4. Network Analysis

8/16/2019 4. Network Analysis

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MICROWAVE NETWORK ANALYSIS


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Outline2

1. Impedance and Admittance Matrix2. Scattering Matrix3. Transmission Matrix4. Signal Flow Graph


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N- port Microwave Network3

Closed wa eg!ide


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Admittance "etwor# 4

$ri ing port j with the c!rrent I j % openother ports &so I k = ' (or k ≠ j )% and open)circ!it oltage at port I => Z ij$ri ing port * with the oltage V * % shortother ports &so V k = ' (or k ≠ j+% and short)circ!it c!rrent at port I => Y ij


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,eciprocal "etwor#s5

Consider the ar-itrar with short circ!its placed at

all terminal planes except those o( ports 1 and 2


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,eciprocal "etwor#s6

/0 is s mmetr matrix / is s mmetr matrix


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Lo le Network7

In are independent


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Lo le Network !Cont"#8

5et all port c!rrents -e 6ero except (or I m and I n 7


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9

8x7 8 al!ation o( Impedance 9aramete

Find the Z parameter o(two port T)networ# shownin the (ig!re

Z 11 can -e (o!nd as port 1 inp!t impedance when port 2 is open)circ!ited

Z 12 can -e (o!nd as meas!ring the open)circ!ited at when I 2 is applied


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10

8x7 8 al!ation o( Impedance 9aramete

Z 11 can -e (o!nd as port 2 inp!t impedance when port 1 is open)circ!ited


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Outline11

1. Impedance and Admittance Matrix2. Scattering Matrix7

,eciprocal and 5ossless "etwor#A Shi(t in ,e(erence 9lanes

9ower :a e and Generali6ed Scattering 9arameters

3. Transmission Matrix4. Signal Flow Graph


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12

Scatterin$ Matri%

:hen tr ing to meas!re oltages and c!rrents at microwa e (re;!encdirect meas!rement in ol e the magnit!de and phase o( a wa e tra elingi en direction or o( the standing wa e8;!i alent oltages% c!rrent and the relate impedance and admmatrices -ecome somewhat o( a-straction with high)(re;!enc networ#

The scattering matrix is more in accord with direct meas!rement awith the ideas o( incident% re(lected and transmitted wa e.


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13

Scatterin$ Matri% &or N - port Netwo


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14

E%' Evaluation o& Scatterin$ (ara)eter

Find the scattering parameters(or the 3d< atten!ator circ!itwith ='> characteristicimpedance shown in the (ig!re


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15

E%' Evaluation o& Scatterin$ (ara)eter


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*eter)ine Scatterin$ Matri% &ro) + ,

The total oltage and c!rrent at nth port


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17

*eter)ine + , . +Y &ro) Scatterin$ M

The total oltage and c!rrent at nth port


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Reciprocal Network an/ Lo le Network18


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Reciprocal Network an/ Lo le Network19


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A S0i&t in Re&erence (lane20

9hase re(erence plane m!st -e speci(ied (or each port o(the networ#.

:hen the re(erence planes are mo ed (rom their original locations how the scattering parameters are trans(ormed?


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A S0i&t in Re&erence (lane !Cont"#21

/S scattering networ# wher e original re(erence planes is located at z n '.

/S’ scattering networ# where original re(erence planes

is located at z n l n


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S nm is shi(t - twice the electrical length o( the shi(t in terminal plane.

:h ???


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Outline24

1. Impedance and Admittance Matrix2. Scattering Matrix7

,eciprocal and 5ossless "etwor#A Shi(t in ,e(erence 9lanes

9ower :a e and Generali6ed Scattering 9arameters

3. Transmission Matrix4. Signal Flow Graph


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(ower Wave an/ 1enerali2e/ Scatterin$ (ara)eter25

The a erage power deli er to a load

Z o is real


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(ower Wave26

The incident and re(lected power wa e amplit!des a and bas the (ollowing linear trans(ormations o( the total oltage and ct7

Z R is #nown as the reference impedanceTotal oltage and c!rrent in term o( the power wa e amplit!de


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(ower Wave !Cont"#27

The power deli ered to the load7

The re(lection coe((icient (or the re(lected power7

9!re Imaginar


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(ower Wave !Cont"#28

Choosing the re(erence impedance as the con*!gate o( the load imp


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(ower Wave !Cont"#

The power deli ered to the load

The power wa e amplit!de ector7

The scattering matrix (or power wa e7


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Outline30



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Tran )i ion Matri%31

Man microwa e networ#s consist o( a cascade connection o( a two)port networ# It is con enient to de(ined a

2 x 2 transmission matrix ( !"#$

The total oltage and c!rrent7


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Tran )i ion Matri% !Cont"#32

In a cascade connection o( 2 two)port networ#%The total oltage and c!rrent7


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A3C* (ara)eter o& 4 e&ul Two-port Circuit33


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A3C* (ara)eter o& 4 e&ul Two-port Circuit34


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Relation to I)pe/ance Matri%35


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E5uivalent Circuit &or Two-port Networ36


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E5uivalent Circuit &or Two-port Network !C37

8;!i alent Circ!it (or ,eciprocal Two)port "etwor#7

% e;!i alent &e;!i ale

O li


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Outline38


Si$ l 6l 1 0


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Si$nal 6low 1rap039

The primar components o( a signal (low graph

are nodes and -ranches "odes7 8ach port i o( a microwa e networ# has two nodes%a i and b i. "ode a i iis identi(ied with a wa

e entering port i% while node b i is identi(ied witha wa e re(lected (rom port i. The oltage at a nodeis e;!al to the s!m o( all signals entering that nod

e.


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Si$nal 6low 1rap0 on a One-port Network40

* ) iti & Si$ l 6l 1 0


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*eco)po ition o& Si$nal 6low 1rap041

Rule 1 &Series ,!le+. Two -ranches% whose common node has onl one iand one o!tgoing wa e &-ranches in series+% ma -e com-ined to (orm a s

nch whose coe((icient is the prod!ct o( the coe((icients o( the original -ranch

* ) iti & Si$ l 6l 1 0 !C t


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*eco)po ition o& Si$nal 6low 1rap0 !Cont42

Rule 2 &9arallel ,!le+. Two -ranches (rom one common node to anoth

on node &-ranches in parallel+ ma -e com-ined into a single -ranch w((icient is the s!m o( the coe((icients o( the original -ranches.

* ) iti & Si$ l 6l 1 0 !C t


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Rule 3 &Sel()5oop ,!le+. :hen a node has a sel()loop &a -ranch that -egd ends on the same node+ o( coe((icient S % the sel()loop can -e elim!ltipl ing coe((icients o( the -ranches (eeding that node - 1 '( 1 @

*eco)po ition o& Si$nal 6low 1rap0 !Cont


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Rule 4 &Splitting ,!le+. A node ma -e split into two separate nodes as les!lting (low graph contains% once and onl once% each com-ination o(sel()loops+ inp!t and o!tp!t -ranches that connect to the original node.

E%a)ple


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E%a)ple45

se signal (low graphs to deri e expressions (or in and o!t (or the microwa e n

E%a)ple


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E%a)ple46

E%a)ple


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E%a)ple47

On ite 7o)ework


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On ite 7o)ework48

4.11% 4.1B% 4.2'% 4.23% 4.2B

4. Network Analysis

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