Software de análisis de circuitos linealesmediante métodos avanzados deresolución para uso docente.

Autor: Ayose Lomba Pérez

Tutores: Jose Miguel Monzón VeronaAntonio Andrés Ocón Carreras

Fecha: Septiembre 2009

Universidad de Las Palmas de Gran CanariaEscuela Técnica Superior de Ingenieros Industriales

Ingeniería Industrial

Manual de Problemas Resueltos

Software de Análisis de Cir uitos Lineales medianteMétodos Avanzados de Resolu ión para Uso Do ente.Manual de Problemas Resueltos.Ayose Lomba PérezSeptiembre 2009

Índi e generalIntrodu ión 71. Cir uito RC on ex ita ión en ontinua. 111.1. Datos Generales. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.1.1. Datos generales del ir uito . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.1.2. Los valores dados al ir uito son: . . . . . . . . . . . . . . . . . . . . . . . . 121.2. Matriz T. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.2.1. Valores de la Matriz T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.2.2. Captura de la Matriz T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131.3. Solu iones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131.3.1. Primer análisis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131.4. Comproba ión de resultados. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162. Cir uito RC sin exita ión. 192.1. Datos Generales. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.2. Solu iones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.2.1. Primer análisis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.3. Comproba ión de resultados. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233. Cir uito RL on exita ión ontínua. 273.1. Datos Generales. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.2. Solu iones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.2.1. Primer análisis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.3. Comproba ión de resultados. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314. Cir uito RC on exita ión senoidal. 354.1. Datos Generales. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.2. Solu iones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364.2.1. Primer análisis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365. Cir uito RL on exita ión senoidal. 415.1. Datos Generales. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415.2. Solu iones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425.2.1. Primer análisis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426. Cir uito RL sin exita ión. 476.1. Datos Generales. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 476.2. Solu iones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 486.2.1. Primer análisis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 486.3. Compara ión. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513

4 ÍNDICE GENERAL7. Cir uito RL on ex ita ión es alón. 537.1. Datos Generales. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 537.2. Solu iones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 547.2.1. Primer análisis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 548. Cir uito RLC serie. 598.1. Datos Generales. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 598.2. Solu iones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 608.2.1. Primer análisis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 609. Cir uito RLC sin ex ita ión. 659.1. Datos Generales. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 659.2. Solu iones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 669.2.1. Primer análisis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6610.Cir uito RLC paralelo. 7910.1. Datos Generales. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7910.2. Solu iones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8010.2.1. Primer análisis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8011.Cir uito RLC paralelo sin ex ita ión. 8911.1. Datos Generales. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8911.2. Solu iones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9011.2.1. Primer análisis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9012.Cir uito RLC paralelo sin ex ita ión on EA. 9712.1. Datos Generales. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9712.2. Solu iones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9812.2.1. Primer análisis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9813.Cir uito on a oplamiento magnéti o simple. 10513.1. Datos Generales. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10513.2. Solu iones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10613.2.1. Primer análisis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10614.Cir uito on a oplamiento magnéti o. 11314.1. Datos Generales. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11314.2. Solu iones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11414.2.1. Primer análisis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11415.Cir uito on fuente de tensión dependiente de tensión. 12715.1. Datos Generales. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12715.2. Solu iones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12815.2.1. Primer análisis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12816.Cir uito on fuente de intensidad dependiente de tensión. 13916.1. Datos Generales. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13916.2. Solu iones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14016.2.1. Primer análisis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14017.Cir uito on transformador. 14717.1. Datos Generales. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14717.2. Solu iones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14817.2.1. Primer análisis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

ÍNDICE GENERAL 518.Cir uito on bipuerto on parámetros híbridos. 15318.1. Datos Generales. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15418.2. Solu iones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15518.2.1. Primer análisis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

Introdu ión.En el presente manual de ejer i ios resueltos se elaboran una ole ión de ejer i ios bási os enlos que se utilizan las apa idades del proye to para el estudio de diferentes ir uitos en régimentransitorio y esta ionario.Para todos ellos se seguirá la misma estru tura de análisis y se presentarán los datos obtenidosde la misma forma, estru turada según:Esquema del ir uitoAr hivo *.sp generado por X ir uitTipo de análisis realizado• Datos introdu idos• Condi iones Ini ialesDatos Generales. En este punto se detallan datos omo el número de nodos, elementos delgrupo A2, et .Matriz T• Valores de la Matriz T ensamblada para la resolu ión.• Captura de la distribu ión de valores en la Matriz.Solu iones• Esta ionario• Transitorio

Fi hero on datos numéri os de solu ión por olumnas. Grá o de salida. S ript utilizado para el grá o.En los primeros ejemplos además se realizará un estudio omparativo de los resultados del pro-grama on las expresiones teóri as obtenidas por métodos tradi ionales de análisis, de esta formase podrá demostrar el orre to fun ionamiento del software.

7

Problemas Resueltos on Ávalon.

9

Capítulo 1Cir uito RC on ex ita ión en ontinua.Sabiendo que la onstante de tiempo de un ir uito de este tipo es τ = RC y que se llegaal permanente pasados aproximadamente 5 ve es este valor (5τ), pasemos a al ular el régimentransitorio de este simple ir uito suponiendo que el ondensador se en uentra ini ialmente des ar-gado, por lo que no existirá diferen ia de poten ial entre sus pla as, he ho que ayuda a estable erlas ondi iones ini iales onsistentes que nos soli itará el programa para el ál ulo del transitorio.Figura 1.1: Cir uito RC on ex ita ión en ontinuaLas expresiones teóri as de las variables del ir uito son:Tensión en resisten ia, que será la diferen ia entre tensión en nudo 1 y en nudo 2 en nuestroprograma

VR = V · e−t

RC (1.1)Tensión en Condensador es la tensión en el nudo 2 en ÁvalonVc = V ·

(

1 − e−t

RC

) (1.2)Intensidad de resisten ia que oin ide on la de la fuente y por tanto la de la úni a malla del ir uitoit =

V

R· e−

t

RC (1.3)Carga del ondensador. Dire tamente nuestro programa no nos fa ilita esta expresión así quesi deseamos al ular la magnitud de arga del ondesador tendremos que tomar los valores de sutensión y multipli arlos por la apa idad tal y omo podemos dedu ir de su e ua ión fundamentalq = V C analizada en el apítulo Teoría bási a previa, de la memoria de este proye to.

qt = V C ·

(

1 − e−t

RC

) (1.4)En este ir uito RC se al ularán las tensiones en los nudos 1 y 2 además de las intensidadque pasa por la malla que forma el ir uito. Nótese que debido al fun ionamiento del programa y11

12 1. Cir uito RC on ex ita ión en ontinua.naturaleza del método, este nos fa ilita las tensiones de los nudos y aquellas intensidades de loselementos que pertene en al Grupo 2, es de ir aquellos que debido a su e ua ión de onstitu iónno es posible ensamblarlos en la matriz T en fun ión de su admitan ia, por lo que ontribuyen alsistema on una nueva e ua ión adi ional que nos propor iona su intensidad.Ar hivo *.sp *SPICE ir uit <ejemplo/ej_01_01>from XCir uit v3.6 rev 1352 1 0 1 0 2 0 11 1 0 2 2 1 0 104 1 0 2 1 0 0 1 rho f a b A B C D.end Tipo de análisis realizadoAnálisis esta ionario ⊠Análisis transitorio ⊠1.1. Datos Generales.1.1.1. Datos generales del ir uitoElementos del Cto: 3EA: 0Nodos: 2A2: 2No nulos: 8Densidad: 0.5Dispersion: 0.51.1.2. Los valores dados al ir uito son:Elemento MagnitudFuente independiente de Tensión 1 VResisten ia 10 ΩCondensador 1 FCuadro 1.1: Datos del Cir uito ej_01_01Tiempo Ini ial 0Tiempo Final 50Paso de Tiempo 0,5Theta 1 (Euler)Cuadro 1.2: Datos del Transitorio ej_01_011.2. Matriz T.1.2.1. Valores de la Matriz Trow 0: (2, -1) (3, 1)

1.3. Solu iones 13row 1: (1, 0 + 1 i) (2, 1)row 2: (0, -1) (1, 1) (2, -10)row 3: (0, 1)1.2.2. Captura de la Matriz T1.3. Solu iones1.3.1. Primer análisis.Esta ionarioTensión en nodo 1: 1 + 3.25261e-19 iTensión en nodo 2: 0.00990099 - 0.0990099 iI Resisten ia entre nodos 2, 1: -0.0990099 - 0.00990099 iI de Fuente tension entre nodos 1, 0: -0.0990099 - 0.00990099 iTransitorio1 0.047619 -0.0952381 -0.0952381 01 0.0929705 -0.0907029 -0.0907029 0.51 0.136162 -0.0863838 -0.0863838 11 0.177298 -0.0822702 -0.0822702 1.51 0.216474 -0.0783526 -0.0783526 21 0.253785 -0.0746215 -0.0746215 2.51 0.289319 -0.0710681 -0.0710681 31 0.323161 -0.0676839 -0.0676839 3.51 0.355391 -0.0644609 -0.0644609 41 0.386087 -0.0613913 -0.0613913 4.51 0.415321 -0.0584679 -0.0584679 51 0.443163 -0.0556837 -0.0556837 5.51 0.469679 -0.0530321 -0.0530321 61 0.494932 -0.0505068 -0.0505068 6.51 0.518983 -0.0481017 -0.0481017 71 0.541888 -0.0458112 -0.0458112 7.51 0.563703 -0.0436297 -0.0436297 81 0.584479 -0.0415521 -0.0415521 8.51 0.604266 -0.0395734 -0.0395734 91 0.623111 -0.0376889 -0.0376889 9.51 0.641058 -0.0358942 -0.0358942 101 0.65815 -0.034185 -0.034185 10.51 0.674429 -0.0325571 -0.0325571 111 0.689932 -0.0310068 -0.0310068 11.51 0.704697 -0.0295303 -0.0295303 121 0.718759 -0.0281241 -0.0281241 12.51 0.732152 -0.0267848 -0.0267848 13

14 1. Cir uito RC on ex ita ión en ontinua.1 0.744906 -0.0255094 -0.0255094 13.51 0.757054 -0.0242946 -0.0242946 141 0.768623 -0.0231377 -0.0231377 14.51 0.779641 -0.0220359 -0.0220359 151 0.790134 -0.0209866 -0.0209866 15.51 0.800127 -0.0199873 -0.0199873 161 0.809645 -0.0190355 -0.0190355 16.51 0.81871 -0.018129 -0.018129 171 0.827343 -0.0172657 -0.0172657 17.51 0.835564 -0.0164436 -0.0164436 181 0.843395 -0.0156605 -0.0156605 18.51 0.850852 -0.0149148 -0.0149148 191 0.857954 -0.0142046 -0.0142046 19.51 0.864718 -0.0135282 -0.0135282 201 0.87116 -0.012884 -0.012884 20.51 0.877296 -0.0122704 -0.0122704 211 0.883139 -0.0116861 -0.0116861 21.51 0.888703 -0.0111297 -0.0111297 221 0.894003 -0.0105997 -0.0105997 22.51 0.899051 -0.0100949 -0.0100949 231 0.903858 -0.00961421 -0.00961421 23.51 0.908436 -0.00915639 -0.00915639 241 0.912796 -0.00872037 -0.00872037 24.51 0.916949 -0.00830512 -0.00830512 251 0.920904 -0.00790964 -0.00790964 25.51 0.92467 -0.00753299 -0.00753299 261 0.928257 -0.00717427 -0.00717427 26.51 0.931674 -0.00683264 -0.00683264 271 0.934927 -0.00650728 -0.00650728 27.51 0.938026 -0.00619741 -0.00619741 281 0.940977 -0.00590229 -0.00590229 28.51 0.943788 -0.00562123 -0.00562123 291 0.946464 -0.00535355 -0.00535355 29.51 0.949014 -0.00509862 -0.00509862 301 0.951442 -0.00485583 -0.00485583 30.51 0.953754 -0.0046246 -0.0046246 311 0.955956 -0.00440438 -0.00440438 31.51 0.958054 -0.00419465 -0.00419465 321 0.960051 -0.0039949 -0.0039949 32.51 0.961953 -0.00380467 -0.00380467 331 0.963765 -0.00362349 -0.00362349 33.51 0.965491 -0.00345095 -0.00345095 341 0.967134 -0.00328662 -0.00328662 34.51 0.968699 -0.00313011 -0.00313011 351 0.970189 -0.00298106 -0.00298106 35.51 0.971609 -0.0028391 -0.0028391 361 0.972961 -0.00270391 -0.00270391 36.51 0.974248 -0.00257515 -0.00257515 371 0.975475 -0.00245252 -0.00245252 37.51 0.976643 -0.00233574 -0.00233574 381 0.977755 -0.00222451 -0.00222451 38.51 0.978814 -0.00211858 -0.00211858 391 0.979823 -0.0020177 -0.0020177 39.51 0.980784 -0.00192162 -0.00192162 40

1.3. Solu iones 151 0.981699 -0.00183011 -0.00183011 40.51 0.98257 -0.00174296 -0.00174296 411 0.9834 -0.00165996 -0.00165996 41.51 0.984191 -0.00158092 -0.00158092 421 0.984944 -0.00150564 -0.00150564 42.51 0.985661 -0.00143394 -0.00143394 431 0.986343 -0.00136566 -0.00136566 43.51 0.986994 -0.00130063 -0.00130063 441 0.987613 -0.00123869 -0.00123869 44.51 0.988203 -0.00117971 -0.00117971 451 0.988765 -0.00112353 -0.00112353 45.51 0.9893 -0.00107003 -0.00107003 461 0.989809 -0.00101907 -0.00101907 46.51 0.990295 -0.000970547 -0.000970547 471 0.990757 -0.000924331 -0.000924331 47.51 0.991197 -0.000880315 -0.000880315 481 0.991616 -0.000838395 -0.000838395 48.51 0.992015 -0.000798471 -0.000798471 491 0.992396 -0.000760449 -0.000760449 50S ript.set gridset autos aleset t i t l e ' Graf i ado por d e f e t o de l a s s o l u i on e s de l i r u i t o 'plot ' so l_trans . data ' using 5 :1 t i t l e 'V en nodo 1 ' with l i n e s , 'so l_trans . data ' using 5 :2 t i t l e 'V en nodo 2 ' with l i n e s , 'so l_trans . data ' using 5 :3 t i t l e ' I Re s i s t en i a ent r e nodos 2 , 1 'with l i n e s , ' so l_trans . data ' using 5 :4 t i t l e ' I de Fuente t ens i on ent r e nodos 1 , 0 ' with l i n e sset terminal po s t s r i p t o l o r s o l i dset output ' /home/ayose/Programa ion/AVALON/debug/ s r / ejemplo/ej_01_01_grafi a . ps 'replotGrá o de salida.

16 1. Cir uito RC on ex ita ión en ontinua.

1.4. Comproba ión de resultados.Ha llegado la hora de omprobar si los datos obtenidos on el programa son orre tos por loque se pro ederá a superponer las grá as de las expresiones teóri as on la de la solu ión aportadapor el software.Empezaremos on la superposi ión de la e ua ión 1.2 on los datos de tensión en nudo 2.

Corriente de la malla del ir uito. Superposi ión de la e ua ión 1.3 on la obtenida on Ávalon.Cabe desta ar que tal y omo se estable e el riterio de signos de los elementos del programa nos

1.4. Comproba ión de resultados. 17sale la intensidad on signo negativo, esto quiere de ir que la misma es en sentido ontrario alque por defe to toma el programa para realizar los ál ulos. Pro edamos a superponer las grá aspara ver los resultados obtenidos.

Tensión en la resisten ia del ir uito. Para su ompara ión se ha e uso de la e ua ión 1.1 ylos datos propor ionados por el programa. Deberemos tener presente que en el Método Nodalmodi ado lo que se obtienen son tensiones en nudos e intensidades en elementos, por lo que parapoder omprobar si los datos que nos ha propor ionado el programa son orre tos, debemos restarlos valores del nodo 1 on el del 2 para así obtener diferen ia de tensión existente en la resisten ia.

Por último nos queda analizar la arga del ondensador a lo largo del tiempo de estudio paraeso nuevamente se solaparán la e ua ión 1.4 on los datos del programa.

18 1. Cir uito RC on ex ita ión en ontinua.

Capítulo 2Cir uito RC sin exita ión.En este ejemplo se analizará la des arga de un ondensador en un ir uito RC simple.Supondremos por tanto que el ondensador está ini ialmente argado.1

0Las expresiones teóri as de las variables del ir uito son:Tensión en resisten iaVR = −V · e−

t

RC (2.1)Tensión en CondensadorVc = V · e−

t

RC (2.2)Intensidad de resisten ia y por tanto la de la úni a malla del ir uitoit = −

V

R· e−

t

RC (2.3)Carga del ondensador. Dire tamente nuestro programa no nos fa ilita esta expresión así quesi deseamos al ular la magnitud de arga del ondesador tendremos que tomar los valores de sutensión y multipli arlos por la apa idad tal y omo podemos dedu ir de su e ua ión fundamentalq = V C analizada en el apítulo teoría bási a previa la memoria de este proye to.

qt = V C · e−t

RC (2.4)2.1. Datos Generales.Ar hivo *.sp ∗SPICE i r u i t <ejemplo02> from XCir uit v3 . 6 rev 1351 1 0 2 0 1 0 52 1 0 1 1 0 0 2. end 19

20 2. Cir uito RC sin exita ión.Tipo de análisis realizadoAnálisis esta ionario ⊠Análisis transitorio ⊠Datos generales del ir uitoElementos del Cto: 2EA: 0Nodos: 1A2: 1No nulos: 4Densidad: 1Dispersion: 0Los valores dados al ir uito son:Elemento MagnitudResisten ia 5 ΩCondensador 2 FCuadro 2.1: Datos del Cir uito ej_02Matriz T.Valores de la Matriz Trow 0: (0, 0 + 2 i) (1, -1)row 1: (0, -1) (1, -5)2.2. Solu iones2.2.1. Primer análisisNuevamente se realizará un análisis omprendido entre 0 segundos y 5 ve es su onstante detiempo, es de ir 50 segundos. Tiempo Ini ial 0Tiempo Final 50Paso de Tiempo 0,5Theta 1 (Euler)Cuadro 2.2: Datos del Transitorio ej_02

2.2. Solu iones 21Esta ionarioResultados sistema esta ionario:Tensión en nodo 1: 0I Resisten ia entre nodos 0, 1: 0Transitorio1.90476 -0.380952 01.81406 -0.362812 0.51.72768 -0.345535 11.6454 -0.329081 1.51.56705 -0.31341 21.49243 -0.298486 2.51.42136 -0.284273 31.35368 -0.270736 3.51.28922 -0.257844 41.22783 -0.245565 4.51.16936 -0.233872 51.11367 -0.222735 5.51.06064 -0.212129 61.01014 -0.202027 6.50.962034 -0.192407 70.916223 -0.183245 7.50.872593 -0.174519 80.831041 -0.166208 8.50.791468 -0.158294 90.753779 -0.150756 9.50.717885 -0.143577 100.6837 -0.13674 10.50.651143 -0.130229 110.620136 -0.124027 11.50.590606 -0.118121 120.562481 -0.112496 12.50.535697 -0.107139 130.510187 -0.102037 13.50.485893 -0.0971785 140.462755 -0.092551 14.50.440719 -0.0881438 150.419732 -0.0839465 15.50.399745 -0.079949 160.38071 -0.0761419 16.50.362581 -0.0725161 170.345315 -0.069063 17.50.328871 -0.0657743 180.313211 -0.0626421 18.50.298296 -0.0596592 190.284091 -0.0568183 19.50.270563 -0.0541126 200.257679 -0.0515358 20.50.245409 -0.0490818 210.233723 -0.0467445 21.50.222593 -0.0445186 220.211993 -0.0423987 22.5

22 2. Cir uito RC sin exita ión.0.201898 -0.0403797 230.192284 -0.0384568 23.50.183128 -0.0366256 240.174407 -0.0348815 24.50.166102 -0.0332205 250.158193 -0.0316385 25.50.15066 -0.0301319 260.143485 -0.0286971 26.50.136653 -0.0273306 270.130146 -0.0260291 27.50.123948 -0.0247896 280.118046 -0.0236092 28.50.112425 -0.0224849 290.107071 -0.0214142 29.50.101972 -0.0203945 300.0971166 -0.0194233 30.50.092492 -0.0184984 310.0880876 -0.0176175 31.50.083893 -0.0167786 320.0798981 -0.0159796 32.50.0760934 -0.0152187 330.0724699 -0.014494 33.50.069019 -0.0138038 340.0657323 -0.0131465 34.50.0626022 -0.0125204 350.0596212 -0.0119242 35.50.0567821 -0.0113564 360.0540782 -0.0108156 36.50.051503 -0.0103006 370.0490505 -0.0098101 37.50.0467147 -0.00934295 380.0444902 -0.00889805 38.50.0423716 -0.00847433 390.040354 -0.00807079 39.50.0384323 -0.00768647 400.0366022 -0.00732044 40.50.0348593 -0.00697185 410.0331993 -0.00663986 41.50.0316184 -0.00632368 420.0301127 -0.00602255 42.50.0286788 -0.00573576 430.0273131 -0.00546263 43.50.0260125 -0.0052025 440.0247738 -0.00495477 44.50.0235941 -0.00471882 450.0224706 -0.00449412 45.50.0214006 -0.00428011 460.0203815 -0.0040763 46.50.0194109 -0.00388219 470.0184866 -0.00369732 47.50.0176063 -0.00352126 480.0167679 -0.00335358 48.50.0159694 -0.00319389 490.015209 -0.0030418 49.5 50

2.3. Comproba ión de resultados. 23Algorithm 1 S ript por defe to del ej_02set terminal pngset output ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/2/ e jemplo02_gra f i a . png 'set en oding iso_8859_1set gridset autos aleset key bottom r i gh t t i t l e ' Var i ab l e s ' boxset t i t l e ' Graf i ado por d e f e t o de l a s s o l u i on e s de l i r u i t o 'plot ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/2/ ejemplo02_x_trans . data ' using 3 :1 t i t l e 'V en nodo 1 ' with l i n e s , ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/2/ ejemplo02_x_trans . data 'using 3 :2 t i t l e ' I Re s i s t en i a ent r e nodos 0 , 1 ' with l i n e sGrá o de salida.

2.3. Comproba ión de resultados.Ha llegado la hora de omprobar si los datos obtenidos on el programa son orre tos por loque se pro ederá a superponer las grá as de las expresiones teóri as on la de la solu ión aportadapor el software.Empezaremos on la superposi ión de la e ua ión 2.2 en la página~19 on los datos de tensiónen nudo 1.

24 2. Cir uito RC sin exita ión.

Corriente de la malla del ir uito superposi ión de la e ua ión 2.3 on la obtenida on Ávalon.Pro edamos a superponer las grá as para ver los resultados obtenidos.

Tensión en la resisten ia del ir uito se ha e uso de la e ua ión 2.1 y los datos propor ionadospor el programa.

2.3. Comproba ión de resultados. 25

Por último nos queda analizar la arga del ondensador a lo largo del tiempo de estudio paraeso nuevamente se solaparán la e ua ión 2.4 on los datos del programa.

Cal ularemos también en este ir uito la poten ia de la resisten ia basándonos en la expresiónp = RI2

26 2. Cir uito RC sin exita ión.

Capítulo 3Cir uito RL on exita ión ontínua.Ahora analizaremos el omportamiento de un ir uito RL on ex ita ión ontínua en el que su onstante de tiempo es τ = L

Rpor lo que el análisis lo realizaremos para in o ve es el mendionadovalor.

Las expresiones teóri as de las variables del ir uito son:Tensión en Resisten iaVR = V ·

(

1 − e−R

Lt

) (3.1)Tensión en la BobinaVL = −V · e−

R

Lt (3.2)Intensidad de resisten ia y por tanto la de la úni a malla del ir uito

it =V

R·

(

1 − e−R

Lt

) (3.3)3.1. Datos Generales.Ar hivo *.sp ∗SPICE i r u i t <ejemplo03> from XCir uit v3 . 6 rev 1353 1 0 2 0 2 0 101 1 0 2 2 1 0 24 1 0 2 1 0 0 2 rho f a b A B C D. end Tipo de análisis realizadoAnálisis esta ionario ⊠Análisis transitorio ⊠27

28 3. Cir uito RL on exita ión ontínua.Datos generales del ir uitoElementos del Cto: 3EA: 0Nodos: 2A2: 3No nulos: 10Densidad: 0.4Dispersion: 0.6Los valores dados al ir uito son:Elemento MagnitudResisten ia 2 ΩBobina 10 HMatriz T.Valores de la Matriz Trow 0: (2, -1) (3, 1)row 1: (2, 1) (4, -1)row 2: (0, -1) (1, 1) (2, -2)row 3: (0, 1)row 4: (1, -1) (4, -0 - 10 i)3.2. Solu iones3.2.1. Primer análisisNuevamente se realizará un análisis omprendido entre 0 segundos y 5 ve es su onstante detiempo, es de ir 50 segundos. Tiempo Ini ial 0Tiempo Final 25Paso de Tiempo 0,25Theta 1 (Euler)Esta ionarioResultados sistema esta ionario:Tensión en nodo 1: 2 - 2.1684e-19 iTensión en nodo 2: 1.92308 + 0.384615 iI Resisten ia entre nodos 2, 1: -0.0384615 + 0.192308 iI de Fuente tension entre nodos 1, 0: -0.0384615 + 0.192308 iI de Bobina entre nodos 0, 2: -0.0384615 + 0.192308 i

3.2. Solu iones 29Transitorio2 1.90476 -0.047619 -0.047619 -0.047619 02 1.81406 -0.0929705 -0.0929705 -0.0929705 0.252 1.72768 -0.136162 -0.136162 -0.136162 0.52 1.6454 -0.177298 -0.177298 -0.177298 0.752 1.56705 -0.216474 -0.216474 -0.216474 12 1.49243 -0.253785 -0.253785 -0.253785 1.252 1.42136 -0.289319 -0.289319 -0.289319 1.52 1.35368 -0.323161 -0.323161 -0.323161 1.752 1.28922 -0.355391 -0.355391 -0.355391 22 1.22783 -0.386087 -0.386087 -0.386087 2.252 1.16936 -0.415321 -0.415321 -0.415321 2.52 1.11367 -0.443163 -0.443163 -0.443163 2.752 1.06064 -0.469679 -0.469679 -0.469679 32 1.01014 -0.494932 -0.494932 -0.494932 3.252 0.962034 -0.518983 -0.518983 -0.518983 3.52 0.916223 -0.541888 -0.541888 -0.541888 3.752 0.872593 -0.563703 -0.563703 -0.563703 42 0.831041 -0.584479 -0.584479 -0.584479 4.252 0.791468 -0.604266 -0.604266 -0.604266 4.52 0.753779 -0.623111 -0.623111 -0.623111 4.752 0.717885 -0.641058 -0.641058 -0.641058 52 0.6837 -0.65815 -0.65815 -0.65815 5.252 0.651143 -0.674429 -0.674429 -0.674429 5.52 0.620136 -0.689932 -0.689932 -0.689932 5.752 0.590606 -0.704697 -0.704697 -0.704697 62 0.562481 -0.718759 -0.718759 -0.718759 6.252 0.535697 -0.732152 -0.732152 -0.732152 6.52 0.510187 -0.744906 -0.744906 -0.744906 6.752 0.485893 -0.757054 -0.757054 -0.757054 72 0.462755 -0.768623 -0.768623 -0.768623 7.252 0.440719 -0.779641 -0.779641 -0.779641 7.52 0.419732 -0.790134 -0.790134 -0.790134 7.752 0.399745 -0.800127 -0.800127 -0.800127 82 0.38071 -0.809645 -0.809645 -0.809645 8.252 0.362581 -0.81871 -0.81871 -0.81871 8.52 0.345315 -0.827343 -0.827343 -0.827343 8.752 0.328871 -0.835564 -0.835564 -0.835564 92 0.313211 -0.843395 -0.843395 -0.843395 9.252 0.298296 -0.850852 -0.850852 -0.850852 9.52 0.284091 -0.857954 -0.857954 -0.857954 9.752 0.270563 -0.864718 -0.864718 -0.864718 102 0.257679 -0.87116 -0.87116 -0.87116 10.252 0.245409 -0.877296 -0.877296 -0.877296 10.52 0.233723 -0.883139 -0.883139 -0.883139 10.752 0.222593 -0.888703 -0.888703 -0.888703 112 0.211993 -0.894003 -0.894003 -0.894003 11.252 0.201898 -0.899051 -0.899051 -0.899051 11.52 0.192284 -0.903858 -0.903858 -0.903858 11.752 0.183128 -0.908436 -0.908436 -0.908436 122 0.174407 -0.912796 -0.912796 -0.912796 12.252 0.166102 -0.916949 -0.916949 -0.916949 12.52 0.158193 -0.920904 -0.920904 -0.920904 12.75

30 3. Cir uito RL on exita ión ontínua.2 0.15066 -0.92467 -0.92467 -0.92467 132 0.143485 -0.928257 -0.928257 -0.928257 13.252 0.136653 -0.931674 -0.931674 -0.931674 13.52 0.130146 -0.934927 -0.934927 -0.934927 13.752 0.123948 -0.938026 -0.938026 -0.938026 142 0.118046 -0.940977 -0.940977 -0.940977 14.252 0.112425 -0.943788 -0.943788 -0.943788 14.52 0.107071 -0.946464 -0.946464 -0.946464 14.752 0.101972 -0.949014 -0.949014 -0.949014 152 0.0971166 -0.951442 -0.951442 -0.951442 15.252 0.092492 -0.953754 -0.953754 -0.953754 15.52 0.0880876 -0.955956 -0.955956 -0.955956 15.752 0.083893 -0.958054 -0.958054 -0.958054 162 0.0798981 -0.960051 -0.960051 -0.960051 16.252 0.0760934 -0.961953 -0.961953 -0.961953 16.52 0.0724699 -0.963765 -0.963765 -0.963765 16.752 0.069019 -0.965491 -0.965491 -0.965491 172 0.0657323 -0.967134 -0.967134 -0.967134 17.252 0.0626022 -0.968699 -0.968699 -0.968699 17.52 0.0596212 -0.970189 -0.970189 -0.970189 17.752 0.0567821 -0.971609 -0.971609 -0.971609 182 0.0540782 -0.972961 -0.972961 -0.972961 18.252 0.051503 -0.974248 -0.974248 -0.974248 18.52 0.0490505 -0.975475 -0.975475 -0.975475 18.752 0.0467147 -0.976643 -0.976643 -0.976643 192 0.0444902 -0.977755 -0.977755 -0.977755 19.252 0.0423716 -0.978814 -0.978814 -0.978814 19.52 0.040354 -0.979823 -0.979823 -0.979823 19.752 0.0384323 -0.980784 -0.980784 -0.980784 202 0.0366022 -0.981699 -0.981699 -0.981699 20.252 0.0348593 -0.98257 -0.98257 -0.98257 20.52 0.0331993 -0.9834 -0.9834 -0.9834 20.752 0.0316184 -0.984191 -0.984191 -0.984191 212 0.0301127 -0.984944 -0.984944 -0.984944 21.252 0.0286788 -0.985661 -0.985661 -0.985661 21.52 0.0273131 -0.986343 -0.986343 -0.986343 21.752 0.0260125 -0.986994 -0.986994 -0.986994 222 0.0247738 -0.987613 -0.987613 -0.987613 22.252 0.0235941 -0.988203 -0.988203 -0.988203 22.52 0.0224706 -0.988765 -0.988765 -0.988765 22.752 0.0214006 -0.9893 -0.9893 -0.9893 232 0.0203815 -0.989809 -0.989809 -0.989809 23.252 0.0194109 -0.990295 -0.990295 -0.990295 23.52 0.0184866 -0.990757 -0.990757 -0.990757 23.752 0.0176063 -0.991197 -0.991197 -0.991197 242 0.0167679 -0.991616 -0.991616 -0.991616 24.252 0.0159694 -0.992015 -0.992015 -0.992015 24.52 0.015209 -0.992396 -0.992396 -0.992396 25set terminal pngset output ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/3/ e jemplo03_gra f i a . png 'set en oding iso_8859_1set grid

3.3. Comproba ión de resultados. 31set autos aleset key top r i gh t t i t l e ' Var i ab l e s ' boxset t i t l e ' Graf i ado por d e f e t o de l a s s o l u i on e s de l i r u i t o 'plot ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/3/ ejemplo03_x_trans . data ' using 6 :1 t i t l e 'V en nodo 1 ' with l i n e s , ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/3/ ejemplo03_x_trans . data 'using 6 :2 t i t l e 'V en nodo 2 ' with l i n e s , ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/3/ejemplo03_x_trans . data ' using 6 :3 t i t l e ' I Re s i s t en i a ent r e nodos 2 , 1 ' with l i n e s , ' /home/ ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/3/ ejemplo03_x_trans . data 'using 6 :4 t i t l e ' I de Fuente t ens i on ent r e nodos 1 , 0 ' with l i n e s ,' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/3/ ejemplo03_x_trans . data ' using 6 :5 t i t l e ' I de Bobina ent r e nodos 0 , 2 ' with l i n e sGrá o de salida.

3.3. Comproba ión de resultados.Ahora se omprobará si los datos obtenidos on el programa son orre tos, por lo que sepro ederá a superponer las grá as de las expresiones teóri as on la de la solu ión aportada porel software.Empezaremos on la superposi ión de la e ua ión 3.2 en la página~27 on los datos de tensiónen nudo 2.

32 3. Cir uito RL on exita ión ontínua.

Corriente de la malla del ir uito superposi ión de la e ua ión 3.3 on la obtenida on Ávalon.Pro edamos a ver las grá as para analizar los resultados obtenidos.

Tensión en la resisten ia del ir uito se ha e uso de la e ua ión 3.1 y los datos propor ionadospor el programa. Debemos tener presente que para la obten ión de esta grá a on el programa sedeben restar las olumnas 1 y 2 que es la diferen ia de tensión a la que se en uentra la resisten ia,re ordemos que el programa sólo porpor iona tensiones e intensidades.

3.3. Comproba ión de resultados. 33

Capítulo 4Cir uito RC on exita ión senoidal.En este ejemplo se analizará un ir uito RL on ondi iones ini iales.4.1. Datos Generales.Ar hivo *.sp ∗SPICE i r u i t <CTOr > from XCir uit v3 . 6 rev 1352 1 0 1 0 2 0 0 ,0011 1 0 2 2 1 0 24 1 0 2 1 0 1 0 0 50 a b 1 B C D. end Tipo de análisis realizadoAnálisis esta ionario ⊠Análisis transitorio ⊠Datos generales del ir uitoElementos del Cto: 3EA: 0Nodos: 2A2: 2No nulos: 8Densidad: 0.5Dispersion: 0.5Los valores dados al ir uito son:Elemento MagnitudResisten ia 2 ΩCondensador 0, 001 F35

36 4. Cir uito RC on exita ión senoidal.Matriz T.Valores de la Matriz Trow 0: (2, -1) (3, 1)row 1: (1, 0 + 0.001 i) (2, 1)row 2: (0, -1) (1, 1) (2, -2)row 3: (0, 1)4.2. Solu iones4.2.1. Primer análisisNuevamente se realizará un análisis omprendido entre 0 segundos y 5 ve es su onstante detiempo, es de ir 50 segundos. Tiempo Ini ial 0Tiempo Final 0, 1Paso de Tiempo 0, 001Theta 1 (Euler)Esta ionarioResultados sistema esta ionario:Tensión en nodo 1: 1 - 2.16841e-19 iTensión en nodo 2: 0.999996 - 0.00199999 iI Resisten ia entre nodos 2, 1: -1.99999e-06 - 0.000999996 iI de Fuente tension entre nodos 1, 0: -1.99999e-06 - 0.000999996 iTransitorio0.309017 0.103006 -0.103006 -0.103006 00.587785 0.264599 -0.161593 -0.161593 0.0010.809017 0.446072 -0.181473 -0.181473 0.0020.951057 0.6144 -0.168328 -0.168328 0.0031 0.742933 -0.128533 -0.128533 0.0040.951056 0.812308 -0.0693744 -0.0693744 0.0050.809017 0.811211 0.00109691 0.00109691 0.0060.587785 0.736736 0.0744752 0.0744752 0.0070.309017 0.594163 0.142573 0.142573 0.008-1.49218e-07 0.396108 0.198054 0.198054 0.009-0.309017 0.161067 0.235042 0.235042 0.01-0.587785 -0.0885508 0.249617 0.249617 0.011-0.809017 -0.328706 0.240155 0.240155 0.012-0.951057 -0.536156 0.20745 0.20745 0.013-1 -0.690771 0.154615 0.154615 0.014-0.951056 -0.777533 0.0867618 0.0867618 0.015-0.809017 -0.788027 0.0104947 0.0104947 0.016-0.587785 -0.72128 -0.0667475 -0.0667475 0.017

4.2. Solu iones 37-0.309017 -0.583859 -0.137421 -0.137421 0.0182.98435e-07 -0.389239 -0.19462 -0.19462 0.0190.309017 -0.156487 -0.232752 -0.232752 0.020.587786 0.0916039 -0.248091 -0.248091 0.0210.809017 0.330742 -0.239138 -0.239138 0.0220.951057 0.537513 -0.206772 -0.206772 0.0231 0.691676 -0.154162 -0.154162 0.0240.951056 0.778136 -0.0864603 -0.0864603 0.0250.809017 0.788429 -0.0102936 -0.0102936 0.0260.587785 0.721548 0.0668815 0.0668815 0.0270.309017 0.584037 0.13751 0.13751 0.028-4.47653e-07 0.389358 0.194679 0.194679 0.029-0.309017 0.156566 0.232792 0.232792 0.03-0.587786 -0.091551 0.248117 0.248117 0.031-0.809017 -0.330706 0.239155 0.239155 0.032-0.951057 -0.53749 0.206783 0.206783 0.033-1 -0.69166 0.15417 0.15417 0.034-0.951056 -0.778125 0.0864655 0.0864655 0.035-0.809017 -0.788422 0.0102971 0.0102971 0.036-0.587785 -0.721543 -0.0668792 -0.0668792 0.037-0.309016 -0.584034 -0.137509 -0.137509 0.0385.96871e-07 -0.389356 -0.194678 -0.194678 0.0390.309018 -0.156565 -0.232791 -0.232791 0.040.587786 0.0915521 -0.248117 -0.248117 0.0410.809017 0.330707 -0.239155 -0.239155 0.0420.951057 0.53749 -0.206783 -0.206783 0.0431 0.69166 -0.15417 -0.15417 0.0440.951056 0.778126 -0.0864653 -0.0864653 0.0450.809017 0.788423 -0.010297 -0.010297 0.0460.587785 0.721543 0.0668793 0.0668793 0.0470.309016 0.584034 0.137509 0.137509 0.048-7.46088e-07 0.389356 0.194678 0.194678 0.049-0.309018 0.156565 0.232791 0.232791 0.05-0.587786 -0.0915522 0.248117 0.248117 0.051-0.809017 -0.330707 0.239155 0.239155 0.052-0.951057 -0.53749 0.206783 0.206783 0.053-1 -0.69166 0.15417 0.15417 0.054-0.951056 -0.778126 0.0864653 0.0864653 0.055-0.809016 -0.788423 0.0102969 0.0102969 0.056-0.587785 -0.721543 -0.0668793 -0.0668793 0.057-0.309016 -0.584034 -0.137509 -0.137509 0.0588.95306e-07 -0.389356 -0.194678 -0.194678 0.0590.309018 -0.156565 -0.232791 -0.232791 0.060.587786 0.0915523 -0.248117 -0.248117 0.0610.809018 0.330707 -0.239155 -0.239155 0.0620.951057 0.537491 -0.206783 -0.206783 0.06299991 0.69166 -0.15417 -0.15417 0.0640.951056 0.778126 -0.0864653 -0.0864653 0.0650.809016 0.788423 -0.0102969 -0.0102969 0.0660.587784 0.721543 0.0668794 0.0668794 0.0670.309016 0.584034 0.137509 0.137509 0.068-1.04452e-06 0.389356 0.194678 0.194678 0.069-0.309018 0.156564 0.232791 0.232791 0.07-0.587786 -0.0915524 0.248117 0.248117 0.071

38 4. Cir uito RC on exita ión senoidal.-0.809018 -0.330708 0.239155 0.239155 0.072-0.951057 -0.537491 0.206783 0.206783 0.073-1 -0.69166 0.15417 0.15417 0.074-0.951056 -0.778126 0.0864653 0.0864653 0.075-0.809016 -0.788423 0.0102969 0.0102969 0.076-0.587784 -0.721543 -0.0668794 -0.0668794 0.077-0.309016 -0.584034 -0.137509 -0.137509 0.0781.19374e-06 -0.389356 -0.194678 -0.194678 0.0790.309018 -0.156564 -0.232791 -0.232791 0.080.587786 0.0915525 -0.248117 -0.248117 0.0810.809018 0.330708 -0.239155 -0.239155 0.0820.951057 0.537491 -0.206783 -0.206783 0.0831 0.69166 -0.15417 -0.15417 0.0840.951056 0.778126 -0.0864652 -0.0864652 0.0850.809016 0.788423 -0.0102968 -0.0102968 0.0860.587784 0.721543 0.0668795 0.0668795 0.0870.309016 0.584034 0.137509 0.137509 0.088-1.34296e-06 0.389356 0.194678 0.194678 0.089-0.309018 0.156564 0.232791 0.232791 0.09-0.587786 -0.0915526 0.248117 0.248117 0.091-0.809018 -0.330708 0.239155 0.239155 0.092-0.951057 -0.537491 0.206783 0.206783 0.093-1 -0.691661 0.15417 0.15417 0.094-0.951056 -0.778126 0.0864652 0.0864652 0.095-0.809016 -0.788423 0.0102968 0.0102968 0.096-0.587784 -0.721543 -0.0668795 -0.0668795 0.097-0.309016 -0.584034 -0.137509 -0.137509 0.0981.49218e-06 -0.389355 -0.194678 -0.194678 0.1set terminal pngset output ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/4/CTOr _grafi a . png 'set en oding iso_8859_1set gridset autos aleset key bottom r i gh t t i t l e ' Var i ab l e s ' boxset t i t l e ' Graf i ado por d e f e t o de l a s s o l u i on e s de l i r u i t o 'plot ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/4/CTOr _x_trans . data ' using 5 :1 t i t l e 'V en nodo 1 ' with l i n e s , ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/4/CTOr _x_trans . data ' using5 :2 t i t l e 'V en nodo 2 ' with l i n e s , ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/4/CTOr _x_trans . data ' using 5 :3 t i t l e ' I Re s i s t en i a ent r e nodos 2 , 1' with l i n e s , ' /home/ ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/4/CTOr _x_trans . data ' using 5 :4 t i t l e 'I de Fuente t ens i on ent r e nodos 1 , 0 ' with po in t sGrá o de salida. Como las variables de intensidad que al ula el ir uito para la fuente y laresisten ia oin iden se ha modi ado el s ript para que la orriente de la tensión se represente on puntos.

4.2. Solu iones 39

Capítulo 5Cir uito RL on exita ión senoidal.En este ejemplo se analizará un ir uito RL on ondi iones ini iales.5.1. Datos Generales.Ar hivo *.sp ∗SPICE i r u i t <ejemplo03> from XCir uit v3 . 6 rev 1353 1 0 2 0 2 0 0 ,0011 1 0 2 2 1 0 24 1 0 2 1 0 1 0 0 50 a b 1 B C D. end Tipo de análisis realizadoAnálisis esta ionario ⊠Análisis transitorio ⊠Datos generales del ir uitoElementos del Cto: 3EA: 0Nodos: 2A2: 3No nulos: 10Densidad: 0.4Dispersion: 0.6Los valores dados al ir uito son:Elemento MagnitudResisten ia 2 ΩBobina 0, 001 H41

42 5. Cir uito RL on exita ión senoidal.Matriz T.Valores de la Matriz Trow 0: (2, -1) (3, 1)row 1: (2, 1) (4, -1)row 2: (0, -1) (1, 1) (2, -2)row 3: (0, 1)row 4: (1, -1) (4, -0 - 0.001 i)5.2. Solu iones5.2.1. Primer análisisNuevamente se realizará un análisis omprendido entre 0 segundos y 5 ve es su onstante detiempo, es de ir 50 segundos. Tiempo Ini ial 0Tiempo Final 0, 1Paso de Tiempo 0, 001Theta 1 (Euler)Esta ionarioResultados sistema esta ionario:Tensión en nodo 1: 1 - 5.46025e-14 iTensión en nodo 2: 2.5e-07 + 0.0005 iI Resisten ia entre nodos 2, 1: -0.5 + 0.00025 iI de Fuente tension entre nodos 1, 0: -0.5 + 0.00025 iI de Bobina entre nodos 0, 2: -0.5 + 0.00025 iTransitorio0.618034 0.206011 -0.206011 -0.206011 -0.206011 00.587785 0.0585875 -0.264599 -0.264599 -0.264599 0.0010.809017 0.0932731 -0.357872 -0.357872 -0.357872 0.0020.951057 0.0784375 -0.43631 -0.43631 -0.43631 0.0031 0.0424603 -0.47877 -0.47877 -0.47877 0.0040.951056 -0.00216106 -0.476609 -0.476609 -0.476609 0.0050.809017 -0.0480669 -0.428542 -0.428542 -0.428542 0.0060.587785 -0.0897662 -0.338776 -0.338776 -0.338776 0.0070.309017 -0.122845 -0.215931 -0.215931 -0.215931 0.008-1.49218e-07 -0.143954 -0.0719769 -0.0719769 -0.0719769 0.009-0.309017 -0.15099 0.0790134 0.0790134 0.0790134 0.01-0.587785 -0.143253 0.222266 0.222266 0.222266 0.011-0.809017 -0.121495 0.343761 0.343761 0.343761 0.012-0.951057 -0.0878448 0.431606 0.431606 0.431606 0.013-1 -0.0455961 0.477202 0.477202 0.477202 0.014-0.951056 0.00111584 0.476086 0.476086 0.476086 0.015

5.2. Solu iones 43-0.809017 0.0477185 0.428368 0.428368 0.428368 0.016-0.587785 0.0896501 0.338718 0.338718 0.338718 0.017-0.309017 0.122806 0.215911 0.215911 0.215911 0.0182.98435e-07 0.143941 0.0719704 0.0719704 0.0719704 0.0190.309017 0.150986 -0.0790156 -0.0790156 -0.0790156 0.020.587786 0.143251 -0.222267 -0.222267 -0.222267 0.0210.809017 0.121494 -0.343761 -0.343761 -0.343761 0.0220.951057 0.0878446 -0.431606 -0.431606 -0.431606 0.0231 0.045596 -0.477202 -0.477202 -0.477202 0.0240.951056 -0.00111586 -0.476086 -0.476086 -0.476086 0.0250.809017 -0.0477185 -0.428368 -0.428368 -0.428368 0.0260.587785 -0.0896501 -0.338718 -0.338718 -0.338718 0.0270.309017 -0.122806 -0.215911 -0.215911 -0.215911 0.028-4.47653e-07 -0.143941 -0.0719703 -0.0719703 -0.0719703 0.029-0.309017 -0.150986 0.0790157 0.0790157 0.0790157 0.03-0.587786 -0.143251 0.222267 0.222267 0.222267 0.031-0.809017 -0.121494 0.343761 0.343761 0.343761 0.032-0.951057 -0.0878446 0.431606 0.431606 0.431606 0.033-1 -0.045596 0.477202 0.477202 0.477202 0.034-0.951056 0.00111589 0.476086 0.476086 0.476086 0.035-0.809017 0.0477185 0.428368 0.428368 0.428368 0.036-0.587785 0.0896501 0.338717 0.338717 0.338717 0.037-0.309016 0.122806 0.215911 0.215911 0.215911 0.0385.96871e-07 0.143941 0.0719702 0.0719702 0.0719702 0.0390.309018 0.150986 -0.0790158 -0.0790158 -0.0790158 0.040.587786 0.143251 -0.222267 -0.222267 -0.222267 0.0410.809017 0.121494 -0.343762 -0.343762 -0.343762 0.0420.951057 0.0878446 -0.431606 -0.431606 -0.431606 0.0431 0.0455959 -0.477202 -0.477202 -0.477202 0.0440.951056 -0.00111592 -0.476086 -0.476086 -0.476086 0.0450.809017 -0.0477185 -0.428368 -0.428368 -0.428368 0.0460.587785 -0.0896502 -0.338717 -0.338717 -0.338717 0.0470.309016 -0.122806 -0.215911 -0.215911 -0.215911 0.048-7.46088e-07 -0.143941 -0.0719702 -0.0719702 -0.0719702 0.049-0.309018 -0.150986 0.0790159 0.0790159 0.0790159 0.05-0.587786 -0.143251 0.222267 0.222267 0.222267 0.051-0.809017 -0.121494 0.343762 0.343762 0.343762 0.052-0.951057 -0.0878445 0.431606 0.431606 0.431606 0.053-1 -0.0455959 0.477202 0.477202 0.477202 0.054-0.951056 0.00111595 0.476086 0.476086 0.476086 0.055-0.809016 0.0477186 0.428368 0.428368 0.428368 0.056-0.587785 0.0896502 0.338717 0.338717 0.338717 0.057-0.309016 0.122806 0.215911 0.215911 0.215911 0.0588.95306e-07 0.143941 0.0719701 0.0719701 0.0719701 0.0590.309018 0.150986 -0.0790159 -0.0790159 -0.0790159 0.060.587786 0.143251 -0.222267 -0.222267 -0.222267 0.0610.809018 0.121494 -0.343762 -0.343762 -0.343762 0.0620.951057 0.0878445 -0.431606 -0.431606 -0.431606 0.06299991 0.0455959 -0.477202 -0.477202 -0.477202 0.0640.951056 -0.00111597 -0.476086 -0.476086 -0.476086 0.0650.809016 -0.0477186 -0.428367 -0.428367 -0.428367 0.0660.587784 -0.0896502 -0.338717 -0.338717 -0.338717 0.0670.309016 -0.122806 -0.215911 -0.215911 -0.215911 0.068-1.04452e-06 -0.143941 -0.07197 -0.07197 -0.07197 0.069

44 5. Cir uito RL on exita ión senoidal.-0.309018 -0.150986 0.079016 0.079016 0.079016 0.07-0.587786 -0.143251 0.222267 0.222267 0.222267 0.071-0.809018 -0.121494 0.343762 0.343762 0.343762 0.072-0.951057 -0.0878445 0.431606 0.431606 0.431606 0.073-1 -0.0455959 0.477202 0.477202 0.477202 0.074-0.951056 0.00111598 0.476086 0.476086 0.476086 0.075-0.809016 0.0477186 0.428367 0.428367 0.428367 0.076-0.587784 0.0896502 0.338717 0.338717 0.338717 0.077-0.309016 0.122806 0.215911 0.215911 0.215911 0.0781.19374e-06 0.143941 0.0719699 0.0719699 0.0719699 0.0790.309018 0.150986 -0.0790161 -0.0790161 -0.0790161 0.080.587786 0.143251 -0.222267 -0.222267 -0.222267 0.0810.809018 0.121494 -0.343762 -0.343762 -0.343762 0.0820.951057 0.0878445 -0.431606 -0.431606 -0.431606 0.0831 0.0455959 -0.477202 -0.477202 -0.477202 0.0840.951056 -0.00111601 -0.476086 -0.476086 -0.476086 0.0850.809016 -0.0477186 -0.428367 -0.428367 -0.428367 0.0860.587784 -0.0896502 -0.338717 -0.338717 -0.338717 0.0870.309016 -0.122806 -0.215911 -0.215911 -0.215911 0.088-1.34296e-06 -0.143941 -0.0719699 -0.0719699 -0.0719699 0.089-0.309018 -0.150986 0.0790161 0.0790161 0.0790161 0.09-0.587786 -0.143251 0.222268 0.222268 0.222268 0.091-0.809018 -0.121494 0.343762 0.343762 0.343762 0.092-0.951057 -0.0878445 0.431606 0.431606 0.431606 0.093-1 -0.0455958 0.477202 0.477202 0.477202 0.094-0.951056 0.00111603 0.476086 0.476086 0.476086 0.095-0.809016 0.0477186 0.428367 0.428367 0.428367 0.096-0.587784 0.0896502 0.338717 0.338717 0.338717 0.097-0.309016 0.122806 0.215911 0.215911 0.215911 0.0981.49218e-06 0.143941 0.0719698 0.0719698 0.0719698 0.1set terminal pngset output ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/5/ e jemplo05_gra f i a . png 'set en oding iso_8859_1set gridset autos aleset yrange [ 1 . 8 : − 1 . 8 set key bottom r i gh t t i t l e ' Var i ab l e s ' boxset t i t l e ' Graf i ado por d e f e t o de l a s s o l u i on e s de l i r u i t o 'plot ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/5/ ejemplo05_x_trans . data ' using 6 :1 t i t l e 'V en nodo 1 ' with l i n e s , ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/5/ ejemplo05_x_trans . data 'using 6 :2 t i t l e 'V en nodo 2 ' with l i n e s , ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/5/ejemplo05_x_trans . data ' using 6 :3 t i t l e ' I Re s i s t en i a ent r e nodos 2 , 1 ' with points , ' /home/ ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/5/ ejemplo05_x_trans . data 'using 6 :4 t i t l e ' I de Fuente t ens i on ent r e nodos 1 , 0 ' with points ,' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/5/ ejemplo05_x_trans . data ' using 6 :5 t i t l e ' I de Bobina ent r e nodos 0 , 2 ' with l i n e s

5.2. Solu iones 45Grá o de salida. Nuevamente se modi ó ligeramente el s ript de ploteo por defe to para quepudiesen apre iarse bien las variables de intensidad que da el programa que obviamente deben seriguales.

Capítulo 6Cir uito RL sin exita ión.En este ejemplo se analizará un ir uito RL on ondi iones ini iales.1

06.1. Datos Generales.Ar hivo *.sp ∗SPICE i r u i t <ejemplo04> from XCir uit v3 . 6 rev 1351 1 0 2 0 1 0 0 ,53 1 0 2 1 0 0 0 ,0001. end Tipo de análisis realizadoAnálisis esta ionario ⊠Análisis transitorio ⊠Datos generales del ir uitoElementos del Cto: 2EA: 0Nodos: 1A2: 2No nulos: 6Densidad: 0.666667Dispersion: 0.3333333333Los valores dados al ir uito son:Elemento MagnitudResisten ia 0, 5 ΩBobina 0, 0001 H47

48 6. Cir uito RL sin exita ión.Matriz T.Valores de la Matriz Trow 0: (1, -1) (2, 1)row 1: (0, -1) (1, -0.5)row 2: (0, 1) (2, -0 - 0.0001 i)6.2. Solu iones6.2.1. Primer análisisTiempo Ini ial 0Tiempo Final 0, 001Paso de Tiempo 0, 00001Theta 1 (Euler) Condi iones Ini iales ValorV nodo 1 0I Resisten ia entre nodos 0, 1 4I Bobina entre nodos 1, 0 4Esta ionarioResultados sistema esta ionario:Tensión en nodo 1: 0I Resisten ia entre nodos 0, 1: 0I de Bobina entre nodos 1, 0: 0Transitorio-1.90476 3.80952 3.80952 0-1.81406 3.62812 3.62812 1e-05-1.72768 3.45535 3.45535 2e-05-1.6454 3.29081 3.29081 3e-05-1.56705 3.1341 3.1341 4e-05-1.49243 2.98486 2.98486 5e-05-1.42136 2.84273 2.84273 6e-05-1.35368 2.70736 2.70736 7e-05-1.28922 2.57844 2.57844 8e-05-1.22783 2.45565 2.45565 9e-05-1.16936 2.33872 2.33872 0.0001-1.11367 2.22735 2.22735 0.00011-1.06064 2.12129 2.12129 0.00012-1.01014 2.02027 2.02027 0.00013-0.962034 1.92407 1.92407 0.00014-0.916223 1.83245 1.83245 0.00015-0.872593 1.74519 1.74519 0.00016-0.831041 1.66208 1.66208 0.00017-0.791468 1.58294 1.58294 0.00018-0.753779 1.50756 1.50756 0.00019-0.717885 1.43577 1.43577 0.0002-0.6837 1.3674 1.3674 0.00021-0.651143 1.30229 1.30229 0.00022

6.2. Solu iones 49-0.620136 1.24027 1.24027 0.00023-0.590606 1.18121 1.18121 0.00024-0.562481 1.12496 1.12496 0.00025-0.535697 1.07139 1.07139 0.00026-0.510187 1.02037 1.02037 0.00027-0.485893 0.971785 0.971785 0.00028-0.462755 0.92551 0.92551 0.00029-0.440719 0.881438 0.881438 0.0003-0.419732 0.839465 0.839465 0.00031-0.399745 0.79949 0.79949 0.00032-0.38071 0.761419 0.761419 0.00033-0.362581 0.725161 0.725161 0.00034-0.345315 0.69063 0.69063 0.00035-0.328871 0.657743 0.657743 0.00036-0.313211 0.626421 0.626421 0.00037-0.298296 0.596592 0.596592 0.00038-0.284091 0.568183 0.568183 0.00039-0.270563 0.541126 0.541126 0.0004-0.257679 0.515358 0.515358 0.00041-0.245409 0.490818 0.490818 0.00042-0.233723 0.467445 0.467445 0.00043-0.222593 0.445186 0.445186 0.00044-0.211993 0.423987 0.423987 0.00045-0.201898 0.403797 0.403797 0.00046-0.192284 0.384568 0.384568 0.00047-0.183128 0.366256 0.366256 0.00048-0.174407 0.348815 0.348815 0.00049-0.166102 0.332205 0.332205 0.0005-0.158193 0.316385 0.316385 0.00051-0.15066 0.301319 0.301319 0.00052-0.143485 0.286971 0.286971 0.00053-0.136653 0.273306 0.273306 0.00054-0.130146 0.260291 0.260291 0.00055-0.123948 0.247896 0.247896 0.00056-0.118046 0.236092 0.236092 0.00057-0.112425 0.224849 0.224849 0.00058-0.107071 0.214142 0.214142 0.00059-0.101972 0.203945 0.203945 0.0006-0.0971166 0.194233 0.194233 0.00061-0.092492 0.184984 0.184984 0.00062-0.0880876 0.176175 0.176175 0.00063-0.083893 0.167786 0.167786 0.00064-0.0798981 0.159796 0.159796 0.00065-0.0760934 0.152187 0.152187 0.00066-0.0724699 0.14494 0.14494 0.00067-0.069019 0.138038 0.138038 0.00068-0.0657323 0.131465 0.131465 0.00069-0.0626022 0.125204 0.125204 0.0007-0.0596212 0.119242 0.119242 0.00071-0.0567821 0.113564 0.113564 0.00072-0.0540782 0.108156 0.108156 0.00073-0.051503 0.103006 0.103006 0.00074-0.0490505 0.098101 0.098101 0.00075-0.0467147 0.0934295 0.0934295 0.00076

50 6. Cir uito RL sin exita ión.-0.0444902 0.0889805 0.0889805 0.00077-0.0423716 0.0847433 0.0847433 0.00078-0.040354 0.0807079 0.0807079 0.00079-0.0384323 0.0768647 0.0768647 0.0008-0.0366022 0.0732044 0.0732044 0.00081-0.0348593 0.0697185 0.0697185 0.00082-0.0331993 0.0663986 0.0663986 0.00083-0.0316184 0.0632368 0.0632368 0.00084-0.0301127 0.0602255 0.0602255 0.00085-0.0286788 0.0573576 0.0573576 0.00086-0.0273131 0.0546263 0.0546263 0.00087-0.0260125 0.052025 0.052025 0.00088-0.0247738 0.0495477 0.0495477 0.00089-0.0235941 0.0471882 0.0471882 0.000900001-0.0224706 0.0449412 0.0449412 0.000910001-0.0214006 0.0428011 0.0428011 0.000920001-0.0203815 0.040763 0.040763 0.000930001-0.0194109 0.0388219 0.0388219 0.000940001-0.0184866 0.0369732 0.0369732 0.000950001-0.0176063 0.0352126 0.0352126 0.000960001-0.0167679 0.0335358 0.0335358 0.000970001-0.0159694 0.0319389 0.0319389 0.000980001-0.015209 0.030418 0.030418 0.000990001set terminal pngset output ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/6/ e jemplo06_gra f i a . png 'set en oding iso_8859_1set gridset autos aleset key bottom r i gh t t i t l e ' Var i ab l e s ' boxset t i t l e ' Graf i ado por d e f e t o de l a s s o l u i on e s de l i r u i t o 'plot ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/6/ ejemplo06_x_trans . data ' using 4 :1 t i t l e 'V en nodo 1 ' with l i n e s , ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/6/ ejemplo06_x_trans . data 'using 4 :2 t i t l e ' I Re s i s t en i a ent r e nodos 0 , 1 ' with l i n e s , ' /home/ ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/6/ ejemplo06_x_trans . data ' using 4 :3 t i t l e ' I de Bobina ent r e nodos 1 , 0 ' with l i n e sGrá o de salida.

6.3. Compara ión. 51

6.3. Compara ión.Comparemos la intensidad obtenida on el programa on su expresión ideal it = V

Re−

R

Lt

Capítulo 7Cir uito RL on ex ita ión es alón.En este ejemplo se analizará un ir uito RL omo el visto anteriormente pero utilizando unafuente de ex ita ión es alón. Los datos obtenidos serán similares a los del ejemplo 3 en la pági-na~27pero teniendo en uenta que la fuente no omenzará a alimentar el ir uito hasta llegado elvalor de salto a los 5 segundos.1 2

07.1. Datos Generales.Ar hivo *.sp ∗SPICE i r u i t <ejemplo07> from XCir uit v3 . 6 rev 1353 1 0 2 0 2 0 101 1 0 2 2 1 0 24 1 0 2 1 0 4 0 rho f 5 b 0 1 C D. endComo vemos se ha es ogido una ex ita ión tipo es alón ya que en la posi ión 7 del ve tor dedeni ión de la fuente hay un 4. A su vez en la posi ión 11 se en uentra un 5 que es el valor detiempo en que salta el es alón. Falta por denir los valores entre los que se mueve di ho es alónque para este ejemplo han sido desde 0 a 1.Tipo de análisis realizadoAnálisis esta ionario ⊠Análisis transitorio ⊠Datos generales del ir uitoElementos del Cto: 3EA: 0Nodos: 2A2: 3 53

54 7. Cir uito RL on ex ita ión es alón.No nulos: 10Densidad: 0.4Dispersion: 0.6Los valores dados al ir uito son:Elemento MagnitudResisten ia 2 ΩBobina 10 HMatriz T.Valores de la Matriz Trow 0: (2, -1) (3, 1)row 1: (2, 1) (4, -1)row 2: (0, -1) (1, 1) (2, -2)row 3: (0, 1)row 4: (1, -1) (4, -0 - 10 i)7.2. Solu iones7.2.1. Primer análisis Tiempo Ini ial 0Tiempo Final 30Paso de Tiempo 0, 3Theta 1 (Euler)Esta ionarioResultados sistema esta ionario:Tensión en nodo 1: 1.26117e-44 - 1.36736e-63 iTensión en nodo 2: 1.21266e-44 + 2.42532e-45 iI Resisten ia entre nodos 2, 1: -2.42532e-46 + 1.21266e-45 iI de Fuente tension entre nodos 1, 0: -2.42532e-46 + 1.21266e-45 iI de Bobina entre nodos 0, 2: -2.42532e-46 + 1.21266e-45 iTransitorio0 0 0 0 0 00 0 0 0 0 0.30 0 0 0 0 0.60 0 0 0 0 0.90 0 0 0 0 1.21 0.943396 -0.0283019 -0.0283019 -0.0283019 1.51 0.889996 -0.0550018 -0.0550018 -0.0550018 1.81 0.839619 -0.0801904 -0.0801904 -0.0801904 2.11 0.792094 -0.103953 -0.103953 -0.103953 2.4

7.2. Solu iones 551 0.747258 -0.126371 -0.126371 -0.126371 2.71 0.704961 -0.14752 -0.14752 -0.14752 31 0.665057 -0.167471 -0.167471 -0.167471 3.31 0.627412 -0.186294 -0.186294 -0.186294 3.61 0.591898 -0.204051 -0.204051 -0.204051 3.91 0.558395 -0.220803 -0.220803 -0.220803 4.21 0.526788 -0.236606 -0.236606 -0.236606 4.51 0.496969 -0.251515 -0.251515 -0.251515 4.81 0.468839 -0.26558 -0.26558 -0.26558 5.11 0.442301 -0.27885 -0.27885 -0.27885 5.41 0.417265 -0.291367 -0.291367 -0.291367 5.71 0.393646 -0.303177 -0.303177 -0.303177 61 0.371364 -0.314318 -0.314318 -0.314318 6.31 0.350344 -0.324828 -0.324828 -0.324828 6.61 0.330513 -0.334743 -0.334743 -0.334743 6.91 0.311805 -0.344098 -0.344098 -0.344098 7.21 0.294155 -0.352922 -0.352922 -0.352922 7.51 0.277505 -0.361247 -0.361247 -0.361247 7.81 0.261797 -0.369101 -0.369101 -0.369101 8.11 0.246979 -0.376511 -0.376511 -0.376511 8.41 0.232999 -0.383501 -0.383501 -0.383501 8.71 0.21981 -0.390095 -0.390095 -0.390095 91 0.207368 -0.396316 -0.396316 -0.396316 9.31 0.19563 -0.402185 -0.402185 -0.402185 9.61 0.184557 -0.407722 -0.407722 -0.407722 9.91 0.17411 -0.412945 -0.412945 -0.412945 10.21 0.164255 -0.417873 -0.417873 -0.417873 10.51 0.154957 -0.422521 -0.422521 -0.422521 10.81 0.146186 -0.426907 -0.426907 -0.426907 11.11 0.137912 -0.431044 -0.431044 -0.431044 11.41 0.130105 -0.434947 -0.434947 -0.434947 11.71 0.122741 -0.43863 -0.43863 -0.43863 121 0.115793 -0.442103 -0.442103 -0.442103 12.31 0.109239 -0.445381 -0.445381 -0.445381 12.61 0.103056 -0.448472 -0.448472 -0.448472 12.91 0.0972222 -0.451389 -0.451389 -0.451389 13.21 0.091719 -0.45414 -0.45414 -0.45414 13.51 0.0865274 -0.456736 -0.456736 -0.456736 13.81 0.0816296 -0.459185 -0.459185 -0.459185 14.11 0.0770091 -0.461495 -0.461495 -0.461495 14.41 0.0726501 -0.463675 -0.463675 -0.463675 14.71 0.0685378 -0.465731 -0.465731 -0.465731 151 0.0646583 -0.467671 -0.467671 -0.467671 15.31 0.0609984 -0.469501 -0.469501 -0.469501 15.61 0.0575457 -0.471227 -0.471227 -0.471227 15.91 0.0542884 -0.472856 -0.472856 -0.472856 16.21 0.0512154 -0.474392 -0.474392 -0.474392 16.51 0.0483164 -0.475842 -0.475842 -0.475842 16.81 0.0455816 -0.477209 -0.477209 -0.477209 17.11 0.0430015 -0.478499 -0.478499 -0.478499 17.41 0.0405674 -0.479716 -0.479716 -0.479716 17.71 0.0382711 -0.480864 -0.480864 -0.480864 181 0.0361049 -0.481948 -0.481948 -0.481948 18.31 0.0340612 -0.482969 -0.482969 -0.482969 18.6

56 7. Cir uito RL on ex ita ión es alón.1 0.0321332 -0.483933 -0.483933 -0.483933 18.91 0.0303143 -0.484843 -0.484843 -0.484843 19.21 0.0285984 -0.485701 -0.485701 -0.485701 19.51 0.0269797 -0.48651 -0.48651 -0.48651 19.81 0.0254525 -0.487274 -0.487274 -0.487274 20.11 0.0240118 -0.487994 -0.487994 -0.487994 20.41 0.0226526 -0.488674 -0.488674 -0.488674 20.71 0.0213704 -0.489315 -0.489315 -0.489315 211 0.0201608 -0.48992 -0.48992 -0.48992 21.31 0.0190196 -0.49049 -0.49049 -0.49049 21.61 0.017943 -0.491028 -0.491028 -0.491028 21.91 0.0169274 -0.491536 -0.491536 -0.491536 22.21 0.0159692 -0.492015 -0.492015 -0.492015 22.51 0.0150653 -0.492467 -0.492467 -0.492467 22.81 0.0142125 -0.492894 -0.492894 -0.492894 23.11 0.0134081 -0.493296 -0.493296 -0.493296 23.41 0.0126491 -0.493675 -0.493675 -0.493675 23.71 0.0119331 -0.494033 -0.494033 -0.494033 241 0.0112577 -0.494371 -0.494371 -0.494371 24.31 0.0106204 -0.49469 -0.49469 -0.49469 24.61 0.0100193 -0.49499 -0.49499 -0.49499 24.91 0.00945215 -0.495274 -0.495274 -0.495274 25.21 0.00891713 -0.495541 -0.495541 -0.495541 25.51 0.00841238 -0.495794 -0.495794 -0.495794 25.81 0.00793621 -0.496032 -0.496032 -0.496032 26.11 0.00748699 -0.496257 -0.496257 -0.496257 26.41 0.0070632 -0.496468 -0.496468 -0.496468 26.71 0.00666339 -0.496668 -0.496668 -0.496668 271 0.00628622 -0.496857 -0.496857 -0.496857 27.31 0.0059304 -0.497035 -0.497035 -0.497035 27.61 0.00559471 -0.497203 -0.497203 -0.497203 27.91 0.00527803 -0.497361 -0.497361 -0.497361 28.21 0.00497928 -0.49751 -0.49751 -0.49751 28.51 0.00469743 -0.497651 -0.497651 -0.497651 28.81 0.00443154 -0.497784 -0.497784 -0.497784 29.11 0.0041807 -0.49791 -0.49791 -0.49791 29.4set terminal pngset output ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/7/ e jemplo07_gra f i a . png 'set en oding iso_8859_1set gridset autos aleset key top r i gh t t i t l e ' Var i ab l e s ' boxset t i t l e ' Graf i ado por d e f e t o de l a s s o l u i on e s de l i r u i t o 'plot ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/7/ ejemplo07_x_trans . data ' using 6 :1 t i t l e 'V en nodo 1 ' with l i n e s , ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/7/ ejemplo07_x_trans . data 'using 6 :2 t i t l e 'V en nodo 2 ' with l i n e s , ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/7/ejemplo07_x_trans . data ' using 6 :3 t i t l e ' I Re s i s t en i a ent r e nodos 2 , 1 ' with l i n e s , ' /home/ ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/7/ ejemplo07_x_trans . data '

7.2. Solu iones 57using 6 :4 t i t l e ' I de Fuente t ens i on ent r e nodos 1 , 0 ' with l i n e s ,' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/7/ ejemplo07_x_trans . data ' using 6 :5 t i t l e ' I de Bobina ent r e nodos 0 , 2 ' with l i n e sGrá o de salida.

Hagamos una modi a ión en el s ript para ha er un zoom sobre los 5 primeros segundos, deesta forma apre iaremos mejor la parte de la grá a que no se ve orre tamente, además pasaremoslas representa iones de la intensidad a puntos para ver omo abe esperar que oin idan entre loselementos.

58 7. Cir uito RL on ex ita ión es alón.

Capítulo 8Cir uito RLC serie.Con este ejemplo se pro edera al analisis ir uitos de segundo orden. Este es un ir uito RLCserie on ex ita ión ontinua y analizaremos su respuesta transitoria y esta ionaria.1 2

308.1. Datos Generales.Ar hivo *.sp ∗SPICE i r u i t <ejemplo08> from XCir uit v3 . 6 rev 1352 1 0 1 0 3 0 0 ,00000013 1 0 2 3 2 0 0 ,00011 1 0 2 2 1 0 34 1 0 2 1 0 0 1 rho f a b A B C D. end Tipo de análisis realizadoAnálisis esta ionario ⊠Análisis transitorio ⊠Datos generales del ir uitoElementos del Cto: 4EA: 0Nodos: 3A2: 3No nulos: 13Densidad: 0.361111Dispersion: 0.6388888889 59

60 8. Cir uito RLC serie.Los valores dados al ir uito son:Elemento MagnitudResisten ia 0, 2 ΩBobina 0, 0001 HCondensador 10−6 FFuente de tensión 1 VMatriz T.Valores de la Matriz Trow 0: (3, -1) (4, 1)row 1: (3, 1) (5, -1)row 2: (2, 0 + 1e-07 i) (5, 1)row 3: (0, -1) (1, 1) (3, -0.2)row 4: (0, 1)row 5: (1, -1) (2, 1) (5, -0 - 0.0001 i)8.2. Solu iones8.2.1. Primer análisis Tiempo Ini ial 0Tiempo Final 0, 0001Paso de Tiempo 0, 000001Theta 1 (Euler)Esta ionarioResultados sistema esta ionario:Tensión en nodo 1: 1 + 1.01526e-13 iTensión en nodo 2: 1 - 2.00001e-08 iTensión en nodo 3: 1 - 2.00001e-08 iI Resisten ia entre nodos 2, 1: -2.00002e-15 - 1.00001e-07 iI de Fuente tension entre nodos 1, 0: -2.00002e-15 - 1.00001e-07 iI de Bobina entre nodos 3, 2: -2.00001e-15 - 1.00002e-07 iTransitorio1 0.998185 0.0907441 -0.00907441 -0.00907441 -0.00907441 01 0.996703 0.255599 -0.0164855 -0.0164855 -0.0164855 1e-061 0.995657 0.472744 -0.0217146 -0.0217146 -0.0217146 2e-061 0.995102 0.717637 -0.0244892 -0.0244892 -0.0244892 3e-061 0.995043 0.965485 -0.0247848 -0.0247848 -0.0247848 4e-061 0.995439 1.19352 -0.022804 -0.022804 -0.022804 5e-061 0.996213 1.3829 -0.0189371 -0.0189371 -0.0189371 6e-061 0.997258 1.51999 -0.0137098 -0.0137098 -0.0137098 7e-061 0.998456 1.59722 -0.00772218 -0.00772218 -0.00772218 8e-06

8.2. Solu iones 611 0.999682 1.6131 -0.00158804 -0.00158804 -0.00158804 9e-061 1.00082 1.57187 0.00412243 0.00412243 0.00412243 1e-051 1.00179 1.48257 0.00893026 0.00893026 0.00893026 1.1e-051 1.0025 1.35774 0.0124827 0.0124827 0.0124827 1.2e-051 1.00291 1.21201 0.0145736 0.0145736 0.0145736 1.3e-051 1.00303 1.06052 0.0151485 0.0151485 0.0151485 1.4e-051 1.00286 0.917565 0.0142956 0.0142956 0.0142956 1.5e-051 1.00244 0.795321 0.0122243 0.0122243 0.0122243 1.6e-051 1.00185 0.702966 0.00923553 0.00923553 0.00923553 1.7e-051 1.00114 0.646113 0.00568529 0.00568529 0.00568529 1.8e-051 1.00039 0.626635 0.00194775 0.00194775 0.00194775 1.9e-051 0.999676 0.642841 -0.0016206 -0.0016206 -0.0016206 2e-051 0.999058 0.689957 -0.0047116 -0.0047116 -0.0047116 2.1e-051 0.998582 0.760847 -0.00708895 -0.00708895 -0.00708895 2.2e-051 0.998279 0.846877 -0.00860298 -0.00860298 -0.00860298 2.3e-051 0.998161 0.938839 -0.0091962 -0.0091962 -0.0091962 2.4e-051 0.99822 1.02784 -0.00890001 -0.00890001 -0.00890001 2.5e-051 0.998435 1.10607 -0.00782361 -0.00782361 -0.00782361 2.6e-051 0.998773 1.16744 -0.0061369 -0.0061369 -0.0061369 2.7e-051 0.99919 1.20794 -0.00404942 -0.00404942 -0.00404942 2.8e-051 0.999642 1.22582 -0.00178769 -0.00178769 -0.00178769 2.9e-051 1.00009 1.22155 0.000426912 0.000426912 0.000426912 3e-051 1.00048 1.19757 0.0023978 0.0023978 0.0023978 3.1e-051 1.00079 1.15788 0.00396867 0.00396867 0.00396867 3.2e-051 1.00101 1.10754 0.00503402 0.00503402 0.00503402 3.3e-051 1.00111 1.0521 0.00554394 0.00554394 0.00554394 3.4e-051 1.0011 0.997066 0.00550359 0.00550359 0.00550359 3.5e-051 1.00099 0.94739 0.00496756 0.00496756 0.00496756 3.6e-051 1.00081 0.907086 0.00403037 0.00403037 0.00403037 3.7e-051 1.00056 0.878945 0.00281418 0.00281418 0.00281418 3.8e-051 1.00029 0.864393 0.0014552 0.0014552 0.0014552 3.9e-051 1.00002 0.863493 8.99512e-05 8.99512e-05 8.99512e-05 4e-051 0.999769 0.875064 -0.00115709 -0.00115709 -0.00115709 4.1e-051 0.999563 0.896901 -0.00218371 -0.00218371 -0.00218371 4.2e-051 0.999417 0.926073 -0.00291715 -0.00291715 -0.00291715 4.3e-051 0.999336 0.959253 -0.00331799 -0.00331799 -0.00331799 4.4e-051 0.999324 0.993059 -0.00338064 -0.00338064 -0.00338064 4.5e-051 0.999374 1.02437 -0.00313071 -0.00313071 -0.00313071 4.6e-051 0.999476 1.05056 -0.00261983 -0.00261983 -0.00261983 4.7e-051 0.999616 1.06975 -0.0019185 -0.0019185 -0.0019185 4.8e-051 0.999778 1.08083 -0.00110799 -0.00110799 -0.00110799 4.9e-051 0.999946 1.08355 -0.000271956 -0.000271956 -0.000271956 5e-051 1.0001 1.07844 0.000511373 0.000511373 0.000511373 5.1e-051 1.00024 1.06668 0.00117579 0.00117579 0.00117579 5.2e-051 1.00033 1.04996 0.00167202 0.00167202 0.00167202 5.3e-051 1.00039 1.03025 0.00197059 0.00197059 0.00197059 5.4e-051 1.00041 1.00962 0.00206271 0.00206271 0.00206271 5.5e-051 1.00039 0.990033 0.00195912 0.00195912 0.00195912 5.6e-051 1.00034 0.97316 0.00168734 0.00168734 0.00168734 5.7e-051 1.00026 0.960284 0.0012876 0.0012876 0.0012876 5.8e-051 1.00016 0.952203 0.000808016 0.000808016 0.000808016 5.9e-051 1.00006 0.949208 0.000299501 0.000299501 0.000299501 6e-051 0.999962 0.9511 -0.000189125 -0.000189125 -0.000189125 6.1e-051 0.999877 0.957253 -0.000615361 -0.000615361 -0.000615361 6.2e-05

62 8. Cir uito RLC serie.1 0.999811 0.966716 -0.000946306 -0.000946306 -0.000946306 6.3e-051 0.999768 0.978324 -0.00116075 -0.00116075 -0.00116075 6.4e-051 0.99975 0.990824 -0.00125001 -0.00125001 -0.00125001 6.5e-051 0.999756 1.003 -0.00121758 -0.00121758 -0.00121758 6.6e-051 0.999784 1.01378 -0.00107766 -0.00107766 -0.00107766 6.7e-051 0.999829 1.02231 -0.000852901 -0.000852901 -0.000852901 6.8e-051 0.999886 1.02802 -0.000571551 -0.000571551 -0.000571551 6.9e-051 0.999947 1.03066 -0.000264377 -0.000264377 -0.000264377 7e-051 1.00001 1.03028 3.83557e-05 3.83557e-05 3.83557e-05 7.1e-051 1.00006 1.02719 0.000309587 0.000309587 0.000309587 7.2e-051 1.00011 1.02191 0.000527621 0.000527621 0.000527621 7.3e-051 1.00014 1.01513 0.000677595 0.000677595 0.000677595 7.4e-051 1.00015 1.00761 0.000752199 0.000752199 0.000752199 7.5e-051 1.00015 1.00009 0.000751641 0.000751641 0.000751641 7.6e-051 1.00014 0.993265 0.000682928 0.000682928 0.000682928 7.7e-051 1.00011 0.987679 0.000558603 0.000558603 0.000558603 7.8e-051 1.00008 0.983728 0.000395095 0.000395095 0.000395095 7.9e-051 1.00004 0.98162 0.000210869 0.000210869 0.000210869 8e-051 1 0.981374 2.45595e-05 2.45595e-05 2.45595e-05 8.1e-051 0.999971 0.982841 -0.000146734 -0.000146734 -0.000146734 8.2e-051 0.999942 0.98573 -0.000288857 -0.000288857 -0.000288857 8.3e-051 0.999922 0.989646 -0.000391614 -0.000391614 -0.000391614 8.4e-051 0.99991 0.994139 -0.000449323 -0.000449323 -0.000449323 8.5e-051 0.999908 0.998748 -0.000460917 -0.000460917 -0.000460917 8.6e-051 0.999914 1.00304 -0.000429612 -0.000429612 -0.000429612 8.7e-051 0.999928 1.00667 -0.00036222 -0.00036222 -0.00036222 8.8e-051 0.999946 1.00935 -0.000268197 -0.000268197 -0.000268197 8.9e-051 0.999968 1.01093 -0.000158539 -0.000158539 -0.000158539 9e-051 0.999991 1.01138 -4.46441e-05 -4.46441e-05 -4.46441e-05 9.1e-051 1.00001 1.01075 6.27598e-05 6.27598e-05 6.27598e-05 9.2e-051 1.00003 1.00921 0.000154527 0.000154527 0.000154527 9.3e-051 1.00004 1.00697 0.000223779 0.000223779 0.000223779 9.4e-051 1.00005 1.00431 0.000266313 0.000266313 0.000266313 9.5e-051 1.00006 1.0015 0.000280745 0.000280745 0.000280745 9.6e-051 1.00005 0.998816 0.000268365 0.000268365 0.000268365 9.7e-051 1.00005 0.996488 0.000232778 0.000232778 0.000232778 9.8e-051 1.00004 0.994694 0.000179362 0.000179362 0.000179362 9.9e-05set terminal pngset output ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/4b/ e jemplo04_gra f i a . png 'set en oding iso_8859_1set gridset autos aleset key bottom r i gh t t i t l e ' Var i ab l e s ' boxset t i t l e ' Graf i ado por d e f e t o de l a s s o l u i on e s de l i r u i t o 'plot ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/4b/ejemplo04_x_trans . data ' using 7 :1 t i t l e 'V en nodo 1 ' with l i n e s , ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/4b/ejemplo04_x_trans . data 'using 7 :2 t i t l e 'V en nodo 2 ' with l i n e s , ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/4b/ejemplo04_x_trans . data ' using 7 :3 t i t l e 'V en nodo 3 ' with l i n e s , '/home/ ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s /

8.2. Solu iones 63 o l e i onprob l emas/4b/ejemplo04_x_trans . data ' using 7 :4 t i t l e ' I Re s i s t en i a ent r e nodos 2 , 1 ' with l i n e s , ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/4b/ejemplo04_x_trans . data ' using 7 :5 t i t l e ' I de Fuente t ens i on ent r e nodos 1 , 0 ' with l i n e s , ' /home/ ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/4b/ejemplo04_x_trans . data 'using 7 :6 t i t l e ' I de Bobina ent r e nodos 3 , 2 ' with l i n e sGrá o de salida.

Como la intensidad posee una amplitud mu ho menor que la onda de tensión representaremosahora por separado la intensidad del ir uito, on esto onseguiremos una visualiza ión de lavariable mu ho mejor en su evolu ión temporal.

64 8. Cir uito RLC serie.

Capítulo 9Cir uito RLC sin ex ita ión.Cir uito de segundo orden, RLC serie on ondi iones ini iales y análisis de su respuesta tran-sitoria y esta ionaria.1 2

09.1. Datos Generales.Ar hivo *.sp ∗SPICE i r u i t <ejemplo09> from XCir uit v3 . 6 rev 1352 1 0 1 1 0 0 0 ,0000013 1 0 2 0 2 0 0 ,00011 1 0 2 2 1 0 0 ,2. end Tipo de análisis realizadoAnálisis esta ionario ⊠Análisis transitorio ⊠Datos generales del ir uitoElementos del Cto: 3EA: 0Nodos: 2A2: 2No nulos: 9Densidad: 0.5625Dispersion: 0.4375 65

66 9. Cir uito RLC sin ex ita ión.Los valores dados al ir uito son:Elemento MagnitudResisten ia 0, 2 ΩBobina 0, 0001 HCondensador 10−6 FMatriz T.row 0: (0, 0 + 1e-06 i) (3, -1)row 1: (2, -1) (3, 1)row 2: (1, -1) (2, -0 - 0.0001 i)row 3: (0, -1) (1, 1) (3, -0.2)9.2. Solu iones9.2.1. Primer análisis Tiempo Ini ial 0Tiempo Final 0, 0006Paso de Tiempo 0, 0000012Theta 1 (Euler)Esta ionarioResultados sistema esta ionario:Tensión en nodo 1: 0Tensión en nodo 2: 0I de Bobina entre nodos 0, 2: 0I Resisten ia entre nodos 2, 1: 0Transitorio1.97168 1.96696 -0.0236035 -0.0236035 01.9159 1.9066 -0.0464827 -0.0464827 1.2e-061.83391 1.82024 -0.0683256 -0.0683256 2.4e-061.7273 1.70953 -0.0888399 -0.0888399 3.6e-061.59799 1.57644 -0.107757 -0.107757 4.8e-061.44819 1.42322 -0.124836 -0.124836 6e-061.28035 1.25238 -0.139864 -0.139864 7.2e-061.09715 1.06662 -0.152664 -0.152664 8.4e-060.901445 0.868827 -0.16309 -0.16309 9.6e-060.696205 0.661998 -0.171034 -0.171034 1.08e-050.484496 0.449211 -0.176424 -0.176424 1.2e-050.269423 0.233578 -0.179227 -0.179227 1.32e-050.0540885 0.0181994 -0.179446 -0.179446 1.44e-05-0.158454 -0.193878 -0.177119 -0.177119 1.56e-05-0.365241 -0.399706 -0.172323 -0.172323 1.68e-05

9.2. Solu iones 67-0.563439 -0.596472 -0.165165 -0.165165 1.8e-05-0.750383 -0.78154 -0.155786 -0.155786 1.92e-05-0.923611 -0.952482 -0.144357 -0.144357 2.04e-05-1.0809 -1.10711 -0.131071 -0.131071 2.16e-05-1.22028 -1.24351 -0.116149 -0.116149 2.28e-05-1.34007 -1.36004 -0.0998288 -0.0998288 2.4e-05-1.43891 -1.45538 -0.0823642 -0.0823642 2.52e-05-1.51573 -1.52854 -0.0640218 -0.0640218 2.64e-05-1.56982 -1.57884 -0.0450757 -0.0450757 2.76e-05-1.60079 -1.60595 -0.0258043 -0.0258043 2.88e-05-1.60857 -1.60987 -0.00648587 -0.00648587 3e-05-1.59345 -1.59092 0.0126052 0.0126052 3.12e-05-1.556 -1.54976 0.0312024 0.0312024 3.24e-05-1.49714 -1.48733 0.0490504 0.0490504 3.36e-05-1.41805 -1.40487 0.0659088 0.0659088 3.48e-05-1.32019 -1.30387 0.0815553 0.0815553 3.6e-05-1.20524 -1.18608 0.0957883 0.0957883 3.72e-05-1.07512 -1.05344 0.10843 0.10843 3.84e-05-0.931932 -0.908067 0.119326 0.119326 3.96e-05-0.777909 -0.752238 0.128353 0.128353 4.08e-05-0.615413 -0.58833 0.135413 0.135413 4.2e-05-0.446886 -0.418799 0.140439 0.140439 4.32e-05-0.274815 -0.246137 0.143392 0.143392 4.44e-05-0.101696 -0.0728423 0.144267 0.144267 4.56e-050.070004 0.0986206 0.143083 0.143083 4.68e-050.237875 0.265854 0.139893 0.139893 4.8e-050.399604 0.426559 0.134774 0.134774 4.92e-050.553002 0.578568 0.127831 0.127831 5.04e-050.696033 0.719872 0.119193 0.119193 5.16e-050.826844 0.848646 0.109009 0.109009 5.28e-050.943784 0.963274 0.0974498 0.0974498 5.4e-051.04543 1.06237 0.0847014 0.0847014 5.52e-051.13058 1.14478 0.0709641 0.0709641 5.64e-051.19832 1.20961 0.0564488 0.0564488 5.76e-051.24797 1.25624 0.0413738 0.0413738 5.88e-051.27912 1.28432 0.025962 0.025962 6e-051.29165 1.29374 0.0104372 0.0104372 6.12e-051.28567 1.28468 -0.00497894 -0.00497894 6.24e-051.26159 1.25758 -0.0200699 -0.0200699 6.36e-051.22004 1.21311 -0.0346272 -0.0346272 6.48e-051.16189 1.1522 -0.0484536 -0.0484536 6.60001e-051.08825 1.07598 -0.0613654 -0.0613654 6.72001e-051.00042 0.985782 -0.0731948 -0.0731948 6.84001e-050.89987 0.883112 -0.0837921 -0.0837921 6.96001e-050.788237 0.769631 -0.0930277 -0.0930277 7.08001e-050.667285 0.647126 -0.100793 -0.100793 7.20001e-050.538882 0.517481 -0.107003 -0.107003 7.32001e-050.404968 0.382649 -0.111595 -0.111595 7.44001e-050.267531 0.244625 -0.11453 -0.11453 7.56001e-050.128577 0.105418 -0.115795 -0.115795 7.68001e-05-0.00990236 -0.0329823 -0.1154 -0.1154 7.80001e-05-0.145954 -0.168629 -0.113376 -0.113376 7.92001e-05-0.27769 -0.299646 -0.10978 -0.10978 8.04001e-05-0.403317 -0.424255 -0.104689 -0.104689 8.16001e-05

68 9. Cir uito RLC sin ex ita ión.-0.521156 -0.540796 -0.0981996 -0.0981996 8.28001e-05-0.629668 -0.647754 -0.0904266 -0.0904266 8.40001e-05-0.72747 -0.74377 -0.0815013 -0.0815013 8.52001e-05-0.813353 -0.827667 -0.0715693 -0.0715693 8.64001e-05-0.886298 -0.898456 -0.0607879 -0.0607879 8.76001e-05-0.945487 -0.955352 -0.0493236 -0.0493236 8.88001e-05-0.990307 -0.997777 -0.0373503 -0.0373503 9.00001e-05-1.02036 -1.02537 -0.0250459 -0.0250459 9.12001e-05-1.03547 -1.03799 -0.01259 -0.01259 9.24001e-05-1.03566 -1.0357 -0.000161634 -0.000161634 9.36001e-05-1.02119 -1.01878 0.0120637 0.0120637 9.48001e-05-0.992488 -0.987705 0.0239161 0.0239161 9.60001e-05-0.950208 -0.943161 0.0352341 0.0352341 9.72001e-05-0.895168 -0.885995 0.045866 0.045866 9.84001e-05-0.828361 -0.817227 0.0556727 0.0556727 9.96001e-05-0.750926 -0.738021 0.064529 0.064529 0.0001008-0.664136 -0.649671 0.072325 0.072325 0.000102-0.569375 -0.553581 0.078968 0.078968 0.0001032-0.468115 -0.451239 0.0843829 0.0843829 0.0001044-0.361899 -0.344197 0.0885132 0.0885132 0.0001056-0.252313 -0.234049 0.0913218 0.0913218 0.0001068-0.140964 -0.122406 0.0927907 0.0927907 0.000108-0.029459 -0.0108747 0.0929212 0.0929212 0.00010920.0806213 0.098968 0.0917336 0.0917336 0.00011040.187741 0.205594 0.0892664 0.0892664 0.00011160.290432 0.307547 0.0855759 0.0855759 0.00011280.387313 0.40346 0.0807343 0.0807343 0.0001140.477109 0.492074 0.0748294 0.0748294 0.00011520.558663 0.572256 0.0679624 0.0679624 0.00011640.630959 0.643008 0.0602463 0.0602463 0.00011760.693124 0.703485 0.0518045 0.0518045 0.00011880.744446 0.753 0.0427685 0.0427685 0.000120.784378 0.791033 0.0332761 0.0332761 0.00012120.812541 0.817235 0.0234692 0.0234692 0.00012240.828731 0.83143 0.0134921 0.0134921 0.00012360.832918 0.833615 0.0034887 0.0034887 0.00012480.825239 0.823959 -0.00639882 -0.00639882 0.0001260.806 0.802794 -0.0160323 -0.0160323 0.00012720.775665 0.770609 -0.0252797 -0.0252797 0.00012840.734845 0.728042 -0.0340162 -0.0340162 0.00012960.684294 0.675868 -0.0421266 -0.0421266 0.00013080.624886 0.614985 -0.0495064 -0.0495064 0.0001320.55761 0.546397 -0.0560632 -0.0560632 0.00013320.483549 0.471205 -0.0617176 -0.0617176 0.00013440.403863 0.390582 -0.0664046 -0.0664046 0.00013560.319775 0.30576 -0.0700737 -0.0700737 0.00013680.232547 0.218009 -0.0726898 -0.0726898 0.0001380.143467 0.12862 -0.0742333 -0.0742333 0.00013920.0538272 0.0388872 -0.0746999 -0.0746999 0.0001404-0.035094 -0.0499142 -0.074101 -0.074101 0.0001416-0.122049 -0.136541 -0.0724625 -0.0724625 0.0001428-0.205839 -0.219804 -0.0698248 -0.0698248 0.000144-0.285329 -0.298577 -0.0662419 -0.0662419 0.0001452-0.359465 -0.371821 -0.06178 -0.06178 0.0001464

9.2. Solu iones 69-0.427285 -0.438589 -0.056517 -0.056517 0.0001476-0.487934 -0.498042 -0.0505405 -0.0505405 0.0001488-0.54067 -0.54946 -0.043947 -0.043947 0.00015-0.584878 -0.592246 -0.03684 -0.03684 0.0001512-0.620073 -0.625939 -0.0293287 -0.0293287 0.0001524-0.645904 -0.65021 -0.0215262 -0.0215262 0.0001536-0.662162 -0.664871 -0.0135478 -0.0135478 0.0001548-0.668773 -0.669875 -0.00550927 -0.00550927 0.000156-0.665803 -0.665309 0.00247443 0.00247443 0.0001572-0.653454 -0.651396 0.0102912 0.0102912 0.0001584-0.632054 -0.628488 0.017833 0.017833 0.0001596-0.602057 -0.597058 0.0249977 0.0249977 0.0001608-0.564029 -0.557691 0.03169 0.03169 0.000162-0.518642 -0.511077 0.0378229 0.0378229 0.0001632-0.466659 -0.457995 0.0433189 0.0433189 0.0001644-0.408926 -0.399304 0.0481105 0.0481105 0.0001656-0.346356 -0.335928 0.0521417 0.0521417 0.0001668-0.279915 -0.268841 0.0553678 0.0553678 0.000168-0.210607 -0.199056 0.0577564 0.0577564 0.0001692-0.139462 -0.127604 0.0592877 0.0592877 0.0001704-0.0675171 -0.0555263 0.059954 0.059954 0.00017160.00419514 0.0161472 0.0597602 0.0597602 0.00017280.0746632 0.0864078 0.0587233 0.0587233 0.0001740.142909 0.154284 0.0568719 0.0568719 0.00017520.208004 0.218853 0.0542457 0.0542457 0.00017640.269078 0.279257 0.0508946 0.0508946 0.00017760.325332 0.334707 0.0468781 0.0468781 0.00017880.376049 0.384501 0.0422641 0.0422641 0.000180.420602 0.428027 0.0371278 0.0371278 0.00018120.458462 0.464773 0.0315505 0.0315505 0.00018240.489205 0.494328 0.0256186 0.0256186 0.00018360.512511 0.516395 0.0194218 0.0194218 0.00018480.528174 0.530784 0.0130524 0.0130524 0.0001860.536098 0.537419 0.00660339 0.00660339 0.00018720.536299 0.536332 0.000167401 0.000167401 0.00018840.528901 0.527668 -0.00616462 -0.00616462 0.00018960.514136 0.511675 -0.0123047 -0.0123047 0.00019080.492333 0.488699 -0.0181691 -0.0181691 0.0001920.463918 0.459182 -0.0236793 -0.0236793 0.00019320.429402 0.423649 -0.0287631 -0.0287631 0.00019440.389375 0.382704 -0.0333555 -0.0333555 0.00019560.344496 0.337016 -0.0373997 -0.0373997 0.00019680.295479 0.287309 -0.0408474 -0.0408474 0.0001980.243087 0.234355 -0.0436597 -0.0436597 0.00019920.188118 0.178957 -0.0458072 -0.0458072 0.00020040.131394 0.12194 -0.0472704 -0.0472704 0.00020160.0737458 0.0641378 -0.0480401 -0.0480401 0.00020280.0160058 0.00638243 -0.0481167 -0.0481167 0.000204-0.0410069 -0.050509 -0.0475106 -0.0475106 0.0002052-0.0964969 -0.105745 -0.0462416 -0.0462416 0.0002064-0.149703 -0.158571 -0.0443388 -0.0443388 0.0002076-0.199911 -0.208279 -0.0418394 -0.0418394 0.0002088-0.246457 -0.254215 -0.0387889 -0.0387889 0.00021-0.288745 -0.295792 -0.0352393 -0.0352393 0.0002112

70 9. Cir uito RLC sin ex ita ión.-0.326244 -0.332494 -0.0312494 -0.0312494 0.0002124-0.358503 -0.36388 -0.0268829 -0.0268829 0.0002136-0.385153 -0.389594 -0.0222077 -0.0222077 0.0002148-0.405907 -0.409366 -0.0172953 -0.0172953 0.000216-0.42057 -0.423014 -0.0122192 -0.0122192 0.0002172-0.429035 -0.430445 -0.00705383 -0.00705383 0.0002184-0.431283 -0.431658 -0.00187393 -0.00187393 0.0002196-0.427387 -0.426738 0.00324692 0.00324692 0.0002208-0.417502 -0.415855 0.00823718 0.00823718 0.000222-0.401868 -0.399263 0.0130283 0.0130283 0.0002232-0.380801 -0.37729 0.0175558 0.0175558 0.0002244-0.35469 -0.350338 0.0217599 0.0217599 0.0002256-0.323986 -0.318869 0.0255863 0.0255863 0.0002268-0.289201 -0.283404 0.0289871 0.0289871 0.000228-0.250896 -0.244512 0.0319213 0.0319213 0.0002292-0.20967 -0.202799 0.0343549 0.0343549 0.0002304-0.166156 -0.158904 0.0362617 0.0362617 0.0002316-0.121008 -0.113483 0.0376235 0.0376235 0.0002328-0.0748918 -0.0672058 0.03843 0.03843 0.000234-0.0284771 -0.0207414 0.0386789 0.0386789 0.00023520.0175739 0.0252491 0.0383759 0.0383759 0.00023640.0626152 0.0701221 0.0375344 0.0375344 0.00023760.106026 0.113261 0.0361753 0.0361753 0.00023880.147217 0.154082 0.0343263 0.0343263 0.000240.185643 0.192048 0.0320217 0.0320217 0.00024120.220805 0.226666 0.0293017 0.0293017 0.00024240.252259 0.257502 0.0262117 0.0262117 0.00024360.279621 0.284182 0.0228015 0.0228015 0.00024480.302571 0.306396 0.0191248 0.0191248 0.0002460.320857 0.323904 0.0152379 0.0152379 0.00024720.334296 0.336536 0.0111995 0.0111995 0.00024840.342779 0.344193 0.0070692 0.0070692 0.00024960.346267 0.346849 0.00290701 0.00290701 0.00025080.344794 0.344549 -0.00122757 -0.00122757 0.0002520.338463 0.337407 -0.00527646 -0.00527646 0.00025320.327442 0.325605 -0.00918373 -0.00918373 0.00025440.311966 0.309387 -0.0128964 -0.0128964 0.00025560.292328 0.289055 -0.016365 -0.016365 0.00025680.268875 0.264966 -0.0195446 -0.0195446 0.0002580.242001 0.237522 -0.0223949 -0.0223949 0.00025920.212144 0.207168 -0.0248809 -0.0248809 0.00026040.179776 0.174381 -0.0269735 -0.0269735 0.00026160.145396 0.139666 -0.0286495 -0.0286495 0.00026280.109526 0.103548 -0.029892 -0.029892 0.0002640.072697 0.0665589 -0.0306908 -0.0306908 0.00026520.0354471 0.0292388 -0.0310416 -0.0310416 0.0002664-0.00168941 -0.00787883 -0.0309471 -0.0309471 0.0002676-0.0381884 -0.0442716 -0.0304158 -0.0304158 0.0002688-0.0735435 -0.079436 -0.0294626 -0.0294626 0.00027-0.107273 -0.112894 -0.0281078 -0.0281078 0.0002712-0.138926 -0.144201 -0.0263774 -0.0263774 0.0002724-0.168088 -0.172949 -0.024302 -0.024302 0.0002736-0.194388 -0.198772 -0.0219168 -0.0219168 0.0002748-0.217501 -0.221353 -0.0192605 -0.0192605 0.000276

9.2. Solu iones 71-0.237152 -0.240427 -0.0163754 -0.0163754 0.0002772-0.253119 -0.25578 -0.0133061 -0.0133061 0.0002784-0.265238 -0.267257 -0.010099 -0.010099 0.0002796-0.2734 -0.27476 -0.00680185 -0.00680185 0.0002808-0.277555 -0.278248 -0.00346288 -0.00346288 0.000282-0.277711 -0.277737 -0.00013003 -0.00013003 0.0002832-0.273932 -0.273302 0.00314959 0.00314959 0.0002844-0.266335 -0.265069 0.00633042 0.00633042 0.0002856-0.255092 -0.253219 0.00936905 0.00936905 0.0002868-0.240423 -0.237978 0.0122248 0.0122248 0.000288-0.222591 -0.219618 0.0148602 0.0148602 0.0002892-0.201901 -0.198452 0.0172416 0.0172416 0.0002904-0.178693 -0.174825 0.0193395 0.0193395 0.0002916-0.153338 -0.149113 0.0211289 0.0211289 0.0002928-0.126231 -0.121713 0.0225894 0.0225894 0.000294-0.097784 -0.0930428 0.023706 0.023706 0.0002952-0.068422 -0.0635283 0.0244683 0.0244683 0.0002964-0.0385762 -0.0336019 0.0248715 0.0248715 0.0002976-0.00867716 -0.00369399 0.0249158 0.0249158 0.00029880.0208507 0.0257721 0.0246066 0.0246066 0.00030.0495955 0.0543863 0.0239539 0.0239539 0.00030120.0771629 0.0817575 0.0229729 0.0229729 0.00030240.103182 0.107519 0.0216826 0.0216826 0.00030360.12731 0.131331 0.0201067 0.0201067 0.00030480.149236 0.152891 0.018272 0.018272 0.0003060.168687 0.171929 0.0162088 0.0162088 0.00030720.185427 0.188217 0.0139502 0.0139502 0.00030840.199265 0.201571 0.0115314 0.0115314 0.00030960.210052 0.21185 0.00898916 0.00898916 0.00031080.217686 0.218958 0.00636167 0.00636167 0.0003120.222111 0.222848 0.00368748 0.00368748 0.00031320.223317 0.223518 0.00100527 0.00100527 0.00031440.221341 0.221012 -0.00164687 -0.00164687 0.00031560.216263 0.215416 -0.00423187 -0.00423187 0.00031680.208206 0.206863 -0.00671422 -0.00671422 0.0003180.197333 0.195521 -0.00906047 -0.00906047 0.00031920.183845 0.181598 -0.0112396 -0.0112396 0.00032040.167977 0.165332 -0.0132236 -0.0132236 0.00032160.149992 0.146995 -0.0149876 -0.0149876 0.00032280.13018 0.126878 -0.0165101 -0.0165101 0.0003240.108852 0.105297 -0.0177737 -0.0177737 0.00032520.086334 0.082581 -0.0187646 -0.0187646 0.00032640.0629658 0.0590711 -0.0194735 -0.0194735 0.00032760.039092 0.035113 -0.0198948 -0.0198948 0.00032880.015059 0.0110535 -0.0200275 -0.0200275 0.00033-0.0087902 -0.0127651 -0.0198743 -0.0198743 0.0003312-0.0321208 -0.0360093 -0.0194422 -0.0194422 0.0003324-0.0546111 -0.0583595 -0.0187419 -0.0187419 0.0003336-0.0759564 -0.0795139 -0.0177877 -0.0177877 0.0003348-0.0958732 -0.0991927 -0.0165974 -0.0165974 0.000336-0.114103 -0.117142 -0.0151917 -0.0151917 0.0003372-0.130416 -0.133135 -0.0135941 -0.0135941 0.0003384-0.144613 -0.146979 -0.0118303 -0.0118303 0.0003396-0.156526 -0.158512 -0.00992819 -0.00992819 0.0003408

72 9. Cir uito RLC sin ex ita ión.-0.166027 -0.16761 -0.00791687 -0.00791687 0.000342-0.173019 -0.174184 -0.00582667 -0.00582667 0.0003432-0.177445 -0.178183 -0.00368848 -0.00368848 0.0003444-0.179285 -0.179592 -0.00153338 -0.00153338 0.0003456-0.178555 -0.178434 0.000607831 0.000607831 0.0003468-0.175309 -0.174768 0.00270505 0.00270505 0.000348-0.169634 -0.168688 0.00472931 0.00472931 0.0003492-0.16165 -0.16032 0.00665315 0.00665315 0.0003504-0.151509 -0.149819 0.00845098 0.00845098 0.0003516-0.13939 -0.13737 0.0100994 0.0100994 0.0003528-0.125497 -0.123181 0.0115776 0.0115776 0.000354-0.110056 -0.107483 0.0128674 0.0128674 0.0003552-0.0933116 -0.0905209 0.0139536 0.0139536 0.0003564-0.0755224 -0.0725576 0.0148243 0.0148243 0.0003576-0.0569576 -0.0538635 0.0154707 0.0154707 0.0003588-0.0378929 -0.0347154 0.0158873 0.0158873 0.00036-0.0186065 -0.0153921 0.016072 0.016072 0.00036120.000624729 0.00382993 0.016026 0.016026 0.00036240.0195294 0.0226801 0.0157539 0.0157539 0.00036360.0378451 0.0408977 0.0152631 0.0152631 0.0003648010.0553222 0.058235 0.0145643 0.0145643 0.0003660010.0717271 0.0744612 0.0136707 0.0136707 0.0003672010.0868451 0.0893648 0.0125984 0.0125984 0.0003684010.100483 0.102756 0.0113653 0.0113653 0.0003696010.112473 0.114472 0.00999162 0.00999162 0.0003708010.122672 0.124372 0.00849915 0.00849915 0.0003720010.130966 0.132348 0.00691098 0.00691098 0.0003732010.137267 0.138317 0.00525117 0.00525117 0.0003744010.14152 0.142229 0.00354442 0.00354442 0.0003756010.143699 0.144062 0.00181568 0.00181568 0.0003768010.143807 0.143825 8.97796e-05 8.97796e-05 0.0003780010.141876 0.141554 -0.00160887 -0.00160887 0.0003792010.137968 0.137317 -0.00325667 -0.00325667 0.0003804010.132171 0.131205 -0.00483113 -0.00483113 0.0003816010.124597 0.123335 -0.00631115 -0.00631115 0.0003828010.115385 0.113849 -0.00767734 -0.00767734 0.0003840010.10469 0.102907 -0.00891223 -0.00891223 0.0003852010.0926893 0.0906892 -0.0100005 -0.0100005 0.0003864010.0795743 0.0773885 -0.0109292 -0.0109292 0.0003876010.0655491 0.0632115 -0.0116877 -0.0116877 0.0003888010.0508273 0.0483736 -0.0122682 -0.0122682 0.0003900010.0356289 0.0330958 -0.0126653 -0.0126653 0.0003912010.020177 0.0176017 -0.0128766 -0.0128766 0.0003924010.00469467 0.00211429 -0.0129019 -0.0129019 0.000393601-0.0105983 -0.0131472 -0.0127442 -0.0127442 0.000394801-0.0254885 -0.0279702 -0.0124085 -0.0124085 0.000396001-0.0397718 -0.0421523 -0.0119027 -0.0119027 0.000397201-0.0532558 -0.0555031 -0.0112367 -0.0112367 0.000398401-0.0657627 -0.0678472 -0.0104225 -0.0104225 0.000399601-0.0771317 -0.0790266 -0.00947417 -0.00947417 0.000400801-0.0872206 -0.088902 -0.00840734 -0.00840734 0.000402001-0.0959074 -0.0973553 -0.00723908 -0.00723908 0.000403201-0.103093 -0.10429 -0.0059876 -0.0059876 0.000404401-0.108699 -0.109633 -0.004672 -0.004672 0.000405601

9.2. Solu iones 73-0.112673 -0.113336 -0.00331197 -0.00331197 0.000406801-0.114986 -0.115372 -0.00192751 -0.00192751 0.000408001-0.115633 -0.11574 -0.000538623 -0.000538623 0.000409201-0.114631 -0.114464 0.000834942 0.000834942 0.000410401-0.112022 -0.111587 0.00217399 0.00217399 0.000411601-0.10787 -0.107178 0.00346012 0.00346012 0.000412801-0.102259 -0.101323 0.004676 0.004676 0.000414001-0.0952919 -0.0941308 0.00580557 0.00580557 0.000415201-0.0870908 -0.085724 0.00683426 0.00683426 0.000416401-0.0777918 -0.076242 0.00774916 0.00774916 0.000417601-0.0675448 -0.0658369 0.00853921 0.00853921 0.000418801-0.0565105 -0.0546714 0.00919526 0.00919526 0.000420001-0.0448581 -0.0429161 0.00971026 0.00971026 0.000421201-0.0327631 -0.0307472 0.0100792 0.0100792 0.000422401-0.0204039 -0.018344 0.0102994 0.0102994 0.000423601-0.00795987 -0.00588588 0.01037 0.01037 0.0004248010.00439123 0.00644975 0.0102926 0.0102926 0.0004260010.0164761 0.0184902 0.0100707 0.0100707 0.0004272010.0281279 0.0300699 0.00970986 0.00970986 0.0004284010.0391889 0.0410324 0.00921748 0.00921748 0.0004296010.0495121 0.0512326 0.00860268 0.00860268 0.0004308010.0589636 0.0605388 0.00787622 0.00787622 0.0004320010.0674238 0.0688339 0.00705021 0.00705021 0.0004332010.0747894 0.076017 0.00613801 0.00613801 0.0004344010.0809742 0.082005 0.00515395 0.00515395 0.0004356010.08591 0.0867326 0.00411316 0.00411316 0.0004368010.0895475 0.0901538 0.00303131 0.00303131 0.0004380010.0918568 0.0922417 0.00192441 0.00192441 0.0004392010.0928271 0.0929888 0.000808545 0.000808545 0.0004404010.0924667 0.0924066 -0.000300334 -0.000300334 0.0004416010.0908027 0.0905254 -0.00138664 -0.00138664 0.0004428010.0878803 0.0873932 -0.00243536 -0.00243536 0.0004440010.0837616 0.0830751 -0.00343226 -0.00343226 0.0004452010.0785247 0.0776519 -0.00436408 -0.00436408 0.0004464010.0722622 0.0712185 -0.0052187 -0.0052187 0.0004476010.0650799 0.0638828 -0.0059853 -0.0059853 0.0004488010.0570945 0.0557636 -0.00665446 -0.00665446 0.0004500010.0484325 0.0469889 -0.00721833 -0.00721833 0.0004512010.0392277 0.0376936 -0.00767065 -0.00767065 0.0004524010.0296195 0.0280181 -0.00800687 -0.00800687 0.0004536010.0197505 0.0181057 -0.00822414 -0.00822414 0.0004548010.00976493 0.00810066 -0.00832134 -0.00832134 0.000456001-0.000193987 -0.00185381 -0.0082991 -0.0082991 0.000457201-0.00998561 -0.0116176 -0.00815969 -0.00815969 0.000458401-0.019474 -0.0210554 -0.00790702 -0.00790702 0.000459601-0.0285299 -0.0300392 -0.00754655 -0.00754655 0.000460801-0.0370321 -0.0384491 -0.00708516 -0.00708516 0.000462001-0.0448694 -0.0461756 -0.00653106 -0.00653106 0.000463201-0.0519417 -0.0531204 -0.00589361 -0.00589361 0.000464401-0.0581616 -0.0591982 -0.00518323 -0.00518323 0.000465601-0.063455 -0.0643372 -0.00441118 -0.00441118 0.000466801-0.0677623 -0.0684802 -0.00358942 -0.00358942 0.000468001-0.0710388 -0.0715849 -0.0027304 -0.0027304 0.000469201-0.0732551 -0.0736245 -0.00184691 -0.00184691 0.000470401

74 9. Cir uito RLC sin ex ita ión.-0.0743973 -0.0745877 -0.000951858 -0.000951858 0.000471601-0.0744671 -0.0744787 -5.81142e-05 -5.81142e-05 0.000472801-0.073481 -0.0733167 0.000821686 0.000821686 0.000474001-0.0714707 -0.0711356 0.00167531 0.00167531 0.000475201-0.0684813 -0.0679831 0.00249111 0.00249111 0.000476401-0.0645715 -0.0639199 0.00325815 0.00325815 0.000477601-0.0598119 -0.0590186 0.00396637 0.00396637 0.000478801-0.0542838 -0.0533625 0.00460672 0.00460672 0.000480001-0.0480783 -0.0470441 0.00517125 0.00517125 0.000481201-0.0412945 -0.0401638 0.00565322 0.00565322 0.000482401-0.0340379 -0.0328284 0.00604716 0.00604716 0.000483601-0.0264191 -0.0251493 0.00634895 0.00634895 0.000484801-0.0185521 -0.017241 0.00655584 0.00655584 0.000486001-0.0105524 -0.00921906 0.00666647 0.00666647 0.000487201-0.00253532 -0.00119915 0.00668086 0.00668086 0.0004884010.00538516 0.00670523 0.0066004 0.0066004 0.0004896010.0130985 0.0143841 0.00642779 0.00642779 0.0004908010.0204989 0.0217323 0.006167 0.006167 0.0004920010.0274867 0.0286514 0.00582319 0.00582319 0.0004932010.0339698 0.0350503 0.00540258 0.00540258 0.0004944010.0398647 0.0408472 0.00491241 0.00491241 0.0004956020.0450977 0.0459698 0.00436078 0.00436078 0.0004968020.0496054 0.0503567 0.0037565 0.0037565 0.0004980020.0533362 0.053958 0.003109 0.003109 0.0004992020.0562501 0.0567357 0.00242817 0.00242817 0.0005004020.0583191 0.0586639 0.0017242 0.0017242 0.0005016020.059528 0.0597295 0.00100745 0.00100745 0.0005028020.059874 0.0599316 0.00028827 0.00028827 0.0005040020.0593662 0.0592816 -0.000423109 -0.000423109 0.0005052020.0580261 0.0578028 -0.00111674 -0.00111674 0.0005064020.0558864 0.0555298 -0.0017831 -0.0017831 0.0005076020.0529906 0.0525079 -0.0024132 -0.0024132 0.0005088020.0493921 0.0487924 -0.0029987 -0.0029987 0.0005100020.0451537 0.0444472 -0.00353207 -0.00353207 0.0005112020.0403457 0.0395444 -0.0040066 -0.0040066 0.0005124020.0350459 0.0341625 -0.00441655 -0.00441655 0.0005136020.0293372 0.0283858 -0.00475718 -0.00475718 0.0005148020.0233075 0.0223025 -0.00502481 -0.00502481 0.0005160020.0170472 0.0160039 -0.00521686 -0.00521686 0.0005172020.010649 0.00958263 -0.00533185 -0.00533185 0.0005184020.00420568 0.0031318 -0.00536943 -0.00536943 0.000519602-0.00219074 -0.00325681 -0.00533035 -0.00533035 0.000520802-0.00845045 -0.00949374 -0.00521643 -0.00521643 0.000522002-0.0144871 -0.0154932 -0.00503051 -0.00503051 0.000523202-0.0202188 -0.0211741 -0.00477642 -0.00477642 0.000524402-0.0255694 -0.0264612 -0.00445889 -0.00445889 0.000525602-0.0304696 -0.0312863 -0.00408345 -0.00408345 0.000526802-0.0348572 -0.0355885 -0.00365639 -0.00365639 0.000528002-0.0386788 -0.0393157 -0.0031846 -0.0031846 0.000529202-0.0418894 -0.0424245 -0.00267551 -0.00267551 0.000530402-0.0444537 -0.0448811 -0.00213693 -0.00213693 0.000531602-0.0463461 -0.0466615 -0.001577 -0.001577 0.000532802-0.0475509 -0.0477517 -0.00100398 -0.00100398 0.000534002-0.0480623 -0.0481475 -0.000426206 -0.000426206 0.000535202

9.2. Solu iones 75-0.0478846 -0.047855 0.000148055 0.000148055 0.000536402-0.0470318 -0.0468896 0.00071073 0.00071073 0.000537602-0.0455269 -0.0452761 0.00125404 0.00125404 0.000538802-0.0434022 -0.043048 0.00177062 0.00177062 0.000540002-0.0406979 -0.0402471 0.00225359 0.00225359 0.000541202-0.0374619 -0.0369225 0.00269666 0.00269666 0.000542402-0.0337488 -0.03313 0.00309422 0.00309422 0.000543602-0.0296192 -0.0289309 0.00344139 0.00344139 0.000544802-0.0251383 -0.0243914 0.00373408 0.00373408 0.000546002-0.0203754 -0.0195816 0.00396906 0.00396906 0.000547202-0.0154026 -0.0145739 0.00414395 0.00414395 0.000548402-0.0102939 -0.00944248 0.00425726 0.00425726 0.000549602-0.00512384 -0.00426216 0.0043084 0.0043084 0.0005508023.33823e-05 0.00089292 0.00429769 0.00429769 0.0005520020.00510493 0.00595018 0.00422629 0.00422629 0.0005532020.0100204 0.0108396 0.00409621 0.00409621 0.0005544020.0147127 0.0154948 0.00391027 0.00391027 0.0005556020.0191191 0.0198536 0.00367203 0.00367203 0.0005568020.023182 0.0238592 0.00338572 0.00338572 0.0005580020.0268494 0.0274607 0.00305619 0.00305619 0.0005592020.030076 0.0306138 0.00268883 0.00268883 0.0005604020.0328234 0.0332813 0.00228945 0.00228945 0.0005616020.0350605 0.0354333 0.00186425 0.00186425 0.0005628020.0367641 0.037048 0.00141968 0.00141968 0.0005640020.0379189 0.0381114 0.00096234 0.00096234 0.0005652020.0385176 0.0386174 0.000498931 0.000498931 0.0005664020.038561 0.0385682 3.61125e-05 3.61125e-05 0.0005676020.0380575 0.0379736 -0.00041957 -0.00041957 0.0005688020.0370233 0.036851 -0.000861782 -0.000861782 0.0005700020.035482 0.0352251 -0.00128448 -0.00128448 0.0005712020.0334635 0.0331271 -0.00168201 -0.00168201 0.0005724020.0310046 0.0305947 -0.00204915 -0.00204915 0.0005736020.0281471 0.0276709 -0.0023812 -0.0023812 0.0005748020.0249383 0.0244035 -0.00267404 -0.00267404 0.0005760020.0214293 0.0208445 -0.00292417 -0.00292417 0.0005772020.0176748 0.017049 -0.00312876 -0.00312876 0.0005784020.013732 0.0130749 -0.00328566 -0.00328566 0.0005796020.00965987 0.00898118 -0.00339343 -0.00339343 0.0005808020.00551822 0.00482795 -0.00345137 -0.00345137 0.0005820020.00136686 0.00067497 -0.00345947 -0.00345947 0.000583202-0.00273526 -0.00341895 -0.00341844 -0.00341844 0.000584402-0.00673088 -0.00739681 -0.00332968 -0.00332968 0.000585602-0.0105652 -0.0112042 -0.00319523 -0.00319523 0.000586802-0.0141864 -0.01479 -0.00301775 -0.00301775 0.000588002-0.017547 -0.0181071 -0.00280046 -0.00280046 0.000589202-0.0206035 -0.021113 -0.00254711 -0.00254711 0.000590402-0.0233178 -0.0237701 -0.00226187 -0.00226187 0.000591602-0.0256569 -0.0260468 -0.0019493 -0.0019493 0.000592802-0.0275941 -0.027917 -0.0016143 -0.0016143 0.000594002-0.0291085 -0.0293609 -0.00126197 -0.00126197 0.000595202-0.0301856 -0.0303651 -0.000897589 -0.000897589 0.000596402-0.0308174 -0.0309227 -0.000526517 -0.000526517 0.000597602-0.0310023 -0.0310332 -0.000154119 -0.000154119 0.0006

76 9. Cir uito RLC sin ex ita ión.set terminal pngset output ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/9/ e jemplo09_gra f i a . png 'set en oding iso_8859_1set gridset autos aleset key bottom r i gh t t i t l e ' Var i ab l e s ' boxset t i t l e ' Graf i ado por d e f e t o de l a s s o l u i on e s de l i r u i t o 'plot ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/9/ ejemplo09_x_trans . data ' using 5 :1 t i t l e 'V en nodo 1 ' with l i n e s , ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/9/ ejemplo09_x_trans . data 'using 5 :2 t i t l e 'V en nodo 2 ' with l i n e s , ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/9/ejemplo09_x_trans . data ' using 5 :3 t i t l e ' I de Bobina ent r e nodos 0 , 2 ' with l i n e s , ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/9/ ejemplo09_x_trans . data 'using 5 :4 t i t l e ' I Re s i s t en i a ent r e nodos 2 , 1 ' with l i n e sGrá o de salida.

Veámos por separado la tensión del nudo 1, la del 2 y la intensidad de la malla

9.2. Solu iones 77

Podríamos pensar que las tensiones en los nudos 1 y 2 son iguales pero esto no es así, tal y omo puede verse en los datos de salida. Sus valores son similares debido a la po a aída de tensiónexistente en la misma debido a su redu ido valor de 0, 2 Ω

78 9. Cir uito RLC sin ex ita ión.

Capítulo 10Cir uito RLC paralelo.Cir uitos de segundo orden, RLC paralelo on ex ita ión de fuente de intensidad.10.1. Datos Generales.Ar hivo *.sp ∗SPICE i r u i t <ejemplo010> from XCir uit v3 . 6 rev 1352 1 0 1 1 0 0 0 ,0000023 1 0 2 1 0 0 0 ,00011 1 0 2 1 0 0 105 1 0 3 1 0 0 1 rho f a b A B C D. end Tipo de análisis realizadoAnálisis esta ionario ⊠Análisis transitorio ⊠Datos generales del ir uitoElementos del Cto: 4EA: 0Nodos: 1A2: 2No nulos: 7Densidad: 0.777778Dispersion: 0.2222222222 79

80 10. Cir uito RLC paralelo.Los valores dados al ir uito son:Elemento MagnitudResisten ia 10 ΩBobina 0, 0001 HCondensador 2 · 10−6 FMatriz T.row 0: (0, 0 + 2e-06 i) (1, 1) (2, 1)row 1: (0, 1) (1, -10)row 2: (0, 1) (2, -0 - 0.0001 i)10.2. Solu iones10.2.1. Primer análisis Tiempo Ini ial 0Tiempo Final 0, 00064Paso de Tiempo 0, 000002Theta 1 (Euler)Esta ionarioResultados sistema esta ionario:Tensión en nodo 1: -1e-10 - 1e-05 iI Resisten ia entre nodos 1, 0: 0.1 - 1e-06 iI de Bobina entre nodos 1, 0: -0.1 + 1e-06 iTransitorio-0.982143 0.00178571 0.980357 0-1.84152 -0.0841518 0.943527 2e-06-2.57593 -0.157593 0.892008 4e-06-3.18566 -0.218566 0.828295 6e-06-3.67318 -0.267318 0.754831 8e-06-4.04286 -0.304286 0.673974 1e-05-4.30075 -0.330075 0.587959 1.2e-05-4.4542 -0.34542 0.498875 1.4e-05-4.51168 -0.351168 0.408642 1.6e-05-4.48243 -0.348243 0.318993 1.8e-05-4.37627 -0.337627 0.231468 2e-05-4.20334 -0.320334 0.147401 2.2e-05-3.97387 -0.297387 0.0679236 2.4e-05-3.69803 -0.269803 -0.00603705 2.6e-05-3.38571 -0.238571 -0.0737512 2.8e-05-3.04639 -0.204639 -0.134679 3e-05-2.68903 -0.168903 -0.18846 3.2e-05

10.2. Solu iones 81-2.32194 -0.132194 -0.234898 3.4e-05-1.95271 -0.0952713 -0.273953 3.6e-05-1.58818 -0.0588179 -0.305716 3.8e-05-1.23434 -0.0234341 -0.330403 4e-05-0.896374 0.0103626 -0.34833 4.2e-05-0.57861 0.042139 -0.359903 4.4e-05-0.28456 0.071544 -0.365594 4.6e-05-0.0169341 0.0983066 -0.365933 4.8e-050.22232 0.122232 -0.361486 5e-050.43197 0.143197 -0.352847 5.2e-050.611443 0.161144 -0.340618 5.4e-050.760769 0.176077 -0.325403 5.6e-050.88051 0.188051 -0.307792 5.8e-050.971699 0.19717 -0.288358 6e-051.03577 0.203577 -0.267643 6.2e-051.07447 0.207447 -0.246154 6.4e-051.08984 0.208984 -0.224357 6.6e-051.08411 0.208411 -0.202675 6.8e-051.05963 0.205963 -0.181482 7e-051.01885 0.201885 -0.161105 7.2e-050.964243 0.196424 -0.14182 7.4e-050.898271 0.189827 -0.123855 7.6e-050.823327 0.182333 -0.107388 7.8e-050.74171 0.174171 -0.0925541 8e-050.655593 0.165559 -0.0794422 8.2e-050.566995 0.1567 -0.0681023 8.4e-050.477766 0.147777 -0.058547 8.6e-050.389565 0.138956 -0.0507557 8.8e-050.303858 0.130386 -0.0446785 9e-050.221907 0.122191 -0.0402404 9.2e-050.144775 0.114477 -0.0373449 9.4e-050.0733211 0.107332 -0.0358785 9.6e-050.00821392 0.100821 -0.0357142 9.8e-05-0.0500642 0.0949936 -0.0367155 0.0001-0.101204 0.0898796 -0.0387396 0.000102-0.145058 0.0854942 -0.0416407 0.000104-0.181622 0.0818378 -0.0452732 0.000106-0.211026 0.0788974 -0.0494937 0.000108-0.233511 0.0766489 -0.0541639 0.00011-0.249417 0.0750583 -0.0591522 0.000112-0.259165 0.0740835 -0.0643355 0.000114-0.263241 0.0736759 -0.0696004 0.000116-0.262179 0.0737821 -0.0748439 0.000118-0.256549 0.0743451 -0.0799749 0.00012-0.246941 0.0753059 -0.0849137 0.000122-0.233953 0.0766047 -0.0895928 0.000124-0.218179 0.0781821 -0.0939564 0.000126-0.200199 0.0799801 -0.0979603 0.000128-0.18057 0.081943 -0.101572 0.00013-0.15982 0.084018 -0.104768 0.000132-0.138439 0.0861561 -0.107537 0.000134-0.116877 0.0883123 -0.109874 0.000136-0.0955378 0.0904462 -0.111785 0.000138-0.0747791 0.0925221 -0.113281 0.00014

82 10. Cir uito RLC paralelo.-0.0549092 0.0945091 -0.114379 0.000142-0.0361877 0.0963812 -0.115103 0.000144-0.0188259 0.0981174 -0.115479 0.000146-0.00298807 0.0997012 -0.115539 0.0001480.0112062 0.101121 -0.115315 0.000150.0236795 0.102368 -0.114841 0.0001520.0343936 0.103439 -0.114153 0.0001540.0433456 0.104335 -0.113287 0.0001560.0505643 0.105056 -0.112275 0.0001580.0561068 0.105611 -0.111153 0.000160.0600534 0.106005 -0.109952 0.0001620.0625049 0.10625 -0.108702 0.0001640.0635775 0.106358 -0.10743 0.0001660.0633999 0.10634 -0.106162 0.0001680.0621092 0.106211 -0.10492 0.000170.0598476 0.105985 -0.103723 0.0001720.0567597 0.105676 -0.102588 0.0001740.0529891 0.105299 -0.101528 0.0001760.0486762 0.104868 -0.100555 0.0001780.0439562 0.104396 -0.0996756 0.000180.038957 0.103896 -0.0988965 0.0001820.0337977 0.10338 -0.0982205 0.0001840.0285877 0.102859 -0.0976488 0.0001860.0234254 0.102343 -0.0971803 0.0001880.0183979 0.10184 -0.0968123 0.000190.0135806 0.101358 -0.0965407 0.0001920.00903684 0.100904 -0.09636 0.0001940.00481857 0.100482 -0.0962636 0.0001960.000966203 0.100097 -0.0962443 0.000198-0.00249066 0.0997509 -0.0962941 0.0002-0.00553267 0.0994467 -0.0964047 0.000202-0.00814995 0.099185 -0.0965677 0.000204-0.0103413 0.0989659 -0.0967745 0.000206-0.0121131 0.0987887 -0.0970168 0.000208-0.0134789 0.0986521 -0.0972864 0.00021-0.0144576 0.0985542 -0.0975755 0.000212-0.0150732 0.0984927 -0.097877 0.000214-0.0153538 0.0984646 -0.0981841 0.000216-0.0153301 0.098467 -0.0984907 0.000218-0.0150352 0.0984965 -0.0987914 0.00022-0.0145034 0.0985497 -0.0990815 0.000222-0.0137696 0.098623 -0.0993568 0.000224-0.0128685 0.0987131 -0.0996142 0.000226-0.0118342 0.0988166 -0.0998509 0.000228-0.0106994 0.0989301 -0.100065 0.00023-0.00949508 0.0990505 -0.100255 0.000232-0.00825026 0.099175 -0.10042 0.000234-0.00699148 0.0993009 -0.10056 0.000236-0.00574273 0.0994257 -0.100674 0.000238-0.00452523 0.0995475 -0.100765 0.00024-0.00335736 0.0996643 -0.100832 0.000242-0.00225467 0.0997745 -0.100877 0.000244-0.00122986 0.099877 -0.100902 0.000246-0.000292892 0.0999707 -0.100908 0.000248

10.2. Solu iones 830.000548917 0.100055 -0.100897 0.000250.00129073 0.100129 -0.100871 0.0002520.00193001 0.100193 -0.100832 0.0002540.00246634 0.100247 -0.100783 0.0002560.00290116 0.10029 -0.100725 0.0002580.00323759 0.100324 -0.10066 0.000260.00348015 0.100348 -0.100591 0.0002620.00363458 0.100363 -0.100518 0.0002640.00370756 0.100371 -0.100444 0.0002660.00370652 0.100371 -0.10037 0.0002680.0036394 0.100364 -0.100297 0.000270.00351448 0.100351 -0.100227 0.0002720.00334019 0.100334 -0.10016 0.0002740.00312492 0.100312 -0.100097 0.0002760.00287692 0.100288 -0.10004 0.0002780.00260412 0.10026 -0.0999876 0.000280.00231404 0.100231 -0.0999413 0.0002820.00201372 0.100201 -0.0999011 0.0002840.00170962 0.100171 -0.0998669 0.0002860.00140757 0.100141 -0.0998387 0.0002880.00111275 0.100111 -0.0998165 0.000290.000829643 0.100083 -0.0997999 0.0002920.000562057 0.100056 -0.0997886 0.0002940.000313104 0.100031 -0.0997824 0.0002968.52329e-05 0.100009 -0.0997807 0.000298-0.000119745 0.099988 -0.099783 0.0003-0.000300623 0.0999699 -0.0997891 0.000302-0.000456753 0.0999543 -0.0997982 0.000304-0.000587998 0.0999412 -0.09981 0.000306-0.000694681 0.0999305 -0.0998238 0.000308-0.000777529 0.0999222 -0.0998394 0.00031-0.000837616 0.0999162 -0.0998562 0.000312-0.000876308 0.0999124 -0.0998737 0.000314-0.000895206 0.0999105 -0.0998916 0.000316-0.000896093 0.0999104 -0.0999095 0.000318-0.000880883 0.0999119 -0.0999271 0.00032-0.000851573 0.0999148 -0.0999442 0.000322-0.000810197 0.099919 -0.0999604 0.000324-0.000758786 0.0999241 -0.0999755 0.000326-0.000699334 0.0999301 -0.0999895 0.000327999-0.000633763 0.0999366 -0.100002 0.000329999-0.000563901 0.0999436 -0.100013 0.000331999-0.000491454 0.0999509 -0.100023 0.000333999-0.000417993 0.0999582 -0.100032 0.000335999-0.000344939 0.0999655 -0.100039 0.000337999-0.000273553 0.0999726 -0.100044 0.000339999-0.00020493 0.0999795 -0.100048 0.000341999-0.000140001 0.099986 -0.100051 0.000343999-7.95275e-05 0.099992 -0.100053 0.000345999-2.41136e-05 0.0999976 -0.100053 0.0003479992.57937e-05 0.100003 -0.100052 0.0003499996.98932e-05 0.100007 -0.100051 0.0003519990.00010802 0.100011 -0.100049 0.0003539990.000140132 0.100014 -0.100046 0.000355999

84 10. Cir uito RLC paralelo.0.000166302 0.100017 -0.100043 0.0003579990.000186698 0.100019 -0.100039 0.0003599990.000201575 0.10002 -0.100035 0.0003619990.000211258 0.100021 -0.100031 0.0003639990.000216131 0.100022 -0.100026 0.0003659990.000216623 0.100022 -0.100022 0.0003679990.000213194 0.100021 -0.100018 0.0003699990.000206325 0.100021 -0.100014 0.0003719990.000196508 0.10002 -0.10001 0.0003739990.000184233 0.100018 -0.100006 0.0003759990.000169984 0.100017 -0.100003 0.0003779990.000154226 0.100015 -0.0999997 0.0003799990.000137402 0.100014 -0.0999969 0.0003819990.000119928 0.100012 -0.0999945 0.0003839990.000102184 0.10001 -0.0999925 0.0003859998.45161e-05 0.100008 -0.0999908 0.0003879996.72323e-05 0.100007 -0.0999894 0.0003899995.05997e-05 0.100005 -0.0999884 0.0003919993.48457e-05 0.100003 -0.0999877 0.0003939992.01573e-05 0.100002 -0.0999873 0.0003959996.68271e-06 0.100001 -0.0999872 0.000397999-5.4675e-06 0.0999995 -0.0999873 0.000399999-1.62183e-05 0.0999984 -0.0999876 0.000401999-2.55275e-05 0.0999974 -0.0999881 0.000403999-3.33835e-05 0.0999967 -0.0999888 0.000405999-3.98017e-05 0.099996 -0.0999896 0.000407999-4.48215e-05 0.0999955 -0.0999905 0.000409999-4.8503e-05 0.0999951 -0.0999915 0.000411999-5.0924e-05 0.0999949 -0.0999925 0.000413999-5.21762e-05 0.0999948 -0.0999935 0.000415999-5.23625e-05 0.0999948 -0.0999946 0.000417999-5.15938e-05 0.0999948 -0.0999956 0.000419999-4.99862e-05 0.099995 -0.0999966 0.000421999-4.76582e-05 0.0999952 -0.0999976 0.000423999-4.47286e-05 0.0999955 -0.0999985 0.000425999-4.13142e-05 0.0999959 -0.0999993 0.000427999-3.75278e-05 0.0999962 -0.1 0.000429999-3.3477e-05 0.0999967 -0.100001 0.000431999-2.92624e-05 0.0999971 -0.100001 0.000433999-2.49768e-05 0.0999975 -0.100002 0.000435999-2.07043e-05 0.0999979 -0.100002 0.000437999-1.65199e-05 0.0999983 -0.100003 0.000439999-1.24889e-05 0.0999988 -0.100003 0.000441999-8.6667e-06 0.0999991 -0.100003 0.000443999-5.09928e-06 0.0999995 -0.100003 0.000445999-1.82303e-06 0.0999998 -0.100003 0.0004479991.13476e-06 0.1 -0.100003 0.0004499993.75537e-06 0.1 -0.100003 0.0004519996.02815e-06 0.100001 -0.100003 0.0004539997.94976e-06 0.100001 -0.100003 0.0004559999.52353e-06 0.100001 -0.100003 0.0004579991.07586e-05 0.100001 -0.100002 0.0004599991.16693e-05 0.100001 -0.100002 0.0004619991.2274e-05 0.100001 -0.100002 0.000463999

10.2. Solu iones 851.25947e-05 0.100001 -0.100002 0.0004659991.26561e-05 0.100001 -0.100001 0.0004679991.2485e-05 0.100001 -0.100001 0.0004699991.21093e-05 0.100001 -0.100001 0.0004719991.15575e-05 0.100001 -0.100001 0.0004739981.08585e-05 0.100001 -0.1 0.0004759981.00405e-05 0.100001 -0.1 0.0004779989.13089e-06 0.100001 -0.1 0.0004799988.15565e-06 0.100001 -0.0999998 0.0004819987.13926e-06 0.100001 -0.0999997 0.0004839986.10428e-06 0.100001 -0.0999996 0.0004859985.07119e-06 0.100001 -0.0999995 0.0004879984.05823e-06 0.1 -0.0999994 0.0004899983.08133e-06 0.1 -0.0999993 0.0004919982.15408e-06 0.1 -0.0999993 0.0004939981.28771e-06 0.1 -0.0999993 0.0004959984.91166e-07 0.1 -0.0999993 0.000497998-2.28802e-07 0.1 -0.0999993 0.000499998-8.67544e-07 0.0999999 -0.0999993 0.000501998-1.42236e-06 0.0999999 -0.0999993 0.000503998-1.89233e-06 0.0999998 -0.0999993 0.000505998-2.27815e-06 0.0999998 -0.0999994 0.000507999-2.58196e-06 0.0999997 -0.0999994 0.000509999-2.8071e-06 0.0999997 -0.0999995 0.000511999-2.958e-06 0.0999997 -0.0999996 0.000513999-3.03991e-06 0.0999997 -0.0999996 0.000515999-3.05876e-06 0.0999997 -0.0999997 0.000517999-3.02097e-06 0.0999997 -0.0999997 0.000519999-2.93328e-06 0.0999997 -0.0999998 0.000521999-2.80261e-06 0.0999997 -0.0999999 0.000523999-2.63589e-06 0.0999997 -0.0999999 0.000525999-2.43996e-06 0.0999998 -0.1 0.000527999-2.22146e-06 0.0999998 -0.1 0.000529999-1.9867e-06 0.0999998 -0.1 0.000531999-1.74161e-06 0.0999998 -0.1 0.000533999-1.49168e-06 0.0999999 -0.1 0.000535999-1.2419e-06 0.0999999 -0.1 0.000537999-9.96699e-07 0.0999999 -0.1 0.000539999-7.59972e-07 0.0999999 -0.1 0.000541999-5.35037e-07 0.0999999 -0.1 0.000543999-3.24649e-07 0.1 -0.1 0.000545999-1.31005e-07 0.1 -0.1 0.0005479994.42307e-08 0.1 -0.1 0.0005499991.99901e-07 0.1 -0.1 0.0005519993.35324e-07 0.1 -0.1 0.0005539994.50248e-07 0.1 -0.1 0.0005559995.44819e-07 0.1 -0.1 0.0005579996.19529e-07 0.1 -0.1 0.0005599996.75171e-07 0.1 -0.1 0.0005619997.12795e-07 0.1 -0.1 0.0005639997.33659e-07 0.1 -0.1 0.0005659997.39186e-07 0.1 -0.1 0.0005679997.30922e-07 0.1 -0.1 0.0005699997.10491e-07 0.1 -0.1 0.000571999

86 10. Cir uito RLC paralelo.6.79562e-07 0.1 -0.1 0.0005739996.39811e-07 0.1 -0.1 0.0005759995.92894e-07 0.1 -0.1 0.0005779995.40417e-07 0.1 -0.1 0.0005799994.83912e-07 0.1 -0.1 0.0005819994.2482e-07 0.1 -0.1 0.0005839993.64473e-07 0.1 -0.1 0.0005859993.04083e-07 0.1 -0.1 0.0005879992.44733e-07 0.1 -0.1 0.0005899991.87373e-07 0.1 -0.1 0.0005919991.32812e-07 0.1 -0.1 0.0005939998.1725e-08 0.1 -0.1 0.0005959993.46525e-08 0.1 -0.1 0.0006set terminal pngset output ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/10/ e jemplo010_graf i a . png 'set en oding iso_8859_1set gridset autos aleset key bottom r i gh t t i t l e ' Var i ab l e s ' boxset t i t l e ' Graf i ado por d e f e t o de l a s s o l u i on e s de l i r u i t o 'plot ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/10/ejemplo010_x_trans . data ' using 4 :1 t i t l e 'V en nodo 1 ' with l i n e s , ' /home/ ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/10/ejemplo010_x_trans . data 'using 4 :2 t i t l e ' I Re s i s t en i a ent r e nodos 1 , 0 ' with l i n e s , ' /home/ ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/10/ejemplo010_x_trans . data ' using 4 :3 t i t l e ' I de Bobina ent r e nodos 1 , 0 ' with l i n e sGrá o de salida.

10.2. Solu iones 87

Veámos por separado la tensión del nudo 1,y las intensidades de la resisten ia y bobina. Po-dríamos obtener la intensidad del ondensador indi ando al programa que este es e ua ión adi- ional.

88 10. Cir uito RLC paralelo.

Capítulo 11Cir uito RLC paralelo sin ex ita ión.Cir uitos de segundo orden, RLC paralelo on ondi iones ini iales.1

011.1. Datos Generales.Ar hivo *.sp ∗SPICE i r u i t <ejemplo011> from XCir uit v3 . 6 rev 1352 1 0 1 1 0 0 0 ,0000023 1 0 2 1 0 0 0 ,00011 1 0 2 1 0 0 10. end Tipo de análisis realizadoAnálisis esta ionario ⊠Análisis transitorio ⊠Datos generales del ir uitoElementos del Cto: 3EA: 0Nodos: 1A2: 2No nulos: 7Densidad: 0.777778Dispersion: 0.2222222222Los valores dados al ir uito son:Elemento MagnitudResisten ia 10 ΩBobina 0, 0001 HCondensador 2 · 10−6 F

Condi iones Ini iales ValorV nodo 1 0I Resisten ia entre nodos 0, 1 0I Bobina entre nodos 1, 0 0, 189

90 11. Cir uito RLC paralelo sin ex ita ión.Matriz T.row 0: (0, 0 + 2e-06 i) (1, 1) (2, 1)row 1: (0, 1) (1, -0 - 0.0001 i)row 2: (0, 1) (2, -10)11.2. Solu iones11.2.1. Primer análisis Tiempo Ini ial 0Tiempo Final 0, 0004Paso de Tiempo 0, 000002Theta 1 (Euler)Esta ionarioResultados sistema esta ionario:Tensión en nodo 1: 0I de Bobina entre nodos 1, 0: 0I Resisten ia entre nodos 1, 0: 0Transitorio-0.0892857 0.0982143 -0.00892857 0-0.167411 0.0948661 -0.0167411 2e-06-0.234176 0.0901826 -0.0234176 4e-06-0.289606 0.0843904 -0.0289606 6e-06-0.333925 0.0777119 -0.0333925 8e-06-0.367533 0.0703613 -0.0367533 1e-05-0.390977 0.0625417 -0.0390977 1.2e-05-0.404927 0.0544432 -0.0404927 1.4e-05-0.410152 0.0462401 -0.0410152 1.6e-05-0.407493 0.0380903 -0.0407493 1.8e-05-0.397843 0.0301334 -0.0397843 2e-05-0.382121 0.022491 -0.0382121 2.2e-05-0.361261 0.0152658 -0.0361261 2.4e-05-0.336185 0.00854209 -0.0336185 2.6e-05-0.307792 0.00238625 -0.0307792 2.8e-05-0.276945 -0.00315264 -0.0276945 3e-05-0.244457 -0.00804178 -0.0244457 3.2e-05-0.211085 -0.0122635 -0.0211085 3.4e-05-0.177519 -0.0158139 -0.0177519 3.6e-05-0.14438 -0.0187015 -0.014438 3.8e-05-0.112213 -0.0209457 -0.0112213 4e-05-0.0814885 -0.0225755 -0.00814885 4.2e-05-0.0526009 -0.0236275 -0.00526009 4.4e-05-0.0258691 -0.0241449 -0.00258691 4.6e-05

11.2. Solu iones 91-0.00153946 -0.0241757 -0.000153946 4.8e-050.0202109 -0.0237715 0.00202109 5e-050.03927 -0.0229861 0.003927 5.2e-050.0555858 -0.0218744 0.00555858 5.4e-050.0691608 -0.0204911 0.00691608 5.6e-050.0800464 -0.0188902 0.00800464 5.8e-050.0883363 -0.0171235 0.00883363 6e-050.0941605 -0.0152403 0.00941605 6.2e-050.0976792 -0.0132867 0.00976792 6.4e-050.0990767 -0.0113052 0.00990767 6.6e-050.0985553 -0.00933405 0.00985553 6.8e-050.0963297 -0.00740746 0.00963297 7e-050.0926225 -0.00555501 0.00926225 7.2e-050.0876585 -0.00380184 0.00876585 7.4e-050.081661 -0.00216862 0.0081661 7.6e-050.0748479 -0.000671659 0.00748479 7.8e-050.0674282 0.000676904 0.00674282 8e-050.0595993 0.00186889 0.00595993 8.2e-050.051545 0.00289979 0.0051545 8.4e-050.0434333 0.00376846 0.00434333 8.6e-050.035415 0.00447676 0.0035415 8.8e-050.0276234 0.00502922 0.00276234 9e-050.0201734 0.00543269 0.00201734 9.2e-050.0131613 0.00569592 0.00131613 9.4e-050.00666556 0.00582923 0.000666556 9.6e-050.00074672 0.00584417 7.4672e-05 9.8e-05-0.00455129 0.00575314 -0.000455129 0.0001-0.00920038 0.00556913 -0.000920038 0.000102-0.0131871 0.00530539 -0.00131871 0.000104-0.0165111 0.00497517 -0.00165111 0.000106-0.0191842 0.00459148 -0.00191842 0.000108-0.0212283 0.00416692 -0.00212283 0.00011-0.0226743 0.00371343 -0.00226743 0.000112-0.0235605 0.00324222 -0.00235605 0.000114-0.023931 0.0027636 -0.0023931 0.000116-0.0238344 0.00228692 -0.00238344 0.000118-0.0233226 0.00182046 -0.00233226 0.00012-0.0224492 0.00137148 -0.00224492 0.000122-0.0212685 0.00094611 -0.00212685 0.000124-0.0198344 0.000549421 -0.00198344 0.000126-0.0181999 0.000185423 -0.00181999 0.000128-0.0164154 -0.000142886 -0.00164154 0.00013-0.0145291 -0.000433467 -0.00145291 0.000132-0.0125854 -0.000685174 -0.00125854 0.000134-0.0106252 -0.000897678 -0.00106252 0.000136-0.00868526 -0.00107138 -0.000868526 0.000138-0.0067981 -0.00120734 -0.00067981 0.00014-0.00499175 -0.00130718 -0.000499175 0.000142-0.00328979 -0.00137298 -0.000328979 0.000144-0.00171144 -0.0014072 -0.000171144 0.000146-0.000271643 -0.00141264 -2.71643e-05 0.0001480.00101875 -0.00139226 0.000101875 0.000150.00215269 -0.00134921 0.000215269 0.0001520.00312669 -0.00128667 0.000312669 0.000154

92 11. Cir uito RLC paralelo sin ex ita ión.0.00394051 -0.00120786 0.000394051 0.0001560.00459676 -0.00111593 0.000459676 0.0001580.00510061 -0.00101392 0.000510061 0.000160.0054594 -0.000904729 0.00054594 0.0001620.00568226 -0.000791084 0.000568226 0.0001640.00577977 -0.000675489 0.000577977 0.0001660.00576363 -0.000560216 0.000576363 0.0001680.00564629 -0.00044729 0.000564629 0.000170.00544069 -0.000338476 0.000544069 0.0001720.00515997 -0.000235277 0.000515997 0.0001740.00481719 -0.000138933 0.000481719 0.0001760.00442511 -5.04309e-05 0.000442511 0.0001780.00399602 2.94894e-05 0.000399602 0.000180.00354154 0.00010032 0.000354154 0.0001820.00307252 0.000161771 0.000307252 0.0001840.00259888 0.000213748 0.000259888 0.0001860.00212958 0.00025634 0.000212958 0.0001880.00167254 0.000289791 0.000167254 0.000190.0012346 0.000314483 0.00012346 0.0001920.000821531 0.000330913 8.21531e-05 0.0001940.000438051 0.000339674 4.38051e-05 0.0001968.78367e-05 0.000341431 8.78367e-06 0.000198-0.000226424 0.000336903 -2.26424e-05 0.0002-0.00050297 0.000326843 -5.0297e-05 0.000202-0.000740905 0.000312025 -7.40905e-05 0.000204-0.000940116 0.000293223 -9.40116e-05 0.000206-0.0011012 0.000271199 -0.00011012 0.000208-0.00122535 0.000246692 -0.000122535 0.00021-0.00131432 0.000220405 -0.000131432 0.000212-0.0013703 0.000193 -0.00013703 0.000214-0.0013958 0.000165084 -0.00013958 0.000216-0.00139364 0.000137211 -0.000139364 0.000218-0.00136684 0.000109874 -0.000136684 0.00022-0.00131849 8.35041e-05 -0.000131849 0.000222-0.00125178 5.84685e-05 -0.000125178 0.000224-0.00116987 3.50712e-05 -0.000116987 0.000226-0.00107584 1.35545e-05 -0.000107584 0.000228-0.00097267 -5.89892e-06 -9.7267e-05 0.00023-0.000863189 -2.31627e-05 -8.63189e-05 0.000232-0.000750023 -3.81632e-05 -7.50023e-05 0.000234-0.000635589 -5.0875e-05 -6.35589e-05 0.000236-0.000522066 -6.13163e-05 -5.22066e-05 0.000238-0.000411384 -6.9544e-05 -4.11384e-05 0.00024-0.000305214 -7.56483e-05 -3.05214e-05 0.000242-0.00020497 -7.97476e-05 -2.0497e-05 0.000244-0.000111805 -8.19838e-05 -1.11805e-05 0.000246-2.66265e-05 -8.25163e-05 -2.66265e-06 0.0002484.99016e-05 -8.15183e-05 4.99016e-06 0.000250.000117339 -7.91715e-05 1.17339e-05 0.0002520.000175456 -7.56624e-05 1.75456e-05 0.0002540.000224213 -7.11781e-05 2.24213e-05 0.0002560.000263742 -6.59033e-05 2.63742e-05 0.0002580.000294326 -6.00167e-05 2.94326e-05 0.000260.000316377 -5.36892e-05 3.16377e-05 0.000262

11.2. Solu iones 930.000330417 -4.70809e-05 3.30417e-05 0.0002640.000337051 -4.03398e-05 3.37051e-05 0.0002660.000336956 -3.36007e-05 3.36956e-05 0.0002680.000330855 -2.69836e-05 3.30855e-05 0.000270.000319498 -2.05937e-05 3.19498e-05 0.0002720.000303654 -1.45206e-05 3.03654e-05 0.0002740.000284084 -8.8389e-06 2.84084e-05 0.0002760.000261538 -3.60813e-06 2.61538e-05 0.0002780.000236738 1.12663e-06 2.36738e-05 0.000280.000210367 5.33397e-06 2.10367e-05 0.0002820.000183065 8.99528e-06 1.83065e-05 0.0002840.00015542 1.21037e-05 1.5542e-05 0.0002860.000127961 1.46629e-05 1.27961e-05 0.0002880.000101159 1.66861e-05 1.01159e-05 0.000297.54221e-05 1.81945e-05 7.54221e-06 0.0002925.10961e-05 1.92164e-05 5.10961e-06 0.0002942.8464e-05 1.97857e-05 2.8464e-06 0.0002967.74844e-06 1.99407e-05 7.74844e-07 0.000298-1.08859e-05 1.9723e-05 -1.08859e-06 0.0003-2.73294e-05 1.91764e-05 -2.73294e-06 0.000302-4.1523e-05 1.83459e-05 -4.1523e-06 0.000304-5.34544e-05 1.72768e-05 -5.34544e-06 0.000306-6.31529e-05 1.60138e-05 -6.31529e-06 0.000308-7.06845e-05 1.46001e-05 -7.06845e-06 0.00031-7.61469e-05 1.30771e-05 -7.61469e-06 0.000312-7.96644e-05 1.14839e-05 -7.96644e-06 0.000314-8.13823e-05 9.85621e-06 -8.13823e-06 0.000316-8.1463e-05 8.22695e-06 -8.1463e-06 0.000318-8.00803e-05 6.62534e-06 -8.00803e-06 0.00032-7.74158e-05 5.07703e-06 -7.74158e-06 0.000322-7.36543e-05 3.60394e-06 -7.36543e-06 0.000324-6.89805e-05 2.22433e-06 -6.89805e-06 0.000326-6.35758e-05 9.52816e-07 -6.35758e-06 0.000327999-5.76148e-05 -1.9948e-07 -5.76148e-06 0.000329999-5.12637e-05 -1.22475e-06 -5.12637e-06 0.000331999-4.46776e-05 -2.11831e-06 -4.46776e-06 0.000333999-3.79994e-05 -2.87829e-06 -3.79994e-06 0.000335999-3.13581e-05 -3.50546e-06 -3.13581e-06 0.000337999-2.48685e-05 -4.00283e-06 -2.48685e-06 0.000339999-1.863e-05 -4.37543e-06 -1.863e-06 0.000341999-1.27273e-05 -4.62997e-06 -1.27273e-06 0.000343999-7.22977e-06 -4.77457e-06 -7.22977e-07 0.000345999-2.19215e-06 -4.81841e-06 -2.19215e-07 0.0003479992.34488e-06 -4.77151e-06 2.34488e-07 0.0003499996.35392e-06 -4.64444e-06 6.35392e-07 0.0003519999.81996e-06 -4.44804e-06 9.81996e-07 0.0003539991.27393e-05 -4.19325e-06 1.27393e-06 0.0003559991.51183e-05 -3.89088e-06 1.51183e-06 0.0003579991.69725e-05 -3.55143e-06 1.69725e-06 0.0003599991.8325e-05 -3.18493e-06 1.8325e-06 0.0003619991.92053e-05 -2.80083e-06 1.92053e-06 0.0003639991.96483e-05 -2.40786e-06 1.96483e-06 0.0003659991.9693e-05 -2.014e-06 1.9693e-06 0.0003679991.93813e-05 -1.62638e-06 1.93813e-06 0.000369999

94 11. Cir uito RLC paralelo sin ex ita ión.1.87568e-05 -1.25124e-06 1.87568e-06 0.0003719991.78643e-05 -8.93956e-07 1.78643e-06 0.0003739991.67485e-05 -5.58986e-07 1.67485e-06 0.0003759991.54531e-05 -2.49924e-07 1.54531e-06 0.0003779991.40205e-05 3.04866e-08 1.40205e-06 0.0003799991.24911e-05 2.80309e-07 1.24911e-06 0.0003819991.09025e-05 4.98359e-07 1.09025e-06 0.0003839999.28942e-06 6.84148e-07 9.28942e-07 0.0003859997.68328e-06 8.37814e-07 7.68328e-07 0.0003879996.11203e-06 9.60054e-07 6.11203e-07 0.0003899994.59997e-06 1.05205e-06 4.59997e-07 0.0003919993.16779e-06 1.11541e-06 3.16779e-07 0.0003939991.83248e-06 1.15206e-06 1.83248e-07 0.0003959996.07519e-07 1.16421e-06 6.07519e-08 0.0004set terminal pngset output ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/11/ e jemplo011_graf i a . png 'set en oding iso_8859_1set gridset autos aleset key bottom r i gh t t i t l e ' Var i ab l e s ' boxset t i t l e ' Graf i ado por d e f e t o de l a s s o l u i on e s de l i r u i t o 'plot ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/11/ejemplo011_x_trans . data ' using 4 :1 t i t l e 'V en nodo 1 ' with l i n e s , ' /home/ ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/11/ejemplo011_x_trans . data 'using 4 :2 t i t l e ' I de Bobina ent r e nodos 1 , 0 ' with l i n e s , ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/11/ejemplo011_x_trans . data ' using 4 :3 t i t l e ' I Re s i s t en i a ent r e nodos 1 , 0 ' with l i n e sGrá o de salida.

11.2. Solu iones 95

Veámos por separado la tensión del nudo 1, la intensidad en la bobina y la de la resisten ia.

96 11. Cir uito RLC paralelo sin ex ita ión.

Capítulo 12Cir uito RLC paralelo sin ex ita ión on EA.Ya que hasta el momento no se había pedido al programa añadir más variables que las que al ula por defe to pro ederemos a añadir al problema anterior el ál ulo de la intensidad del ondensador a través de una e ua ión adi ional EA. Para ello simplemente, una vez argado el ir uito le indi amos en la tabla MDG (Matriz de Datos Generales) que el ondensador tiene unaEA poniendo un 1 en la olumna orrespondiente a este tipo de valores.Re ordemos que el ondensador se ensambla en el sistema omo elemento del tipo A1, lo quese tradu e en que su intensidad no es al ulada por defe to, a no ser que se le indique al programaque pro eda de otra forma.Tomando el ejemplo anterior:1

012.1. Datos Generales.Ar hivo *.sp ∗SPICE i r u i t <ejemplo011> from XCir uit v3 . 6 rev 1352 1 1 1 1 0 0 0 ,0000023 1 0 2 1 0 0 0 ,00011 1 0 2 1 0 0 10. end Tipo de análisis realizadoAnálisis esta ionario ⊠Análisis transitorio ⊠Datos generales del ir uitoElementos del Cto: 3EA: 1Nodos: 1 97

98 12. Cir uito RLC paralelo sin ex ita ión on EA.A2: 2No nulos: 9Densidad: 0.5625Dispersion: 0.4375Los valores dados al ir uito son:Elemento MagnitudResisten ia 10 ΩBobina 0, 0001 HCondensador 2 · 10−6 F

Condi iones Ini iales ValorV nodo 1 0I Resisten ia entre nodos 0, 1 0I Bobina entre nodos 1, 0 0, 1I de Condensador 1, 0 0Matriz T.row 0: (1, 1) (2, 1) (3, 1)row 1: (0, 1) (1, -0 - 0.0001 i)row 2: (0, 1) (2, -10)row 3: (0, 0 + 2e-06 i) (3, -1)12.2. Solu iones12.2.1. Primer análisis Tiempo Ini ial 0Tiempo Final 0, 0004Paso de Tiempo 0, 000002Theta 1 (Euler)Esta ionarioResultados sistema esta ionario:Tensión en nodo 1: 0I de Bobina entre nodos 1, 0: 0I Resisten ia entre nodos 1, 0: 0Intensidad de Condensador entre nodos 1, 0: 0Transitorio-0.0892857 0.0982143 -0.00892857 -0.0892857 0-0.167411 0.0948661 -0.0167411 -0.078125 2e-06-0.234176 0.0901826 -0.0234176 -0.066765 4e-06-0.289606 0.0843904 -0.0289606 -0.0554299 6e-06-0.333925 0.0777119 -0.0333925 -0.0443194 8e-06-0.367533 0.0703613 -0.0367533 -0.033608 1e-05-0.390977 0.0625417 -0.0390977 -0.023444 1.2e-05-0.404927 0.0544432 -0.0404927 -0.0139504 1.4e-05-0.410152 0.0462401 -0.0410152 -0.00522491 1.6e-05

12.2. Solu iones 99-0.407493 0.0380903 -0.0407493 0.00265906 1.8e-05-0.397843 0.0301334 -0.0397843 0.00965082 2e-05-0.382121 0.022491 -0.0382121 0.0157211 2.2e-05-0.361261 0.0152658 -0.0361261 0.0208603 2.4e-05-0.336185 0.00854209 -0.0336185 0.0250764 2.6e-05-0.307792 0.00238625 -0.0307792 0.0283929 2.8e-05-0.276945 -0.00315264 -0.0276945 0.0308471 3e-05-0.244457 -0.00804178 -0.0244457 0.0324875 3.2e-05-0.211085 -0.0122635 -0.0211085 0.033372 3.4e-05-0.177519 -0.0158139 -0.0177519 0.0335658 3.6e-05-0.14438 -0.0187015 -0.014438 0.0331395 3.8e-05-0.112213 -0.0209457 -0.0112213 0.032167 4e-05-0.0814885 -0.0225755 -0.00814885 0.0307244 4.2e-05-0.0526009 -0.0236275 -0.00526009 0.0288876 4.4e-05-0.0258691 -0.0241449 -0.00258691 0.0267318 4.6e-05-0.00153946 -0.0241757 -0.000153946 0.0243296 4.8e-050.0202109 -0.0237715 0.00202109 0.0217504 5e-050.03927 -0.0229861 0.003927 0.0190591 5.2e-050.0555858 -0.0218744 0.00555858 0.0163158 5.4e-050.0691608 -0.0204911 0.00691608 0.0135751 5.6e-050.0800464 -0.0188902 0.00800464 0.0108856 5.8e-050.0883363 -0.0171235 0.00883363 0.00828986 6e-050.0941605 -0.0152403 0.00941605 0.00582423 6.2e-050.0976792 -0.0132867 0.00976792 0.00351877 6.4e-050.0990767 -0.0113052 0.00990767 0.00139748 6.6e-050.0985553 -0.00933405 0.00985553 -0.000521475 6.8e-050.0963297 -0.00740746 0.00963297 -0.00222552 7e-050.0926225 -0.00555501 0.00926225 -0.00370724 7.2e-050.0876585 -0.00380184 0.00876585 -0.00496401 7.4e-050.081661 -0.00216862 0.0081661 -0.00599748 7.6e-050.0748479 -0.000671659 0.00748479 -0.00681313 7.8e-050.0674282 0.000676904 0.00674282 -0.00741972 8e-050.0595993 0.00186889 0.00595993 -0.00782882 8.2e-050.051545 0.00289979 0.0051545 -0.00805429 8.4e-050.0434333 0.00376846 0.00434333 -0.00811178 8.6e-050.035415 0.00447676 0.0035415 -0.00801826 8.8e-050.0276234 0.00502922 0.00276234 -0.00779157 9e-050.0201734 0.00543269 0.00201734 -0.00745003 9.2e-050.0131613 0.00569592 0.00131613 -0.00701205 9.4e-050.00666556 0.00582923 0.000666556 -0.00649579 9.6e-050.00074672 0.00584417 7.4672e-05 -0.00591884 9.8e-05-0.00455129 0.00575314 -0.000455129 -0.00529801 0.0001-0.00920038 0.00556913 -0.000920038 -0.00464909 0.000102-0.0131871 0.00530539 -0.00131871 -0.00398668 0.000104-0.0165111 0.00497517 -0.00165111 -0.00332406 0.000106-0.0191842 0.00459148 -0.00191842 -0.00267307 0.000108-0.0212283 0.00416692 -0.00212283 -0.00204409 0.00011-0.0226743 0.00371343 -0.00226743 -0.001446 0.000112-0.0235605 0.00324222 -0.00235605 -0.000886178 0.000114-0.023931 0.0027636 -0.0023931 -0.000370507 0.000116-0.0238344 0.00228692 -0.00238344 9.65285e-05 0.000118-0.0233226 0.00182046 -0.00233226 0.000511801 0.00012-0.0224492 0.00137148 -0.00224492 0.000873441 0.000122-0.0212685 0.00094611 -0.00212685 0.00118074 0.000124

100 12. Cir uito RLC paralelo sin ex ita ión on EA.-0.0198344 0.000549421 -0.00198344 0.00143402 0.000126-0.0181999 0.000185423 -0.00181999 0.00163456 0.000128-0.0164154 -0.000142886 -0.00164154 0.00178443 0.00013-0.0145291 -0.000433467 -0.00145291 0.00188637 0.000132-0.0125854 -0.000685174 -0.00125854 0.00194371 0.000134-0.0106252 -0.000897678 -0.00106252 0.00196019 0.000136-0.00868526 -0.00107138 -0.000868526 0.00193991 0.000138-0.0067981 -0.00120734 -0.00067981 0.00188715 0.00014-0.00499175 -0.00130718 -0.000499175 0.00180635 0.000142-0.00328979 -0.00137298 -0.000328979 0.00170195 0.000144-0.00171144 -0.0014072 -0.000171144 0.00157835 0.000146-0.000271643 -0.00141264 -2.71643e-05 0.0014398 0.0001480.00101875 -0.00139226 0.000101875 0.00129039 0.000150.00215269 -0.00134921 0.000215269 0.00113394 0.0001520.00312669 -0.00128667 0.000312669 0.000974006 0.0001540.00394051 -0.00120786 0.000394051 0.000813814 0.0001560.00459676 -0.00111593 0.000459676 0.000656254 0.0001580.00510061 -0.00101392 0.000510061 0.000503856 0.000160.0054594 -0.000904729 0.00054594 0.000358789 0.0001620.00568226 -0.000791084 0.000568226 0.000222858 0.0001640.00577977 -0.000675489 0.000577977 9.75113e-05 0.0001660.00576363 -0.000560216 0.000576363 -1.61466e-05 0.0001680.00564629 -0.00044729 0.000564629 -0.000117339 0.000170.00544069 -0.000338476 0.000544069 -0.000205593 0.0001720.00515997 -0.000235277 0.000515997 -0.000280721 0.0001740.00481719 -0.000138933 0.000481719 -0.000342786 0.0001760.00442511 -5.04309e-05 0.000442511 -0.00039208 0.0001780.00399602 2.94894e-05 0.000399602 -0.000429091 0.000180.00354154 0.00010032 0.000354154 -0.000454475 0.0001820.00307252 0.000161771 0.000307252 -0.000469023 0.0001840.00259888 0.000213748 0.000259888 -0.000473637 0.0001860.00212958 0.00025634 0.000212958 -0.000469299 0.0001880.00167254 0.000289791 0.000167254 -0.000457045 0.000190.0012346 0.000314483 0.00012346 -0.000437943 0.0001920.000821531 0.000330913 8.21531e-05 -0.000413066 0.0001940.000438051 0.000339674 4.38051e-05 -0.00038348 0.0001968.78367e-05 0.000341431 8.78367e-06 -0.000350215 0.000198-0.000226424 0.000336903 -2.26424e-05 -0.00031426 0.0002-0.00050297 0.000326843 -5.0297e-05 -0.000276546 0.000202-0.000740905 0.000312025 -7.40905e-05 -0.000237935 0.000204-0.000940116 0.000293223 -9.40116e-05 -0.000199211 0.000206-0.0011012 0.000271199 -0.00011012 -0.000161079 0.000208-0.00122535 0.000246692 -0.000122535 -0.000124157 0.00021-0.00131432 0.000220405 -0.000131432 -8.89729e-05 0.000212-0.0013703 0.000193 -0.00013703 -5.597e-05 0.000214-0.0013958 0.000165084 -0.00013958 -2.55037e-05 0.000216-0.00139364 0.000137211 -0.000139364 2.15384e-06 0.000218-0.00136684 0.000109874 -0.000136684 2.68096e-05 0.00022-0.00131849 8.35041e-05 -0.000131849 4.83449e-05 0.000222-0.00125178 5.84685e-05 -0.000125178 6.67096e-05 0.000224-0.00116987 3.50712e-05 -0.000116987 8.19153e-05 0.000226-0.00107584 1.35545e-05 -0.000107584 9.40291e-05 0.000228-0.00097267 -5.89892e-06 -9.7267e-05 0.000103166 0.00023-0.000863189 -2.31627e-05 -8.63189e-05 0.000109482 0.000232

12.2. Solu iones 101-0.000750023 -3.81632e-05 -7.50023e-05 0.000113165 0.000234-0.000635589 -5.0875e-05 -6.35589e-05 0.000114434 0.000236-0.000522066 -6.13163e-05 -5.22066e-05 0.000113523 0.000238-0.000411384 -6.9544e-05 -4.11384e-05 0.000110682 0.00024-0.000305214 -7.56483e-05 -3.05214e-05 0.00010617 0.000242-0.00020497 -7.97476e-05 -2.0497e-05 0.000100245 0.000244-0.000111805 -8.19838e-05 -1.11805e-05 9.31643e-05 0.000246-2.66265e-05 -8.25163e-05 -2.66265e-06 8.51789e-05 0.0002484.99016e-05 -8.15183e-05 4.99016e-06 7.65281e-05 0.000250.000117339 -7.91715e-05 1.17339e-05 6.74376e-05 0.0002520.000175456 -7.56624e-05 1.75456e-05 5.81168e-05 0.0002540.000224213 -7.11781e-05 2.24213e-05 4.87568e-05 0.0002560.000263742 -6.59033e-05 2.63742e-05 3.95291e-05 0.0002580.000294326 -6.00167e-05 2.94326e-05 3.05842e-05 0.000260.000316377 -5.36892e-05 3.16377e-05 2.20515e-05 0.0002620.000330417 -4.70809e-05 3.30417e-05 1.40392e-05 0.0002640.000337051 -4.03398e-05 3.37051e-05 6.63471e-06 0.0002660.000336956 -3.36007e-05 3.36956e-05 -9.49285e-08 0.0002680.000330855 -2.69836e-05 3.30855e-05 -6.10184e-06 0.000270.000319498 -2.05937e-05 3.19498e-05 -1.13562e-05 0.0002720.000303654 -1.45206e-05 3.03654e-05 -1.58448e-05 0.0002740.000284084 -8.8389e-06 2.84084e-05 -1.95695e-05 0.0002760.000261538 -3.60813e-06 2.61538e-05 -2.25457e-05 0.0002780.000236738 1.12663e-06 2.36738e-05 -2.48004e-05 0.000280.000210367 5.33397e-06 2.10367e-05 -2.63707e-05 0.0002820.000183065 8.99528e-06 1.83065e-05 -2.73018e-05 0.0002840.00015542 1.21037e-05 1.5542e-05 -2.76457e-05 0.0002860.000127961 1.46629e-05 1.27961e-05 -2.7459e-05 0.0002880.000101159 1.66861e-05 1.01159e-05 -2.6802e-05 0.000297.54221e-05 1.81945e-05 7.54221e-06 -2.57367e-05 0.0002925.10961e-05 1.92164e-05 5.10961e-06 -2.4326e-05 0.0002942.8464e-05 1.97857e-05 2.8464e-06 -2.26321e-05 0.0002967.74844e-06 1.99407e-05 7.74844e-07 -2.07155e-05 0.000298-1.08859e-05 1.9723e-05 -1.08859e-06 -1.86344e-05 0.0003-2.73294e-05 1.91764e-05 -2.73294e-06 -1.64434e-05 0.000302-4.1523e-05 1.83459e-05 -4.1523e-06 -1.41936e-05 0.000304-5.34544e-05 1.72768e-05 -5.34544e-06 -1.19314e-05 0.000306-6.31529e-05 1.60138e-05 -6.31529e-06 -9.69849e-06 0.000308-7.06845e-05 1.46001e-05 -7.06845e-06 -7.53163e-06 0.00031-7.61469e-05 1.30771e-05 -7.61469e-06 -5.46245e-06 0.000312-7.96644e-05 1.14839e-05 -7.96644e-06 -3.51742e-06 0.000314-8.13823e-05 9.85621e-06 -8.13823e-06 -1.71798e-06 0.000316-8.1463e-05 8.22695e-06 -8.1463e-06 -8.06504e-08 0.000318-8.00803e-05 6.62534e-06 -8.00803e-06 1.38269e-06 0.00032-7.74158e-05 5.07703e-06 -7.74158e-06 2.66455e-06 0.000322-7.36543e-05 3.60394e-06 -7.36543e-06 3.76148e-06 0.000324-6.89805e-05 2.22433e-06 -6.89805e-06 4.67372e-06 0.000326-6.35758e-05 9.52816e-07 -6.35758e-06 5.40476e-06 0.000327999-5.76148e-05 -1.9948e-07 -5.76148e-06 5.96096e-06 0.000329999-5.12637e-05 -1.22475e-06 -5.12637e-06 6.35112e-06 0.000331999-4.46776e-05 -2.11831e-06 -4.46776e-06 6.58607e-06 0.000333999-3.79994e-05 -2.87829e-06 -3.79994e-06 6.67823e-06 0.000335999-3.13581e-05 -3.50546e-06 -3.13581e-06 6.64127e-06 0.000337999-2.48685e-05 -4.00283e-06 -2.48685e-06 6.48967e-06 0.000339999

102 12. Cir uito RLC paralelo sin ex ita ión on EA.-1.863e-05 -4.37543e-06 -1.863e-06 6.23843e-06 0.000341999-1.27273e-05 -4.62997e-06 -1.27273e-06 5.90271e-06 0.000343999-7.22977e-06 -4.77457e-06 -7.22977e-07 5.49755e-06 0.000345999-2.19215e-06 -4.81841e-06 -2.19215e-07 5.03763e-06 0.0003479992.34488e-06 -4.77151e-06 2.34488e-07 4.53703e-06 0.0003499996.35392e-06 -4.64444e-06 6.35392e-07 4.00904e-06 0.0003519999.81996e-06 -4.44804e-06 9.81996e-07 3.46604e-06 0.0003539991.27393e-05 -4.19325e-06 1.27393e-06 2.91932e-06 0.0003559991.51183e-05 -3.89088e-06 1.51183e-06 2.37905e-06 0.0003579991.69725e-05 -3.55143e-06 1.69725e-06 1.85418e-06 0.0003599991.8325e-05 -3.18493e-06 1.8325e-06 1.35244e-06 0.0003619991.92053e-05 -2.80083e-06 1.92053e-06 8.80303e-07 0.0003639991.96483e-05 -2.40786e-06 1.96483e-06 4.43034e-07 0.0003659991.9693e-05 -2.014e-06 1.9693e-06 4.47037e-08 0.0003679991.93813e-05 -1.62638e-06 1.93813e-06 -3.11747e-07 0.0003699991.87568e-05 -1.25124e-06 1.87568e-06 -6.24439e-07 0.0003719991.78643e-05 -8.93956e-07 1.78643e-06 -8.92478e-07 0.0003739991.67485e-05 -5.58986e-07 1.67485e-06 -1.11586e-06 0.0003759991.54531e-05 -2.49924e-07 1.54531e-06 -1.29538e-06 0.0003779991.40205e-05 3.04866e-08 1.40205e-06 -1.43254e-06 0.0003799991.24911e-05 2.80309e-07 1.24911e-06 -1.52942e-06 0.0003819991.09025e-05 4.98359e-07 1.09025e-06 -1.58861e-06 0.0003839999.28942e-06 6.84148e-07 9.28942e-07 -1.61309e-06 0.0003859997.68328e-06 8.37814e-07 7.68328e-07 -1.60614e-06 0.0003879996.11203e-06 9.60054e-07 6.11203e-07 -1.57126e-06 0.0003899994.59997e-06 1.05205e-06 4.59997e-07 -1.51205e-06 0.0003919993.16779e-06 1.11541e-06 3.16779e-07 -1.43219e-06 0.0003939991.83248e-06 1.15206e-06 1.83248e-07 -1.33531e-06 0.0003959996.07519e-07 1.16421e-06 6.07519e-08 -1.22496e-06 0.0004set terminal pngset output ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/12/ e jemplo012_graf i a . png 'set en oding iso_8859_1set gridset autos aleset key bottom r i gh t t i t l e ' Var i ab l e s ' boxset t i t l e ' Graf i ado por d e f e t o de l a s s o l u i on e s de l i r u i t o 'plot ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/12/ejemplo012_x_trans . data ' using 5 :1 t i t l e 'V en nodo 1 ' with l i n e s , ' /home/ ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/12/ejemplo012_x_trans . data 'using 5 :2 t i t l e ' I de Bobina ent r e nodos 1 , 0 ' with l i n e s , ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/12/ejemplo012_x_trans . data ' using 5 :3 t i t l e ' I Re s i s t en i a ent r e nodos 1 , 0 ' with l i n e s , ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/12/ejemplo012_x_trans . data ' using 5 :4 t i t l e ' I n t ens idad de Condensador ent r e nodos 1 , 0 ' with l i n e sGrá o de salida.

12.2. Solu iones 103

Veámos la nueva grá a de la evolu ión temporal de la intensidad del ondensador

Capítulo 13Cir uito on a oplamiento magnéti osimple.Ahora pasaremos al análsis de ir uitos on elementos bipuertos o uatripolos, el primero quevamos a analizar será un ir uito on ex ita ión es alón y unas bobinas a opladas.1

0

2 3

013.1. Datos Generales.Ar hivo *.sp ∗SPICE i r u i t <ejemplo013> from XCir uit v3 . 6 rev 1351 1 0 2 0 3 0 11 2 0 2 2 1 0 112 1 0 2 2 0 3 0 0 0 0 0 0 0 2 3 14 1 0 2 1 0 4 Cte rho f 0 b 0 1 C D. end Tipo de análisis realizadoAnálisis esta ionario ⊠Análisis transitorio ⊠Datos generales del ir uitoElementos del Cto: 4EA: 0Nodos: 3A2: 5No nulos: 18Densidad: 0.28125Dispersion: 0.71875 105

106 13. Cir uito on a oplamiento magnéti o simple.Los valores dados al ir uito son:Elemento MagnitudResisten ias 1 ΩBobinas a opladas L1 = 2, L2 = 3, M = 1Fuente de tensión, ex ita ión es alón unidad 1 VMatriz T.row 0: (5, 1) (7, -1)row 1: (3, 1) (7, 1)row 2: (4, 1) (6, -1)row 3: (1, 1) (3, -0 - 2 i) (4, -0 - 1 i)row 4: (2, 1) (3, -0 - 1 i) (4, -0 - 3 i)row 5: (0, 1)row 6: (2, -1) (6, -1)row 7: (0, -1) (1, 1) (7, -1)13.2. Solu iones13.2.1. Primer análisis Tiempo Ini ial 0Tiempo Final 20Paso de Tiempo 0, 13Theta 1 (Euler)Esta ionarioResultados sistema esta ionario:Tensión en nodo 1: 1.26117e-44 - 4.70372e-61 iTensión en nodo 2: 9.22806e-45 + 5.22924e-45 iTensión en nodo 3: 1.53801e-45 - 1.23041e-45 iI de Bobinas A opladas entre nodos 2, 0: 3.38362e-45 - 5.22924e-45 iI de Bobinas A opladas entre nodos 3, 0: -1.53801e-45 + 1.23041e-45 iI de Fuente tension entre nodos 1, 0: -3.38362e-45 + 5.22924e-45 iI Resisten ia entre nodos 0, 3: -1.53801e-45 + 1.23041e-45 iI Resisten ia entre nodos 2, 1: -3.38362e-45 + 5.22924e-45 iTransitorio1 0.928197 0.0229402 0.0718029 -0.0229402 -0.0718029 -0.0229402 -0.0718029 01 0.862076 0.0431124 0.137924 -0.0431124 -0.137924 -0.0431124 -0.137924 0.131 0.801165 0.060782 0.198835 -0.060782 -0.198835 -0.060782 -0.198835 0.261 0.745034 0.076191 0.254966 -0.076191 -0.254966 -0.076191 -0.254966 0.391 0.693286 0.0895593 0.306714 -0.0895593 -0.306714 -0.0895593 -0.306714 0.521 0.645561 0.101087 0.354439 -0.101087 -0.354439 -0.101087 -0.354439 0.651 0.601526 0.110957 0.398474 -0.110957 -0.398474 -0.110957 -0.398474 0.78

13.2. Solu iones 1071 0.56088 0.119335 0.43912 -0.119335 -0.43912 -0.119335 -0.43912 0.911 0.523345 0.12637 0.476655 -0.12637 -0.476655 -0.12637 -0.476655 1.041 0.488666 0.132201 0.511334 -0.132201 -0.511334 -0.132201 -0.511334 1.171 0.456611 0.136952 0.543389 -0.136952 -0.543389 -0.136952 -0.543389 1.31 0.426967 0.140735 0.573033 -0.140735 -0.573033 -0.140735 -0.573033 1.431 0.399538 0.143653 0.600462 -0.143653 -0.600462 -0.143653 -0.600462 1.561 0.374146 0.145799 0.625854 -0.145799 -0.625854 -0.145799 -0.625854 1.691 0.350625 0.147258 0.649375 -0.147258 -0.649375 -0.147258 -0.649375 1.821 0.328828 0.148106 0.671172 -0.148106 -0.671172 -0.148106 -0.671172 1.951 0.308614 0.148412 0.691386 -0.148412 -0.691386 -0.148412 -0.691386 2.081 0.28986 0.14824 0.71014 -0.14824 -0.71014 -0.14824 -0.71014 2.211 0.272448 0.147646 0.727552 -0.147646 -0.727552 -0.147646 -0.727552 2.341 0.256272 0.146682 0.743728 -0.146682 -0.743728 -0.146682 -0.743728 2.471 0.241236 0.145394 0.758764 -0.145394 -0.758764 -0.145394 -0.758764 2.61 0.22725 0.143823 0.77275 -0.143823 -0.77275 -0.143823 -0.77275 2.731 0.214232 0.142009 0.785768 -0.142009 -0.785768 -0.142009 -0.785768 2.861 0.202107 0.139984 0.797893 -0.139984 -0.797893 -0.139984 -0.797893 2.991 0.190807 0.137781 0.809193 -0.137781 -0.809193 -0.137781 -0.809193 3.121 0.180267 0.135426 0.819733 -0.135426 -0.819733 -0.135426 -0.819733 3.251 0.17043 0.132944 0.82957 -0.132944 -0.82957 -0.132944 -0.82957 3.381 0.161242 0.130357 0.838758 -0.130357 -0.838758 -0.130357 -0.838758 3.511 0.152655 0.127687 0.847345 -0.127687 -0.847345 -0.127687 -0.847345 3.641 0.144623 0.12495 0.855377 -0.12495 -0.855377 -0.12495 -0.855377 3.771 0.137105 0.122162 0.862895 -0.122162 -0.862895 -0.122162 -0.862895 3.91 0.130063 0.119338 0.869937 -0.119338 -0.869937 -0.119338 -0.869937 4.031 0.123462 0.11649 0.876538 -0.11649 -0.876538 -0.11649 -0.876538 4.161 0.117269 0.113631 0.882731 -0.113631 -0.882731 -0.113631 -0.882731 4.291 0.111456 0.110769 0.888544 -0.110769 -0.888544 -0.110769 -0.888544 4.421 0.105994 0.107913 0.894006 -0.107913 -0.894006 -0.107913 -0.894006 4.551 0.100859 0.105071 0.899141 -0.105071 -0.899141 -0.105071 -0.899141 4.681 0.0960271 0.102251 0.903973 -0.102251 -0.903973 -0.102251 -0.903973 4.811 0.0914777 0.0994577 0.908522 -0.0994577 -0.908522 -0.0994577 -0.908522 4.941 0.0871909 0.0966965 0.912809 -0.0966965 -0.912809 -0.0966965 -0.912809 5.071 0.0831486 0.0939718 0.916851 -0.0939718 -0.916851 -0.0939718 -0.916851 5.21 0.079334 0.0912876 0.920666 -0.0912876 -0.920666 -0.0912876 -0.920666 5.331 0.0757318 0.0886469 0.924268 -0.0886469 -0.924268 -0.0886469 -0.924268 5.461 0.0723276 0.0860527 0.927672 -0.0860527 -0.927672 -0.0860527 -0.927672 5.591 0.0691083 0.0835072 0.930892 -0.0835072 -0.930892 -0.0835072 -0.930892 5.721 0.0660618 0.0810121 0.933938 -0.0810121 -0.933938 -0.0810121 -0.933938 5.851 0.0631768 0.0785691 0.936823 -0.0785691 -0.936823 -0.0785691 -0.936823 5.981 0.0604429 0.0761793 0.939557 -0.0761793 -0.939557 -0.0761793 -0.939557 6.111 0.0578505 0.0738436 0.942149 -0.0738436 -0.942149 -0.0738436 -0.942149 6.241 0.0553907 0.0715625 0.944609 -0.0715625 -0.944609 -0.0715625 -0.944609 6.371 0.0530551 0.0693364 0.946945 -0.0693364 -0.946945 -0.0693364 -0.946945 6.51 0.0508362 0.0671656 0.949164 -0.0671656 -0.949164 -0.0671656 -0.949164 6.631 0.0487268 0.0650499 0.951273 -0.0650499 -0.951273 -0.0650499 -0.951273 6.761 0.0467203 0.0629892 0.95328 -0.0629892 -0.95328 -0.0629892 -0.95328 6.891 0.0448107 0.0609831 0.955189 -0.0609831 -0.955189 -0.0609831 -0.955189 7.021 0.0429921 0.0590313 0.957008 -0.0590313 -0.957008 -0.0590313 -0.957008 7.151 0.0412593 0.0571331 0.958741 -0.0571331 -0.958741 -0.0571331 -0.958741 7.281 0.0396074 0.0552879 0.960393 -0.0552879 -0.960393 -0.0552879 -0.960393 7.411 0.0380318 0.053495 0.961968 -0.053495 -0.961968 -0.053495 -0.961968 7.541 0.0365282 0.0517536 0.963472 -0.0517536 -0.963472 -0.0517536 -0.963472 7.671 0.0350926 0.0500627 0.964907 -0.0500627 -0.964907 -0.0500627 -0.964907 7.8

108 13. Cir uito on a oplamiento magnéti o simple.1 0.0337213 0.0484215 0.966279 -0.0484215 -0.966279 -0.0484215 -0.966279 7.930011 0.0324108 0.0468291 0.967589 -0.0468291 -0.967589 -0.0468291 -0.967589 8.060011 0.0311579 0.0452844 0.968842 -0.0452844 -0.968842 -0.0452844 -0.968842 8.190011 0.0299595 0.0437865 0.97004 -0.0437865 -0.97004 -0.0437865 -0.97004 8.320011 0.0288128 0.0423342 0.971187 -0.0423342 -0.971187 -0.0423342 -0.971187 8.450011 0.0277151 0.0409266 0.972285 -0.0409266 -0.972285 -0.0409266 -0.972285 8.580011 0.026664 0.0395626 0.973336 -0.0395626 -0.973336 -0.0395626 -0.973336 8.710011 0.025657 0.0382412 0.974343 -0.0382412 -0.974343 -0.0382412 -0.974343 8.840011 0.024692 0.0369612 0.975308 -0.0369612 -0.975308 -0.0369612 -0.975308 8.970011 0.0237669 0.0357216 0.976233 -0.0357216 -0.976233 -0.0357216 -0.976233 9.100011 0.0228799 0.0345214 0.97712 -0.0345214 -0.97712 -0.0345214 -0.97712 9.230011 0.022029 0.0333594 0.977971 -0.0333594 -0.977971 -0.0333594 -0.977971 9.360011 0.0212125 0.0322348 0.978788 -0.0322348 -0.978788 -0.0322348 -0.978788 9.490011 0.0204288 0.0311463 0.979571 -0.0311463 -0.979571 -0.0311463 -0.979571 9.620011 0.0196765 0.030093 0.980324 -0.030093 -0.980324 -0.030093 -0.980324 9.750011 0.018954 0.029074 0.981046 -0.029074 -0.981046 -0.029074 -0.981046 9.880011 0.01826 0.0280882 0.98174 -0.0280882 -0.98174 -0.0280882 -0.98174 10.011 0.0175932 0.0271346 0.982407 -0.0271346 -0.982407 -0.0271346 -0.982407 10.141 0.0169525 0.0262123 0.983048 -0.0262123 -0.983048 -0.0262123 -0.983048 10.271 0.0163366 0.0253204 0.983663 -0.0253204 -0.983663 -0.0253204 -0.983663 10.41 0.0157444 0.024458 0.984256 -0.024458 -0.984256 -0.024458 -0.984256 10.531 0.015175 0.0236241 0.984825 -0.0236241 -0.984825 -0.0236241 -0.984825 10.661 0.0146273 0.0228178 0.985373 -0.0228178 -0.985373 -0.0228178 -0.985373 10.791 0.0141005 0.0220384 0.9859 -0.0220384 -0.9859 -0.0220384 -0.9859 10.921 0.0135936 0.0212851 0.986406 -0.0212851 -0.986406 -0.0212851 -0.986406 11.051 0.0131058 0.0205569 0.986894 -0.0205569 -0.986894 -0.0205569 -0.986894 11.181 0.0126364 0.019853 0.987364 -0.019853 -0.987364 -0.019853 -0.987364 11.311 0.0121845 0.0191728 0.987816 -0.0191728 -0.987816 -0.0191728 -0.987816 11.441 0.0117494 0.0185155 0.988251 -0.0185155 -0.988251 -0.0185155 -0.988251 11.571 0.0113305 0.0178803 0.988669 -0.0178803 -0.988669 -0.0178803 -0.988669 11.71 0.0109271 0.0172666 0.989073 -0.0172666 -0.989073 -0.0172666 -0.989073 11.831 0.0105386 0.0166736 0.989461 -0.0166736 -0.989461 -0.0166736 -0.989461 11.961 0.0101644 0.0161006 0.989836 -0.0161006 -0.989836 -0.0161006 -0.989836 12.091 0.00980394 0.0155471 0.990196 -0.0155471 -0.990196 -0.0155471 -0.990196 12.221 0.00945664 0.0150123 0.990543 -0.0150123 -0.990543 -0.0150123 -0.990543 12.351 0.00912201 0.0144957 0.990878 -0.0144957 -0.990878 -0.0144957 -0.990878 12.481 0.00879956 0.0139967 0.9912 -0.0139967 -0.9912 -0.0139967 -0.9912 12.611 0.00848881 0.0135146 0.991511 -0.0135146 -0.991511 -0.0135146 -0.991511 12.741 0.00818932 0.013049 0.991811 -0.013049 -0.991811 -0.013049 -0.991811 12.871 0.00790065 0.0125992 0.992099 -0.0125992 -0.992099 -0.0125992 -0.992099 131 0.00762239 0.0121648 0.992378 -0.0121648 -0.992378 -0.0121648 -0.992378 13.131 0.00735414 0.0117453 0.992646 -0.0117453 -0.992646 -0.0117453 -0.992646 13.261 0.00709553 0.0113401 0.992904 -0.0113401 -0.992904 -0.0113401 -0.992904 13.391 0.0068462 0.0109488 0.993154 -0.0109488 -0.993154 -0.0109488 -0.993154 13.521 0.00660579 0.0105708 0.993394 -0.0105708 -0.993394 -0.0105708 -0.993394 13.651 0.00637397 0.0102058 0.993626 -0.0102058 -0.993626 -0.0102058 -0.993626 13.781 0.00615042 0.00985338 0.99385 -0.00985338 -0.99385 -0.00985338 -0.99385 13.911 0.00593485 0.00951301 0.994065 -0.00951301 -0.994065 -0.00951301 -0.994065 14.041 0.00572694 0.00918433 0.994273 -0.00918433 -0.994273 -0.00918433 -0.994273 14.171 0.00552642 0.00886693 0.994474 -0.00886693 -0.994474 -0.00886693 -0.994474 14.31 0.00533301 0.00856045 0.994667 -0.00856045 -0.994667 -0.00856045 -0.994667 14.431 0.00514647 0.0082645 0.994854 -0.0082645 -0.994854 -0.0082645 -0.994854 14.561 0.00496652 0.00797874 0.995033 -0.00797874 -0.995033 -0.00797874 -0.995033 14.691 0.00479295 0.00770281 0.995207 -0.00770281 -0.995207 -0.00770281 -0.995207 14.82

13.2. Solu iones 1091 0.0046255 0.00743638 0.995374 -0.00743638 -0.995374 -0.00743638 -0.995374 14.951 0.00446397 0.00717913 0.995536 -0.00717913 -0.995536 -0.00717913 -0.995536 15.081 0.00430814 0.00693074 0.995692 -0.00693074 -0.995692 -0.00693074 -0.995692 15.211 0.00415779 0.00669092 0.995842 -0.00669092 -0.995842 -0.00669092 -0.995842 15.341 0.00401274 0.00645936 0.995987 -0.00645936 -0.995987 -0.00645936 -0.995987 15.471 0.00387279 0.00623579 0.996127 -0.00623579 -0.996127 -0.00623579 -0.996127 15.61 0.00373777 0.00601994 0.996262 -0.00601994 -0.996262 -0.00601994 -0.996262 15.731 0.00360748 0.00581153 0.996393 -0.00581153 -0.996393 -0.00581153 -0.996393 15.861 0.00348177 0.00561032 0.996518 -0.00561032 -0.996518 -0.00561032 -0.996518 15.991 0.00336047 0.00541606 0.99664 -0.00541606 -0.99664 -0.00541606 -0.99664 16.121 0.00324343 0.00522851 0.996757 -0.00522851 -0.996757 -0.00522851 -0.996757 16.251 0.00313048 0.00504743 0.99687 -0.00504743 -0.99687 -0.00504743 -0.99687 16.381 0.00302149 0.00487262 0.996979 -0.00487262 -0.996979 -0.00487262 -0.996979 16.511 0.00291632 0.00470384 0.997084 -0.00470384 -0.997084 -0.00470384 -0.997084 16.641 0.00281483 0.0045409 0.997185 -0.0045409 -0.997185 -0.0045409 -0.997185 16.771 0.00271688 0.00438359 0.997283 -0.00438359 -0.997283 -0.00438359 -0.997283 16.91 0.00262236 0.00423172 0.997378 -0.00423172 -0.997378 -0.00423172 -0.997378 17.031 0.00253115 0.00408511 0.997469 -0.00408511 -0.997469 -0.00408511 -0.997469 17.161 0.00244312 0.00394356 0.997557 -0.00394356 -0.997557 -0.00394356 -0.997557 17.291 0.00235816 0.00380692 0.997642 -0.00380692 -0.997642 -0.00380692 -0.997642 17.421 0.00227617 0.003675 0.997724 -0.003675 -0.997724 -0.003675 -0.997724 17.551 0.00219704 0.00354764 0.997803 -0.00354764 -0.997803 -0.00354764 -0.997803 17.681 0.00212067 0.0034247 0.997879 -0.0034247 -0.997879 -0.0034247 -0.997879 17.811 0.00204696 0.003306 0.997953 -0.003306 -0.997953 -0.003306 -0.997953 17.941 0.00197582 0.00319142 0.998024 -0.00319142 -0.998024 -0.00319142 -0.998024 18.071 0.00190717 0.00308081 0.998093 -0.00308081 -0.998093 -0.00308081 -0.998093 18.21 0.0018409 0.00297402 0.998159 -0.00297402 -0.998159 -0.00297402 -0.998159 18.331 0.00177694 0.00287093 0.998223 -0.00287093 -0.998223 -0.00287093 -0.998223 18.461 0.00171521 0.00277141 0.998285 -0.00277141 -0.998285 -0.00277141 -0.998285 18.591 0.00165563 0.00267534 0.998344 -0.00267534 -0.998344 -0.00267534 -0.998344 18.721 0.00159813 0.0025826 0.998402 -0.0025826 -0.998402 -0.0025826 -0.998402 18.851 0.00154262 0.00249307 0.998457 -0.00249307 -0.998457 -0.00249307 -0.998457 18.981 0.00148905 0.00240664 0.998511 -0.00240664 -0.998511 -0.00240664 -0.998511 19.111 0.00143734 0.0023232 0.998563 -0.0023232 -0.998563 -0.0023232 -0.998563 19.241 0.00138743 0.00224266 0.998613 -0.00224266 -0.998613 -0.00224266 -0.998613 19.371 0.00133925 0.0021649 0.998661 -0.0021649 -0.998661 -0.0021649 -0.998661 19.51 0.00129276 0.00208984 0.998707 -0.00208984 -0.998707 -0.00208984 -0.998707 19.631 0.00124787 0.00201738 0.998752 -0.00201738 -0.998752 -0.00201738 -0.998752 19.76set terminal pngset output ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/13/ e jemplo013_graf i a . png 'set en oding iso_8859_1set gridset autos aleset key bottom r i gh t t i t l e ' Var i ab l e s ' boxset t i t l e ' Graf i ado por d e f e t o de l a s s o l u i on e s de l i r u i t o 'plot ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/13/ejemplo013_x_trans . data ' using 9 :1 t i t l e 'V en nodo 1 ' with l i n e s , ' /home/ ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/13/ejemplo013_x_trans . data 'using 9 :2 t i t l e 'V en nodo 2 ' with l i n e s , ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/13/ejemplo013_x_trans . data ' using 9 :3 t i t l e 'V en nodo 3 ' with l i n e s ,

110 13. Cir uito on a oplamiento magnéti o simple.' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/13/ejemplo013_x_trans . data ' using 9 :4 t i t l e ' I de Bobinas A opladas ent r e nodos 2 , 0 ' with l i n e s , ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/13/ejemplo013_x_trans . data ' using 9 :5 t i t l e ' I de Bobinas A opladas ent r e nodos 3 , 0 ' with l i n e s , ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/13/ejemplo013_x_trans . data ' using 9 :6 t i t l e ' I de Fuente t ens i on ent r e nodos 1 , 0 ' with l i n e s , ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/13/ejemplo013_x_trans . data 'using 9 :7 t i t l e ' I Re s i s t en i a ent r e nodos 0 , 3 ' with l i n e s , ' /home/ ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/13/ejemplo013_x_trans . data ' using 9 :8 t i t l e ' I Re s i s t en i a ent r e nodos 2 , 1 ' with l i n e sGrá o de salida.

Veámos las intensidades de las bobinas a opladas on mayor detalle.

13.2. Solu iones 111

Capítulo 14Cir uito on a oplamientomagnéti o.Ahora se pro ederá al análsis de un ir uito on bobinas a opladas un po o más ompli adoque el anterior.1

2 3

0 014.1. Datos Generales.Ar hivo *.sp ∗SPICE i r u i t <ejemplo014> from XCir uit v3 . 6 rev 1351 1 0 2 0 3 0 12 1 0 1 0 3 0 22 2 0 1 2 0 0 11 2 0 2 2 1 0 112 1 0 2 2 0 3 0 0 0 0 0 0 0 1 3 1 04 1 0 2 1 0 0 1 rho f a b A B C D. end Tipo de análisis realizadoAnálisis esta ionario ⊠Análisis transitorio ⊠Datos generales del ir uitoElementos del Cto: 6EA: 0Nodos: 3A2: 5No nulos: 20 113

114 14. Cir uito on a oplamiento magnéti o.Densidad: 0.3125Dispersion: 0.6875Los valores dados al ir uito son:Elemento MagnitudResisten ias 1 ΩCondensador entre nodos 2, 0 1 FCondensador entre nodos 3, 0 2 FBobinas a opladas L1 = 1, L2 = 3, M = 1Fuente de tensión 1 VMatriz T.row 0: (5, 1) (7, -1)row 1: (1, 0 + 1 i) (3, 1) (7, 1)row 2: (2, 0 + 2 i) (4, 1) (6, -1)row 3: (1, 1) (3, -0 - 1 i) (4, -0 - 1 i)row 4: (2, 1) (3, -0 - 1 i) (4, -0 - 3 i)row 5: (0, 1)row 6: (2, -1) (6, -1)row 7: (0, -1) (1, 1) (7, -1)14.2. Solu iones14.2.1. Primer análisis Tiempo Ini ial 0Tiempo Final 20Paso de Tiempo 0, 05Theta 1 (Euler)Esta ionarioResultados sistema esta ionario:Tensión en nodo 1: 1 + 5.0307e-17 iTensión en nodo 2: 0.7 + 0.4 iTensión en nodo 3: -0.1 - 0.2 iI de Bobinas A opladas entre nodos 2, 0: 0.7 - 1.1 iI de Bobinas A opladas entre nodos 3, 0: -0.3 + 0.4 iI de Fuente tension entre nodos 1, 0: -0.3 + 0.4 iI Resisten ia entre nodos 0, 3: 0.1 + 0.2 iI Resisten ia entre nodos 2, 1: -0.3 + 0.4 i

14.2. Solu iones 115Transitorio1 0.0474496 2.89151e-05 0.003558 -0.00118552 -0.95255 -2.89151e-05 -0.95255 01 0.0923102 0.000113342 0.0104784 -0.00349044 -0.90769 -0.000113342 -0.90769 0.051 0.134554 0.000277587 0.0205631 -0.00684736 -0.865446 -0.000277587 -0.865446 0.11 0.174165 0.000543692 0.0336119 -0.0111879 -0.825835 -0.000543692 -0.825835 0.151 0.211137 0.000931481 0.0494239 -0.016443 -0.788863 -0.000931481 -0.788863 0.21 0.245474 0.0014586 0.067798 -0.0225434 -0.754526 -0.0014586 -0.754526 0.251 0.277188 0.00214058 0.0885335 -0.0294196 -0.722812 -0.00214058 -0.722812 0.31 0.306301 0.00299087 0.111431 -0.0370024 -0.693699 -0.00299087 -0.693699 0.351 0.332844 0.00402092 0.136294 -0.0452229 -0.667156 -0.00402092 -0.667156 0.41 0.356855 0.00524024 0.162927 -0.0540133 -0.643145 -0.00524024 -0.643145 0.451 0.378379 0.00665649 0.191139 -0.0633064 -0.621621 -0.00665649 -0.621621 0.51 0.397469 0.00827551 0.220743 -0.0730362 -0.602531 -0.00827551 -0.602531 0.551 0.414182 0.0101014 0.251554 -0.0831382 -0.585818 -0.0101014 -0.585818 0.61 0.428583 0.0121367 0.283394 -0.0935494 -0.571417 -0.0121367 -0.571417 0.651 0.440741 0.0143824 0.31609 -0.104208 -0.559259 -0.0143824 -0.559259 0.71 0.450731 0.0168378 0.349474 -0.115056 -0.549269 -0.0168378 -0.549269 0.751 0.45863 0.0195012 0.383384 -0.126034 -0.54137 -0.0195012 -0.54137 0.81 0.464521 0.0223691 0.417664 -0.137088 -0.535479 -0.0223691 -0.535479 0.851 0.468489 0.0254373 0.452164 -0.148164 -0.531511 -0.0254373 -0.531511 0.91 0.47062 0.0287001 0.486743 -0.159212 -0.52938 -0.0287001 -0.52938 0.951 0.471007 0.0321509 0.521265 -0.170183 -0.528993 -0.0321509 -0.528993 11 0.46974 0.0357822 0.555601 -0.181032 -0.53026 -0.0357822 -0.53026 1.051 0.466913 0.0395854 0.58963 -0.191716 -0.533087 -0.0395854 -0.533087 1.11 0.46262 0.0435514 0.623237 -0.202192 -0.53738 -0.0435514 -0.53738 1.151 0.456956 0.0476703 0.656317 -0.212424 -0.543044 -0.0476703 -0.543044 1.21 0.450017 0.0519314 0.68877 -0.222377 -0.549983 -0.0519314 -0.549983 1.251 0.441897 0.0563237 0.720505 -0.232016 -0.558103 -0.0563237 -0.558103 1.31 0.43269 0.0608356 0.751435 -0.241312 -0.56731 -0.0608356 -0.56731 1.351 0.422492 0.0654552 0.781486 -0.250238 -0.577508 -0.0654552 -0.577508 1.41 0.411393 0.0701702 0.810586 -0.258769 -0.588607 -0.0701702 -0.588607 1.451 0.399485 0.074968 0.838673 -0.266882 -0.600515 -0.074968 -0.600515 1.51 0.386857 0.079836 0.865692 -0.274557 -0.613143 -0.079836 -0.613143 1.551 0.373598 0.0847614 0.891592 -0.281778 -0.626402 -0.0847614 -0.626402 1.61 0.359792 0.0897314 0.916333 -0.28853 -0.640208 -0.0897314 -0.640208 1.651 0.345521 0.0947331 0.939879 -0.294799 -0.654479 -0.0947331 -0.654479 1.71 0.330868 0.0997536 0.962201 -0.300577 -0.669132 -0.0997536 -0.669132 1.751 0.315909 0.104781 0.983274 -0.305855 -0.684091 -0.104781 -0.684091 1.81 0.300719 0.109801 1.00308 -0.310628 -0.699281 -0.109801 -0.699281 1.851 0.28537 0.114803 1.02162 -0.314892 -0.71463 -0.114803 -0.71463 1.91 0.26993 0.119775 1.03887 -0.318646 -0.73007 -0.119775 -0.73007 1.951 0.254465 0.124705 1.05483 -0.32189 -0.745535 -0.124705 -0.745535 21 0.239037 0.129581 1.06952 -0.324627 -0.760963 -0.129581 -0.760963 2.051 0.223705 0.134393 1.08294 -0.326859 -0.776295 -0.134393 -0.776295 2.11 0.208523 0.139129 1.0951 -0.328594 -0.791477 -0.139129 -0.791477 2.151 0.193545 0.143781 1.10602 -0.329838 -0.806455 -0.143781 -0.806455 2.21 0.178818 0.148337 1.11572 -0.3306 -0.821182 -0.148337 -0.821182 2.251 0.164387 0.15279 1.12423 -0.33089 -0.835613 -0.15279 -0.835613 2.31 0.150293 0.15713 1.13158 -0.330719 -0.849707 -0.15713 -0.849707 2.351 0.136575 0.161348 1.13779 -0.3301 -0.863425 -0.161348 -0.863425 2.41 0.123267 0.165439 1.1429 -0.329046 -0.876733 -0.165439 -0.876733 2.451 0.1104 0.169393 1.14694 -0.327571 -0.8896 -0.169393 -0.8896 2.51 0.0980018 0.173205 1.14996 -0.325691 -0.901998 -0.173205 -0.901998 2.55

116 14. Cir uito on a oplamiento magnéti o.1 0.0860971 0.176869 1.152 -0.323422 -0.913903 -0.176869 -0.913903 2.61 0.0747072 0.180379 1.15309 -0.32078 -0.925293 -0.180379 -0.925293 2.651 0.0638504 0.18373 1.15329 -0.317783 -0.93615 -0.18373 -0.93615 2.71 0.0535418 0.186919 1.15263 -0.314448 -0.946458 -0.186919 -0.946458 2.751 0.0437939 0.18994 1.15116 -0.310795 -0.956206 -0.18994 -0.956206 2.81 0.034616 0.192791 1.14894 -0.30684 -0.965384 -0.192791 -0.965384 2.851 0.026015 0.19547 1.14601 -0.302604 -0.973985 -0.19547 -0.973985 2.91 0.0179949 0.197973 1.14241 -0.298105 -0.982005 -0.197973 -0.982005 2.951 0.0105575 0.200299 1.13819 -0.293361 -0.989442 -0.200299 -0.989442 31 0.00370208 0.202448 1.13341 -0.288392 -0.996298 -0.202448 -0.996298 3.051 -0.00257436 0.204418 1.1281 -0.283218 -1.00257 -0.204418 -1.00257 3.11 -0.00827689 0.206209 1.12233 -0.277855 -1.00828 -0.206209 -1.00828 3.151 -0.0134126 0.207822 1.11613 -0.272325 -1.01341 -0.207822 -1.01341 3.21 -0.0179903 0.209256 1.10955 -0.266643 -1.01799 -0.209256 -1.01799 3.251 -0.0220208 0.210514 1.10263 -0.26083 -1.02202 -0.210514 -1.02202 3.31 -0.0255163 0.211597 1.09543 -0.254902 -1.02552 -0.211597 -1.02552 3.351 -0.0284907 0.212506 1.08798 -0.248877 -1.02849 -0.212506 -1.02849 3.41 -0.030959 0.213244 1.08032 -0.242772 -1.03096 -0.213244 -1.03096 3.451 -0.0329375 0.213814 1.07251 -0.236603 -1.03294 -0.213814 -1.03294 3.51 -0.0344439 0.214218 1.06457 -0.230387 -1.03444 -0.214218 -1.03444 3.551 -0.0354964 0.21446 1.05655 -0.224138 -1.0355 -0.21446 -1.0355 3.61 -0.0361144 0.214543 1.04847 -0.217872 -1.03611 -0.214543 -1.03611 3.651 -0.0363179 0.214472 1.04039 -0.211602 -1.03632 -0.214472 -1.03632 3.71 -0.0361277 0.214249 1.03232 -0.205342 -1.03613 -0.214249 -1.03613 3.751 -0.0355649 0.21388 1.02431 -0.199106 -1.03556 -0.21388 -1.03556 3.81 -0.0346511 0.213368 1.01638 -0.192906 -1.03465 -0.213368 -1.03465 3.851 -0.0334083 0.212719 1.00855 -0.186753 -1.03341 -0.212719 -1.03341 3.91 -0.0318585 0.211937 1.00086 -0.180658 -1.03186 -0.211937 -1.03186 3.951 -0.0300242 0.211027 0.993337 -0.174631 -1.03002 -0.211027 -1.03002 41 -0.0279274 0.209994 0.985992 -0.168683 -1.02793 -0.209994 -1.02793 4.051 -0.0255905 0.208844 0.978852 -0.162823 -1.02559 -0.208844 -1.02559 4.11 -0.0230354 0.207581 0.971935 -0.157057 -1.02304 -0.207581 -1.02304 4.151 -0.0202841 0.20621 0.965258 -0.151395 -1.02028 -0.20621 -1.02028 4.21 -0.0173581 0.204738 0.958838 -0.145842 -1.01736 -0.204738 -1.01736 4.251 -0.0142786 0.203169 0.952688 -0.140406 -1.01428 -0.203169 -1.01428 4.31 -0.0110662 0.201508 0.94682 -0.135092 -1.01107 -0.201508 -1.01107 4.351 -0.00774144 0.199762 0.941245 -0.129904 -1.00774 -0.199762 -1.00774 4.41 -0.00432388 0.197935 0.935973 -0.124848 -1.00432 -0.197935 -1.00432 4.451 -0.000832711 0.196032 0.931009 -0.119926 -1.00083 -0.196032 -1.00083 4.51 0.00271354 0.194059 0.926361 -0.115142 -0.997286 -0.194059 -0.997286 4.551 0.00629703 0.192021 0.922033 -0.110499 -0.993703 -0.192021 -0.993703 4.61 0.00990062 0.189923 0.918028 -0.105999 -0.990099 -0.189923 -0.990099 4.651 0.0135079 0.18777 0.914346 -0.101642 -0.986492 -0.18777 -0.986492 4.71 0.0171032 0.185567 0.91099 -0.0974307 -0.982897 -0.185567 -0.982897 4.751 0.0206718 0.183318 0.907958 -0.0933645 -0.979328 -0.183318 -0.979328 4.81 0.0241995 0.181028 0.905247 -0.0894438 -0.975801 -0.181028 -0.975801 4.851 0.0276731 0.178702 0.902855 -0.0856681 -0.972327 -0.178702 -0.972327 4.91 0.0310802 0.176345 0.900777 -0.0820365 -0.96892 -0.176345 -0.96892 4.951 0.0344093 0.173959 0.899009 -0.0785477 -0.965591 -0.173959 -0.965591 51 0.0376496 0.17155 0.897544 -0.0752002 -0.96235 -0.17155 -0.96235 5.051 0.0407913 0.169122 0.896375 -0.0719919 -0.959209 -0.169122 -0.959209 5.11 0.0438253 0.166678 0.895495 -0.0689206 -0.956175 -0.166678 -0.956175 5.151 0.0467434 0.164222 0.894895 -0.0659836 -0.953257 -0.164222 -0.953257 5.21 0.0495381 0.161758 0.894567 -0.0631782 -0.950462 -0.161758 -0.950462 5.25

14.2. Solu iones 1171 0.052203 0.159288 0.8945 -0.060501 -0.947797 -0.159288 -0.947797 5.31 0.0547322 0.156816 0.894684 -0.0579489 -0.945268 -0.156816 -0.945268 5.351 0.0571207 0.154346 0.89511 -0.0555183 -0.942879 -0.154346 -0.942879 5.41 0.0593642 0.151879 0.895765 -0.0532054 -0.940636 -0.151879 -0.940636 5.451 0.0614593 0.149419 0.896639 -0.0510064 -0.938541 -0.149419 -0.938541 5.51 0.0634032 0.146967 0.89772 -0.0489173 -0.936597 -0.146967 -0.936597 5.551 0.0651937 0.144528 0.898996 -0.046934 -0.934806 -0.144528 -0.934806 5.61 0.0668294 0.142101 0.900456 -0.0450522 -0.933171 -0.142101 -0.933171 5.651 0.0683096 0.139691 0.902087 -0.0432677 -0.93169 -0.139691 -0.93169 5.71 0.069634 0.137298 0.903877 -0.0415761 -0.930366 -0.137298 -0.930366 5.751 0.0708032 0.134924 0.905814 -0.0399731 -0.929197 -0.134924 -0.929197 5.81 0.071818 0.132571 0.907886 -0.0384542 -0.928182 -0.132571 -0.928182 5.851 0.0726799 0.13024 0.910081 -0.0370152 -0.92732 -0.13024 -0.92732 5.91 0.073391 0.127933 0.912387 -0.0356517 -0.926609 -0.127933 -0.926609 5.951 0.0739537 0.125651 0.914792 -0.0343592 -0.926046 -0.125651 -0.926046 61 0.0743709 0.123395 0.917285 -0.0331336 -0.925629 -0.123395 -0.925629 6.051 0.0746458 0.121165 0.919855 -0.0319707 -0.925354 -0.121165 -0.925354 6.100011 0.0747823 0.118962 0.922489 -0.0308662 -0.925218 -0.118962 -0.925218 6.150011 0.0747841 0.116788 0.925178 -0.0298161 -0.925216 -0.116788 -0.925216 6.200011 0.0746558 0.114642 0.927912 -0.0288164 -0.925344 -0.114642 -0.925344 6.250011 0.0744018 0.112526 0.930679 -0.0278633 -0.925598 -0.112526 -0.925598 6.300011 0.0740269 0.110439 0.93347 -0.026953 -0.925973 -0.110439 -0.925973 6.350011 0.0735364 0.108381 0.936275 -0.0260819 -0.926464 -0.108381 -0.926464 6.400011 0.0729353 0.106353 0.939087 -0.0252464 -0.927065 -0.106353 -0.927065 6.450011 0.0722291 0.104356 0.941895 -0.0244433 -0.927771 -0.104356 -0.927771 6.500011 0.0714233 0.102388 0.944692 -0.0236692 -0.928577 -0.102388 -0.928577 6.550011 0.0705236 0.100449 0.94747 -0.022921 -0.929476 -0.100449 -0.929476 6.600011 0.0695358 0.0985409 0.950222 -0.0221959 -0.930464 -0.0985409 -0.930464 6.650011 0.0684655 0.0966616 0.95294 -0.021491 -0.931535 -0.0966616 -0.931535 6.700011 0.0673186 0.0948114 0.955619 -0.0208037 -0.932681 -0.0948114 -0.932681 6.750011 0.066101 0.0929899 0.958251 -0.0201314 -0.933899 -0.0929899 -0.933899 6.800011 0.0648184 0.0911968 0.960833 -0.019472 -0.935182 -0.0911968 -0.935182 6.850011 0.0634767 0.0894316 0.963358 -0.0188231 -0.936523 -0.0894316 -0.936523 6.900011 0.0620815 0.0876938 0.965822 -0.0181828 -0.937918 -0.0876938 -0.937918 6.950011 0.0606386 0.085983 0.96822 -0.0175492 -0.939361 -0.085983 -0.939361 7.000011 0.0591535 0.0842985 0.970549 -0.0169206 -0.940847 -0.0842985 -0.940847 7.050011 0.0576316 0.0826399 0.972805 -0.0162954 -0.942368 -0.0826399 -0.942368 7.100011 0.0560784 0.0810066 0.974986 -0.0156722 -0.943922 -0.0810066 -0.943922 7.150011 0.054499 0.0793979 0.977089 -0.0150497 -0.945501 -0.0793979 -0.945501 7.200011 0.0528986 0.0778132 0.979111 -0.0144268 -0.947101 -0.0778132 -0.947101 7.250011 0.051282 0.076252 0.98105 -0.0138026 -0.948718 -0.076252 -0.948718 7.300011 0.0496539 0.0747135 0.982907 -0.0131761 -0.950346 -0.0747135 -0.950346 7.350011 0.0480191 0.0731973 0.984678 -0.0125466 -0.951981 -0.0731973 -0.951981 7.400011 0.0463818 0.0717025 0.986364 -0.0119136 -0.953618 -0.0717025 -0.953618 7.450011 0.0447462 0.0702287 0.987965 -0.0112765 -0.955254 -0.0702287 -0.955254 7.500011 0.0431165 0.0687752 0.989479 -0.0106351 -0.956884 -0.0687752 -0.956884 7.550011 0.0414963 0.0673414 0.990908 -0.00998894 -0.958504 -0.0673414 -0.958504 7.600011 0.0398892 0.0659267 0.992251 -0.00933801 -0.960111 -0.0659267 -0.960111 7.650011 0.0382988 0.0645305 0.99351 -0.00868222 -0.961701 -0.0645305 -0.961701 7.700011 0.0367281 0.0631522 0.994686 -0.00802161 -0.963272 -0.0631522 -0.963272 7.750011 0.0351801 0.0617913 0.99578 -0.00735633 -0.96482 -0.0617913 -0.96482 7.800011 0.0336576 0.0604473 0.996793 -0.00668659 -0.966342 -0.0604473 -0.966342 7.850011 0.0321631 0.0591197 0.997727 -0.00601267 -0.967837 -0.0591197 -0.967837 7.900011 0.0306989 0.0578078 0.998584 -0.00533495 -0.969301 -0.0578078 -0.969301 7.95001

118 14. Cir uito on a oplamiento magnéti o.1 0.0292672 0.0565114 0.999367 -0.00465384 -0.970733 -0.0565114 -0.970733 8.000011 0.0278699 0.0552299 1.00008 -0.00396985 -0.97213 -0.0552299 -0.97213 8.050011 0.0265087 0.0539629 1.00072 -0.00328349 -0.973491 -0.0539629 -0.973491 8.100011 0.0251851 0.05271 1.00129 -0.00259537 -0.974815 -0.05271 -0.974815 8.150011 0.0239005 0.0514709 1.00179 -0.00190611 -0.976099 -0.0514709 -0.976099 8.200011 0.022656 0.0502452 1.00224 -0.00121638 -0.977344 -0.0502452 -0.977344 8.250011 0.0214524 0.0490326 1.00262 -0.000526874 -0.978548 -0.0490326 -0.978548 8.300011 0.0202907 0.0478327 1.00294 0.000161676 -0.979709 -0.0478327 -0.979709 8.350011 0.0191713 0.0466454 1.00322 0.000848527 -0.980829 -0.0466454 -0.980829 8.400011 0.0180948 0.0454703 1.00344 0.00153291 -0.981905 -0.0454703 -0.981905 8.450011 0.0170613 0.0443072 1.00361 0.00221406 -0.982939 -0.0443072 -0.982939 8.500011 0.016071 0.0431561 1.00373 0.00289119 -0.983929 -0.0431561 -0.983929 8.550011 0.0151239 0.0420166 1.00382 0.00356351 -0.984876 -0.0420166 -0.984876 8.600011 0.0142198 0.0408886 1.00386 0.00423023 -0.98578 -0.0408886 -0.98578 8.650011 0.0133583 0.039772 1.00387 0.00489057 -0.986642 -0.039772 -0.986642 8.700021 0.0125392 0.0386668 1.00384 0.00554376 -0.987461 -0.0386668 -0.987461 8.750021 0.0117617 0.0375727 1.00379 0.00618903 -0.988238 -0.0375727 -0.988238 8.800021 0.0110254 0.0364898 1.0037 0.00682565 -0.988975 -0.0364898 -0.988975 8.850021 0.0103294 0.0354181 1.00359 0.00745286 -0.989671 -0.0354181 -0.989671 8.900021 0.00967285 0.0343574 1.00346 0.00806998 -0.990327 -0.0343574 -0.990327 8.950021 0.00905492 0.0333078 1.0033 0.0086763 -0.990945 -0.0333078 -0.990945 9.000021 0.00847456 0.0322693 1.00313 0.00927116 -0.991525 -0.0322693 -0.991525 9.050021 0.0079307 0.0312419 1.00295 0.00985394 -0.992069 -0.0312419 -0.992069 9.100021 0.00742222 0.0302256 1.00275 0.010424 -0.992578 -0.0302256 -0.992578 9.150021 0.00694792 0.0292206 1.00254 0.0109808 -0.993052 -0.0292206 -0.993052 9.200021 0.00650657 0.0282268 1.00232 0.0115239 -0.993493 -0.0282268 -0.993493 9.250021 0.0060969 0.0272444 1.0021 0.0120525 -0.993903 -0.0272444 -0.993903 9.300021 0.0057176 0.0262734 1.00187 0.0125664 -0.994282 -0.0262734 -0.994282 9.350021 0.00536732 0.0253139 1.00164 0.0130651 -0.994633 -0.0253139 -0.994633 9.400021 0.00504472 0.0243661 1.00141 0.0135481 -0.994955 -0.0243661 -0.994955 9.450021 0.00474841 0.0234299 1.00118 0.0140152 -0.995252 -0.0234299 -0.995252 9.500021 0.00447701 0.0225057 1.00095 0.0144659 -0.995523 -0.0225057 -0.995523 9.550021 0.00422914 0.0215933 1.00073 0.0149 -0.995771 -0.0215933 -0.995771 9.600021 0.00400341 0.0206931 1.00051 0.0153172 -0.995997 -0.0206931 -0.995997 9.650021 0.00379844 0.019805 1.0003 0.0157174 -0.996202 -0.019805 -0.996202 9.700021 0.00361286 0.0189293 1.0001 0.0161003 -0.996387 -0.0189293 -0.996387 9.750021 0.00344532 0.018066 0.999905 0.0164658 -0.996555 -0.018066 -0.996555 9.800021 0.00329449 0.0172152 0.999722 0.0168138 -0.996706 -0.0172152 -0.996706 9.850021 0.00315906 0.0163772 0.99955 0.0171443 -0.996841 -0.0163772 -0.996841 9.900021 0.00303774 0.015552 0.999389 0.0174572 -0.996962 -0.015552 -0.996962 9.950021 0.00292928 0.0147397 0.99924 0.0177524 -0.997071 -0.0147397 -0.997071 101 0.00283247 0.0139404 0.999104 0.0180301 -0.997168 -0.0139404 -0.997168 10.051 0.00274611 0.0131543 0.998981 0.0182903 -0.997254 -0.0131543 -0.997254 10.11 0.00266908 0.0123814 0.998872 0.0185331 -0.997331 -0.0123814 -0.997331 10.151 0.00260027 0.0116219 0.998776 0.0187587 -0.9974 -0.0116219 -0.9974 10.21 0.00253861 0.0108758 0.998695 0.0189671 -0.997461 -0.0108758 -0.997461 10.251 0.0024831 0.0101433 0.998627 0.0191586 -0.997517 -0.0101433 -0.997517 10.31 0.00243276 0.00942435 0.998574 0.0193334 -0.997567 -0.00942435 -0.997567 10.351 0.00238667 0.00871908 0.998535 0.0194917 -0.997613 -0.00871908 -0.997613 10.41 0.00234397 0.00802755 0.99851 0.0196338 -0.997656 -0.00802755 -0.997656 10.451 0.00230382 0.00734981 0.998499 0.0197599 -0.997696 -0.00734981 -0.997696 10.51 0.00226545 0.0066859 0.998502 0.0198705 -0.997735 -0.0066859 -0.997735 10.551 0.00222813 0.00603586 0.998518 0.0199656 -0.997772 -0.00603586 -0.997772 10.61 0.0021912 0.00539972 0.998548 0.0200459 -0.997809 -0.00539972 -0.997809 10.65

14.2. Solu iones 1191 0.00215401 0.0047775 0.99859 0.0201114 -0.997846 -0.0047775 -0.997846 10.71 0.00211601 0.0041692 0.998644 0.0201628 -0.997884 -0.0041692 -0.997884 10.751 0.00207665 0.00357482 0.99871 0.0202002 -0.997923 -0.00357482 -0.997923 10.81 0.00203547 0.00299436 0.998788 0.0202242 -0.997965 -0.00299436 -0.997965 10.851 0.00199202 0.00242779 0.998877 0.0202351 -0.998008 -0.00242779 -0.998008 10.91 0.00194592 0.00187508 0.998976 0.0202333 -0.998054 -0.00187508 -0.998054 10.951 0.00189683 0.00133619 0.999085 0.0202193 -0.998103 -0.00133619 -0.998103 111 0.00184446 0.000811074 0.999203 0.0201935 -0.998156 -0.000811074 -0.998156 11.051 0.00178855 0.000299676 0.99933 0.0201563 -0.998211 -0.000299676 -0.998211 11.11 0.00172889 -0.000198074 0.999464 0.0201081 -0.998271 0.000198074 -0.998271 11.151 0.00166532 -0.000682253 0.999606 0.0200494 -0.998335 0.000682253 -0.998335 11.21 0.00159769 -0.00115294 0.999755 0.0199806 -0.998402 0.00115294 -0.998402 11.251 0.00152592 -0.00161024 0.99991 0.0199022 -0.998474 0.00161024 -0.998474 11.31 0.00144994 -0.00205425 1.00007 0.0198146 -0.99855 0.00205425 -0.99855 11.351 0.00136973 -0.00248508 1.00023 0.0197182 -0.99863 0.00248508 -0.99863 11.41 0.00128529 -0.00290285 1.0004 0.0196135 -0.998715 0.00290285 -0.998715 11.451 0.00119666 -0.00330768 1.00058 0.0195009 -0.998803 0.00330768 -0.998803 11.51 0.00110391 -0.00369971 1.00075 0.0193808 -0.998896 0.00369971 -0.998896 11.551 0.00100712 -0.00407907 1.00093 0.0192537 -0.998993 0.00407907 -0.998993 11.61 0.000906404 -0.00444592 1.00111 0.0191199 -0.999094 0.00444592 -0.999094 11.651 0.00080191 -0.00480041 1.00129 0.0189798 -0.999198 0.00480041 -0.999198 11.71 0.000693791 -0.00514269 1.00147 0.0188339 -0.999306 0.00514269 -0.999306 11.751 0.000582225 -0.00547293 1.00165 0.0186825 -0.999418 0.00547293 -0.999418 11.81 0.000467409 -0.0057913 1.00183 0.0185261 -0.999533 0.0057913 -0.999533 11.851 0.000349552 -0.00609797 1.00201 0.0183649 -0.99965 0.00609797 -0.99965 11.91 0.00022888 -0.00639313 1.00218 0.0181993 -0.999771 0.00639313 -0.999771 11.951 0.000105627 -0.00667695 1.00236 0.0180298 -0.999894 0.00667695 -0.999894 121 -1.99582e-05 -0.00694962 1.00253 0.0178565 -1.00002 0.00694962 -1.00002 12.051 -0.000147621 -0.00721133 1.0027 0.0176799 -1.00015 0.00721133 -1.00015 12.11 -0.000277099 -0.00746228 1.00287 0.0175003 -1.00028 0.00746228 -1.00028 12.151 -0.000408123 -0.00770266 1.00303 0.0173179 -1.00041 0.00770266 -1.00041 12.21 -0.000540422 -0.00793268 1.00319 0.0171331 -1.00054 0.00793268 -1.00054 12.251 -0.00067372 -0.00815252 1.00334 0.0169462 -1.00067 0.00815252 -1.00067 12.31 -0.00080774 -0.00836239 1.00349 0.0167573 -1.00081 0.00836239 -1.00081 12.351 -0.000942208 -0.0085625 1.00363 0.0165668 -1.00094 0.0085625 -1.00094 12.41 -0.00107685 -0.00875304 1.00377 0.0163749 -1.00108 0.00875304 -1.00108 12.451 -0.00121138 -0.00893423 1.0039 0.0161818 -1.00121 0.00893423 -1.00121 12.51 -0.00134555 -0.00910627 1.00403 0.0159878 -1.00135 0.00910627 -1.00135 12.551 -0.00147908 -0.00926936 1.00415 0.015793 -1.00148 0.00926936 -1.00148 12.61 -0.00161171 -0.00942371 1.00426 0.0155977 -1.00161 0.00942371 -1.00161 12.651 -0.0017432 -0.00956953 1.00437 0.0154021 -1.00174 0.00956953 -1.00174 12.71 -0.00187328 -0.00970701 1.00448 0.0152062 -1.00187 0.00970701 -1.00187 12.751 -0.00200174 -0.00983636 1.00457 0.0150104 -1.002 0.00983636 -1.002 12.81 -0.00212833 -0.00995778 1.00466 0.0148146 -1.00213 0.00995778 -1.00213 12.851 -0.00225284 -0.0100715 1.00474 0.0146192 -1.00225 0.0100715 -1.00225 12.91 -0.00237505 -0.0101776 1.00482 0.0144241 -1.00238 0.0101776 -1.00238 12.951 -0.00249477 -0.0102765 1.00489 0.0142296 -1.00249 0.0102765 -1.00249 131 -0.0026118 -0.0103681 1.00495 0.0140356 -1.00261 0.0103681 -1.00261 13.051 -0.00272596 -0.0104529 1.00501 0.0138425 -1.00273 0.0104529 -1.00273 13.11 -0.0028371 -0.0105309 1.00506 0.0136501 -1.00284 0.0105309 -1.00284 13.151 -0.00294504 -0.0106023 1.0051 0.0134587 -1.00295 0.0106023 -1.00295 13.21 -0.00304965 -0.0106673 1.00514 0.0132683 -1.00305 0.0106673 -1.00305 13.251 -0.0031508 -0.0107261 1.00517 0.0130789 -1.00315 0.0107261 -1.00315 13.31 -0.00324836 -0.0107789 1.0052 0.0128906 -1.00325 0.0107789 -1.00325 13.35

120 14. Cir uito on a oplamiento magnéti o.1 -0.00334223 -0.0108259 1.00522 0.0127035 -1.00334 0.0108259 -1.00334 13.41 -0.00343231 -0.0108671 1.00523 0.0125176 -1.00343 0.0108671 -1.00343 13.451 -0.00351851 -0.0109029 1.00524 0.012333 -1.00352 0.0109029 -1.00352 13.51 -0.00360076 -0.0109333 1.00525 0.0121497 -1.0036 0.0109333 -1.0036 13.551 -0.003679 -0.0109585 1.00524 0.0119677 -1.00368 0.0109585 -1.00368 13.61 -0.00375318 -0.0109787 1.00524 0.0117871 -1.00375 0.0109787 -1.00375 13.651 -0.00382327 -0.0109941 1.00522 0.0116078 -1.00382 0.0109941 -1.00382 13.71 -0.00388922 -0.0110047 1.00521 0.0114299 -1.00389 0.0110047 -1.00389 13.751 -0.00395103 -0.0110108 1.00519 0.0112535 -1.00395 0.0110108 -1.00395 13.81 -0.0040087 -0.0110124 1.00516 0.0110784 -1.00401 0.0110124 -1.00401 13.851 -0.00406221 -0.0110098 1.00513 0.0109047 -1.00406 0.0110098 -1.00406 13.91 -0.00411159 -0.011003 1.0051 0.0107324 -1.00411 0.011003 -1.00411 13.951 -0.00415686 -0.0109923 1.00506 0.0105615 -1.00416 0.0109923 -1.00416 141 -0.00419805 -0.0109776 1.00502 0.010392 -1.0042 0.0109776 -1.0042 14.051 -0.0042352 -0.0109592 1.00498 0.0102239 -1.00424 0.0109592 -1.00424 14.11 -0.00426836 -0.0109372 1.00493 0.0100572 -1.00427 0.0109372 -1.00427 14.151 -0.00429758 -0.0109117 1.00488 0.00989183 -1.0043 0.0109117 -1.0043 14.21 -0.00432293 -0.0108829 1.00483 0.00972783 -1.00432 0.0108829 -1.00432 14.251 -0.00434447 -0.0108507 1.00478 0.00956518 -1.00434 0.0108507 -1.00434 14.31 -0.00436228 -0.0108154 1.00472 0.00940385 -1.00436 0.0108154 -1.00436 14.351 -0.00437644 -0.0107771 1.00466 0.00924383 -1.00438 0.0107771 -1.00438 14.41 -0.00438704 -0.0107358 1.0046 0.00908511 -1.00439 0.0107358 -1.00439 14.451 -0.00439417 -0.0106917 1.00454 0.00892767 -1.00439 0.0106917 -1.00439 14.51 -0.00439792 -0.0106449 1.00447 0.0087715 -1.0044 0.0106449 -1.0044 14.551 -0.00439841 -0.0105954 1.00441 0.00861657 -1.0044 0.0105954 -1.0044 14.61 -0.00439572 -0.0105434 1.00434 0.00846288 -1.0044 0.0105434 -1.0044 14.651 -0.00438997 -0.0104889 1.00427 0.00831041 -1.00439 0.0104889 -1.00439 14.71 -0.00438126 -0.0104321 1.00421 0.00815914 -1.00438 0.0104321 -1.00438 14.751 -0.00436971 -0.010373 1.00414 0.00800905 -1.00437 0.010373 -1.00437 14.81 -0.00435543 -0.0103117 1.00407 0.00786015 -1.00436 0.0103117 -1.00436 14.851 -0.00433854 -0.0102483 1.004 0.0077124 -1.00434 0.0102483 -1.00434 14.91 -0.00431915 -0.0101829 1.00393 0.00756581 -1.00432 0.0101829 -1.00432 14.951 -0.00429738 -0.0101155 1.00386 0.00742035 -1.0043 0.0101155 -1.0043 151 -0.00427334 -0.0100463 1.00379 0.00727603 -1.00427 0.0100463 -1.00427 15.051 -0.00424715 -0.00997521 1.00372 0.00713283 -1.00425 0.00997521 -1.00425 15.11 -0.00421893 -0.00990242 1.00365 0.00699074 -1.00422 0.00990242 -1.00422 15.151 -0.0041888 -0.00982796 1.00359 0.00684976 -1.00419 0.00982796 -1.00419 15.21 -0.00415686 -0.00975191 1.00352 0.00670989 -1.00416 0.00975191 -1.00416 15.251 -0.00412324 -0.00967433 1.00345 0.00657111 -1.00412 0.00967433 -1.00412 15.31 -0.00408804 -0.00959529 1.00338 0.00643343 -1.00409 0.00959529 -1.00409 15.351 -0.00405137 -0.00951484 1.00332 0.00629684 -1.00405 0.00951484 -1.00405 15.41 -0.00401334 -0.00943304 1.00325 0.00616135 -1.00401 0.00943304 -1.00401 15.451 -0.00397407 -0.00934997 1.00319 0.00602695 -1.00397 0.00934997 -1.00397 15.51 -0.00393365 -0.00926567 1.00313 0.00589365 -1.00393 0.00926567 -1.00393 15.551 -0.00389218 -0.0091802 1.00306 0.00576145 -1.00389 0.0091802 -1.00389 15.61 -0.00384976 -0.00909362 1.003 0.00563035 -1.00385 0.00909362 -1.00385 15.651 -0.00380648 -0.00900598 1.00294 0.00550037 -1.00381 0.00900598 -1.00381 15.71 -0.00376245 -0.00891733 1.00288 0.00537149 -1.00376 0.00891733 -1.00376 15.751 -0.00371775 -0.00882773 1.00282 0.00524375 -1.00372 0.00882773 -1.00372 15.81 -0.00367246 -0.00873723 1.00277 0.00511713 -1.00367 0.00873723 -1.00367 15.851 -0.00362666 -0.00864587 1.00271 0.00499165 -1.00363 0.00864587 -1.00363 15.91 -0.00358045 -0.00855371 1.00266 0.00486731 -1.00358 0.00855371 -1.00358 15.951 -0.00353388 -0.0084608 1.0026 0.00474414 -1.00353 0.0084608 -1.00353 161 -0.00348704 -0.00836717 1.00255 0.00462214 -1.00349 0.00836717 -1.00349 16.05

14.2. Solu iones 1211 -0.00343999 -0.00827288 1.0025 0.00450132 -1.00344 0.00827288 -1.00344 16.11 -0.00339281 -0.00817797 1.00245 0.00438169 -1.00339 0.00817797 -1.00339 16.151 -0.00334554 -0.00808249 1.0024 0.00426326 -1.00335 0.00808249 -1.00335 16.21 -0.00329825 -0.00798648 1.00235 0.00414606 -1.0033 0.00798648 -1.0033 16.251 -0.003251 -0.00788999 1.00231 0.00403008 -1.00325 0.00788999 -1.00325 16.31 -0.00320383 -0.00779304 1.00226 0.00391535 -1.0032 0.00779304 -1.0032 16.351 -0.00315679 -0.0076957 1.00222 0.00380188 -1.00316 0.0076957 -1.00316 16.41 -0.00310994 -0.00759799 1.00217 0.00368968 -1.00311 0.00759799 -1.00311 16.451 -0.0030633 -0.00749996 1.00213 0.00357876 -1.00306 0.00749996 -1.00306 16.51 -0.00301692 -0.00740165 1.00209 0.00346914 -1.00302 0.00740165 -1.00302 16.551 -0.00297083 -0.00730309 1.00205 0.00336084 -1.00297 0.00730309 -1.00297 16.61 -0.00292507 -0.00720433 1.00201 0.00325385 -1.00293 0.00720433 -1.00293 16.651 -0.00287966 -0.0071054 1.00197 0.00314821 -1.00288 0.0071054 -1.00288 16.71 -0.00283463 -0.00700634 1.00193 0.00304392 -1.00283 0.00700634 -1.00283 16.751 -0.00279 -0.00690718 1.0019 0.00294099 -1.00279 0.00690718 -1.00279 16.81 -0.0027458 -0.00680797 1.00186 0.00283943 -1.00275 0.00680797 -1.00275 16.851 -0.00270203 -0.00670873 1.00183 0.00273927 -1.0027 0.00670873 -1.0027 16.91 -0.00265873 -0.00660951 1.00179 0.0026405 -1.00266 0.00660951 -1.00266 16.951 -0.00261589 -0.00651033 1.00176 0.00254314 -1.00262 0.00651033 -1.00262 171 -0.00257354 -0.00641123 1.00173 0.00244719 -1.00257 0.00641123 -1.00257 17.051 -0.00253167 -0.00631224 1.00169 0.00235268 -1.00253 0.00631224 -1.00253 17.11 -0.00249031 -0.00621339 1.00166 0.0022596 -1.00249 0.00621339 -1.00249 17.151 -0.00244944 -0.00611473 1.00163 0.00216797 -1.00245 0.00611473 -1.00245 17.21 -0.00240908 -0.00601626 1.0016 0.00207779 -1.00241 0.00601626 -1.00241 17.251 -0.00236922 -0.00591804 1.00157 0.00198907 -1.00237 0.00591804 -1.00237 17.31 -0.00232987 -0.00582008 1.00154 0.00190182 -1.00233 0.00582008 -1.00233 17.351 -0.00229102 -0.00572242 1.00151 0.00181603 -1.00229 0.00572242 -1.00229 17.41 -0.00225268 -0.00562509 1.00149 0.00173172 -1.00225 0.00562509 -1.00225 17.451 -0.00221483 -0.00552811 1.00146 0.00164889 -1.00221 0.00552811 -1.00221 17.51 -0.00217747 -0.00543151 1.00143 0.00156754 -1.00218 0.00543151 -1.00218 17.551 -0.0021406 -0.00533532 1.0014 0.00148767 -1.00214 0.00533532 -1.00214 17.61 -0.00210421 -0.00523956 1.00138 0.00140929 -1.0021 0.00523956 -1.0021 17.651 -0.00206828 -0.00514426 1.00135 0.00133239 -1.00207 0.00514426 -1.00207 17.71 -0.00203282 -0.00504945 1.00132 0.00125697 -1.00203 0.00504945 -1.00203 17.751 -0.00199781 -0.00495515 1.0013 0.00118304 -1.002 0.00495515 -1.002 17.81 -0.00196325 -0.00486138 1.00127 0.00111058 -1.00196 0.00486138 -1.00196 17.851 -0.00192912 -0.00476817 1.00125 0.00103961 -1.00193 0.00476817 -1.00193 17.91 -0.0018954 -0.00467553 1.00122 0.000970104 -1.0019 0.00467553 -1.0019 17.951 -0.00186211 -0.00458349 1.0012 0.00090207 -1.00186 0.00458349 -1.00186 181 -0.00182921 -0.00449208 1.00117 0.000835498 -1.00183 0.00449208 -1.00183 18.051 -0.0017967 -0.00440131 1.00115 0.000770382 -1.0018 0.00440131 -1.0018 18.11 -0.00176457 -0.00431119 1.00112 0.000706717 -1.00176 0.00431119 -1.00176 18.151 -0.0017328 -0.00422176 1.0011 0.000644493 -1.00173 0.00422176 -1.00173 18.21 -0.0017014 -0.00413303 1.00107 0.000583702 -1.0017 0.00413303 -1.0017 18.251 -0.00167033 -0.00404501 1.00105 0.000524335 -1.00167 0.00404501 -1.00167 18.31 -0.00163961 -0.00395773 1.00103 0.000466382 -1.00164 0.00395773 -1.00164 18.351 -0.00160921 -0.00387119 1.001 0.000409832 -1.00161 0.00387119 -1.00161 18.41 -0.00157912 -0.00378543 1.00098 0.000354675 -1.00158 0.00378543 -1.00158 18.451 -0.00154933 -0.00370044 1.00095 0.000300897 -1.00155 0.00370044 -1.00155 18.51 -0.00151985 -0.00361624 1.00093 0.000248487 -1.00152 0.00361624 -1.00152 18.551 -0.00149065 -0.00353286 1.00091 0.000197432 -1.00149 0.00353286 -1.00149 18.61 -0.00146172 -0.00345029 1.00088 0.000147717 -1.00146 0.00345029 -1.00146 18.651 -0.00143307 -0.00336856 1.00086 9.93301e-05 -1.00143 0.00336856 -1.00143 18.71 -0.00140467 -0.00328768 1.00084 5.2255e-05 -1.0014 0.00328768 -1.0014 18.75

122 14. Cir uito on a oplamiento magnéti o.1 -0.00137654 -0.00320765 1.00081 6.47727e-06 -1.00138 0.00320765 -1.00138 18.81 -0.00134865 -0.00312849 1.00079 -3.80187e-05 -1.00135 0.00312849 -1.00135 18.851 -0.001321 -0.0030502 1.00077 -8.12488e-05 -1.00132 0.0030502 -1.00132 18.91 -0.00129358 -0.0029728 1.00075 -0.000123229 -1.00129 0.0029728 -1.00129 18.951 -0.0012664 -0.00289629 1.00072 -0.000163976 -1.00127 0.00289629 -1.00127 191 -0.00123944 -0.00282069 1.0007 -0.000203507 -1.00124 0.00282069 -1.00124 19.051 -0.00121271 -0.00274599 1.00068 -0.00024184 -1.00121 0.00274599 -1.00121 19.11 -0.00118619 -0.00267221 1.00066 -0.00027899 -1.00119 0.00267221 -1.00119 19.151 -0.00115989 -0.00259935 1.00063 -0.000314977 -1.00116 0.00259935 -1.00116 19.21 -0.0011338 -0.00252742 1.00061 -0.000349817 -1.00113 0.00252742 -1.00113 19.251 -0.00110792 -0.00245642 1.00059 -0.00038353 -1.00111 0.00245642 -1.00111 19.31 -0.00108224 -0.00238636 1.00057 -0.000416133 -1.00108 0.00238636 -1.00108 19.351 -0.00105678 -0.00231724 1.00055 -0.000447644 -1.00106 0.00231724 -1.00106 19.41 -0.00103152 -0.00224906 1.00053 -0.000478083 -1.00103 0.00224906 -1.00103 19.451 -0.00100646 -0.00218183 1.00051 -0.000507467 -1.00101 0.00218183 -1.00101 19.51 -0.000981617 -0.00211554 1.00048 -0.000535815 -1.00098 0.00211554 -1.00098 19.551 -0.000956975 -0.00205021 1.00046 -0.000563146 -1.00096 0.00205021 -1.00096 19.61 -0.00093254 -0.00198583 1.00044 -0.000589478 -1.00093 0.00198583 -1.00093 19.651 -0.000908313 -0.0019224 1.00042 -0.00061483 -1.00091 0.0019224 -1.00091 19.71 -0.000884296 -0.00185992 1.0004 -0.000639221 -1.00088 0.00185992 -1.00088 19.751 -0.00086049 -0.00179839 1.00038 -0.000662668 -1.00086 0.00179839 -1.00086 19.81 -0.000836898 -0.00173782 1.00037 -0.000685191 -1.00084 0.00173782 -1.00084 19.851 -0.000813522 -0.00167819 1.00035 -0.000706808 -1.00081 0.00167819 -1.00081 19.91 -0.000790364 -0.00161952 1.00033 -0.000727537 -1.00079 0.00161952 -1.00079 20set terminal pngset output ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/14/ e jemplo014_graf i a . png 'set en oding iso_8859_1set gridset autos aleset key bottom r i gh t t i t l e ' Var i ab l e s ' boxset t i t l e ' Graf i ado por d e f e t o de l a s s o l u i on e s de l i r u i t o 'plot ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/14/ejemplo014_x_trans . data ' using 9 :1 t i t l e 'V en nodo 1 ' with l i n e s , ' /home/ ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/14/ejemplo014_x_trans . data 'using 9 :2 t i t l e 'V en nodo 2 ' with l i n e s , ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/14/ejemplo014_x_trans . data ' using 9 :3 t i t l e 'V en nodo 3 ' with l i n e s ,' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/14/ejemplo014_x_trans . data ' using 9 :4 t i t l e ' I de Bobinas A opladas ent r e nodos 2 , 0 ' with l i n e s , ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/14/ejemplo014_x_trans . data ' using 9 :5 t i t l e ' I de Bobinas A opladas ent r e nodos 3 , 0 ' with l i n e s , ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/14/ejemplo014_x_trans . data ' using 9 :6 t i t l e ' I de Fuente t ens i on ent r e nodos 1 , 0 ' with l i n e s , ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/14/ejemplo014_x_trans . data 'using 9 :7 t i t l e ' I Re s i s t en i a ent r e nodos 0 , 3 ' with l i n e s , ' /home/ ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/14/ejemplo014_x_trans . data ' using 9 :8 t i t l e ' I Re s i s t en i a ent r e nodos 2 , 1 ' with l i n e s

14.2. Solu iones 123Grá o de salida.

Veámos las variables al uladas on mayor detalle. Empezaremos por las tensiones en los nodos.Tensión en nodo 1

Tensión en nodo 2

124 14. Cir uito on a oplamiento magnéti o.

Tensión en nodo 3

Intensidades de las bobinas a opladas

14.2. Solu iones 125

Intensidad de la malla 1 y de la malla2

126 14. Cir uito on a oplamiento magnéti o.

Capítulo 15Cir uito on fuente de tensióndependiente de tensión.1 2

3 0

3

1

4 5

015.1. Datos Generales.Ar hivo *.sp ∗SPICE i r u i t <ejemplo015> from XCir uit v3 . 6 rev 1352 1 0 1 0 5 0 0 ,0000051 1 0 2 0 5 0 201 2 0 2 5 4 0 509 1 0 2 3 1 4 0 0 31 3 0 2 0 2 0 1002 2 0 1 2 1 0 0 ,0000021 4 0 2 1 3 0 104 1 0 2 3 0 0 1 rho f a b A B C D. end Tipo de análisis realizadoAnálisis esta ionario ⊠Análisis transitorio ⊠Datos generales del ir uitoElementos del Cto: 8EA: 0Nodos: 5A2: 6No nulos: 27Densidad: 0.22314 127

128 15. Cir uito on fuente de tensión dependiente de tensión.Dispersion: 0.7768595041Los valores dados al ir uito son:Elemento MagnitudResisten ia entre nodos 1, 2 10 ΩCondensador entre nodos 2, 3 2 · 10−6 FResisten ia entre nodos 3, 0 100 ΩFuente de V dependiente de V 100Resisten ia entre nodos 4, 5 50 ΩResisten ia entre nodos 5, 0 20 ΩCondensador entre nodos 3, 0 5 · 10−6 FMatriz T.row 0: (0, 0 + 2e-06 i) (1, -0 - 2e-06 i) (5, 1)row 1: (0, -0 - 2e-06 i) (1, 0 + 2e-06 i) (10, -1)row 2: (5, -1) (6, 1)row 3: (8, -1) (9, 1)row 4: (4, 0 + 5e-06 i) (7, -1) (8, 1)row 5: (0, 1) (2, -1) (5, -10)row 6: (2, 1)row 7: (4, -1) (7, -20)row 8: (3, -1) (4, 1) (8, -50)row 9: (0, 3) (2, -3) (3, 1)row 10: (1, -1) (10, -100)15.2. Solu iones15.2.1. Primer análisis Tiempo Ini ial 0Tiempo Final 0, 001Paso de Tiempo 0, 00001Theta 1 (Euler)Esta ionarioResultados sistema esta ionario:Tensión en nodo 1: 1 - 2e-05 iTensión en nodo 2: 4.4e-08 + 0.0002 iTensión en nodo 3: 1 - 5.60615e-21 iTensión en nodo 4: 1.32e-08 + 6e-05 iTensión en nodo 5: 4.99592e-09 + 1.71429e-05 iI Resisten ia entre nodos 1, 3: -4.4e-10 - 2e-06 iI de Fuente tension entre nodos 3, 0: -4.4e-10 - 2e-06 iI Resisten ia entre nodos 0, 5: -2.49796e-10 - 8.57143e-07 iI Resisten ia entre nodos 5, 4: -1.64082e-10 - 8.57143e-07 i

15.2. Solu iones 129I de Fuente de V dependiente de V entre nodos 3, 1: -1.64082e-10 - 8.57143e-07 iI Resisten ia entre nodos 0, 2: -4.4e-10 - 2e-06 iTransitorio0.913043 0.869565 1 0.26087 0.00915332 -0.00869565 -0.00869565 -0.000457666 -0.00503432 -0.00503432 -0.00869565 00.916824 0.831758 1 0.249527 0.0167846 -0.00831758 -0.00831758 -0.000839229 -0.00465486 -0.00465486 -0.00831758 1e-050.920441 0.795595 1 0.238678 0.023098 -0.00795595 -0.00795595 -0.0011549 -0.00431161 -0.00431161-0.00795595 2e-050.9239 0.761004 1 0.228301 0.028272 -0.00761004 -0.00761004 -0.0014136 -0.00400058 -0.00400058-0.00761004 3e-050.927208 0.727916 1 0.218375 0.0324622 -0.00727916 -0.00727916 -0.00162311 -0.00371825 -0.00371825 -0.00727916 4e-050.930373 0.696268 1 0.20888 0.0358048 -0.00696268 -0.00696268 -0.00179024 -0.00346151 -0.00346151 -0.00696268 5e-050.9334 0.665995 1 0.199799 0.0384182 -0.00665995 -0.00665995 -0.00192091 -0.00322761 -0.00322761-0.00665995 6e-050.936296 0.637039 1 0.191112 0.0404058 -0.00637039 -0.00637039 -0.00202029 -0.00301412 -0.00301412 -0.00637039 7e-050.939066 0.609342 1 0.182803 0.0418578 -0.00609342 -0.00609342 -0.00209289 -0.00281889 -0.00281889 -0.00609342 8e-050.941715 0.582849 1 0.174855 0.0428527 -0.00582849 -0.00582849 -0.00214263 -0.00264004 -0.00264004 -0.00582849 9e-050.944249 0.557507 1 0.167252 0.0434585 -0.00557507 -0.00557507 -0.00217293 -0.00247587 -0.00247587 -0.00557507 0.00010.946673 0.533268 1 0.15998 0.0437349 -0.00533268 -0.00533268 -0.00218674 -0.00232491 -0.00232491 -0.00533268 0.000110.948992 0.510082 1 0.153025 0.0437332 -0.00510082 -0.00510082 -0.00218666 -0.00218583 -0.00218583 -0.00510082 0.000120.95121 0.487905 1 0.146371 0.0434983 -0.00487905 -0.00487905 -0.00217492 -0.00205746 -0.00205746 -0.00487905 0.000130.953331 0.466692 1 0.140007 0.043069 -0.00466692 -0.00466692 -0.00215345 -0.00193877 -0.00193877 -0.00466692 0.000140.95536 0.446401 1 0.13392 0.0424787 -0.00446401 -0.00446401 -0.00212394 -0.00182883 -0.00182883-0.00446401 0.000150.957301 0.426992 1 0.128098 0.0417567 -0.00426992 -0.00426992 -0.00208784 -0.00172682 -0.00172682 -0.00426992 0.000160.959157 0.408427 1 0.122528 0.0409279 -0.00408427 -0.00408427 -0.0020464 -0.001632 -0.001632-0.00408427 0.000170.960933 0.390669 1 0.117201 0.040014 -0.00390669 -0.00390669 -0.0020007 -0.00154374 -0.00154374-0.00390669 0.000180.962632 0.373684 1 0.112105 0.0390335 -0.00373684 -0.00373684 -0.00195168 -0.00146143 -0.00146143 -0.00373684 0.000190.964256 0.357437 1 0.107231 0.0380024 -0.00357437 -0.00357437 -0.00190012 -0.00138457 -0.00138457 -0.00357437 0.00020.96581 0.341896 1 0.102569 0.0369344 -0.00341896 -0.00341896 -0.00184672 -0.00131269 -0.00131269 -0.00341896 0.000210.967297 0.327031 1 0.0981093 0.035841 -0.00327031 -0.00327031 -0.00179205 -0.00124537 -0.00124537 -0.00327031 0.000220.968719 0.312812 1 0.0938436 0.0347322 -0.00312812 -0.00312812 -0.00173661 -0.00118223 -0.00118223 -0.00312812 0.00023

130 15. Cir uito on fuente de tensión dependiente de tensión.0.970079 0.299212 1 0.0897635 0.0336165 -0.00299212 -0.00299212 -0.00168082 -0.00112294 -0.00112294 -0.00299212 0.000240.97138 0.286202 1 0.0858607 0.0325008 -0.00286202 -0.00286202 -0.00162504 -0.0010672 -0.0010672 -0.00286202 0.000250.972624 0.273759 1 0.0821276 0.0313911 -0.00273759 -0.00273759 -0.00156956 -0.00101473 -0.00101473 -0.00273759 0.000260.973814 0.261856 1 0.0785569 0.0302925 -0.00261856 -0.00261856 -0.00151462 -0.000965288-0.000965288 -0.00261856 0.000270.974953 0.250471 1 0.0751414 0.0292089 -0.00250471 -0.00250471 -0.00146044 -0.00091865 -0.00091865 -0.00250471 0.000280.976042 0.239581 1 0.0718743 0.0281437 -0.00239581 -0.00239581 -0.00140719 -0.000874613-0.000874613 -0.00239581 0.000290.977084 0.229165 1 0.0687494 0.0270997 -0.00229165 -0.00229165 -0.00135499 -0.000832993-0.000832993 -0.00229165 0.00030.97808 0.219201 1 0.0657603 0.0260791 -0.00219201 -0.00219201 -0.00130395 -0.000793624 -0.000793624 -0.00219201 0.000310.979033 0.20967 1 0.0629011 0.0250834 -0.0020967 -0.0020967 -0.00125417 -0.000756354 -0.000756354 -0.0020967 0.000320.979945 0.200554 1 0.0601663 0.0241141 -0.00200554 -0.00200554 -0.00120571 -0.000721044-0.000721044 -0.00200554 0.000330.980817 0.191835 1 0.0575504 0.023172 -0.00191835 -0.00191835 -0.0011586 -0.000687567 -0.000687567 -0.00191835 0.000340.981651 0.183494 1 0.0550482 0.0222579 -0.00183494 -0.00183494 -0.00111289 -0.000655806-0.000655806 -0.00183494 0.000350.982448 0.175516 1 0.0526548 0.021372 -0.00175516 -0.00175516 -0.0010686 -0.000625656 -0.000625656 -0.00175516 0.000360.983212 0.167885 1 0.0503654 0.0205146 -0.00167885 -0.00167885 -0.00102573 -0.000597018-0.000597018 -0.00167885 0.000370.983941 0.160585 1 0.0481756 0.0196856 -0.00160585 -0.00160585 -0.00098428 -0.000569801-0.000569801 -0.00160585 0.000380.98464 0.153603 1 0.046081 0.018885 -0.00153603 -0.00153603 -0.000944248 -0.000543922 -0.000543922 -0.00153603 0.000390.985307 0.146925 1 0.0440775 0.0181123 -0.00146925 -0.00146925 -0.000905616 -0.000519304-0.000519304 -0.00146925 0.00040.985946 0.140537 1 0.0421611 0.0173673 -0.00140537 -0.00140537 -0.000868367 -0.000495875-0.000495875 -0.00140537 0.000410.986557 0.134427 1 0.040328 0.0166495 -0.00134427 -0.00134427 -0.000832476 -0.00047357 -0.00047357 -0.00134427 0.000420.987142 0.128582 1 0.0385746 0.0159583 -0.00128582 -0.00128582 -0.000797917 -0.000452326-0.000452326 -0.00128582 0.000430.987701 0.122992 1 0.0368975 0.0152932 -0.00122992 -0.00122992 -0.00076466 -0.000432085-0.000432085 -0.00122992 0.000440.988236 0.117644 1 0.0352932 0.0146534 -0.00117644 -0.00117644 -0.000732672 -0.000412796-0.000412796 -0.00117644 0.000450.988747 0.112529 1 0.0337587 0.0140384 -0.00112529 -0.00112529 -0.000701921 -0.000394407-0.000394407 -0.00112529 0.000460.989236 0.107637 1 0.032291 0.0134474 -0.00107637 -0.00107637 -0.000672371 -0.000376871-0.000376871 -0.00107637 0.000470.989704 0.102957 1 0.030887 0.0128797 -0.00102957 -0.00102957 -0.000643987 -0.000360146-0.000360146 -0.00102957 0.000480.990152 0.0984803 1 0.0295441 0.0123346 -0.000984803 -0.000984803 -0.000616732 -0.000344189-0.000344189 -0.000984803 0.000490.99058 0.0941986 1 0.0282596 0.0118114 -0.000941986 -0.000941986 -0.000590572 -0.000328963-0.000328963 -0.000941986 0.0005

15.2. Solu iones 1310.99099 0.090103 1 0.0270309 0.0113094 -0.00090103 -0.00090103 -0.000565468 -0.000314431-0.000314431 -0.00090103 0.000510.991381 0.0861855 1 0.0258556 0.0108277 -0.000861855 -0.000861855 -0.000541385 -0.000300559-0.000300559 -0.000861855 0.000520.991756 0.0824383 1 0.0247315 0.0103658 -0.000824383 -0.000824383 -0.000518288 -0.000287315-0.000287315 -0.000824383 0.000530.992115 0.078854 1 0.0236562 0.00992281 -0.00078854 -0.00078854 -0.000496141 -0.000274668-0.000274668 -0.00078854 0.000540.992457 0.0754256 1 0.0226277 0.00949817 -0.000754256 -0.000754256 -0.000474909 -0.00026259-0.00026259 -0.000754256 0.000550.992785 0.0721462 1 0.0216439 0.00909117 -0.000721462 -0.000721462 -0.000454558 -0.000251054-0.000251054 -0.000721462 0.000560.993099 0.0690094 1 0.0207028 0.00870112 -0.000690094 -0.000690094 -0.000435056 -0.000240034-0.000240034 -0.000690094 0.000570.993399 0.066009 1 0.0198027 0.00832739 -0.00066009 -0.00066009 -0.00041637 -0.000229506-0.000229506 -0.00066009 0.000580.993686 0.063139 1 0.0189417 0.00796935 -0.00063139 -0.00063139 -0.000398468 -0.000219447-0.000219447 -0.00063139 0.000590.993961 0.0603939 1 0.0181182 0.00762639 -0.000603939 -0.000603939 -0.000381319 -0.000209835-0.000209835 -0.000603939 0.00060.994223 0.057768 1 0.0173304 0.0072979 -0.00057768 -0.00057768 -0.000364895 -0.00020065-0.00020065 -0.00057768 0.000610.994474 0.0552564 1 0.0165769 0.00698331 -0.000552564 -0.000552564 -0.000349166 -0.000191872-0.000191872 -0.000552564 0.000620.994715 0.0528539 1 0.0158562 0.00668207 -0.000528539 -0.000528539 -0.000334103 -0.000183482-0.000183482 -0.000528539 0.000630.994944 0.0505559 1 0.0151668 0.00639363 -0.000505559 -0.000505559 -0.000319682 -0.000175463-0.000175463 -0.000505559 0.000640.995164 0.0483579 1 0.0145074 0.00611748 -0.000483579 -0.000483579 -0.000305874 -0.000167798-0.000167798 -0.000483579 0.000650.995374 0.0462553 1 0.0138766 0.00585311 -0.000462553 -0.000462553 -0.000292655 -0.00016047-0.00016047 -0.000462553 0.000660.995576 0.0442442 1 0.0132733 0.00560003 -0.000442442 -0.000442442 -0.000280002 -0.000153465-0.000153465 -0.000442442 0.000670.995768 0.0423206 1 0.0126962 0.00535779 -0.000423206 -0.000423206 -0.000267889 -0.000146768-0.000146768 -0.000423206 0.000680.995952 0.0404806 1 0.0121442 0.00512593 -0.000404806 -0.000404806 -0.000256296 -0.000140365-0.000140365 -0.000404806 0.000690.996128 0.0387205 1 0.0116162 0.00490401 -0.000387205 -0.000387205 -0.000245201 -0.000134243-0.000134243 -0.000387205 0.00070.996296 0.037037 1 0.0111111 0.00469163 -0.00037037 -0.00037037 -0.000234581 -0.00012839-0.00012839 -0.00037037 0.000710.996457 0.0354267 1 0.010628 0.00448838 -0.000354267 -0.000354267 -0.000224419 -0.000122793-0.000122793 -0.000354267 0.000720.996611 0.0338864 1 0.0101659 0.00429387 -0.000338864 -0.000338864 -0.000214694 -0.000117441-0.000117441 -0.000338864 0.000730.996759 0.0324131 1 0.00972393 0.00410774 -0.000324131 -0.000324131 -0.000205387 -0.000112324-0.000112324 -0.000324131 0.000740.9969 0.0310038 1 0.00930115 0.00392964 -0.000310038 -0.000310038 -0.000196482 -0.00010743-0.00010743 -0.000310038 0.000750.997034 0.0296558 1 0.00889675 0.00375922 -0.000296558 -0.000296558 -0.000187961 -0.000102751-0.000102751 -0.000296558 0.000760.997163 0.0283665 1 0.00850994 0.00359616 -0.000283665 -0.000283665 -0.000179808 -9.82757e-05 -9.82757e-05 -0.000283665 0.00077

132 15. Cir uito on fuente de tensión dependiente de tensión.0.997287 0.0271331 1 0.00813994 0.00344013 -0.000271331 -0.000271331 -0.000172007 -9.39961e-05 -9.39961e-05 -0.000271331 0.000780.997405 0.0259534 1 0.00778603 0.00329086 -0.000259534 -0.000259534 -0.000164543 -8.99035e-05 -8.99035e-05 -0.000259534 0.000790.997517 0.024825 1 0.00744751 0.00314803 -0.00024825 -0.00024825 -0.000157402 -8.59895e-05-8.59895e-05 -0.00024825 0.00080.997625 0.0237457 1 0.0071237 0.00301139 -0.000237457 -0.000237457 -0.000150569 -8.22464e-05 -8.22464e-05 -0.000237457 0.000810.997729 0.0227133 1 0.00681398 0.00288065 -0.000227133 -0.000227133 -0.000144033 -7.86665e-05 -7.86665e-05 -0.000227133 0.000820.997827 0.0217257 1 0.00651772 0.00275558 -0.000217257 -0.000217257 -0.000137779 -7.52427e-05 -7.52427e-05 -0.000217257 0.000830.997922 0.0207811 1 0.00623434 0.00263593 -0.000207811 -0.000207811 -0.000131796 -7.19683e-05 -7.19683e-05 -0.000207811 0.000840.998012 0.0198776 1 0.00596328 0.00252145 -0.000198776 -0.000198776 -0.000126073 -6.88365e-05 -6.88365e-05 -0.000198776 0.000850.998099 0.0190134 1 0.00570401 0.00241194 -0.000190134 -0.000190134 -0.000120597 -6.58413e-05 -6.58413e-05 -0.000190134 0.000860.998181 0.0181867 1 0.00545601 0.00230718 -0.000181867 -0.000181867 -0.000115359 -6.29766e-05 -6.29766e-05 -0.000181867 0.000870.99826 0.017396 1 0.00521879 0.00220695 -0.00017396 -0.00017396 -0.000110348 -6.02367e-05-6.02367e-05 -0.00017396 0.000880.998336 0.0166396 1 0.00499189 0.00211108 -0.000166396 -0.000166396 -0.000105554 -5.76161e-05 -5.76161e-05 -0.000166396 0.000890.998408 0.0159162 1 0.00477485 0.00201936 -0.000159162 -0.000159162 -0.000100968 -5.51097e-05 -5.51097e-05 -0.000159162 0.0009000010.998478 0.0152241 1 0.00456724 0.00193162 -0.000152241 -0.000152241 -9.65812e-05 -5.27124e-05 -5.27124e-05 -0.000152241 0.0009100010.998544 0.0145622 1 0.00436867 0.00184769 -0.000145622 -0.000145622 -9.23847e-05 -5.04195e-05 -5.04195e-05 -0.000145622 0.0009200010.998607 0.0139291 1 0.00417873 0.00176741 -0.000139291 -0.000139291 -8.83703e-05 -4.82264e-05 -4.82264e-05 -0.000139291 0.0009300010.998668 0.0133235 1 0.00399704 0.0016906 -0.000133235 -0.000133235 -8.45302e-05 -4.61288e-05 -4.61288e-05 -0.000133235 0.0009400010.998726 0.0127442 1 0.00382326 0.00161714 -0.000127442 -0.000127442 -8.08568e-05 -4.41225e-05 -4.41225e-05 -0.000127442 0.0009500010.998781 0.0121901 1 0.00365703 0.00154686 -0.000121901 -0.000121901 -7.73428e-05 -4.22035e-05 -4.22035e-05 -0.000121901 0.0009600010.998834 0.0116601 1 0.00349803 0.00147963 -0.000116601 -0.000116601 -7.39815e-05 -4.0368e-05 -4.0368e-05 -0.000116601 0.0009700010.998885 0.0111531 1 0.00334594 0.00141532 -0.000111531 -0.000111531 -7.07661e-05 -3.86124e-05 -3.86124e-05 -0.000111531 0.0009800010.998933 0.0106682 1 0.00320046 0.00135381 -0.000106682 -0.000106682 -6.76904e-05 -3.69331e-05 -3.69331e-05 -0.000106682 0.000990001set terminal pngset output ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/15/ e jemplo015_graf i a . png 'set en oding iso_8859_1set gridset autos aleset key bottom r i gh t t i t l e ' Var i ab l e s ' boxset t i t l e ' Graf i ado por d e f e t o de l a s s o l u i on e s de l i r u i t o '

15.2. Solu iones 133plot ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/15/ejemplo015_x_trans . data ' using 12 :1 t i t l e 'V en nodo 1 ' with l i n e s , ' /home/ ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/15/ejemplo015_x_trans . data 'using 12 :2 t i t l e 'V en nodo 2 ' with l i n e s , ' /home/ ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/15/ejemplo015_x_trans . data ' using 12 :3 t i t l e 'V en nodo 3 ' withl i n e s , ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/15/ejemplo015_x_trans . data ' using 12 :4t i t l e 'V en nodo 4 ' with l i n e s , ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/15/ejemplo015_x_trans . data ' using 12 :5 t i t l e 'V en nodo 5 ' with l i n e s ,' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/15/ejemplo015_x_trans . data ' using 12 :6 t i t l e ' I Re s i s t en i a ent r e nodos 1 , 3 ' with l i n e s , ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/15/ejemplo015_x_trans . data ' using 12 :7 t i t l e ' I de Fuente t ens i on ent r e nodos 3 , 0 ' with l i n e s , ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/15/ejemplo015_x_trans . data ' using 12 :8 t i t l e ' I Re s i s t en i a ent r e nodos 0 , 5 ' with l i n e s , ' /home/ ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/15/ejemplo015_x_trans . data 'using 12 :9 t i t l e ' I Re s i s t en i a ent r e nodos 5 , 0 ' with l i n e s , ' /home/ ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/15/ejemplo015_x_trans . data ' using 12 :10 t i t l e ' I de Fuente de V dependiente de V ent r e nodos 3 , 1 ' with l i n e s , ' /home/ ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/15/ejemplo015_x_trans . data ' using 12 :11 t i t l e ' I Re s i s t en i a ent r e nodos 0 , 2 ' with l i n e s

Grá o de salida.

134 15. Cir uito on fuente de tensión dependiente de tensión.

Veámos las variables al uladas on mayor detalle. Empezaremos por las tensiones en los nodos.Tensión en nodo 1

Tensión en nodo 2

15.2. Solu iones 135

Tensión en nodo 3

Tensión en nodo 4

136 15. Cir uito on fuente de tensión dependiente de tensión.

Tensión en nodo 5

Intensidad en la malla 1

15.2. Solu iones 137

Intensidad de la malla 2 y 3

Capítulo 16Cir uito on fuente de intensidaddependiente de tensión.La fuente de intensidad dependiente de tensión en el método nodal no se trabaja omo unelemento bipuerto en sí, pertene e a los elementos del grupo A1 por lo que puede expresarse enfun ión de admitan ia y si se desea añadir una e ua ión adi ional.1

0

2

1

2

4 5

016.1. Datos Generales.Ar hivo *.sp ∗SPICE i r u i t <ejemplo016> from XCir uit v3 . 6 rev 1351 1 0 2 0 2 0 103 1 0 2 0 4 0 0 ,00011 2 0 2 4 3 0 508 1 0 1 1 2 3 0 0 22 1 0 1 2 1 0 0 ,00024 1 0 2 1 0 0 1 rho f a b A B C D. end Tipo de análisis realizadoAnálisis esta ionario ⊠Análisis transitorio ⊠Datos generales del ir uitoElementos del Cto: 6EA: 0Nodos: 4A2: 4 139

140 16. Cir uito on fuente de intensidad dependiente de tensión.No nulos: 19Densidad: 0.296875Dispersion: 0.7031Los valores dados al ir uito son:Elemento MagnitudResisten ia entre nodos 2, 0 10 ΩBobina entre nodos 0, 4 0, 0001 HResisten ia entre nodos 4, 3 50 ΩFuente de I dependiente de V 2Condensador entre nodos 2, 1 0, 0002 FFuente de tensión 1 VMatriz T.row 0: (0, 0 + 0.0002 i) (1, -0 - 0.0002 i) (4, 1)row 1: (0, -0 - 0.0002 i) (1, 0 + 0.0002 i) (5, -1)row 2: (0, 2) (1, -2) (7, -1)row 3: (6, -1) (7, 1)row 4: (0, 1)row 5: (1, -1) (5, -10)row 6: (3, -1) (6, -0 - 0.0001 i)row 7: (2, -1) (3, 1) (7, -50)16.2. Solu iones16.2.1. Primer análisis Tiempo Ini ial 0Tiempo Final 0, 01Paso de Tiempo 0, 00005Theta 1 (Euler)Esta ionarioResultados sistema esta ionario:Tensión en nodo 1: 1 - 8.67776e-19 iTensión en nodo 2: 3.99998e-06 + 0.00199999 iTensión en nodo 3: -99.9996 + 0.199799 iTensión en nodo 4: -3.99998e-07 - 0.000199999 iI de Fuente tension entre nodos 1, 0: -3.99998e-07 - 0.000199999 iI Resisten ia entre nodos 0, 2: -3.99998e-07 - 0.000199999 iI de Bobina entre nodos 0, 4: 1.99999 - 0.00399998 iI Resisten ia entre nodos 4, 3: 1.99999 - 0.00399998 i

16.2. Solu iones 141Transitorio1 0.952381 -104.857 -0.0952381 -0.0952381 -0.0952381 2.09524 2.09524 01 -0.0453515 -104.531 0.00453515 0.00453515 0.00453515 2.0907 2.0907 0.00011 -0.0431919 -104.315 0.00431919 0.00431919 0.00431919 2.08638 2.08638 0.00021 -0.0411351 -104.109 0.00411351 0.00411351 0.00411351 2.08227 2.08227 0.00031 -0.0391763 -103.914 0.00391763 0.00391763 0.00391763 2.07835 2.07835 0.00041 -0.0373108 -103.727 0.00373108 0.00373108 0.00373108 2.07462 2.07462 0.00051 -0.0355341 -103.55 0.00355341 0.00355341 0.00355341 2.07107 2.07107 0.00061 -0.033842 -103.381 0.0033842 0.0033842 0.0033842 2.06768 2.06768 0.00071 -0.0322304 -103.22 0.00322304 0.00322304 0.00322304 2.06446 2.06446 0.00081 -0.0306957 -103.066 0.00306957 0.00306957 0.00306957 2.06139 2.06139 0.00091 -0.029234 -102.92 0.0029234 0.0029234 0.0029234 2.05847 2.05847 0.0011 -0.0278419 -102.781 0.00278419 0.00278419 0.00278419 2.05568 2.05568 0.00111 -0.0265161 -102.649 0.00265161 0.00265161 0.00265161 2.05303 2.05303 0.00121 -0.0252534 -102.523 0.00252534 0.00252534 0.00252534 2.05051 2.05051 0.00131 -0.0240509 -102.403 0.00240509 0.00240509 0.00240509 2.0481 2.0481 0.00141 -0.0229056 -102.288 0.00229056 0.00229056 0.00229056 2.04581 2.04581 0.00151 -0.0218148 -102.179 0.00218148 0.00218148 0.00218148 2.04363 2.04363 0.00161 -0.020776 -102.076 0.0020776 0.0020776 0.0020776 2.04155 2.04155 0.00171 -0.0197867 -101.977 0.00197867 0.00197867 0.00197867 2.03957 2.03957 0.00181 -0.0188445 -101.883 0.00188445 0.00188445 0.00188445 2.03769 2.03769 0.00191 -0.0179471 -101.793 0.00179471 0.00179471 0.00179471 2.03589 2.03589 0.0021 -0.0170925 -101.708 0.00170925 0.00170925 0.00170925 2.03418 2.03418 0.00211 -0.0162786 -101.626 0.00162786 0.00162786 0.00162786 2.03256 2.03256 0.00221 -0.0155034 -101.549 0.00155034 0.00155034 0.00155034 2.03101 2.03101 0.00231 -0.0147651 -101.475 0.00147651 0.00147651 0.00147651 2.02953 2.02953 0.00241 -0.014062 -101.405 0.0014062 0.0014062 0.0014062 2.02812 2.02812 0.00251 -0.0133924 -101.338 0.00133924 0.00133924 0.00133924 2.02678 2.02678 0.00261 -0.0127547 -101.274 0.00127547 0.00127547 0.00127547 2.02551 2.02551 0.00271 -0.0121473 -101.214 0.00121473 0.00121473 0.00121473 2.02429 2.02429 0.00281 -0.0115689 -101.156 0.00115689 0.00115689 0.00115689 2.02314 2.02314 0.00291 -0.011018 -101.101 0.0011018 0.0011018 0.0011018 2.02204 2.02204 0.0031 -0.0104933 -101.048 0.00104933 0.00104933 0.00104933 2.02099 2.02099 0.00311 -0.00999363 -100.998 0.000999363 0.000999363 0.000999363 2.01999 2.01999 0.00321 -0.00951774 -100.951 0.000951774 0.000951774 0.000951774 2.01904 2.01904 0.00331 -0.00906451 -100.906 0.000906451 0.000906451 0.000906451 2.01813 2.01813 0.00341 -0.00863287 -100.862 0.000863287 0.000863287 0.000863287 2.01727 2.01727 0.00351 -0.00822178 -100.821 0.000822178 0.000822178 0.000822178 2.01644 2.01644 0.00361 -0.00783027 -100.782 0.000783027 0.000783027 0.000783027 2.01566 2.01566 0.00371 -0.0074574 -100.745 0.00074574 0.00074574 0.00074574 2.01491 2.01491 0.00381 -0.00710228 -100.71 0.000710228 0.000710228 0.000710228 2.0142 2.0142 0.00391 -0.00676408 -100.676 0.000676408 0.000676408 0.000676408 2.01353 2.01353 0.0041 -0.00644198 -100.644 0.000644198 0.000644198 0.000644198 2.01288 2.01288 0.00411 -0.00613522 -100.613 0.000613522 0.000613522 0.000613522 2.01227 2.01227 0.00421 -0.00584307 -100.584 0.000584307 0.000584307 0.000584307 2.01169 2.01169 0.00431 -0.00556483 -100.556 0.000556483 0.000556483 0.000556483 2.01113 2.01113 0.00441 -0.00529983 -100.529 0.000529983 0.000529983 0.000529983 2.0106 2.0106 0.00451 -0.00504746 -100.504 0.000504746 0.000504746 0.000504746 2.01009 2.01009 0.00461 -0.00480711 -100.48 0.000480711 0.000480711 0.000480711 2.00961 2.00961 0.00471 -0.0045782 -100.457 0.00045782 0.00045782 0.00045782 2.00916 2.00916 0.00481 -0.00436019 -100.436 0.000436019 0.000436019 0.000436019 2.00872 2.00872 0.00491 -0.00415256 -100.415 0.000415256 0.000415256 0.000415256 2.00831 2.00831 0.0051 -0.00395482 -100.395 0.000395482 0.000395482 0.000395482 2.00791 2.00791 0.0051

142 16. Cir uito on fuente de intensidad dependiente de tensión.1 -0.00376649 -100.376 0.000376649 0.000376649 0.000376649 2.00753 2.00753 0.00521 -0.00358714 -100.358 0.000358714 0.000358714 0.000358714 2.00717 2.00717 0.00531 -0.00341632 -100.341 0.000341632 0.000341632 0.000341632 2.00683 2.00683 0.00541 -0.00325364 -100.325 0.000325364 0.000325364 0.000325364 2.00651 2.00651 0.00551 -0.0030987 -100.31 0.00030987 0.00030987 0.00030987 2.0062 2.0062 0.00561 -0.00295115 -100.295 0.000295115 0.000295115 0.000295115 2.0059 2.0059 0.00571 -0.00281061 -100.281 0.000281061 0.000281061 0.000281061 2.00562 2.00562 0.00581 -0.00267678 -100.267 0.000267678 0.000267678 0.000267678 2.00535 2.00535 0.00591 -0.00254931 -100.255 0.000254931 0.000254931 0.000254931 2.0051 2.0051 0.0061 -0.00242791 -100.243 0.000242791 0.000242791 0.000242791 2.00486 2.00486 0.00611 -0.0023123 -100.231 0.00023123 0.00023123 0.00023123 2.00462 2.00462 0.00621 -0.00220219 -100.22 0.000220219 0.000220219 0.000220219 2.0044 2.0044 0.00631 -0.00209732 -100.21 0.000209732 0.000209732 0.000209732 2.00419 2.00419 0.00641 -0.00199745 -100.2 0.000199745 0.000199745 0.000199745 2.00399 2.00399 0.00651 -0.00190233 -100.19 0.000190233 0.000190233 0.000190233 2.0038 2.0038 0.00661 -0.00181175 -100.181 0.000181175 0.000181175 0.000181175 2.00362 2.00362 0.00671 -0.00172547 -100.172 0.000172547 0.000172547 0.000172547 2.00345 2.00345 0.00681 -0.00164331 -100.164 0.000164331 0.000164331 0.000164331 2.00329 2.00329 0.00691 -0.00156506 -100.156 0.000156506 0.000156506 0.000156506 2.00313 2.00313 0.0071 -0.00149053 -100.149 0.000149053 0.000149053 0.000149053 2.00298 2.00298 0.00711 -0.00141955 -100.142 0.000141955 0.000141955 0.000141955 2.00284 2.00284 0.00721 -0.00135195 -100.135 0.000135195 0.000135195 0.000135195 2.0027 2.0027 0.00731 -0.00128758 -100.129 0.000128758 0.000128758 0.000128758 2.00258 2.00258 0.007399991 -0.00122626 -100.123 0.000122626 0.000122626 0.000122626 2.00245 2.00245 0.007499991 -0.00116787 -100.117 0.000116787 0.000116787 0.000116787 2.00234 2.00234 0.007599991 -0.00111226 -100.111 0.000111226 0.000111226 0.000111226 2.00222 2.00222 0.007699991 -0.00105929 -100.106 0.000105929 0.000105929 0.000105929 2.00212 2.00212 0.007799991 -0.00100885 -100.101 0.000100885 0.000100885 0.000100885 2.00202 2.00202 0.007899991 -0.000960808 -100.096 9.60808e-05 9.60808e-05 9.60808e-05 2.00192 2.00192 0.007999991 -0.000915056 -100.091 9.15056e-05 9.15056e-05 9.15056e-05 2.00183 2.00183 0.008099991 -0.000871482 -100.087 8.71482e-05 8.71482e-05 8.71482e-05 2.00174 2.00174 0.008199991 -0.000829982 -100.083 8.29982e-05 8.29982e-05 8.29982e-05 2.00166 2.00166 0.008299991 -0.000790459 -100.079 7.90459e-05 7.90459e-05 7.90459e-05 2.00158 2.00158 0.008399991 -0.000752819 -100.075 7.52819e-05 7.52819e-05 7.52819e-05 2.00151 2.00151 0.008499991 -0.00071697 -100.072 7.1697e-05 7.1697e-05 7.1697e-05 2.00143 2.00143 0.008599991 -0.000682829 -100.068 6.82829e-05 6.82829e-05 6.82829e-05 2.00137 2.00137 0.008699991 -0.000650313 -100.065 6.50313e-05 6.50313e-05 6.50313e-05 2.0013 2.0013 0.008799991 -0.000619346 -100.062 6.19346e-05 6.19346e-05 6.19346e-05 2.00124 2.00124 0.008899991 -0.000589853 -100.059 5.89853e-05 5.89853e-05 5.89853e-05 2.00118 2.00118 0.008999991 -0.000561765 -100.056 5.61765e-05 5.61765e-05 5.61765e-05 2.00112 2.00112 0.009099991 -0.000535014 -100.053 5.35014e-05 5.35014e-05 5.35014e-05 2.00107 2.00107 0.009199991 -0.000509537 -100.051 5.09537e-05 5.09537e-05 5.09537e-05 2.00102 2.00102 0.009299991 -0.000485274 -100.048 4.85274e-05 4.85274e-05 4.85274e-05 2.00097 2.00097 0.009399991 -0.000462165 -100.046 4.62165e-05 4.62165e-05 4.62165e-05 2.00092 2.00092 0.009499991 -0.000440157 -100.044 4.40157e-05 4.40157e-05 4.40157e-05 2.00088 2.00088 0.009599991 -0.000419198 -100.042 4.19198e-05 4.19198e-05 4.19198e-05 2.00084 2.00084 0.009699991 -0.000399236 -100.04 3.99236e-05 3.99236e-05 3.99236e-05 2.0008 2.0008 0.009799991 -0.000380224 -100.038 3.80224e-05 3.80224e-05 3.80224e-05 2.00076 2.00076 0.0098999set terminal pngset output ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/16/ e jemplo016_graf i a . png 'set en oding iso_8859_1set grid

16.2. Solu iones 143set autos aleset key bottom r i gh t t i t l e ' Var i ab l e s ' boxset t i t l e ' Graf i ado por d e f e t o de l a s s o l u i on e s de l i r u i t o 'plot ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/16/ejemplo016_x_trans . data ' using 9 :1 t i t l e 'V en nodo 1 ' with l i n e s , ' /home/ ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/16/ejemplo016_x_trans . data 'using 9 :2 t i t l e 'V en nodo 2 ' with l i n e s , ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/16/ejemplo016_x_trans . data ' using 9 :3 t i t l e 'V en nodo 3 ' with l i n e s ,' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/16/ejemplo016_x_trans . data ' using 9 :4 t i t l e 'V en nodo 4 ' with l i n e s , ' /home/ ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/16/ejemplo016_x_trans . data 'using 9 :5 t i t l e ' I de Fuente t ens i on ent r e nodos 1 , 0 ' with l i n e s ,' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/16/ejemplo016_x_trans . data ' using 9 :6 t i t l e ' I Re s i s t en i a ent r e nodos 0 , 2 ' with l i n e s , ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/16/ejemplo016_x_trans . data ' using 9 :7 t i t l e ' I de Bobina ent r e nodos 0 , 4 ' with l i n e s , ' /home/ ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/16/ejemplo016_x_trans . data 'using 9 :8 t i t l e ' I Re s i s t en i a ent r e nodos 4 , 3 ' with l i n e sGrá o de salida.

Veámos las variables por separado para apre iar mejor su evolu ión temporalTensión en nodo 1 y 2

144 16. Cir uito on fuente de intensidad dependiente de tensión.

Tensión en nodo 3 y4

Intensidad de la malla 1

16.2. Solu iones 145

Intensidad de la malla 2

Capítulo 17Cir uito on transformador.El transformador es también un elemento biterminal implementado en el programa de resolu- ión. Se pro ederá a analizar un ir uitos on este elemento tan ara terísti o en los ál ulos deespe ialidad. A su vez aprove haremos este ir uito para usar un elemento que aún no se habíautilizado en ejemplos anteriores la ondu tan ia.1

0 0

2

17.1. Datos Generales.Ar hivo *.sp ∗SPICE i r u i t <ejemplo017> from XCir uit v3 . 6 rev 1354 1 0 2 0 1 1 Cte 0 50 a b 1 B C D0 1 0 1 0 2 0 107 1 0 2 1 0 2 0 0 0 ,5. end Tipo de análisis realizadoAnálisis esta ionario ⊠Análisis transitorio ⊠Datos generales del ir uitoElementos del Cto: 3EA: 0Nodos: 2A2: 3No nulos: 9Densidad: 0.36Dispersion: 0.64 147

148 17. Cir uito on transformador.Los valores dados al ir uito son:Elemento MagnitudCondu tan ia entre nodos 2, 0 10 Ω−1Transformador a = 0, 5Fuente de tensión alterna sin(2π · 50)VMatriz T.row 0: (2, 1) (4, -1)row 1: (1, 10) (3, 1)row 2: (0, 1) (1, -0.5)row 3: (2, 1) (3, -2)row 4: (0, -1)17.2. Solu iones17.2.1. Primer análisis Tiempo Ini ial 0Tiempo Final 0, 04Paso de Tiempo 0, 0004Theta 1 (Euler)Esta ionarioResultados sistema esta ionario:Tensión en nodo 1: -1Tensión en nodo 2: -2I de Trafo entre nodos 1, 0: 40I de Trafo entre nodos 2, 0: 20I de Fuente tension entre nodos 0, 1: 40Transitorio-0.125333 -0.250666 5.01333 2.50666 5.01333 0-0.24869 -0.49738 9.9476 4.9738 9.9476 0.0004-0.368125 -0.736249 14.725 7.36249 14.725 0.0008-0.481754 -0.963507 19.2701 9.63507 19.2701 0.0012-0.587785 -1.17557 23.5114 11.7557 23.5114 0.0016-0.684547 -1.36909 27.3819 13.6909 27.3819 0.002-0.770513 -1.54103 30.8205 15.4103 30.8205 0.0024-0.844328 -1.68866 33.7731 16.8866 33.7731 0.0028-0.904827 -1.80965 36.1931 18.0965 36.1931 0.0032-0.951056 -1.90211 38.0423 19.0211 38.0423 0.0036-0.982287 -1.96457 39.2915 19.6457 39.2915 0.004-0.998027 -1.99605 39.9211 19.9605 39.9211 0.0044-0.998027 -1.99605 39.9211 19.9605 39.9211 0.0048

17.2. Solu iones 149-0.982287 -1.96457 39.2915 19.6457 39.2915 0.0052-0.951057 -1.90211 38.0423 19.0211 38.0423 0.0056-0.904827 -1.80965 36.1931 18.0965 36.1931 0.006-0.844328 -1.68866 33.7731 16.8866 33.7731 0.0064-0.770513 -1.54103 30.8205 15.4103 30.8205 0.0068-0.684547 -1.36909 27.3819 13.6909 27.3819 0.0072-0.587785 -1.17557 23.5114 11.7557 23.5114 0.0076-0.481754 -0.963507 19.2701 9.63507 19.2701 0.008-0.368125 -0.736249 14.725 7.36249 14.725 0.0084-0.24869 -0.49738 9.9476 4.9738 9.9476 0.0088-0.125333 -0.250667 5.01333 2.50667 5.01333 0.0092-7.93633e-08 -1.58727e-07 3.17453e-06 1.58727e-06 3.17453e-06 0.00960.125333 0.250666 -5.01333 -2.50666 -5.01333 0.010.24869 0.49738 -9.94759 -4.9738 -9.94759 0.01040.368124 0.736249 -14.725 -7.36249 -14.725 0.01080.481754 0.963507 -19.2701 -9.63507 -19.2701 0.01120.587785 1.17557 -23.5114 -11.7557 -23.5114 0.01160.684547 1.36909 -27.3819 -13.6909 -27.3819 0.0120.770513 1.54103 -30.8205 -15.4103 -30.8205 0.01240.844328 1.68866 -33.7731 -16.8866 -33.7731 0.01280.904827 1.80965 -36.1931 -18.0965 -36.1931 0.01320.951056 1.90211 -38.0423 -19.0211 -38.0423 0.01360.982287 1.96457 -39.2915 -19.6457 -39.2915 0.0140.998027 1.99605 -39.9211 -19.9605 -39.9211 0.01440.998027 1.99605 -39.9211 -19.9605 -39.9211 0.01480.982287 1.96457 -39.2915 -19.6457 -39.2915 0.01520.951057 1.90211 -38.0423 -19.0211 -38.0423 0.01560.904827 1.80965 -36.1931 -18.0965 -36.1931 0.0160.844328 1.68866 -33.7731 -16.8866 -33.7731 0.01640.770513 1.54103 -30.8205 -15.4103 -30.8205 0.01680.684547 1.36909 -27.3819 -13.6909 -27.3819 0.01720.587785 1.17557 -23.5114 -11.7557 -23.5114 0.01760.481754 0.963508 -19.2702 -9.63508 -19.2702 0.0180.368125 0.736249 -14.725 -7.36249 -14.725 0.01840.24869 0.49738 -9.9476 -4.9738 -9.9476 0.01880.125333 0.250667 -5.01334 -2.50667 -5.01334 0.01921.58727e-07 3.17453e-07 -6.34906e-06 -3.17453e-06 -6.34906e-06 0.0196-0.125333 -0.250666 5.01332 2.50666 5.01332 0.02-0.24869 -0.497379 9.94759 4.97379 9.94759 0.0204-0.368124 -0.736249 14.725 7.36249 14.725 0.0208-0.481754 -0.963507 19.2701 9.63507 19.2701 0.0212-0.587785 -1.17557 23.5114 11.7557 23.5114 0.0216-0.684547 -1.36909 27.3819 13.6909 27.3819 0.022-0.770513 -1.54103 30.8205 15.4103 30.8205 0.0224-0.844328 -1.68866 33.7731 16.8866 33.7731 0.0228-0.904827 -1.80965 36.1931 18.0965 36.1931 0.0232-0.951056 -1.90211 38.0423 19.0211 38.0423 0.0236-0.982287 -1.96457 39.2915 19.6457 39.2915 0.024-0.998027 -1.99605 39.9211 19.9605 39.9211 0.0244-0.998027 -1.99605 39.9211 19.9605 39.9211 0.0248-0.982287 -1.96457 39.2915 19.6457 39.2915 0.0252-0.951057 -1.90211 38.0423 19.0211 38.0423 0.0256-0.904827 -1.80965 36.1931 18.0965 36.1931 0.026-0.844328 -1.68866 33.7731 16.8866 33.7731 0.0264

150 17. Cir uito on transformador.-0.770513 -1.54103 30.8205 15.4103 30.8205 0.0268-0.684547 -1.36909 27.3819 13.6909 27.3819 0.0272-0.587785 -1.17557 23.5114 11.7557 23.5114 0.0276-0.481754 -0.963508 19.2702 9.63508 19.2702 0.028-0.368125 -0.73625 14.725 7.3625 14.725 0.0284-0.24869 -0.49738 9.9476 4.9738 9.9476 0.0288-0.125333 -0.250667 5.01334 2.50667 5.01334 0.0292-2.3809e-07 -4.7618e-07 9.5236e-06 4.7618e-06 9.5236e-06 0.02960.125333 0.250666 -5.01332 -2.50666 -5.01332 0.030.24869 0.497379 -9.94759 -4.97379 -9.94759 0.03040.368124 0.736249 -14.725 -7.36249 -14.725 0.03080.481753 0.963507 -19.2701 -9.63507 -19.2701 0.03120.587785 1.17557 -23.5114 -11.7557 -23.5114 0.03160.684547 1.36909 -27.3819 -13.6909 -27.3819 0.0320.770513 1.54103 -30.8205 -15.4103 -30.8205 0.03240.844328 1.68866 -33.7731 -16.8866 -33.7731 0.03280.904827 1.80965 -36.1931 -18.0965 -36.1931 0.03320.951056 1.90211 -38.0423 -19.0211 -38.0423 0.03360.982287 1.96457 -39.2915 -19.6457 -39.2915 0.0340.998027 1.99605 -39.9211 -19.9605 -39.9211 0.03440.998027 1.99605 -39.9211 -19.9605 -39.9211 0.03480.982287 1.96457 -39.2915 -19.6457 -39.2915 0.03520.951057 1.90211 -38.0423 -19.0211 -38.0423 0.03560.904827 1.80965 -36.1931 -18.0965 -36.1931 0.0360.844328 1.68866 -33.7731 -16.8866 -33.7731 0.03640.770513 1.54103 -30.8205 -15.4103 -30.8205 0.03680.684547 1.36909 -27.3819 -13.6909 -27.3819 0.03720.587785 1.17557 -23.5114 -11.7557 -23.5114 0.03760.481754 0.963508 -19.2702 -9.63508 -19.2702 0.0380.368125 0.73625 -14.725 -7.3625 -14.725 0.03840.24869 0.49738 -9.94761 -4.9738 -9.94761 0.03880.125334 0.250667 -5.01334 -2.50667 -5.01334 0.03923.17453e-07 6.34906e-07 -1.26981e-05 -6.34906e-06 -1.26981e-05set terminal pngset output ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/17/ e jemplo017_graf i a . png 'set en oding iso_8859_1set gridset autos aleset yrange [−55 :45 set key bottom r i gh t t i t l e ' Var i ab l e s ' boxset t i t l e ' Graf i ado por d e f e t o de l a s s o l u i on e s de l i r u i t o 'plot ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/17/ejemplo017_x_trans . data ' using 6 :1 t i t l e 'V en nodo 1 ' with l i n e s , ' /home/ ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/17/ejemplo017_x_trans . data 'using 6 :2 t i t l e 'V en nodo 2 ' with l i n e s , ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/17/ejemplo017_x_trans . data ' using 6 :3 t i t l e ' I de Trafo ent r e nodos 1 , 0 ' with l i n e s , ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/17/ejemplo017_x_trans . data 'using 6 :4 t i t l e ' I de Trafo ent r e nodos 2 , 0 ' with l i n e s , ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s /

17.2. Solu iones 151 o l e i onprob l emas/17/ejemplo017_x_trans . data ' using 6 :5 t i t l e ' I de Fuente t ens i on ent r e nodos 0 , 1 ' with l i n e sGrá o de salida.

Veámos las variables por separado para apre iar mejor su evolu ión temporalTensión en nodo 1 y 2

152 17. Cir uito on transformador.Intensidades en las mallas del ir uito

Capítulo 18Cir uito on bipuerto onparámetros híbridos.Para ir nalizando on este manual de ejer i ios resueltos on Ávalon realizaremos un estudiode un ir uito on un uadripolo denido por parámetros híbridos.h

0

1 2

0En este uadripolo simularemos al al ular sus parámetros un ir uito en π de resisten iasmuy utilizado en ele tri idad en la simula ión de líneas de distribu ión. El poten ial de estetipo de elementos es muy amplio debido a que sabiendo alular los parámetros híbridos de un ir uito determinado podremos realizar análisis aún más omplejos. Además por otro lado de lasimpli a ión visual que esto supone ya que al onvertir una parte de un ir uito en uno de estoselementos el alumno puede entrarse y fo alizar el análisis en la parte del ir uito que más le onvenga.

El á ulo de los parámetros híbridos sería el siguiente:Para V2 = 0

V1

20= I1 + I2

V1

5= I1 + I2

⇒

I1 = 5

40V1

I2 = 3

40V1Para I1 = 0

V2 = 25·15

25∗15I2

V1 = 20

25V2

⇒

V2 = 375

40I2

V1 = 20

25V2153

154 18. Cir uito on bipuerto on parámetros híbridos.Con estas expresiones, se está en disposi ión de sustituir en las fórmulas de los parámetros y al ularlosh11 = V1

I1o ∣

∣

∣

V2=0

= V1

5

40V1

= 80

h12 = V1

V2

∣

∣

∣

I1=0

=20

25V2

V2= 0,8

h21 = I2

I1

∣

∣

∣

V2=0

=3

40V1

5

40V1

= 0,6

h22 = I2

V2

∣

∣

∣

I1=0

= I2375

40I2V1

= 0,1118.1. Datos Generales.Ar hivo *.sp ∗SPICE i r u i t <ejemplo018> from XCir uit v3 . 6 rev 1353 1 0 2 0 2 0 0 ,00014 1 0 2 1 0 0 2 rho f a b A B C D16 1 0 2 1 0 2 0 0 0 0 0 0 0 80 0 ,8 0 ,6 0 ,11. end Tipo de análisis realizadoAnálisis esta ionario ⊠Análisis transitorio ⊠Datos generales del ir uitoElementos del Cto: 3EA: 0Nodos: 2A2: 3No nulos: 11Densidad: 0.44Dispersion: 0.56Los valores dados al ir uito son:Elemento MagnitudBobina entre nodo 2, 0 0, 0001 H uadripolo a través de h h11 = 80 h12 = 0, 8 h21 = 0, 6 h22 = 0, 11Fuente de tensión ontínua 2 VMatriz T.row 0: (2, 1) (3, 1)row 1: (1, 0.11) (3, 0.6) (4, -1)row 2: (0, 1)row 3: (0, 1) (1, -0.8) (3, -80)row 4: (1, -1) (4, -0 - 0.0001 i)

18.2. Solu iones 15518.2. Solu iones18.2.1. Primer análisis Tiempo Ini ial 0Tiempo Final 0, 0001Paso de Tiempo 0, 000001Theta 1 (Euler)Esta ionarioResultados sistema esta ionario:Tensión en nodo 1: 2 - 7.75482e-26 iTensión en nodo 2: -1.56e-11 - 1.5e-06 iI de Fuente tension entre nodos 1, 0: -0.025 - 1.5e-08 iI de uadripolo en h entre nodos 1, 0: 0.025 + 1.5e-08 iI de Bobina entre nodos 0, 2: 0.015 - 1.56e-07 iTransitorio4 -0.263158 -0.0526316 0.0526316 0.00263158 02 -0.108495 -0.0260849 0.0260849 0.00371653 1e-062 -0.0989778 -0.0259898 0.0259898 0.00470631 2e-062 -0.0902956 -0.025903 0.025903 0.00560926 3e-062 -0.0823749 -0.0258237 0.0258237 0.00643301 4e-062 -0.075149 -0.0257515 0.0257515 0.0071845 5e-062 -0.068557 -0.0256856 0.0256856 0.00787007 6e-062 -0.0625432 -0.0256254 0.0256254 0.0084955 7e-062 -0.057057 -0.0255706 0.0255706 0.00906607 8e-062 -0.052052 -0.0255205 0.0255205 0.00958659 9e-062 -0.047486 -0.0254749 0.0254749 0.0100615 1e-052 -0.0433206 -0.0254332 0.0254332 0.0104947 1.1e-052 -0.0395205 -0.0253952 0.0253952 0.0108899 1.2e-052 -0.0360538 -0.0253605 0.0253605 0.0112504 1.3e-052 -0.0328912 -0.0253289 0.0253289 0.0115793 1.4e-052 -0.030006 -0.0253001 0.0253001 0.0118794 1.5e-052 -0.0273739 -0.0252737 0.0252737 0.0121531 1.6e-052 -0.0249727 -0.0252497 0.0252497 0.0124028 1.7e-052 -0.0227821 -0.0252278 0.0252278 0.0126307 1.8e-052 -0.0207837 -0.0252078 0.0252078 0.0128385 1.9e-052 -0.0189605 -0.0251896 0.0251896 0.0130281 2e-052 -0.0172973 -0.025173 0.025173 0.0132011 2.1e-052 -0.01578 -0.0251578 0.0251578 0.0133589 2.2e-052 -0.0143958 -0.025144 0.025144 0.0135028 2.3e-052 -0.013133 -0.0251313 0.0251313 0.0136342 2.4e-052 -0.011981 -0.0251198 0.0251198 0.013754 2.5e-052 -0.01093 -0.0251093 0.0251093 0.0138633 2.6e-052 -0.00997126 -0.0250997 0.0250997 0.013963 2.7e-05

156 18. Cir uito on bipuerto on parámetros híbridos.2 -0.00909659 -0.025091 0.025091 0.014054 2.8e-052 -0.00829864 -0.025083 0.025083 0.0141369 2.9e-052 -0.00757069 -0.0250757 0.0250757 0.0142126 3e-052 -0.0069066 -0.0250691 0.0250691 0.0142817 3.1e-052 -0.00630075 -0.025063 0.025063 0.0143447 3.2e-052 -0.00574806 -0.0250575 0.0250575 0.0144022 3.3e-052 -0.00524384 -0.0250524 0.0250524 0.0144546 3.4e-052 -0.00478385 -0.0250478 0.0250478 0.0145025 3.5e-052 -0.00436422 -0.0250436 0.0250436 0.0145461 3.6e-052 -0.00398139 -0.0250398 0.0250398 0.0145859 3.7e-052 -0.00363215 -0.0250363 0.0250363 0.0146223 3.8e-052 -0.00331354 -0.0250331 0.0250331 0.0146554 3.9e-052 -0.00302288 -0.0250302 0.0250302 0.0146856 4e-052 -0.00275771 -0.0250276 0.0250276 0.0147132 4.1e-052 -0.00251581 -0.0250252 0.0250252 0.0147384 4.2e-052 -0.00229512 -0.025023 0.025023 0.0147613 4.3e-052 -0.0020938 -0.0250209 0.0250209 0.0147822 4.4e-052 -0.00191013 -0.0250191 0.0250191 0.0148013 4.5e-052 -0.00174257 -0.0250174 0.0250174 0.0148188 4.6e-052 -0.00158972 -0.0250159 0.0250159 0.0148347 4.7e-052 -0.00145027 -0.0250145 0.0250145 0.0148492 4.8e-052 -0.00132305 -0.0250132 0.0250132 0.0148624 4.9e-052 -0.00120699 -0.0250121 0.0250121 0.0148745 5e-052 -0.00110112 -0.025011 0.025011 0.0148855 5.1e-052 -0.00100453 -0.02501 0.02501 0.0148955 5.2e-052 -0.000916412 -0.0250092 0.0250092 0.0149047 5.3e-052 -0.000836025 -0.0250084 0.0250084 0.0149131 5.4e-052 -0.000762689 -0.0250076 0.0250076 0.0149207 5.5e-052 -0.000695787 -0.025007 0.025007 0.0149276 5.6e-052 -0.000634753 -0.0250063 0.0250063 0.014934 5.7e-052 -0.000579073 -0.0250058 0.0250058 0.0149398 5.8e-052 -0.000528277 -0.0250053 0.0250053 0.0149451 5.9e-052 -0.000481937 -0.0250048 0.0250048 0.0149499 6e-052 -0.000439662 -0.0250044 0.0250044 0.0149543 6.1e-052 -0.000401095 -0.025004 0.025004 0.0149583 6.2e-052 -0.000365911 -0.0250037 0.0250037 0.0149619 6.3e-052 -0.000333814 -0.0250033 0.0250033 0.0149653 6.4e-052 -0.000304532 -0.025003 0.025003 0.0149683 6.5e-052 -0.000277818 -0.0250028 0.0250028 0.0149711 6.6e-052 -0.000253448 -0.0250025 0.0250025 0.0149736 6.7e-052 -0.000231216 -0.0250023 0.0250023 0.014976 6.8e-052 -0.000210934 -0.0250021 0.0250021 0.0149781 6.9e-052 -0.000192431 -0.0250019 0.0250019 0.01498 7e-052 -0.000175551 -0.0250018 0.0250018 0.0149817 7.1e-052 -0.000160152 -0.0250016 0.0250016 0.0149833 7.2e-052 -0.000146103 -0.0250015 0.0250015 0.0149848 7.3e-052 -0.000133287 -0.0250013 0.0250013 0.0149861 7.4e-052 -0.000121596 -0.0250012 0.0250012 0.0149874 7.5e-052 -0.000110929 -0.0250011 0.0250011 0.0149885 7.6e-052 -0.000101199 -0.025001 0.025001 0.0149895 7.7e-052 -9.23215e-05 -0.0250009 0.0250009 0.0149904 7.8e-052 -8.42231e-05 -0.0250008 0.0250008 0.0149912 7.9e-052 -7.68352e-05 -0.0250008 0.0250008 0.014992 8e-052 -7.00952e-05 -0.0250007 0.0250007 0.0149927 8.1e-05

18.2. Solu iones 1572 -6.39465e-05 -0.0250006 0.0250006 0.0149933 8.2e-052 -5.83372e-05 -0.0250006 0.0250006 0.0149939 8.3e-052 -5.32199e-05 -0.0250005 0.0250005 0.0149945 8.4e-052 -4.85515e-05 -0.0250005 0.0250005 0.014995 8.5e-052 -4.42926e-05 -0.0250004 0.0250004 0.0149954 8.6e-052 -4.04073e-05 -0.0250004 0.0250004 0.0149958 8.7e-052 -3.68628e-05 -0.0250004 0.0250004 0.0149962 8.8e-052 -3.36292e-05 -0.0250003 0.0250003 0.0149965 8.9e-052 -3.06793e-05 -0.0250003 0.0250003 0.0149968 9e-052 -2.79881e-05 -0.0250003 0.0250003 0.0149971 9.1e-052 -2.5533e-05 -0.0250003 0.0250003 0.0149973 9.2e-052 -2.32933e-05 -0.0250002 0.0250002 0.0149976 9.3e-052 -2.125e-05 -0.0250002 0.0250002 0.0149978 9.4e-052 -1.9386e-05 -0.0250002 0.0250002 0.014998 9.5e-052 -1.76854e-05 -0.0250002 0.0250002 0.0149982 9.6e-052 -1.61341e-05 -0.0250002 0.0250002 0.0149983 9.7e-052 -1.47188e-05 -0.0250001 0.0250001 0.0149985 9.8e-052 -1.34277e-05 -0.0250001 0.0250001 0.0149986 9.9e-05set terminal pngset output ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/18/ e jemplo018_graf i a . png 'set en oding iso_8859_1set gridset autos aleset key bottom r i gh t t i t l e ' Var i ab l e s ' boxset t i t l e ' Graf i ado por d e f e t o de l a s s o l u i on e s de l i r u i t o 'plot ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/18/ejemplo018_x_trans . data ' using 6 :1 t i t l e 'V en nodo 1 ' with l i n e s , ' /home/ ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/18/ejemplo018_x_trans . data 'using 6 :2 t i t l e 'V en nodo 2 ' with l i n e s , ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/18/ejemplo018_x_trans . data ' using 6 :3 t i t l e ' I de Fuente t ens i on ent r e nodos 1 , 0 ' with l i n e s , ' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/18/ejemplo018_x_trans . data 'using 6 :4 t i t l e ' I de Cuatr ipo lo en h ent r e nodos 1 , 0 ' with l i n e s ,' /home/ayose/Programa ion/AVALON/debug/ s r / o l e i o n/Gra f i o s / o l e i onprob l emas/18/ejemplo018_x_trans . data ' using 6 :5 t i t l e ' I de Bobina ent r e nodos 0 , 2 ' with l i n e sGrá o de salida.

158 18. Cir uito on bipuerto on parámetros híbridos.

Veamos la tensión en el nodo 2