ECE 563 & TCOM 590 Microwave Engineering Microwave Passive Components October 21, November 4, 2004.

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


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

-


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

-


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

-


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


-

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


-

*

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


-

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


-

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


-

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


-

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


-

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


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.


-

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


-

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

ECE 563 & TCOM 590 Microwave Engineering Microwave Passive Components October 21, November 4, 2004.

Documents

n portscattering matrices

tee junctionwaveguide

n portphysical interpretation

coupled temtransmission

secondary line

primary line

power dividers

power fed