2013/1/8

1

Two-Port Networks

Instructor: Chia-Ming TsaiElectronics Engineering

National Chiao Tung UniversityHsinchu, Taiwan

Contents•Introduction•Impedance Parameters•Admittance Parameters•Hybrid Parameters•Transmission Parameters•Interconnection of Networks•Application•Scattering Parameters

2013/1/8

2

Introduction•One-Port Networks

–Two-terminal circuits–Resistors, capacitors,

inductors

•Two-Port Networks–Three (or four)-terminal

circuits–Op amps, transistors,

transformers

Withoutindependentsources.

Impedance (z) Parameters

impedanceoutputimpedancetransfer

,

impedanceransfertimpedanceinput

,

:ionsuperpositBy

02

222

01

221

02

112

01

111

2

1

2

1

2221

1211

2

1

2221212

2121111

12

12

II

II

IV

zIV

z

IV

zIV

z

II

zII

zzzz

VV

IzIzV

IzIzV

Open-circuit

Open-circuit

=

2013/1/8

3

z Parameters

2

1

2221

1211

2

1

2221212

2121111

orII

zzzz

VV

IzIzV

IzIzVz11 z22

z12I2 z21I1V1 V2

I1 I2

z Parameters

parameter.znohasertransformidealThe

1

21

21

II

VV

nn

2013/1/8

4

Admittance (y) Parameters

,

,

02

222

01

221

02

112

01

111

2

1

2

1

2221

1211

2

1

2221212

2121111

12

12

VV

VV

VI

yVI

y

VI

yVI

y

VV

yVV

yyyy

II

VyVyI

VyVyI

Short-circuit

Short-circuit

y Parameters

2

1

2221

1211

2

1

VV

yyyy

II

y11 y22

y12V2

y21V1

V1 V2

I1 I2

2013/1/8

5

Hybrid (h) Parameters

admittanceoutputgaincurrentforward

,

gainvoltagereverseimpedanceinput

,

02

222

01

221

02

112

01

111

2

1

2

1

2221

1211

2

1

2221212

2121111

12

12

IV

IV

VI

hII

h

VV

hIV

h

VI

hVI

hhhh

IV

VhIhI

VhIhV

)(

,

,

02

222

01

221

02

112

01

111

2

1

2

1

2221

1211

2

1

2221212

2121111

12

12

etersbrid paramInverse hy

VI

VI

IV

gVV

g

II

gVI

g

IV

gIV

gggg

VI

IgVgV

IgVgI

h Parameters

2

1

2221

1211

2

1

VI

hhhh

IV

2

1

2221

1211

2

1

IV

gggg

VI

h11

h22

h12V2

h21I1

V1 V2

I1 I2

g11

g22

g12I2

g21V1

V1 V2

I1 I2

2013/1/8

6

Transmission (T) Parameters

)(

,

,

02

1

02

1

02

1

02

1

2

2

2

2

1

1

22

22

erson parametTransmissi

VI

VI

II

DVI

C

IV

BVV

A

IV

TI

VDCBA

IV

)(

,

,

01

2

01

2

01

2

01

2

1

1

1

1

2

2

11

11

sparameteransmissionInverse tr

VI

VI

II

dVI

c

IV

bVV

a

IV

tI

Vdcba

IV

Interconnection of Networks•Series Connection

–[z] parameters preferred

•Parallel Connection–[y] parameters preferred

•Cascade Connection–[T] parameters preferred

2013/1/8

7

Series Connection

ba

baba

baba

baba

ba

baba

ba

ba

ba

bbbbb

bbbbb

aaaaa

aaaaa

zzz

zzzzzzzz

zzzz

IzzIzz

VVV

IzzIzzVVV

IIIIII

IzIzVIzIzV

IzIzVIzIzV

or

)()(

)()(

22222121

12121111

2221

1211

2222212121

222

2121211111

111

222

111

2221212

2121111

2221212

2121111

n

nzzzz 21

networks,connected-seriesFor

Parallel Connection

ba

baba

baba

baba

ba

baba

ba

ba

ba

bbbbb

bbbbb

aaaaa

aaaaa

yyy

yyyyyyyy

yyyy

VyyVyy

III

VyyVyy

III

VVVVVV

VyVyIVyVyI

VyVyIVyVyI

or

)()(

)()(

22222121

12121111

2221

1211

2222212121

222

2121211111

111

222

111

2221212

2121111

2221212

2121111

n

nyyyy 21

networks,connected-parallelFor

2013/1/8

8

Cascade Connection

2

2

1

1

2

2

1

1

givesparametersiontransmissThe

IV

DCBA

DCBA

IV

IV

DCBA

IV

IV

DCBA

IV

bb

bb

aa

aa

bb

bb

a

a

a

a

aa

aa

n

ba

bb

bb

aa

aa

nTTTT

TTT

DCBA

DCBA

DCBA

21

networks,connected-cascadeFor

or

Application

c

b

oefe

reie

c

b

VI

hhhh

IV

2013/1/8

9

Scattering (S) Parameters

2

1

2

1

2221

1211

2

1

2221212

2121111

waveReflectedon wavetrasmissiForward

on wavetrasmissiReversewaveReflected

aa

Saa

SSSS

bb

aSaSb

aSaSb

Incident wave Incident wave