TWO-PORT NETWORK

TKT 419/3Sem 1 Sidang Akademik 2010/2011

Lecturer: Pn. Wan Nur Suryani Firuz Bt Wan Ariffin (012-4820815)

TWO-PORT NETWORKTerminal equationsTwo-port parametersRelationships among two-port

parametersAnalysis of terminated two-port

circuitInterconnected two-port circuits

TERMINAL EQUATIONS

s -d o m ain

c ir c u it

1V

2V

1I2I

s-domain two-port basic building block

Terminal equations relationships1st Relationship:

2221212

2121111

IzIzVIzIzV

2nd Relationship:

2221212

2121111

VyVyIVyVyI

3rd Relationship:

2222211

2122111

IaVaIIaVaV

4th Relationship:

1221212

1121112

IbVbIIbVbV

5th Relationship:

2221212

2121111

VhIhIVhIhV

6th Relationship:

2221212

2121111

IgVgVIgVgI

TWO PORT NETWORK:

Terminal equationsTwo-port parametersRelationships between

parametersAnalysis of terminated two-port

circuitInterconnected two-port circuits

IMPEDANCE PARAMETERS

z parameters

02

222

01

221

02

112

01

111

12

12

II

II

IVz

IVz

IVz

IVz

2221212

2121111

IzIzVIzIzV

ADMITTANCE PARAMETERSy parameters

SVIyS

VIy

SVIyS

VIy

VV

VV

02

222

01

221

02

112

01

111

12

12

2221212

2121111

VyVyIVyVyI

a parameters

02

122

02

121

02

112

02

111

22

22

VI

VI

IIaS

VIa

IVa

VVa

b parameters

01

222

01

221

01

212

01

211

21

11

VI

VI

IIbS

VIb

IVb

VVb

a and b parameters are called transmission parameters

HYBRID PARAMETERSh parameters

SVIh

IIh

VVh

IVh

IV

IV

02

222

01

221

02

112

01

111

12

12

INVERSE HYBRID PARAMETERSg parameters

02

222

01

221

02

112

01

111

12

12

VI

VI

IVg

VVg

IIgS

VIg

Example 1Find z parameter for the

below circuit:

1V

2V

1I 2I

20

5

15

Solutions:

When port 2 open-circuit, I2=0 so,

1040

)20(20

01

111

2IIVz

When I2=0, thus V2

112 75.0515

15 VVV

5.710/

75.0

1

1

01

221

2V

VIVz

I

Now, when I1=0,so

375.940

)25(15

02

222

1IIVz

When port 1 open-circuit, I1=0, so:

221 8.0205

20 VVV

375.9

22

VI

5.7375.9/

8.0

2

2

02

112

1V

VIVz

I

TWO-PORT NETWORKTerminal equationsTwo-port parametersRelationships between parameters

Analysis of terminated two-port circuit

Interconnected two-port circuits

RELATIONSHIPS BETWEEN PARAMETERS

yIy

yIy

yyyyyIyI

V

212122

2221

1211

222

121

1

yIy

yIy

yyyyIyIy

V

121211

2221

1211

221

111

2

Compare these two above equations:

yyz

yyz

yyz

yyz

1122

2121

1212

2211

Find z parameters as functions of a parameters

221

221

212

1 IaaI

aV

21221

22111

21

111 Ia

aaaI

aaV

Therefore,

21

2222

2121

2112

21

1111

1aaz

az

aaz

aaz

RECIPROCAL TWO-PORT CIRCUITS

If a two-port circuit is reciprocal, the following relationships exist among port parameters:

21122112

21122211

21122211

21122112

11

gghhbbbbbaaaaayyzz

Symmetric of a reciprocal two-port circuitsFollowing relationships exist among

port parameters:

11

21122211

21122211

22112211

22112211

ggggghhhhhbbaayyzz

Example of symmetric two-port circuits

Z a

Z b

Z a

1V

2V

1I 2ISymmetric tee

Symmetric pi

Z b

1V

2V

1I 2I

Z a Z a

Symmetric bridge tee

Z b

1V

2V

1I2I

Z a Z a

Z c

Symmetric lattice

Z b

1V

2V

1I2I

Z a

Z a

Z b

TWO-PORT NETWORKTerminal equationsTwo-port parametersRelationships between

parametersAnalysis of terminated two-port circuit

Interconnected two-port circuits

ANALYSIS OF TERMINATED TWO-PORT CIRCUITS

T w o - p o r t m o d elo f a

n e tw o r k

1V

2V

1I2I

Z L

Z g

gV

6 characteristics of terminated two-port circuitInput impedance (Zin=V1/I1) or

admittance (Yin=I1/V1)Output current, I2

Thevenin voltage and impedance (ZTh, VTh) with respect to port 2

Current gain I2/I1

Voltage gain V2/V1

Voltage gain V2/Vg

6 characteristics in term of z parameters

4 parameter equations that describe the circuit:

L

gg

ZIV

ZIVVIzIzVIzIzV

22

11

2221212

2121111

1st characteristic (input impedance)

22

1212 zZ

IzIL

Lin Zz

zzzZ

22

211211

2nd characteristic (output current, I2)

g

g

ZzIzV

I

11

2121

21122211

212 ))(( zzZzZz

VzI

Lg

g

3rd characteristic (Thevenin voltage @ impedance)

11

12112102

2 zVzIzV

I

11

2102

2 zZzVVVg

gThI

Impedance Thevenin

gZzIzI

11

2121

gTh

VZzzzzZ

IV

g

11

211222

02

2

4th characteristic (current gain)

22

21

1

2

zZz

II

L

5th characteristic (voltage gain V2/V1)

LZVzIzV 2

221212

L

L

ZzVz

zVI

ZVzVIz

11

212

11

11

2121111

zZzZz

zzzzZzZz

VV

L

L

L

L

11

21

2112221111

21

1

2

6th characteristic (voltage gain V2/Vg)

222

11

21

11

212212 )(

VZz

ZzVz

ZzZVzzV

Lg

g

gL

g

g

gL ZzV

ZzZVzI

1111

2121 )(

21122211

212

))(( zzZzZzZz

VV

Lg

L

g

TWO-PORT NETWORKTerminal equationsTwo-port parametersRelationships between parametersAnalysis of terminated two-port

circuitInterconnected two-port circuits

INTERCONNECTED TWO-PORT CIRCUITS

Cascade connection

Two-port parameters

2222211

2122111

IaVaIIaVaV

2222211

2122111

IaVaIIaVaV

Interconnection (V’2=V’1 and I’2= -I’1)

1221211

1121111

IaVaIIaVaV

Relationship V’1 and I’1 with V2 and I2 in second circuit :

2222211

2122111

IaVaIIaVaV

2222212212212211211

2221212112211211111

)()()()(IaaaaVaaaaIIaaaaVaaaaV

2222122122

2122112121

2212121112

2112111111

aaaaaaaaaaaaaaaaaaaa

Reference book

Electric Circuits, James W. Nilsson and Susan A. Riedel, Prentice Hall