ece 563 & tcom 590 microwave engineering microwave passive components october 21, november 4,...
TRANSCRIPT
ECE 563 & TCOM 590Microwave Engineering
Microwave Passive Components
October 21, November 4, 2004
Two-PortDevice
I1+V1
-
+V2
-
I2
Network Matrices
Low frequency circuits - use Z, Y, H parameters
Z: V1 = z11I1 + z12I2 Y: I1 = y11V1 + y12V2
V2 = z21I1 + z22I2 I2 = y21V1 + y22V2
H: V1 = h11I1 + h12V2 I2 = h21I1 + h22V2
Network Matrices
achieve todifficult bemay opens & shortsbut
ports,at measured becan they difficult, sonot I&V
directly, measure todifficult EH,Y, Z,microwavesFor
circuited)-open(input
shorted)(output
02
112
01
111
1
2
I
V
V
Vh
I
Vh
Network Matricesmatrix scattering and aves,consider w Instead,
E Y1+
E Y1- E Y2
-E Y2
+
)eEeE(Z
1H
)understood(e eEeEE
zj1y
zj1y
TE1x
tjzj1y
zj1y1y
Network Matrices
outpower -port intopower port nth at power
)aaaa(2
1HE Re
2
1P
)aa(Z
1H & )aa(ZE
:ports-n todgeneralize be can
)aa(Z
1H & )aa(ZE
Z
eEa ,
Z
eEa Define
*nn
*nn
*xyn portave
nn
TE
xnnnTEyn
11
TE
1x11TE1y
TE
zj1y
1
TE
zj1y
1
Scattering Matrices for a 2 port
port.-2 afor Matrix Scattering a
of formsimpliest theis which a
a
S S
S S
a
a
aSaSa
aSaSa
:port 2 aConsider .a waves
incident of in terms a wavesreflected all Describe
2
1
2221
1211
2
1
2221212
2121111
n
n
a1+
a1-
a2+
a2-
Scattering Matrices for an n port
nn2n1n
2221
n11211
n
2
1
n
2
1
--
SS S
:
S S
SS S
matrix scatteringS
;
a
:
a
a
a ;
a
:
a
a
aaSa
-
Physical Interpretation for a 2 port
matched). 2port (with
oneport at t coefficienon transmissia/a
so ,0a since aaaa
Also,
one.port at t coefficien reflectiona/a
0a since a aaa
:matched 2port With
1221
21212221212
1111
21112121111
S
SSS
S
SSS
a1+
a1-
a2+=0
a2-
ZL=ZTE
Matchedload
Scattering Matrices for an n port
nnnn
nn
nn
nn
nnnn
nn
/aaS matched; others all
n with port at t coefficien reflectionS
general)(in t coefficien reflection Where
dB)(in log 20- RL LossReturn
1
1or VSWR note
;/aaS matched; others all
n with port at t coefficien reflectionS
generalIn
VSWR
VSWR
a
a
aa
aa
j
j
jj
jj
-
Scattering Matrices for an n port
iport tojport at t coefficienon transmissiST
then,matched ports all If
general)(in t coefficienion transmiss T where
dB)(in T log 20- LossInsertion
aa circuit theofout power
aa circuit theintopower
:portjth At the matched. others allwith
iport tojport at t coefficienon transmissiS
generalIn
ijij
ij
ij
*jj
*jj
ij
-
Scattering Matrices for an n port
ces.circumstan these
under jport at cofficient reflection powerSS
1port in power / 2port out power
aa/aaSS Example, matched. are
others all and jport tofed ispower when iport
tojport from cofficient coupling powerSS
lyrespective2,3,...n ports to1port fromt coefficien
coupling powerSS,...,SS, SS
*jjjj
*
11
*
22*
2121
*ijij
*1n1n
*3131
*2121
-
Scattering Matrices for an n port
ns.combinatio their and components microwave
individual theofmany of tiverepresenta
are which networks losslessfor derived
becan matrix -S theof elements variousthe
between ionshipsinterrelat gsimplifyinCertain
-
Basic Properties of Scattering Matrix Elements (S parameters): Lossless System
*
jj
*
nn
*
22
*
11
th
i
th
T
aaaaaaaa
port. j in the fedpower the
toup sum should ports all leavingpower allthen
j) ofexception (with then , ... 2, 1,i ,0a
erminatedproperly t are others all andport
j at thein fed ispower if system, lossless Since 2)
ji transpose T whereS Sor , ,
)components ferrite no (ex. system Reciprocal )1
jiSS jiij
-
Basic Properties (continued)
-
)(unity ismatrix S row ofcolumn any in
termsof squared amplitude of sum 1
1
find aaaaaaaa
expressionpower with
or
of termsurvivingonly theis where
2*
1
*
*1
*22
*11
*
jj
*
nn
*
22
*
11
22
11
ijijij
n
iijij
jnjjjjj
jnjnjj
jjj
SSS
SS
SSSSSS
to
combine
aSaaSa
aaaSa
aSaBy
Basic Properties (continued)
-
kjn
k2j22k1j11
*2222
*1212
*2121
*1111
*2222
*2121
*1212
*1111
aaa
, ,aaa ,aaa
matched. are others all
andk & j portsonly into fed ispower Assume )3
using equations 1
first two thefrom follows also 1
1
1
:port twoaFor
nknj
kjkj
jiij
SS
SSSS
SSSSSS
SSSS
SSSS
SSSS
Basic Properties (continued)
-
*
kk
*
jjk*
j
n
1i
**
kj
n
1i
*
*
kk
n
1i
**
jj
n
1i
*
*
kk
*
jj
*
nn
*
22
*
11
aaaaaaaa
aaaa
find toipsrelationsh theseCombine
aaaaaaaaaa
k & j portsat input powers total
equals ports all leaving powers all of Sum
ikijikij
ikikijij
SSSS
SSSS
Basic Properties (continued)
-
constant)c ,a c j- a anda c j a(let phase
ofout 90 and zero-non are a and a that sok & j ports
at fed are signals theifor (1) eqn. ,0SSSS
phase-in and zero-nonboth select wephase and
magnitude toregardswith arbitrary area and a Since
0aaSSaaSS
find to1SS Use
*
k
*
jkj
kj
n
1iik
*ij
*ikij
kj
k*
j
n
1iik
*ij
*
kj
n
1i
*ikij
n
1i
*ijij
Basic Properties (continued)
-
zero. is row)(or column other any
of termsingcorrespond of conjugatecomplex by the
multiplied row)(or column any of termsof Sum
0SSSS
(2) and (1) eqns. From
(2) eqn. 0,SSSS
,0aa c j SSSS
n
1iik
*ij
n
1i
*ikij
n
1iik
*ij
*ikij
*
kk
n
1iik
*ij
*ikij
Basic Properties (continued)
-
n , ... 2, 1, k j,k ,0
2)column in termingcorrespond of
conjugate(complex 1)(column 0
2) rowin termingcorrespond
of conjugate(complex 1) (row 0
:port For two
n
1i
*
*2221
*1211
*2212
*2111
ijikSS
SSSS
SSSS
Examples: Tee Junction
• Waveguide, coax, stripline, junction with 3 ports and used for power dividers, mixers, sampling junctions
• axis of side arm (2) is parallel to E of main guide [(1) to (3)]. Power fed at port 2 appears at (1) & (3) as = magnitude, opposite phase.
H Plane Tee Junction
-
desired). is (this ports allat
matchedperfectly i.e. ,0S that Assume
symmetry todueequality
entering) 2 leaving, 1 ,subscripts (note
332211
3212
SS
SS
H Plane Tee Junction
-
3not but 2any match - matched bet can'
Tee"" plane H for the inputs 3 all ,impossible
2/1SSbut ,0SS0SS)0(S(0)S
col.2& col.1 choose ,0 SS also
,2/1S find ,2/1S and 1 rowby and
,2/1S1S0S :2 rowby 1, SS Since
system) reciprocal(by S recall
0
0
0
1213*
1213*
1213*
12*
12
*n
1i
*ijik
2
13
2
12
2
12
2
12
2
12
n
1i
*ijij
ij
1213
1212
1312
jiS
SS
SS
SS
S
H Plane Tee Junction
-
2/1SS4/1S2/1SS
SS0S)2/1(S)2/1(
0SS)0(SSS and ,2/1SS
1SSS also ,2/1S
1S0Sagain ,
0
(matched) , 0 and
l)symmetrica are 3 & (1 ,SS with again,Try
1311
2
11
2
11
2
11
13111311
*121312
*1211
2
11
2
13
2
11
2
12
2
13
2
12
2
12
2
12
111213
1212
131211
22
3311
SSS
SS
SSS
S
S
H Plane Tee Junction
tee.hybrid the
isjunction port 4important an port tee, -3 matched
completely a obtaining of difficulty theof Because
TEE HYBRID
lsymmetrica 3 &1 and matched 2port with Tee Plane
H ofMatrix Scattering ,
/21 2/1 /21
2/1 0 2/1
/21 - 2/1 /21
S
Hybrid Tee
-
0S ,SS 4,at none and 2, and 1at
phase opposite amplitude, equal produces 3at Input )3
0S ,SS 3,at none
and 2 & 1at amplitude equal produces 4at Input )2
0SSSS
junctions 4 allat matched bemay it that Assume )1
432313
342414
44332211
Hybrid Tee
-
0 0 1 1
0 0 1- 1
1 1- 0 0
1 1 0 0
)2/1(
2/1SS,1SS ,
0 0 S S
0 0 S- S
S S- 0 0
S S 0 0
.propagate)
tcan' charge sobroken boundary (note ,0SS
versa. viceand 2at output no produces 1at Input )4
1413
2
13
2
13
1414
1313
1413
1413
2112
S
S
Hybrid Tee
-
oscillator theoffrequency the
stabilize tof ~output tor discrimina microwave a)
: tees2 of use 4)
isolation.
source also Note 4.&3at signals same use Doubler, 3)
2&1at crystals 3 into LO & 4 into signal Mixer with 2)
) 2, & 1in phase ofout 3 into
or 2&1equally out 4 into(power divider Power )1
sketch) previous refer to (numbers nsApplicatio
Hybrid Tee
-
circulatorport -4 b)
: tees2 of use 4)
)(Continued nsApplicatio
Directional Coupler
4 port microwave junction
Power in 1 couples to port 2 with a fraction to port 4 and virtually none to 3
Power in 2 couples to port 1 with fraction to 3 and none to 4
All ports well matched so Sii=0
Directional Coupler
-
34122314
2
34
2
14
2
34
2
23
2
23
2
12
2
14
2
12
3414
3423
2312
1412
44332211
SS and ,SS ,So
1SS
1SS
1SS
1SS
0 S 0 S
S 0 S 0
0 S 0 S
S 0 S 0
S
0SSSS Matrix, Scattering
Directional Coupler
-
constants
real are c ,c and
1cc where
0 c 0 jc
c 0 cj 0
0 cj 0 c
cj 0 c 0
S
1cc and jcS 0SS ,0c if
0)S(Sc,0ScSc
cconstantSS Let
)same( ,0SSSS0SSSS
0SSSS0SSSS Also
21
22
21
12
12
21
21
22
2121414
*141
14*
141141*
141
13412
*1214
*1412
*3414
*2312
*1214
*1412
*3423
*1412
Directional Coupler (D/C)
From this S matrix– Power coupled to port 4 is 90o out of phase relative to
power at port 2. (Same for power coupled to 3 compared to 1 for power in reverse direction.
– Lines 1&2 and 3&4 are identical and any can be used as primary line while others serve as secondary
– D/C with c2 small(<<1): widely used for power moni-toring in forward and reverse directions. Reflections from imperfectly matched load or antenna.
– D/C with c2 significant fraction of unity used as power dividers
Directional Coupler Parameters
Balanced Amplifier Configuration (ref: Gonzalez,
Microwave Transistor Amplifiers)
Branch Line Coupler (ref: Gonzalez, Microwave
Transistor Amplifiers)
Branch-Line Coupler
2
0
01
0
01
0
02
2001
ZZ
1
ZZ
Z
Z
and ])/(Z-1/[1 log 10C
tcoefficien couplingCLet
Z
(ref. Pozar, Microwave Electronics)
Lange Directional Coupler
Lange Directional Coupler
• Popular implementation of the quadrature hybrid in microstrip line form.
• The interdigital form of the microstrips permits a very compact geometric size and provides for tight coupling.
• Typically coupling values range between –5 and – 1 dB.
• Octave or more of bandwidth.
TEM Directional Couplers
Pair of coupled transmission lines has coupling with wave induced on secondary line is in a direction opposite to that of primary
TEM Directional Coupler
1sincos)1(
1sin
:conserved isPower
sincos1
1
/2 length line electrical andt coefficien
coupling ,sincos1
sin
222
222
*
11
*
22*
11
*
44
2
2
1
2
g
21
4
aa
aa
aa
aa
ja
a
wherej
j
a
a
TEM Directional Coupler
-
sectionsouter 2 theof coupling theis
sectioncenter theof coupling theis )(
coupler) /43( ,)3sin(sin
coupler) /4( ,sin
1for
3
31
3
1
3
1
4
j
j
ej
eja
a
Coupled Coplanar Striplines
Power on a coupled TEM-transmission line propagates as a composite of two possible modes: one even and one odd.
Coupled Coplanar Striplines
-
2o
'oo
2e
'ee
o
'o
r
ooe
'e
r
oe
oooooe
oooeooooe
oooe
k1k ),b
sw
2(cotanh)
b
w
2tanh(k
k1k ),b
sw
2tanh()
b
w
2tanh(k
where)k(K
)k(K30Z and
)k(K
)k(K30Z
1
1ZZ and
1
1ZZ
;ZZ Z;ZZ
ZZ
Coupled Coplanar Striplines
-
s/b. amd then w/b
,k and k then ),K(k and )K(k then found, becan
Zand Z two the, Zand desired aFor :Design
)nomographs of use is ve(Alternati
)2sin1(
)]1)(1[()K(k
KindFirst
theof Integral elliptic complete)K(k where
oeoe
oooe0
2/12/
0
0
2/120
1
0
2o
o
dk
dttkt