Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test...
Transcript of Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test...
![Page 1: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/1.jpg)
Curs 5 2019/2020
![Page 2: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/2.jpg)
2C/1L, DCMR (CDM)
Minim 7 prezente (curs+laborator)
Curs - conf. Radu Damian Marti 14-16, P7
E – 50% din nota
probleme + (2p prez. curs) + (3 teste) + (bonus activitate) primul test L1 (t2 si t3 neanuntate)
3pz (C) = +0.5p
toate materialele permise
![Page 3: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/3.jpg)
2C/1L, DCMR (CDM) Laborator – conf. Radu Damian
Miercuri 10-14 impar II.12 (par eng.)
Joi 14- 16 par
L – 25% din nota
prezenta + rezultate personale
P – 25% din nota
tema personala
![Page 4: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/4.jpg)
http://rf-opto.etti.tuiasi.ro
![Page 5: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/5.jpg)
http://rf-opto.etti.tuiasi.ro Irinel Casian-Botez: "Microunde vol. 1:
Proiectarea de circuit", Ed. TEHNOPRES, 2008
David Pozar, Microwave Engineering, Wiley; 4th edition , 2011, ISBN : 978-1-118-29813-8 (E), ISBN : 978-0-470-63155-3 (P)
![Page 6: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/6.jpg)
![Page 7: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/7.jpg)
Personalizat
![Page 8: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/8.jpg)
0 dBm = 1 mW 3 dBm = 2 mW 5 dBm = 3 mW 10 dBm = 10 mW 20 dBm = 100 mW -3 dBm = 0.5 mW -10 dBm = 100 W -30 dBm = 1 W -60 dBm = 1 nW
0 dB = 1 + 0.1 dB = 1.023 (+2.3%) + 3 dB = 2 + 5 dB = 3 + 10 dB = 10 -3 dB = 0.5 -10 dB = 0.1 -20 dB = 0.01 -30 dB = 0.001
dB = 10 • log10 (P2 / P1) dBm = 10 • log10 (P / 1 mW)
[dBm] + [dB] = [dBm]
[dBm/Hz] + [dB] = [dBm/Hz]
[x] + [dB] = [x]
![Page 9: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/9.jpg)
Operatii cu numere complexe! z = a + j · b ; j2 = -1
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abscisa – partea reala ordonata – partea imaginara oricare poate fi negativa, intregul plan, 4
cadrane
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Reprezentare polara
modul
faza sincos jzbjaz
0,2
,2
0,0,arctan
0,0,arctan
0,arctan
arg
anedefinit
baa
b
baa
b
aa
b
z
22 baz
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Comportarea (descrierea) unui circuit depinde de lungimea sa electrica la frecventele de interes E≈0 Kirchhoff
E>0 propagare
lllE 2
2
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mod TEM, doi conductori I(z,t)
V(z,t)
Δz
I(z+Δz,t)
V(z+Δz,t)
L·Δz R·Δz
G·Δz C·Δz
![Page 15: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/15.jpg)
Impedanta caracteristica a liniei
zz eVeVzV 00
zz eIeIzI 00
zILjR
dz
zdV
zz eVeVzV 00
zz eVeVLjR
zI
00
CjG
LjRLjRZ
0
CjGLjRj
2 fv f
0
00
0
0
I
VZ
I
V
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impedanta la intrarea liniei de impedanta caracteristica Z0 , de lungime l , terminata cu impedanta ZL
lZjZ
lZjZZZ
L
Lin
tan
tan
0
00
ΓL
Z0 ZL
-l 0
Zin
![Page 17: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/17.jpg)
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Transfer de putere
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Ei
Zi
ZL Pa
PL
aL
iL
PP
ZZ
*
Ei
Zi
ZL Pa
Pa
aL
iL
PP
ZZ
*
![Page 20: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/20.jpg)
Generatorul are posibilitatea de a oferi o anumita putere maxima de semnal Pa
Pentru o sarcina oarecare, acesteia i se ofera o putere de semnal mai mica PL < Pa
Se intampla “ca si cum” (model) o parte din putere se reflecta Pr = Pa – PL
Puterea este o marime scalara!
Ei
Zi Pa
aL
iL
PP
ZZ
*
Ei
Zi ZL
PL
Ei
Zi
ZL
Pa PL
Pr
+
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Ei
Zi
ZL Pa
PL
Pr
i
ia
R
EP
4
2
22
2
LiLi
iLL
XXRR
ERP
22
2
22
224
144
LiLi
iL
i
i
LiLi
iL
i
iLar
XXRR
RR
R
E
XXRR
ER
R
EPPP
|Γ|2 este un coeficient de reflexie in putere
2
22
222
4
a
LiLi
LiLi
i
ir P
XXRR
XXRR
R
EP
![Page 22: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/22.jpg)
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![Page 25: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/25.jpg)
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are ca scop separarea unui circuit complex in blocuri individuale
acestea se analizeaza separat (decuplate de restul circuitului) si se caracterizeaza doar prin intermediul porturilor (cutie neagra)
analiza la nivel de retea permite cuplarea rezultatelor individuale si obtinerea unui rezultat total pentru circuit
[Z] [ABCD] [S] [Z]
![Page 27: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/27.jpg)
Z11 – impedanta de intrare cu iesirea in gol
2
1
2221
1211
2
1
I
I
ZZ
ZZ
V
V
2221212
2121111
IZIZV
IZIZV
011112
I
IZV
01
111
2
II
VZ
02
112
1
II
VZ
01
221
2
II
VZ
02
222
1
II
VZ
01
111
2
II
VZ
I1
V1 [Z]
I2
V2
![Page 28: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/28.jpg)
Y11 – admitanta de intrare cu iesirea in scurtcircuit
2
1
2221
1211
2
1
V
V
YY
YY
I
I
2221212
2121111
VYVYI
VYVYI
011112
V
VYI
01
111
2
VV
IY
02
112
1
VV
IY
01
221
2
VV
IY
02
222
1
VV
IY
01
111
2
VV
IY
I1
V1 [Y]
I2
V2
![Page 29: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/29.jpg)
2
2
1
1
I
V
DC
BA
I
V
221
221
IDVCI
IBVAV
02
1
2
VI
VB
02
1
2
IV
IC
02
1
2
VI
ID
I1
V1
I2
V2
DC
BA
02
1
2
IV
VA
1
1
2
2 1
I
V
AC
BD
CBDAI
V
![Page 30: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/30.jpg)
I1
V1
I2
V2
11
11
DC
BA
I3
V3
22
22
DC
BA
22
22
11
11
DC
BA
DC
BA
DC
BA
I1
V1
I3
V3
DC
BA
![Page 31: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/31.jpg)
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Determinati tensiunea pe sarcina in circuitul urmator
![Page 34: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/34.jpg)
Sectionare circuit in elemente simple Generatoarele raman in exterior Daca e necesar, se creaza porturi de intrare si iesire
lasate in gol
1 2 3 4
I2 = 0
4321 MMMMDC
BA
0221
2
IIBVAV
A
VVVAV LL
![Page 35: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/35.jpg)
1 2 3 4
I2 = 0
901
3
03
jA
VVL
025
253
125
101
050
500
20
02
1
10
501j
jj
j
j
DC
BA
![Page 36: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/36.jpg)
Scattering parameters
2
1
2221
1211
2
1
V
V
SS
SS
V
V
01
111
2
VV
VS
[S]
01
221
2
VV
VS
V1 +
V1 -
V2 +
V2 -
are semnificatia: la portul 2 este conectata impedanta care realizeaza conditia de adaptare (complex conjugat)
02 V
Γ2
00 22 V
![Page 37: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/37.jpg)
S11 este coeficientul de reflexie la portul 1 cand cand portul 2 este terminat pe impedanta care realizeaza adaptarea
S21 este coeficientul de transmisie de la portul 1 (al doilea indice!) la portul 2 (primul indice!) cand se depune semnal la portul 1 portul 2 este terminat pe impedanta care realizeaza adaptarea
2
1
2221
1211
2
1
V
V
SS
SS
V
V
01
01
111
2
2
V
V
VS[S]
V1 +
V1 -
V2 +
V2 -
Γ2 Γ1
021
01
221
2
2
TV
VS
V
![Page 38: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/38.jpg)
Matricea S poate fi extinsa (generalizata) pentru multiporti (n-porturi)
ikVi
iii
k
V
VS
,0 jkVj
iij
k
V
VS
,0
Sii este coeficientul de reflexie la portul i cand toate celelalte porturi sunt conectate la impedanta care realizeaza adaptarea
Sij este coeficientul de transmisie de la portul j (al doilea indice!) la portul i (primul indice!) cand se depune semnal la portul j si toate celelalte porturi sunt conectate la impedanta care realizeaza adaptarea
![Page 39: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/39.jpg)
Daca portul i este conectat la o linie cu impedanta caracteristica Zoi
Curs 2
Legatura cu matricea Z
zjzj eVeVzV 00 zjzj e
Z
Ve
Z
VzI
0
0
0
0
iii VVVi
i
i
ii
Z
V
Z
VI
00
VZZVZZIZ
1
0
1
0
VZZVZZ 00
100
ZZZZS
nZ
Z
Z
0
01
0
0
0
VIZ
VVVZZVZZ
1
0
1
0
VVV
VSV
In planul de referinta al portului, z=0
![Page 40: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/40.jpg)
Definim undele de putere
Tensiuni si curenti
R
R
R
IZVa
2
R
R
R
IZVb
2
*
RRR XjRZ O impedanta de referinta oarecare, complexa
R
RR
R
bZaZV
*
RR
baI
unda incidenta de putere
unda reflectata de putere
![Page 41: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/41.jpg)
legatura intre undele de putere incidenta si reflectata
tipic
aFZZZZFb RR 11*
11* FZZZZFS RRp
100
ZZZZS
iRZZ Rii ,00
500R SS p
aSb p
coincid!!!
![Page 42: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/42.jpg)
Daca in plus generatorul este adaptat conjugat cu sarcina
Reflexie in putere C3
Reflexie in putere C4
*Lg ZZ
L
LR
VaP
82
1 2
02
max
221 aaaraL PPPPPP
*iL ZZ aL PP max
2 ar PP
0
*0
ZZ
ZZ
*
iL ZZ
2
max2
1aPP aL
22
2
1
2
1baPL
RL
RL
R
Rp
ZZ
ZZ
IZV
IZV
a
b
**
222
2
1
2
1pL aaP 2
1 paL PP 22
2
1bPP par
![Page 43: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/43.jpg)
S11 si S22 sunt coeficienti de reflexie la intrare si iesire cand celalalt port este adaptat
2
1
2221
1211
2
1
a
a
SS
SS
b
b
01
111
2
aa
bS
[S]
a1 a2
b1 b2
02
222
1
aa
bS
![Page 44: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/44.jpg)
S21 si S12 sunt amplificari de semnal cand celalalt port este adaptat
2
1
2221
1211
2
1
a
a
SS
SS
b
b
01
221
2
aa
bS
[S]
a1 a2
b1 b2
02
112
1
aa
bS
![Page 45: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/45.jpg)
a,b informatia despre putere SI faza
Sij influenta circuitului asupra puterii semnalului
incluzand informatiile relativ la faza
2
1
2221
1211
2
1
a
a
SS
SS
b
b
0
02
21ZsursaPutere
ZsarcinaPutereS
[S]
a1 a2
b1 b2
![Page 46: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/46.jpg)
Vector Network Analyzer
![Page 47: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/47.jpg)
![Page 48: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/48.jpg)
Funcționalitatea dorită:
divizarea
combinarea
puterii semnalului
![Page 49: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/49.jpg)
numite si joncțiune in T caracterizate de o matrice S 3x3
circuitul este reciproc dacă nu conține: materiale anizotrope (de obicei ferite)
circuite active e de dorit să obținem funcționalitatea dorită de
divizare/combinare de putere fără pierderi interne e de dorit sa obținem circuitul adaptat simultan la
toate porțile evitarea unor pierderi externe de putere
333231
232221
131211
SSS
SSS
SSS
S
![Page 50: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/50.jpg)
circuit reciproc
adaptat simultan la toate portile
matricea S devine:
0
0
0
2313
2312
1312
SS
SS
SS
S
ijSS jiij , tSS
322331132112 ,, SSSSSS
iSii ,0 0,0,0 332211 SSS
![Page 51: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/51.jpg)
reciproc, adaptat, matricea S:
circuit unitar (fără pierderi)
toata puterea introdusa pe un port se regaseste la celelalte porturi
jiSS ij
N
k
kjki ,,1
*
11
*
N
k
kiki SS jiSSN
k
kjki
,01
*
]1[*
t
SS
0
0
0
2313
2312
1312
SS
SS
SS
S
![Page 52: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/52.jpg)
circuit unitar (fără pierderi)
6 ecuatii / 3 necunoscute
nici o solutie posibila
11
*
N
k
kiki SS
jiSSN
k
kjki
,01
*
0
0
0
2313
2312
1312
SS
SS
SS
S
12
13
2
12 SS
12
23
2
12 SS
12
23
2
13 SS
023
*
13 SS
012
*
23 SS
013
*
12 SS
![Page 53: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/53.jpg)
6 ecuații / 3 necunoscute nici o soluție posibila
Un circuit cu 3 porți NU poate fi simultan: reciproc
fara pierderi
adaptat simultan la toate cele 3 porți Renunțarea la una din cele 3 condiții conduce la
circuite realizabile
0
0
0
2313
2312
1312
SS
SS
SS
S
![Page 54: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/54.jpg)
de obicei cu materiale anizotrope, ferite nereciproc, dar adaptat simultan si fara
pierderi matricea S
6 ecuatii / 6 necunoscute
jiij SS
0
0
0
3231
2321
1312
SS
SS
SS
S
032
*
31 SS
023
*
21 SS
013
*
12 SS
12
13
2
12 SS
12
23
2
21 SS
12
32
2
31 SS
![Page 55: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/55.jpg)
doua solutii posibile circulatoare
in sens orar direct
in sens orar invers
0312312 SSS
1133221 SSS
0133221 SSS
1312312 SSS
![Page 56: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/56.jpg)
Un circuit cu 3 porți reciproc si fara pierderi poate fi adaptat numai la 2 porți
332313
2312
1312
0
0
SSS
SS
SS
S
023
*
13 SS
0332313
*
12 SSSS
013
*
3312
*
23 SSSS
12
13
2
12 SS
12
23
2
12 SS
12
33
2
23
2
13 SSS2313 SS
02313 SS
13312 SS
![Page 57: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/57.jpg)
Un circuit cu 3 porți reciproc si fara pierderi
332313
2312
1312
0
0
SSS
SS
SS
S
02313 SS 13312 SS
jeS 12
jeS 33
j
j
j
e
e
e
S
00
00
00
Un circuit cu 3 porți reciproc si fara pierderi degenereaza in doua componente separate: o linie fara pierderi, adaptata, intre
doua dintre porturi al treilea port e separat si
dezadaptat
![Page 58: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/58.jpg)
caracterizate de o matrice S 4x4
circuitul este reciproc dacă nu conține: materiale anizotrope (de obicei ferite)
circuite active e de dorit să obținem funcționalitatea dorită de
divizare/combinare de putere fără pierderi interne e de dorit sa obținem circuitul adaptat simultan la
toate porțile evitarea unor pierderi externe de putere
44434241
34333231
24232221
14131211
SSSS
SSSS
SSSS
SSSS
S
![Page 59: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/59.jpg)
circuit reciproc
adaptat simultan la toate portile
matricea S devine:
ijSS jiij , tSS
322331132112 ,, SSSSSS
iSii ,0 0,0,0,0 44332211 SSSS
0
0
0
0
342414
342313
242312
141312
SSS
SSS
SSS
SSS
S
![Page 60: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/60.jpg)
reciproc, adaptat, matricea S:
circuit unitar (fără pierderi)
toata puterea introdusa pe un port se regaseste la celelalte porturi
jiSS ij
N
k
kjki ,,1
*
11
*
N
k
kiki SS jiSSN
k
kjki
,01
*
]1[*
t
SS
0
0
0
0
342414
342313
242312
141312
SSS
SSS
SSS
SSS
S
![Page 61: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/61.jpg)
o solutie: cuplorul rezulta directional
*
2424
*
1423
*
13 /0 SSSSS
*
1323
*
2413
*
14 /0 SSSSS
02
24
2
13
*
14 SSS
1234
*
1423
*
12 /0 SSSSS
*
3423
*
3412
*
14 /0 SSSSS
02
34
2
1223 SSS
02314 SS
12
13
2
12 SS
12
24
2
12 SS
12
34
2
13 SS
12
34
2
24 SS
2413 SS
3412 SS
00
00
00
00
3424
3413
2412
1312
SS
SS
SS
SS
S
![Page 62: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/62.jpg)
Alegem referintele de faza
3412 SS jeS 13
jeS 24
00
00
00
00
3424
3413
2412
1312
SS
SS
SS
SS
S 2413 SS 3412 SS
034
*
2413
*
12 SSSS n2
12
24
2
12 SS 122
Cealalta solutie posibila pentru ecuatiile anterioare ofera fie aceeasi solutie (cu alta referinta de faza) fie un caz degenerat 0
2
24
2
13
*
14 SSS 02
34
2
1223 SSS
β – coeficientul de cuplaj în tensiune
![Page 63: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/63.jpg)
Un circuit cu 4 porti care este simultan: adaptat la toate portile
reciproc
fara pierderi este intotdeauna directional puterea de semnal introdusa pe un port este
trimisa numai spre doua din celelalte trei porturi
00
00
00
00
j
j
j
j
e
e
e
e
S
![Page 64: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/64.jpg)
![Page 65: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/65.jpg)
consta in separarea unei linii incidente in doua linii separate
se poate implementa in diverse tehnologii
![Page 66: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/66.jpg)
daca liniile sunt fără pierderi, diportul este reciproc, deci nu poate fi adaptat la toate porțile simultan
la nivelul joncțiunii câmpurile sunt neuniforme, generând moduri de ordin superior localizate
aceasta energie localizata poate fi modelata cu o reactanța concentrata la nivelul joncțiunii: B
Proiectarea divizorului presupune adaptarea la linia de intrare cu Z0 ieșirile pot fi adaptate mai
departe cu circuite suplimentare (/4, binomial, Cebișev)
![Page 67: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/67.jpg)
daca liniile sunt fără pierderi, impedantele caracteristice sunt reale
conditia de adaptare poate fi indeplinita doar daca B 0 caz in care conditia de adaptare este:
021
111
ZZZBjYin
021
111
ZZZ
In practica daca B nu poate fi neglijat, se introduce o reactanta externa de compensare, reglabila, cu efect macar intr-o banda ingusta de frecventa.
![Page 68: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/68.jpg)
daca V0 e amplitudinea semnalului la jonctiune
0
2
0
2
1
Z
VPin 1
2
01
2
1
Z
VP
2
2
02
2
1
Z
VP
21 PPPin
deci:
(fara pierderi)
1
2
2
1
Z
Z
P
P (impartirea puterii pe cele doua linii de iesire)
21
21
ZZ
ZPP in
21
12
ZZ
ZPP in
1
1 inPP
1
12 inPP
1101 ZZ 102 ZZ
![Page 69: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/69.jpg)
matricea S fara pierderi (matrice unitara) reciproc (matrice simetrica) portul de intrare este adaptat
1
12 PP
1
113 PP
1
2
3
011 S
11221 SS
1
11331 SS
Coeficienti de reflexie la iesiri
1
1
||
||
120
120122
ZZZ
ZZZS
1||
||
210
210233
ZZZ
ZZZS
![Page 70: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/70.jpg)
1
2
3
Matrice unitara, coloanele 1 si 2
11
1
1
1
1
1
1
10
x
xS0
1
1
11
10
x
13223 SS
111
1
11
1
1
1
1
10
S
![Page 71: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/71.jpg)
divizor de 3dB impartire egala a puterii intre cele
doua iesiri Z1 = Z2 = 2·Z0 , α = 1
1
2
3
2
1
2
1
2
12
1
2
1
2
12
1
2
10
S
2
1
2
1
2
2
1
2
1
2
220
j
j
jj
S
Daca se adauga transformatoare in /4 pentru a adapta iesirile la Z0 matricea S devine:
![Page 72: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/72.jpg)
Proiectați un divizor cu joncțiune în T care are o impedanță a sursei de 30Ω, pentru a obține un raport de puteri la ieşire de 3 :1. Proiectați transformatoare in sfert de lungime de undă care să convertească impedanța liniilor de ieşire la 30Ω.
0
2
0
2
1
Z
VPin
inPZ
VP
4
1
2
1
1
2
01
inPZ
VP
4
3
2
1
2
2
02
1204 01 ZZ
4034 02 ZZ
in
inin
PP
PP
PP
PPP
4
3
4
1
1:3:2
1
21
21
30120||40inZ
Li
i
c ZZZ
60301201
1
Lc ZZZ 64.3430402
2
Lc ZZZ
Verificare
Transformatoare
![Page 73: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/73.jpg)
Introducerea elementelor disipative (pierderi) permite realizarea divizorului: reciproc adaptat la toate cele porti
Impedanta Z vazuta de la nivelul jonctiunii spre una din linii:
3
4
3
00
0 ZZ
ZZ
Linia de intrare va vedea la capat o rezistenta in serie cu doua astfel de linii in paralel
000
3
4
2
1
3Z
ZZZin
deci va fi adaptata: 011 S
din simetrie: 0332211 SSS
![Page 74: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/74.jpg)
Introducerea elementelor disipative (pierderi) permite realizarea divizorului: reciproc (matricea S e simetrica) adaptat la toate cele porti
V1 e tensiunea la intrarea in portul 1, calculam tensiunea la nivelul jonctiunii V
1
00
01
0
13
2
332
32
32
2V
ZZ
ZV
ZZ
ZVV
Tensiunile de iesire se obtin tot prin divizare:
2
13121 SS
din simetrie: 2
1233121 SSS
0332211 SSS
1
00
032
2
1
4
3
3VV
ZZ
ZVVV
![Page 75: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/75.jpg)
Introducerea elementelor disipative (pierderi) permite realizarea divizorului: reciproc (matricea S e simetrica) adaptat la toate cele porti
Matricea S
2
1233121 SSS
0332211 SSS
011
101
110
2
1S
Puteri:
0
2
1
2
1
Z
VPin
inP
Z
V
Z
VPP
4
1
8
121
2
1
0
2
1
0
2
132
Jumatate din putere se disipa pe cei 3 rezistori
![Page 76: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/76.jpg)
Divizoarele de putere anteroare au un dezavantaj major, nu exista izolare intre cele doua porturi de iesire acest deziderat e important in anumite aplicatii
Divizorul Wilkinson este introdus pentru rezolvarea acestui impediment
03223 SS
o proprietate utila suplimentara este ca “pare” fara pierderi daca porturile de iesire sunt adaptate
numai energia reflectata din iesiri este disipata
![Page 77: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/77.jpg)
utila/necesara pentru multiporti exemplu, rezistori, circuit cu 2 porturi
E1 E2
100 Ω
50 Ω 50 Ω
25 Ω
1 2
![Page 78: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/78.jpg)
presupunem ca doresc Y11 E2 = 0
E1 E2
100 Ω
50 Ω 50 Ω
25 Ω
1 2
01
111
2
VV
IY
E1
25 Ω
1
50 Ω
50 Ω
100 Ω
4067.66||100)67.1650(||100
)50||2550(||100echR
SV
IY
V
025.0
01
111
2
![Page 79: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/79.jpg)
analiza pe mod par/impar beneficiaza de existenta in circuit a unor plane de simetrie initiale create
E1 E2
100 Ω
50 Ω 50 Ω
25 Ω
1 2
E1 E2
50 Ω 50 Ω
50 Ω
1 2
50 Ω
50 Ω 50 Ω
plan de simetrie
![Page 80: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/80.jpg)
la atacul porturilor cu surse simetrice/antisimetrice planele de simetrie se transforma in gol virtual
masa virtuala
E1 E2
50 Ω 50 Ω
50 Ω
1 2
50 Ω
50 Ω 50 Ω plan de simetrie Vx
Rech Rech
+
_ Vx
+
_
+Vx +Vx
0V 0V
plan de simetrie gol
xVI ,0
Vx
Rech Rech
+
_ Vx
+
_
+Vx -Vx
0V 0V
I=0
V V
P=0V
0V
plan de simetrie masa
xVP ,0
Aceeasi polaritate pentru surse
Polaritate diferita pentru surse
![Page 81: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/81.jpg)
orice combinatie de 2 surse poate fi echivalata pentru circuitele liniare cu o suprapunere: o sursa simetrica o sursa antisimetrica
E1 E2
50 Ω 50 Ω
50 Ω
1 2
50 Ω
50 Ω 50 Ω plan de simetrie E1
+
_
Ee _
+ oe EEE 1
Eo _
+
E2
+
_
Ee _
+
Eo
_
+
oe EEE 2
2
21 EEEe
2
21 EEEo
![Page 82: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/82.jpg)
In circuite liniare putem aplica suprapunerea efectelor
Efect ( Sursa1 + Sursa2 ) = Efect ( Sursa1 ) + Efect ( Sursa2 )
Efect ( PAR+ IMPAR ) = Efect ( PAR ) + Efect ( IMPAR )
Putem beneficia de avantajele simetriilor!!
![Page 83: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/83.jpg)
exemplu
E1 E2
100 Ω
50 Ω 50 Ω
25 Ω
1 2
01
111
2
VV
IY
V1
I1
E1 E2
50 Ω 50 Ω
50 Ω
1 2
50 Ω
50 Ω 50 Ω plan de simetrie
022 EV 2
1EE e
2
1EEo
![Page 84: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/84.jpg)
analiza pe mod par/impar
Ee
50 Ω
50 Ω
1
50 Ω
V1
I1e
Eo
50 Ω
50 Ω
1
50 Ω
V1
I1o
1005050e
echR 2550||50o
echR
200100
2 111
EE
R
EI
e
ech
ee
5025
2 111
EE
R
EI
o
ech
oo
PAR plan de simetrie gol IMPAR plan de simetrie masa
![Page 85: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/85.jpg)
suprapunerea efectelor
E1 E2
100 Ω
50 Ω 50 Ω
25 Ω
1 2
SV
IY 025.0
40
1
1
111
V1
I1
4050200
111111
EEEIII oe
oe III 111
oe VVV 111
1111 EVVV oe
![Page 86: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/86.jpg)
In circuite liniare putem aplica suprapunerea efectelor
avantaje
reducerea complexitatii circuitului
reducerea numarului de porturi (principalul avantaj)
Efect ( PAR+ IMPAR ) = Efect ( PAR ) + Efect ( IMPAR )
Putem beneficia de avantajele simetriilor!!
![Page 87: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/87.jpg)
o linie de intrare doua transformatoare /4 o rezistenta intre liniile de iesire
![Page 88: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/88.jpg)
schema normalizata si “simetrizata”
![Page 89: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/89.jpg)
analiza pe mod par si impar
![Page 90: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/90.jpg)
mod par, plan de simetrie gol
2
2
2
ZZ e
in privind din portul 2, transformator /4
daca 2Z portul 2 este adaptat
xjxj eeVxV x=0 la portul 1 x=-/4 la portul 2
02 14 VjVVV e 1
110 01
jVVVV e
12 e
inZ
22
22
201 jVV e : coeficientul de reflexie vazut dinspre transformatorul cu
spre impedanta normalizata 2 2Z
12 e
inZ
![Page 91: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/91.jpg)
mod impar, plan de simetrie masa
linia in /4 este scurtcircuitata la capat impedanta vazuta dinspre portul 2 este 2/2 rZ o
in daca 2r portul 2 este adaptat
12 o
inZ 02 VV o
01 oV in modul impar toata puterea se disipa in rezistorul r/2
![Page 92: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/92.jpg)
impedanta de intrare in portul 1
122
1 2
1 inZ
doua transformatoare /4 in paralel
![Page 93: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/93.jpg)
parametrii S
122
1 2
1 inZ 011 S
03322 SS
222
112112
j
VV
VVSS
oe
oe
23113
jSS
03223 SS
12 o
inZ12 e
inZ si similar 13 o
inZ13 e
inZ
scurt sau gol intre porturile 2 si 3 elimina orice transfer de putere + circuit reciproc
si similar
![Page 94: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/94.jpg)
la frecventa de proiectare (lungimile transformatoarelor egale cu 0/4) avem izolare intre cele doua linii de iesire
002
002
220
j
j
jj
S
![Page 95: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/95.jpg)
3 X Wilkinson = divizor de putere pe 4 porturi
![Page 96: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/96.jpg)
![Page 97: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/97.jpg)
![Page 98: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/98.jpg)
Un circuit cu 4 porti care este simultan: adaptat la toate portile
reciproc
fara pierderi este intotdeauna directional puterea de semnal introdusa pe un port este
trimisa numai spre doua din celelalte trei porturi
00
00
00
00
j
j
j
j
e
e
e
e
S
![Page 99: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/99.jpg)
2 cazuri mai des intalnite in practica
cuplor simetric
cuplor asimetric
2
00
00
00
00
j
j
j
j
S
,0
00
00
00
00
S
![Page 100: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/100.jpg)
![Page 101: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/101.jpg)
[dB]log20log103
1 P
PC
[dB]log20log10144
3
SP
PD
[dB]log20log10 14
4
1 SP
PI
22
13 S
222
12 1 S
Cuplaj
Directivitate
Izolare
dBCDI ,
![Page 102: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/102.jpg)
,0
21
Cuplorul hibrid este cuplorul directional de 3 dB
Cuplor hibrid in cuadratura Cuplor hibrid in inel
2
010
100
001
010
2
1
j
j
j
j
S
0110
1001
1001
0110
2
1S
![Page 103: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/103.jpg)
010
001
100
010
2
1
j
j
j
j
S
![Page 104: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/104.jpg)
![Page 105: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/105.jpg)
oeb 2
1
2
11 oe TTb
2
1
2
12 oe TTb
2
1
2
13 oeb
2
1
2
14
![Page 106: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/106.jpg)
![Page 107: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/107.jpg)
1
1
Y
Y'Y S
pentru modul par
pentru modul impar
Y0 ,Z0Y0 ,Z0
Y0 ,Z0Z0
2, Z2
2,
jY’S jY’S jY’S jY’S
Ie Is
Ve Vs
a) b)
S
S
SSe
e
I
V
'jYjY
jZ
'jYI
V
1
01
0
0
1
01
2
2
S
S
SS
S
e
e
I
V
Z'YjYZ'jY
jZZ'Y
I
V
2222
22
22
0
0
22
222
0
0
2
11
2 jY'jYZZ
ZjZ'Y
jYZ'jYZZ
Zj
S
SS
S
222
0
0
22
222
2
2
212
2
2
jYZ'jYZZ
ZjZ'Y
jYZ'jYjZZ'YS
SS
SS
222S0
0
22S
21
jYZ'jYZZ
ZjZ'Y2
2S
222
0
0
22
222
0
0
2
22
2 jYZ'jYZZ
ZjZ'Y
jYZ'jYZZ
Zj
S
SS
S
22
22
222
22
2211
)'('2
'S
zyyzjzy
zyyzjS
SS
S
12
22
222
212
2S
)z'yyz(jz'yST
SS
![Page 108: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/108.jpg)
21
2211
02
01
2
1
S
SSS
Z
ZA
21
22110201
2
1
S
SSSZZB
01020102
0102010211
DZZCZBAZ
DZZCZBAZS
21
2211
02012
11
S
SSS
ZZC
21122211 SSSSS
21
2211
01
02
2
1
S
SSS
Z
ZD
01020102
0201
12
)(2
DZZCZBAZ
ZZBCADS
01020102
0201
21
2
DZZCZBAZ
ZZS
01020102
0102010222
DZZCZBAZ
DZZCZBAZS
![Page 109: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/109.jpg)
2212221
22122
2 zyyzjzy
zyyzje
22122212
2
zyyzjzyTe
2
212221
22122
2 zyyzjzy
zyyzjo
22122212
2
zyyzjzyTo
22
2122
221
2
2212
22
1
22
zyyzzy
zyyzb oe
22
2122
221
22122
2
2
2
2zyyzzy
zyyzjTTb oe
222122
221
213
2
4
2zyyzzy
zyTTb oe
22
2122
221
2212221
4
2
2
2zyyzzy
zyyzzjyb oe
21
222
21221
1
100
yzzyyzb
2221341 00 jzbzybbb
21
22 1 yy
22
2
22
3 ,1
y
jb
y
yb
dBbP
PC ,log20log10 3
3
1
2
2
2 1
y
yC
Cb 3
22 1 Cjb
010
100
001
010
2
2
2
2
CjC
CjC
CCj
CCj
S
![Page 110: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/110.jpg)
2
1
2
2 1 yy
2
2
2 1
y
y
2
2
2
10
1log20dB
y
yC
![Page 111: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/111.jpg)
este frecvenţa de proiectare la care liniile cuplorului
sunt de lungime
05.0 f 05.1 f 0f
4
Proiectaţi un cuplor în scară pe impedanţa caracteristică
de 50 Ω, şi reprezentati mărimea parametrilor S între
şi , unde
.
![Page 112: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/112.jpg)
21C
22 y 11 y
500Z
Un cuplor în scară cu C = 3dB, are . Atunci
şi
Astfel matricea S din relaţia (&.47) devine cea din relaţia (&.38). În plus, pentru
, impedanţele caracteristice ale liniilor cuplorului vor fi:
5001 ZZ 4.352
ZZ 0
2
![Page 113: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/113.jpg)
![Page 114: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/114.jpg)
![Page 115: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/115.jpg)
![Page 116: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/116.jpg)
Modul par
Modul impar
![Page 117: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/117.jpg)
22222
2222211
zjyzyyyjjzyjz
zjyzyyyjjzyjzS
eses
eses
2222212
2
zjyzyyyjjzyjzS
eses
2222221
2
zjyzyyyjjzyjzS
eses
22222
2222222
zjyzyyyjjzyjz
zjyzyyyjjzyjzS
eses
eses
1jyye
1jyys
Pentru modul par:
22122
1222122
22
22122
2112
22122
1222122
11
2
2
2
zyyz
yjzzyyzS
zyyz
jSS
zyyz
yjzzyyzS
e
ee
e
1jyye
1jyys
Pe modul impar:
22122
1222122
o11zyyz
yjz2zyyzS
22122
1222122
o22
22122
o21o12
zyyz
yjz2zyyzS
zyyz
j2SS
00
00
00
00
21
12
21
12
jyjy
jyjy
jyjy
jyjy
S
12
2
2
1 yy
Conditia de adaptare
![Page 118: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/118.jpg)
00
00
00
00
00
00
00
00
21
21
12
12
j
jyjy
jyjy
jyjy
jyjy
S
)log(20log20)( 1ydBC
![Page 119: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/119.jpg)
Proiectaţi un cuplor în inel hibrid (3dB) pe impedanţa de
50 Ω şi reprezentati mărimea parametrilor S între 0.5 si
1.5 din frecventa centrala.
.
7.70Z2 0
)log(20[dB] 1yC
![Page 120: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/120.jpg)
.
)(log20[dB] 110 yC
12
2
2
1 yy
1y
![Page 121: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/121.jpg)
![Page 122: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/122.jpg)
Z0 Z0
Z0+
_E
Z0 1
2 3
4
l
![Page 123: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/123.jpg)
Mod par – caracterizeaza semnalul de mod comun de pe cele doua linii
Mod impar – caracterizeaza semnalul de mod diferential dintre cele doua linii
Fiecare din cele doua moduri e caracterizat de impedante caracteristice diferite
![Page 124: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/124.jpg)
++
+
Z0 Z0
Z0
Z0
Z0
Z0
Z0
Z0
+E/ 2
E/ 2 E/ 2
E/ 2
V V
VV
I I
II
1 1
4 4
2 2
3 3
Zco Z
Z
ce
ceZco
-
- 1
1o
1o
1o
o
1e
1
1
1e
e
e
oe
coce ZZZ 20
![Page 125: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/125.jpg)
+
1
1
1+
1/ 2
1/ 2
1 4
2 3
1
/2e
T /2e
T /2e /2e
1/2
1/2
+
+
1/ 2
1/ 2
1/ 21 4
2 3
/2o
/2o
T /2
T /2-1/2
-
1
1
1
1
o
o-
modul par modul impar
0,1 432111 aaaaaa oe
02
1b oe1
sin1cos
sin
2
1
22
jC
jCb oe
0TT2
1b oe3
sin1cos
1
2
1
2
2
4jC
CTTb oe
coce
coce
ZZ
ZZC
001
010
010
100
2
2
2
2
CCj
CCj
CjC
CjC
S
2
![Page 126: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/126.jpg)
010
100
001
010
2
1
j
j
j
j
S
010
100
001
010
2
2
2
2
CjC
CjC
jCC
jCC
jS
![Page 127: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/127.jpg)
![Page 128: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/128.jpg)
![Page 129: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/129.jpg)
![Page 130: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/130.jpg)
coce
coce
ZZ
ZZ
2
0ZZZ coce
coce
coce
ZZ
ZZC 10log20[dB]
![Page 131: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/131.jpg)
Proiectaţi un cuplor prin proximitate de 20 dB, în tehnologie
stripline, folosind o distanta între planele de masă de 0.158 cm
şi cu o permitivitate electrică relativa de 2.56, pe o impedanţa de
50 Ω, la frecvenţa de 3 GHz. Reprezentaţi cuplajul şi
directivitatea între 1 si 5 GHz.
![Page 132: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/132.jpg)
1.010C 2020
28.559.0
1.150Zce
23.451.1
9.050Zco
C
CZZ
C
CZZ coce
1
1,
1
100
![Page 133: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/133.jpg)
![Page 134: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/134.jpg)
j33 2 2
1
V jCsin jCtg jCtgb jCsin e
V 1 jtgcos 1 C jsin 1 C jtg
2j2
2 21
V 1 C 1b e
V cos jsincos 1 C jsin
C<<1
j N 1j3
1 2 N 11 2
V 1C 2jsin e e C cos N 1 C cos N 3 C
V 2
![Page 135: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/135.jpg)
Să se proiecteze un cuplor cu trei secţiuni, avînd un cuplaj de 20
dB, cu caracteristică binomiala (maxim plat), pe o impedanţă de
50 Ω, la frecvenţa centrală de 3 GHz. Să se reprezinte grafic
cuplajul şi directivitatea între 1 şi 5 GHz.
![Page 136: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/136.jpg)
3N
2,1,0
2
nCd
d
n
n
sinsin3sin
2
12cossin2 2121
1
3 CCCCV
VC
0cos3cos32121
CCC
d
dC
010sin3sin9 2121212
2
CCCCC
d
Cd
010
1.02
21
12
CC
CC
125.0
0125.0
2
31
C
CC
10.44125.1
875.050
69.56875.0
125.150
38.490125.1
9875.050
63.509875.0
0125.150
20
20
30
10
30
10
o
e
oo
ee
Z
Z
ZZ
ZZ
dBC 200 2
![Page 137: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/137.jpg)
![Page 138: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/138.jpg)
![Page 139: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/139.jpg)
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mex
mexexin
CC
CCCC
inexe CCC 4
minexo CCCC 64
44
1
ee
vCZ
44
1
oo
vCZ
exe CC
mexo CCC 2
oe
oeee
CC
CCCC
34
oe
eooo
CC
CCCC
34
eo
oeee
ZZ
ZZZZ
00
0004
3
oe
oeoo
ZZ
ZZZZ
00
0004
3
oeeo
eooeoe
ZZZZ
ZZZZZZZ
0000
20000
44033
oeoe
oe
oe
oe
ZZZZ
ZZ
ZZ
ZZC
0020
20
20
20
44
44
23
3
0
2
0112
8934Z
CCC
CCZ e
0
2
0112
8934Z
CCC
CCZ o
![Page 141: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/141.jpg)
Cuploare directionale
![Page 142: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/142.jpg)
[dB]log20log103
1 P
PC
[dB]log20log10144
3
SP
PD
[dB]log20log10 14
4
1 SP
PI
22
13 S
222
12 1 S
Cuplaj
Directivitate
Izolare
dBCDI ,
![Page 143: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/143.jpg)
2
1
2
2 1 yy
2
2
2 1
y
y
2
2
2
10
1log20dB
y
yC
![Page 144: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/144.jpg)
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.
)(log20[dB] 110 yC
12
2
2
1 yy
1y
![Page 146: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/146.jpg)
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coce
coce
ZZ
ZZ
2
0ZZZ coce
coce
coce
ZZ
ZZC 10log20[dB]
![Page 148: Curs 5 2019/2020rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 5_2019.pdf · 2019-12-12 · primul test L1 (t2 si t3 neanuntate) 3pz (C) = +0.5p ... Operatii cu numere complexe!](https://reader034.fdocumento.com/reader034/viewer/2022042217/5ec0e23035000f57542340d6/html5/thumbnails/148.jpg)
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Laboratorul de microunde si optoelectronica http://rf-opto.etti.tuiasi.ro [email protected]