Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente...
Transcript of Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente...
![Page 1: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/1.jpg)
Curs 9-10 2016/2017
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2C/1L, DCMR (CDM) Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2
E – 50% din nota
probleme + (2p prez. curs) ▪ 3prez.=+0.5p
toate materialele permise Laborator – sl. 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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RF-OPTO
http://rf-opto.etti.tuiasi.ro
Fotografie
de trimis prin email: [email protected]
necesara la laborator/curs
▪ <=C3, +1p
▪ <=C5, +0.5p
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Personalizat
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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]
![Page 7: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/7.jpg)
![Page 8: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/8.jpg)
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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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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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)
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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
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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
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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.
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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
Tabel echiriplu 0.5dB sau relatii de calcul: g1 = 1.5963 = L1, g2 = 1.0967 = C2, g3 = 1.5963 = L3, g4=1.000 =RL
![Page 42: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/42.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 43: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/43.jpg)
ω0 = 1 rad/s (f0 = ω0 / 2π = 0.159 Hz)
![Page 44: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/44.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 45: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/45.jpg)
![Page 46: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/46.jpg)
![Page 47: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/47.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 48: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/48.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 49: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/49.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 50: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/50.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 51: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/51.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 52: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/52.jpg)
permite obtinerea cu sectiuni de linii a inductantelor si capacitatilor dupa scalarea prototipului pentru functia corespunzatoare (FTJ/FTS/FTB /FOB)
![Page 53: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/53.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 54: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/54.jpg)
![Page 55: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/55.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 56: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/56.jpg)
![Page 57: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/57.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 58: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/58.jpg)
![Page 59: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/59.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 60: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/60.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 61: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/61.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 62: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/62.jpg)
maxim plat (ord 4)
echiriplu 3dB (ord 4)
![Page 63: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/63.jpg)
Filtrele echiriplu au nevoie de adaptare la iesire spre 50Ω pentru a functiona precis. Exemplu:
RL = 50Ω
RL = 295.48Ω
![Page 64: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/64.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 65: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/65.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 66: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/66.jpg)
4 echivalente de circuit
![Page 67: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/67.jpg)
4 echivalente de circuit
![Page 68: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/68.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 69: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/69.jpg)
![Page 70: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/70.jpg)
Matrici ABCD, C4
1
01
YDC
BA
llYj
lZjl
DC
BA
cossin
sincos
0
0
+
![Page 71: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/71.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 72: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/72.jpg)
10
1 Z
DC
BA
llYj
lZjl
DC
BA
cossin
sincos
0
0
+
![Page 73: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/73.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 74: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/74.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 75: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/75.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 76: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/76.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 77: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/77.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 78: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/78.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 79: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/79.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 80: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/80.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 81: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/81.jpg)
![Page 82: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/82.jpg)
![Page 83: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/83.jpg)
![Page 84: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/84.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 85: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/85.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 86: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/86.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 87: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/87.jpg)
Inversoarele de impedanta/admitanta pot fi utilizate pentru a schimba structura filtrelor in forme realizabile
Exemplu FOB
![Page 88: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/88.jpg)
Elementele serie pot fi eliminate prin introducerea unui inversor de admitanta
![Page 89: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/89.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 90: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/90.jpg)
Cel mai uzual se foloseste transformatorul in sfert de lungime de unda
Realizare cu elemente concentrate
![Page 91: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/91.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 92: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/92.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 93: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/93.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 94: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/94.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 95: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/95.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 96: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/96.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 97: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/97.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 98: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/98.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 99: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/99.jpg)
![Page 100: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/100.jpg)
![Page 101: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/101.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 102: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/102.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 103: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/103.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 104: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/104.jpg)
![Page 105: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/105.jpg)
Filtru trece banda cu rezonanta la θ=π/2 (l=λ/4)
![Page 106: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/106.jpg)
Un filtru cu N+1 sectiuni de linii cuplate
![Page 107: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/107.jpg)
Se modeleaza
liniile
inversoarele
![Page 108: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/108.jpg)
Se obtine comportare de tip FTB de ordin 2 cu 3 sectiuni de linii cuplate
![Page 109: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/109.jpg)
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
![Page 110: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/110.jpg)
Similar cu o tema de proiect Continuarea amplificatorului C11 Filtru trece banda de ordinul 4, f0 = 5GHz,
banda 10 % Tabel echiriplu 0.5dB sau 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
![Page 111: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/111.jpg)
![Page 112: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/112.jpg)
![Page 113: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/113.jpg)
![Page 114: Curs 9-10 2016/2017rf-opto.etti.tuiasi.ro/docs/files/DCMR Curs 10_2016.pdf · Minim 7 prezente (curs+laborator) Curs - sl. Radu Damian Marti 18-20, P2 E – 50% din nota probleme](https://reader034.fdocument.pub/reader034/viewer/2022052310/604a49300f0c3347583ff89b/html5/thumbnails/114.jpg)
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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linii microstrip
strat dielectric
metalizare totala (plan de masa)
trasee care fixeaza
▪ impedanta caracteristica
▪ lungime fizica/electrica
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Linie quasi TEM
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Se echivaleaza linia cu o linie cu dielectric omogen echivalent
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~ Aproximativ TEM
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~ Aproximativ TEM
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Calcul empiric
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Calcul empiric
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Pentru impedante mari e nevoie de latimi mici ale traseelor Pentru impedante mici e nevoie de latimi mari ale traseelor
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Standardizare
dimensiuni in mil
1 mil = 10-3 inch
1 inch = 2.54 cm
Inaltimea conductoarelor
in functie de greutatea cuprului
uncii / picioare pătrate (oz/ft2)
1oz=28.35g şi 1ft=30.48cm
Greutatea cuprului depus
Grosimea stratului
oz/ft2 g/ft2 inch mm
0.5 14.175 0.0007 0.0178
1.0 28.35 0.0014 0.0356
2.0 56.7 0.0028 0.0712
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Tipic inaltimea straturilor de dielectric de asemenea standardizat in mil
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Constanta dielectrică
relativă
Factorul de pierderi
dielectrice
Conductivi-tate termică
Coeficient liniar de
expansiune
Coeficient de temperatură a
lui r
Material - - W/cm/K ppm/K ppm/K
Al2O3 (99.5%) 9.8 0.0001 0.37 6.3 +136
Al2O3 (96%) 9.4 0.001 0.35 6.4 -
Safir 9.4;11.6 0.0001 0.42 6.0 +110-+140
Sticlă quarţ 3.78 0.0001 0.017 0.55 +13
Sticlă Corning 7059
5.75 0.0036 0.012 4.6 -
BeO Ceramic (98%)
6.3 0.006 2.1 6.1 +107
TiO2 85 0.004 0.05 7.5 -575
Tetratitanat de Ba (BaTi4O9)
37 0.0005 0.02 9.4 -26
Zirconat 20-40 0.002 - 5.0 -130-+100
GaAs 12.9 0.002 0.46 5.7 -
Si 11.9 0.015 1.45 4.2 -
Ferită 9-16 0.001 - - -
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In scheme: >Tools>LineCalc>Start
Pentru linii Microstrip >Tools>LineCalc>Send to Linecalc
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1. Definire (receptie din schema) substrat 2. Introducere frecventa 3. Introducere date de intrare Analiza: W,L Z0,E sau Ze,Zo,E / la f [GHz] Sinteza: Z0,E W,L / la f [GHz]
1
2
3
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Se poate utiliza pentru:
linii microstrip MLIN: W,L Z0,E
linii cuplate microstrip MCLIN: W,L Ze,Zo,E
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http://rf-opto.etti.tuiasi.ro linii de transmisie Rogers
relatii dependente de
▪ t, inaltimea metalizarilor
▪ f, frecventa
relatii pentru
▪ microstrip
▪ strip
▪ linii cuplate
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http://rf-opto.etti.tuiasi.ro note de aplicatii importante Agilent
decuplarea circuit de semnal/circuit de polarizare
detalii de implementare a circuitelor de polarizare pentru tranzistoarele cu microunde
Appcad contine instrumente pentru calculul schemelor de polarizare
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Unirea celor doua scheme
C11 – amplificator (var 4/S36-37)
C13 – filtre
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scopul: echilibrarea caracteristicii amplificatorului (maxim la frecventa centrala)
se prefera reglarea lungimii liniilor de la iesirea amplificatorului
▪ micsorarea afectarii zgomotului
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Se introduce modelul de substrat Liniile/liniile cuplate se calculeaza cu Linecalc
pentru acelasi substrat
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Se folosesc componente din paleta Transmission Lines – Microstrip
MSUB - substrat
MLIN – linie serie
MLOC – stub paralel in gol
MTEE – modelare conexiune cu stub in paralel
MCFIL – sectiune de filtru cu linii cuplate (alternativa mai precisa decat MCLIN – se tine cont de faptul ca doua sectiuni succesive sunt in fizic alaturate)
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E necesara atentie la completarea parametrilor pentru MTEE si MCFIL prin verificarea in schema a latimii liniilor conectate la fiecare terminal
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Se constata o deplasare a benzii obtinute (albastru) spre frecvente mai mici fata de modelele ideale (rosu) datorat diferentei MCFIL / MCLIN
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Reglaj de lungimi la elementele filtrului pentru reglarea frecventelor in jurul f0 = 5GHz
Introducere L (soc RF) si C (decuplare)
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Inlocuirea (fictiva) a tranzistoarelor si elementelor concentrate (LC) cu elemente pentru care ADS are informatii despre capsule
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Laboratorul de microunde si optoelectronica http://rf-opto.etti.tuiasi.ro [email protected]