Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de...
Transcript of Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de...
![Page 1: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/1.jpg)
Curs 12 2018/2019
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2C/1L, DCMR (CDM) Minim 7 prezente (curs+laborator) Curs - conf. Radu Damian Vineri 11-13, P7
E – 50% din nota
probleme + (2p prez. curs) + (3 teste) + (bonus activitate) ▪ 3pz=+0.5p
toate materialele permise Laborator – conf. Radu Damian Joi 8-14 impar II.13
L – 25% din nota
P – 25% din nota
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http://rf-opto.etti.tuiasi.ro
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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]
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Operatii cu numere complexe! z = a + j · b ; j2 = -1
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In domeniul microundelor se utilizeaza doua strategii de implementare a filtrelor structuri specifice microundelor (linii cuplate,
rezonatori dielectrici, structuri periodice)
sinteza de filtre cu elemente concentrate urmate de implementare cu linii de transmisie
prima strategie duce la obtinerea unor filtre mai eficiente dar e caracterizata de generalitate mai mica
proiectare deseori dificila (lipsa relatiilor analitice)
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Sinteza filtrelor cu elemente concentrate, urmata de implementarea acestora cu elemente distribuite (linii)
generala
relatii analitice usor de implementat pe calculator
eficienta
Metoda preferata este metoda pierderilor de insertie
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|Γ(ω)|2 este o functie para de ω
Alegerea corespunzatoare a polinoamelor M si N determina comportarea filtrului
21
1
L
SLR
P
PP
22
22
NM
M
2
2
1
N
MPLR
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Se aleg polinoamele pentru implementarea unui FTJ (prototip)
Acest filtru poate fi convertit la alte functii, scalat in frecventa pentru a obtine alte tipuri de functii
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Maxim plat (Butterworth, binomial) ofera cea mai plata comportare in banda de trecere
Echiriplu (Cebasev) ofera atenuare mai mare in banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere
Filtre eliptice, caracterizate de variatii (riplu) si in banda de taiere si in banda de trecere
Filtru cu raspuns liniar in faza, ofera intarziere de grup de maxim plat, cu dezavantajul unei atenuari in putere mai mica, necesar in anumite aplicatii
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Polinomul
pentru
atenuarea creste cu 20N dB/decada
k ofera atenuarea la limita benzii de trecere (3dB implica k = 1)
N
c
LR kP
2
21
NcLR kP
22
c
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Polinomul
pentru
atenuarea creste cu 20N dB/decada
atenuarea este mai mare de (22N)/4 decat cea a filtrului binomial la frecventele
c
c
NLR TkP
221
N
c
LR
kP
22 2
4
c
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cu atenuarile in dB
1
10
10
'
'log2
110
110log
s
L
L
Ar
As
n
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cu atenuarile in dB
1
1
10
101
'
'cosh
110
110cosh
s
L
L
Ar
As
n
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Filtrele prototip sunt filtre care implementeaza : filtru FTJ
frecventa de taiere ω0 = 1 rad/s (f0 = 0.159 Hz)
conectate la intrare la o rezistenta R = 1 Numarul total de elemente reactive (L/C) este
ordinul filtrului Elementele se introduc in alternanta L serie / C
paralel Exista doua filtre prototip care ofera acelasi
raspuns, o varianta care incepe cu C, o varianta care incepe cu L
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Se definesc parametrii gi, i=0,N+1
paralelrcondensatounuiacapacitate
seriebobineuneiinductantag
Nkk ,1
110
1100
''
''
LgdacaGluigeneratoruaconductant
CgdacaRluigeneratorurezistentag
NNN
NNNN
LgdacaGsarcinadeaconductant
CgdacaRsarcinaderezistentag
''
''
1
11
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Calculul elementelor filtrului
10 g
Nk
N
kgk ,1,
2
12sin2
11 Ng
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Calculul elementelor filtrului (iterativ)
1
1
2 ag
Nkgb
aag
kk
kkk ,1,
4
11
1
parNpentru
imparNpentru
gN
4coth
1
21
37,17cothln ArL
N2sinh
Nk
N
kak ,1,
2
12sin
NkN
kbk ,1,sin22
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Pentru ordin par al filtrului (N = 2, 4, 6, 8 ...) filtrele echiriplu trebuie sa fie inchise pe o impedanta de terminatie diferita de cea standard gN+1 ≠ 1
Daca aplicatia nu suporta aceasta comportare, e necesara introducerea unei adaptari de impedanta suplimentare (transformator in sfert de lungime de unda, binomial ...)
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Să se proiecteze un filtru trece-bandă de ordinul 3, avand riplurile în bandă de 0.5 dB. Frecvenţa centrala a filtrului sa fie de 1 GHz. Banda să fie de 10%, şi impedanţa de 50 Ω.
Tabel echiriplu 0.5dB sau relatii de calcul:
g1 = 1.5963 = L1,
g2 = 1.0967 = C2,
g3 = 1.5963 = L3,
g4=1.000 =RL
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Tabel echiriplu 0.5dB sau relatii de calcul:
g1 = 1.5963 = L1/C3,
g2 = 1.0967 = C2/L4,
g3 = 1.5963 = L3/C5,
g4=1.000 =RL
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ω0 = 1 rad/s (f0 = ω0 / 2π = 0.159 Hz)
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Dupa determinarea coeficientilor filtrului prototip
filtru FTJ
frecventa de taiere ω0 = 1 rad/s (f0 = 0.159 Hz)
conectate la intrare la o rezistenta R = 1
Se pot calcula valorile necesare pentru componente pentru implementarea altor conditii
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FTJ (prototip) are utilitate doar ca pas intermediar
filtru FTJ
frecventa de taiere ω0 = 1 rad/s (f0 = 0.159 Hz)
conectate la intrare la o rezistenta R = 1
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Pentru a determina filtrul care lucreaza cu o alta rezistenta de intrare (R0) se multiplica toate impedantele din circuit cu aceasta impedanta (cu " ' " se noteaza elementele noi)
LRL 0
0R
CC
0RRs LL RRR 0
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modificarea frecventei de taiere – (fig. b) modificarea caracteristicii de atenuare (de
exemplu FTJ FTS – fig. c)
scalare
scalare si conversie
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Pentru FTJ cu alta frecventa de taiere se face schimbarea de variabila:
Echivalent cu largirea caracteristicii de frecventa
c
c
LRLR PP
kk
c
k LjLjXj
kk
c
k CjCjBj
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Noile valori cu scalarea in frecventa
Daca se aplica simultan si scalarea in impedanta
c
kk
LL
c
kk
CC
c
kk
LRL
0
c
kk
R
CC
0
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Se face schimbarea de variabila:
Daca se aplica simultan si scalarea in impedanta
In schema inductantele serie se transforma in capacitati serie, iar capacitatile paralel se transforma in inductante paralel
c
k
kc
kCj
LjXj
1
k
kc
kLj
CjBj
1
kc
kLR
C
0
1
kc
kC
RL
0
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Se face schimbarea de variabila:
unde intervin banda fractionara si frecventa centrala
0
0
0
012
0 1
0
12
210
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01 0
0
0
111
10
20
210
0
1
111
20
20
220
0
2
FTB FOB
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O inductanta serie in filtrul prototip se transforma intr-un circuit LC serie
O capacitate paralel in filtrul prototip se transforma intr-un circuit LC paralel
k
kkk
kkC
jLjL
jL
jLj
Xj
10
0
0
0
k
kkk
kkL
jCjC
jC
jCj
Bj
10
0
0
0
0 k
k
LL
k
kL
C
0
0
k
kC
L
0
kk
CC
![Page 41: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/41.jpg)
O inductanta serie in filtrul prototip se transforma intr-un circuit LC paralel
O capacitate paralel in filtrul prototip se transforma intr-un circuit LC serie
k
kC
L
0
1
0k
k
CC
0k
k
LL
k
kL
C
0
1
1
0
0
![Page 42: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/42.jpg)
![Page 43: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/43.jpg)
Să se proiecteze un filtru trece-bandă de ordinul 3, avînd riplurile în bandă de 0.5 dB. Frecvenţa centrala a filtrului sa fie de 1 GHz. Banda să fie de 10%, şi impedanţa de 50 Ω.
sradGHz /10283.612 9
0
1.0
![Page 44: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/44.jpg)
Tabel echiriplu 0.5dB sau relatii de calcul:
g1 = 1.5963 = L1/C3,
g2 = 1.0967 = C2/L4,
g3 = 1.5963 = L3/C5,
g4=1.000 =RL
![Page 45: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/45.jpg)
ω0 = 1 rad/s (f0 = ω0 / 2π = 0.159 Hz)
![Page 46: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/46.jpg)
pFR
CC 91.34
00
22
nH
C
RL 726.0
20
02
sradGHz /10283.612 9
0 1.000
f
f
nHRL
L 0.1270
011
pF
RLC 199.0
010
1
g1 = 1.5963 = L1, g2 = 1.0967 = C2,
nHRL
L 0.1270
033
pF
RLC 199.0
030
3
g3 = 1.5963 = L3, g4=1.000 =RL
500R
![Page 47: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/47.jpg)
![Page 48: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/48.jpg)
![Page 49: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/49.jpg)
Implementarea cu elemente concentrate (L, C) este utilizabila mai ales in zona frecventelor ceva mai reduse (RF) datorita: dificultatii de implementare a valorilor rezultante
pentru componente
dificultatii de a asigura toleranta (foarte mica) necesara pentru componente
![Page 50: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/50.jpg)
Impedanta vazuta la intrarea unei linii terminate cu ZL
Tehnologic e preferabil ca impedanta de capat sa fie: gol (ZL = ∞)
scurtcircuit (ZL = 0) Se obtine comportare: capacitiva
inductiva
lZjZ
lZjZZZ
L
Lin
tan
tan
0
00
lZjZ scin tan0,
lZjZ gin cot0,
Lscin XjZ ,
C
CginBj
XjZ
1
, l
CZ tan
10
lLZ tan0
![Page 51: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/51.jpg)
Schimbare de variabila
Cu aceasta schimbare de variabila definim reactanta unei inductante
susceptanta unei capacitati
Filtrul echivalent in Ω are frecventa de taiere la:
pv
ll
tantan
lLjLjXj L tan
lCjCjBj C tan
84tan1
lll
![Page 52: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/52.jpg)
Alegand sectiunile de linie in gol sau scurtcircuit sa fie λ/8 la frecventa de taiere dorita (ωc) si impedantele caracteristice corespunzatoare (L/C) vom obtine foarte precis la frecvente in jurul lui ωc o comportare similara cu a filtrului prototip La frecvente departate de ωc comportarea filtrului nu va
mai fi identica cu a prototipului (in situatii specifice trebuie verificata o comportare potrivita cu tipul de filtru dorit)
Scalarea in frecventa se simplifica: alegerea lungimii fizice pentru indeplinirea lungimii electrice λ/8 la frecventa dorita
Toate sectiunile de linii vor avea lungimi electrice egale (λ/8 ) si lungimi fizice comparabile, deci liniile se numesc linii comensurabile
![Page 53: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/53.jpg)
la frecventa ω=2∙ωc lungimile liniilor sunt λ/4
apare un pol suplimentar de atenuare la 2∙ωc (FTJ)
inductantele (de obicei in serie)
capacitatile (de obicei in paralel)
lll
tan24
lZjZ scin tan0,
0cot0, lZjZ gin
![Page 54: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/54.jpg)
periodicitatea functiei tangenta genereaza periodicitatea raspunsului in frecventa al circuitelor cu linii
raspunsul filtrului se repeta la fiecare 4∙ωc
tantan
p
c
p
c
v
l
v
ll
c
4
44
cLRLR PP 4 cinin ZZ 4
04 LRcLR PP cLRcLR PP 3 cLRcLR PP 5
![Page 55: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/55.jpg)
permite obtinerea cu sectiuni de linii a inductantelor si capacitatilor dupa scalarea prototipului pentru functia corespunzatoare (FTJ/FTS/FTB /FOB)
![Page 56: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/56.jpg)
Filtru trece jos de ordinul 4, cu frecventa de taiere de 4 GHz, de tip maxim plat (care sa functioneze pe 50Ω la intrare si iesire)
Tabel maxim plat sau relatii de calcul: g1 = 0.7654 = L1
g2 = 1.8478 = C2
g3 = 1.8478 = L3
g4 = 0.7654 = C4
g5 = 1 (nu are nevoie de adaptare suplimentara la iesire – apare la filtrele de ordin par echiriplu)
![Page 57: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/57.jpg)
![Page 58: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/58.jpg)
sradGHzc /105133.242 10
g1 = 0.7654 = L1, g2 = 1.8478 = C2,
g3 = 1.8478 = L3, g4 = 0.7654 = C4, g5 = 1 = RL
nHLR
Lc
523.1101
pF
R
CC
c
470.10
22
nHLR
Lc
676.3303
pF
R
CC
c
609.00
44
![Page 59: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/59.jpg)
![Page 60: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/60.jpg)
Parametrii filtrului prototip: g1 = 0.7654 = L1
g2 = 1.8478 = C2
g3 = 1.8478 = L3
g4 = 0.7654 = C4 Impedantele raportate ale liniilor z1 = 0.7654 = serie / scurt circuit
z2 = 1 / 1.8478 = 0.5412 = paralel / gol
z3 = 1.8478 = serie / scurt circuit
z4 = 1/ 0.7654 = 1.3065 = paralel / gol Scalarea in impedanta presupune inmultirea cu Z0 = 50Ω Toate liniile au lungimea λ/8 (lungime electrica 45°) la
4GHz
![Page 61: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/61.jpg)
![Page 62: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/62.jpg)
Filtrele realizate cu transformarea Richards beneficiaza de polul suplimentar de atenuare 2∙ωc
au dezavantajul periodicitatii in frecventa, de obicei se prevede un filtru trece jos suplimentar neperiodic daca e necesar
elemente concentrate
linii comensurate Richards
![Page 63: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/63.jpg)
Pentru ordin par al filtrului (N = 2, 4, 6, 8 ...) filtrele echiriplu trebuie sa fie inchise pe o impedanta de terminatie diferita de cea standard
Daca aplicatia nu suporta aceasta comportare, e necesara introducerea unei adaptari de impedanta suplimentare (transformator in sfert de lungime de unda, binomial ...)
)50(1 01 RRgN
![Page 64: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/64.jpg)
Acelasi filtru, echiriplu 3dB Tabel echiriplu 3dB sau relatii de calcul: g1 = 3.4389 = L1 g2 = 0.7483 = C2 g3 = 4.3471 = L3 g4 = 0.5920 = C4 g5 = 5.8095 = RL
Impedantele liniilor Z1 = 3.4389∙50Ω = 171.945Ω = serie / scurt circuit Z2 = 50Ω / 0.7483 = 66.818Ω = paralel / gol Z3 = 4.3471∙50Ω = 217.355Ω = serie / scurt circuit Z4 = 50Ω / 0.5920 = 84.459Ω = paralel / gol RL = 5.8095∙50Ω = 295.475Ω = sarcina
![Page 65: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/65.jpg)
maxim plat (ord 4)
echiriplu 3dB (ord 4)
![Page 66: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/66.jpg)
Filtrele echiriplu au nevoie de adaptare la iesire spre 50Ω pentru a functiona precis. Exemplu:
RL = 50Ω
RL = 295.48Ω
![Page 67: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/67.jpg)
Filtrele implementate cu transformarea Richards au anumite dezavantaje in ceea ce priveste implementarea practica
Identitatile/Transformarile Kuroda pot fi utilizate pentru a elimina o parte din aceste dezavantaje
l
l
l
l
V0
50Ω
50Ω
38.3Ω
27.1Ω
92.4Ω
65.3Ω
Se utilizeaza sectiuni de linie suplimentare pentru a obtine sisteme mai simplu de implementat in practica
Liniile suplimentare se numesc elemente unitare si au lungimi de λ/8 la frecventa de taiere dorita (ωc) fiind comensurate cu celelalte sectiuni de linie
![Page 68: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/68.jpg)
Identitatile Kuroda pot fi utilizate pentru a realiza urmatoarele operatii:
Separarea fizica a diferitelor stub-uri
l
l
l
l
V0
50Ω
50Ω
38.3Ω
27.1Ω
92.4Ω
65.3Ω
Transformarea stub-urilor serie in stub-uri paralel sau invers
Obtinerea unor impedante caracteristice mai “realizabile” pentru linii (~50Ω)
![Page 69: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/69.jpg)
4 echivalente de circuit
![Page 70: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/70.jpg)
4 echivalente de circuit
![Page 71: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/71.jpg)
In toate echivalentele de scheme Kuroda:
n:
inductantele si capacitatile reprezinta stub-uri scurtcircuitate sau in gol (obtinute prin transformarea Richards, de lungime λ/8)
blocurile reprezinta elemente unitare (linii de transmisie de impedanta caracteristica indicata si lungime λ/8)
1
22 1Z
Zn
![Page 72: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/72.jpg)
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Matrici ABCD, C4
1
01
YDC
BA
llYj
lZjl
DC
BA
cossin
sincos
0
0
+
![Page 74: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/74.jpg)
221
21
2
2
1
1
1
111
1
1
01
Zj
Zj
Z
jDC
BA
l tan
21
1cos
l
21sin
l
2
2, cotZ
jlZjZ gin
2
12
21
1
2
1
1
2
2 111
1
1
1
1
1
1
01
1
1
Z
Z
ZZj
Zj
Z
j
Zj
Z
jDC
BA
![Page 75: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/75.jpg)
10
1 Z
DC
BA
llYj
lZjl
DC
BA
cossin
sincos
0
0
+
![Page 76: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/76.jpg)
10
1
1
1
1
11
1
2
1
222
2
22
2
2
n
Zj
Z
nj
n
Zj
DC
BA
l tan
21
1cos
l
21sin
l
2
12
2
2
212
2
2
1
2
2
2
2
21
1
1
1
10
1
1
1
1
1
Z
Z
Z
nj
ZZn
j
n
Zj
Z
njn
Zj
DC
BA
2
1
2
1, tan
n
Zjl
n
ZjZ scin
![Page 77: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/77.jpg)
Prima schema
A doua schema
Rezultatele sunt identice daca alegem
Similar se pot demonstra si celelalte trei identitati
2
12
21
1
2 111
1
1
1
Z
Z
ZZj
Zj
DC
BA
2
12
2
2
212
21
1
1
1
Z
Z
Z
nj
ZZn
j
DC
BA
1
22 1Z
Zn
![Page 78: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/78.jpg)
Filtru trece jos de ordinul 4, cu frecventa de taiere de 4 GHz, de tip maxim plat (care sa functioneze pe 50Ω la intrare si iesire)
Tabel maxim plat sau relatii de calcul: g1 = 0.7654 = L1
g2 = 1.8478 = C2
g3 = 1.8478 = L3
g4 = 0.7654 = C4
g5 = 1 (nu are nevoie de adaptare suplimentara la iesire – apare la filtrele de ordin par echiriplu)
![Page 79: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/79.jpg)
Probleme: stub-urile in serie sunt extrem de
dificil de implementat in tehnologie microstrip
cu tehnologia microstrip e preferabil sa avem stub-uri in gol (scurtcircuit necesita un via-hole spre planul de masa)
cele 4 stub-uri sunt conectate in acelasi punct, o implementare care sa elimine/micsoreze cuplajul intre aceste linii e imposibila
nu e cazul aici, dar pot aparea situatii cand impedantele raportate sunt mult diferite de 1. Majoritatea tehnologiilor sunt concepute pentru linii cu impedante caracteristice in jur de 50Ω
l
l
l
l
V0
1
1
0.7654
0.5412
1.8478
1.3065
Se aplica transformarea Richards
![Page 80: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/80.jpg)
Identitatile Kuroda se refera intotdeauna la o schema cu o sectiune de linie in serie: se adauga elementele unitare (z = 1, l = λ/8) la fiecare capat al circuitului (adaugarea
nu modifica proprietatile filtrului acesta fiind adaptat la z = 1 la fiecare capat) se aplica una din identitatile Kuroda la fiecare capat si se continua un indicator al opririi procedurii este aparitia unei sectiuni de linie intre toate stub-
urile obtinute cu transformarea Richards
l
l
l
l
V0
1
1
0.7654
0.5412
1.8478
1.3065
l l
1 1
adaugat suplimentar
adaugat suplimentar
![Page 81: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/81.jpg)
Se aplica : Kuroda 2 (L,Z cunoscut C,Z) in partea stanga
Kuroda 1 (C,Z cunoscut L,Z) in partea dreapta
l
l
l
l
0.7654
0.5412
1.8478
1.3065
l l
1 1 K 2 (b) Z1=0.7654 Z2=1 n2=2.3065
1
22 1Z
Zn
K 1 (a) Z1=1 Z2=1.3065 n2=2.3065
l
l l
l
![Page 82: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/82.jpg)
Se mai adauga un element unitar in partea dreapta si se aplica Kuroda 2 de doua ori
l
l
l
l
1.8478
0.5412
0.4336
2.3065
l l
1 1.7654
l
0.5667
l
l K 2 (b) Z1=1.8478 Z2=0.5667 n2=1.3067
1
22 1Z
Zn
K 2 (b) Z1=0.4336 Z2=1 n2=3.3063
adaugat suplimentar
![Page 83: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/83.jpg)
Scalare la 50Ω
l l
0.5412 2.3065
l l
1.4336 1.7654
l
2.4145
l
0.7405
l
3.3063
V0
1
1
l l
27.06Ω 115.33Ω
l l
71.68Ω 88.27Ω
l
120.73Ω
l
37.03Ω
l
165.32Ω
V0
50Ω
50Ω
![Page 84: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/84.jpg)
![Page 85: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/85.jpg)
![Page 86: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/86.jpg)
![Page 87: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/87.jpg)
Transformarea Richard si identitatile Kuroda sunt utile mai ales pentru filtrele trece jos in tehnologiile in care stub-urile serie sunt dificil/imposibil de realizat (microstrip)
De exemplu in cazul filtrului trece banda de ordinul 3: se poate implementa inductanta serie utilizand K1-K2 capacitatea serie in schimb nu poate fi echivalata cu
un stub paralel
![Page 88: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/88.jpg)
Pentru situatiile in care implementarea cu Richards + Kuroda nu ofera solutii practice se folosesc structuri de circuit numite inversoare de impedanta si admitanta
L
inZ
KZ
2
L
inY
JY
2
![Page 89: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/89.jpg)
Cel mai simplu exemplu de inversor de impedanta/admitanta este transformatorul in sfert de lungime de unda (C2)
Lin
R
ZZ
21
L
inZ
KZ
2
L
inY
JY
2
![Page 90: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/90.jpg)
Inversoarele de impedanta/admitanta pot fi utilizate pentru a schimba structura filtrelor in forme realizabile
Exemplu FOB
![Page 91: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/91.jpg)
Elementele serie pot fi eliminate prin introducerea unui inversor de admitanta
![Page 92: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/92.jpg)
1
0
1
1
2
2
1
1
1
1
Z
LjCj
CjLj
Y
1
0
1
1
2
0
2
2
1
1
11
1
1
Z
CjLj
Z
CjLj
Y
2
0
1
nnnn CLCL 1
1
1
1
2
0
1
L
C
C
L
Z
2
2
2
2
C
L
C
L
YY
Rezultat similar se obtine si pentru filtrul trece banda
Un grup LC serie introdus in serie se poate inlocui cu un grup LC paralel introdus in paralel incadrat de doua inversoare de admitanta
Echivalenta celor doua scheme se demonstreaza prin obtinerea aceleiasi admitante de intrare
Echivalenta completa se obtine prin incadrarea grupului simulat intre doua invertoare de admitanta
![Page 93: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/93.jpg)
Cel mai uzual se foloseste transformatorul in sfert de lungime de unda
Realizare cu elemente concentrate
![Page 94: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/94.jpg)
Realizare cu linii
2tan0
ZK
2
0
1
Z
K
KX
0
1 2tan
Z
X
2tan0
YJ
2
0
1
Y
J
JB
0
1 2tan
Y
B 0
![Page 95: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/95.jpg)
Utilizand inversoare de admitanta se pot implementa filtrele prototip utilizand un singur tip de element
10
1,
1,0gg
LRK
aA
1
,
1,
nn
Bna
nngg
RLK
1
1,,
1,11,
kk
kaka
nkkkgg
LLK
![Page 96: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/96.jpg)
Utilizand inversoare de admitanta se pot implementa filtrele prototip utilizand un singur tip de element
10
1,
1,0gg
CGJ
aA
1
,
1,
nn
Bna
nngg
gCJ
1
1,,
1,11,
kk
kaka
nkkkgg
CCJ
![Page 97: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/97.jpg)
Pentru filtrele prototip cu inversoare exista 2∙N+1 parametri si N+1 ecuatii care asigura echivalenta raspunsului deci N parametri pot fi alesi din considerente oarecare se pot alege valorile reactantelor, urmand ca parametrii inversoarelor
sa rezulte din calcul se pot alege convenabil inversoarele, urmand ca reactantele sa rezulte
din ecuatiile de echivalare Principiul se poate aplica si pentru filtrele trece banda/opreste
banda, acestea putand fi realizate din N+1 inversoare si N rezonatori (grupuri LC serie sau paralel cu frecventa de rezonanta ω0) conectate fie in serie fie in paralel intre inversoare FTB se realizeaza cu
▪ grup LC serie conectat in serie intre inversoare ▪ grup LC paralel conectat in paralel intre inversoare
FOB se realizeaza cu ▪ grup LC paralel conectat in serie intre inversoare ▪ grup LC serie conectat in paralel intre inversoare
![Page 98: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/98.jpg)
Impedanta de intrare intr-o linie (stub) scurtcircuitata sau lasata in gol la capat manifesta comportament rezonant care poate fi utilizat pentru implementarea rezonatoarelor
lZjZ
lZjZZZ
L
Lin
tan
tan
0
00
lZjZ scin tan0,lZjZ gin cot0,
![Page 99: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/99.jpg)
Linie in scurtcircuit Pentru frecventa (ω0) la
care l = λ/4 se obtine un circuit rezonant LC paralel linia are comportament
capacitiv pentru frecvente mai mici (l>λ/4)
linia are comportament inductiv pentru frecvente mai mari (l<λ/4)
Discutie similara pentru linia in gol (LC serie la frecventa la care l=λ/4)
![Page 100: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/100.jpg)
Pentru cazul particular in care se implementeaza inversoarele de admitanta cu transformatoare in sfert de lungime de unda si impedanta caracteristica Z0
FTB – stub-uri paralel scurticuitate la l = λ/4
FOB – stub-uri paralel in gol de lungime l = λ/4 n
ng
ZZ
4
00
n
ng
ZZ
0
0
4
![Page 101: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/101.jpg)
Similar cu o tema de proiect Continuarea amplificatorului C9 Filtru trece banda de ordinul 4, f0 = 5GHz,
banda 10 % Tabel maxim plat sau relatii de calcul:
n gn Z0n(Ω)
1 0.7654 5.131
2 1.8478 2.125
3 1.8478 2.125
4 0.7654 5.131
![Page 102: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/102.jpg)
![Page 103: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/103.jpg)
![Page 104: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/104.jpg)
Problemele filtrelor realizate cu linii ca rezonatoare si invertoare de impedanta stub-uri in scurtcircuit (via-hole) pentru FTB
deseori impedantele caracteristice pentru stub-uri rezulta de valori dificil de realizat in practica (2.125Ω)
24
ll
l l
2.125Ω 5.131Ω
l l
50Ω 50Ω
l
50Ω
l
2.125Ω
l
5.131Ω
V0
50Ω
50Ω
![Page 105: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/105.jpg)
Analiza sectiunilor de linii cuplate se face punand in evidenta comportarea pe modul par si pe modul impar
Aceste moduri sunt caracterizate de impedantele caracteristice de mod par/impar a caror valoare va impune in functie de tehnologia utilizata geometria liniilor (latime/distanta dintre linii)
![Page 106: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/106.jpg)
Mod par – caracterizeaza semnalul de mod comun de pe cele doua linii
Mod impar – caracterizeaza semnalul de mod diferential dintre cele doua linii
![Page 107: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/107.jpg)
![Page 108: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/108.jpg)
Filtru trece banda cu rezonanta la θ=π/2 (l=λ/4)
![Page 109: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/109.jpg)
Un filtru cu N+1 sectiuni de linii cuplate
![Page 110: Curs 12 2018/2019rf-opto.etc.tuiasi.ro/docs/files/DCMR Curs 12_2018.pdf · 2019-01-11 · banda de taiere cu dezavantajul existentei unor variatii (riplu) in banda de trecere Filtre](https://reader034.fdocumento.com/reader034/viewer/2022042108/5e88b5f9f6969a7c323096f6/html5/thumbnails/110.jpg)
Se modeleaza
liniile
inversoarele
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Se obtine comportare de tip FTB de ordin 2 cu 3 sectiuni de linii cuplate
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Se calculeaza inversoarele
Se calculeaza liniile cuplate (toate de lungime l=λ/4)
1
102 g
JZ
Nn
ggJZ
nn
n ,2,2 1
0
1
102
NN
Ngg
JZ
2
000,0 1 ZJZJZZ nnne
2
000,0 1 ZJZJZZ nnno 1,1 Nn
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Similar cu o tema de proiect Continuarea amplificatorului C10 Filtru trece banda de ordinul 4, f0 = 5GHz,
banda 10 % Tabel echiriplu 0.5dB (gi) plus relatii de calcul:
n g Z0Jn Z0e Z0o 1 1.6703 0.306664 70.04 39.37 2 1.1926 0.111295 56.18 45.05 3 2.3661 0.09351 55.11 45.76 4 0.8419 0.111294 56.18 45.05 5 1.9841 0.306653 70.03 39.37
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Separarea fizica a doua sectiuni de linie produce un cuplaj capacitiv intre cele doua linii
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Din lungimea fizica a rezonatoarelor o portiune se foloseste pentru a crea schema de inversor (ramane φ=π, l=λ/2)
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Se calculeaza inversoarele (similar linii cuplate)
Se calculeaza susceptantele cuplajului
Se calculeaza lungimile de linii care trebuie “imprumutate” pentru realizarea inversoarelor
Se calculeaza lungimile electrice ale liniilor
1
102 g
JZ
Nn
ggJZ
nn
n ,2,2 1
0
1
102
NN
Ngg
JZ
1,1,
12
0
NnJZ
JB
n
nn
1,1,2tan 0
1 NnBZ nn
NiBZBZ iiiii ,1,2tan2tan2
1
2
110
1
0
1
1
1,1,0 Nnn
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Parametri ABCD (C4) linie scurta, model cu elemente concentrate valid
lA cos
lYjC sin0
lZjB sin0
lD cos
3
11Z
ZA
3
1
ZC
3
2121
Z
ZZZZB
3
21Z
ZD
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Element paralel capacitiv
Elementele in serie egale, inductive
Schema echivalenta
lYjZ
sin
1
0
3
3
2
3
1 11cosZ
Z
Z
Zl
2
tansin
1cos1cos 00321
lZj
l
lZjlZZZ
2tan
20
lZ
X
lZ
B sin1
0
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In functie de valoarea impedantei caracteristice
impedanta ridicata Z0 >>
impedanta scazuta Z0 <<
lZX 0
lYB 0
hZZ 0
4
l
lZZ 0
4
l
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Se pot crea filtre trece jos Se utilizeaza
linii cu impedanta caracteristica mare pentru a implementa o inductanta
linii cu impedanta caracteristica mica pentru a implementa o capacitate
De obicei se utilizeaza cea mai mare si cea mai mica impedanta permisa de tehnologie
hZ
RLl 0
0R
ZCl l
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Nu toate liniile au aceeasi lungime deci problema periodicitatii in frecventa a raspunsului e mai putin importanta
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FTJ cu frecventa de taiere 8GHz, de ordinul 6. Impedanta maxima realizabila este 150Ω iar cea minima 15Ω.
n gn L/Cn Z θn[rad] θn[°]
1 0.5176 0.206pF 15 0.155 8.90
2 1.4142 1.407nH 150 0.471 27.01
3 1.9318 0.769pF 15 0.580 33.21
4 1.9318 1.922nH 150 0.644 36.89
5 1.4142 0.563pF 15 0.424 24.31
6 0.5176 0.515nH 150 0.173 9.89
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Laboratorul de microunde si optoelectronica http://rf-opto.etti.tuiasi.ro [email protected]