Chapter 18

Two-port Networks

four-terminal network

the four terminals have been paired into ports two-port

network

At all times, the instantaneous current flowing into one terminal is equal to the instantaneous current flowing out the other.

KCL

i1

i2 i3

i4 i1 i4

i1+i2+i3+i4=0(KCL)i1=-i2 ; i3=-i4

2221212

2121111

2221212

2121111

VyVyI

VyVyI

IzIzV

IzIzV

2221212

2121111

2221212

2121111

IgVgV

IgVgI

VhIhI

VhIhV

112

112

221

221

dIcVI

bIaVV

DICVI

BIAVV

The network is linear(without independent sources).

Impedance ParametersImpedance or z parameters are defined by

 

                                      

impedance matrix Z

2221212

2121111

IzIzV

IzIzV

022

021

012

011

12

2

21

2

12

1

21

1

IIV

IIV

IIV

IIV

z

z

z

zOpen-circuit input impedance.

Open-circuit transfer impedance from port 1 to port 2

Open-circuit transfer impedance from port 2 to port 1

Open-circuit output impedance.

22221212

12121111

oc

oc

VIzIzV

VIzIzV

Determining of the z parameters: (a) finding z11 and z21, (b) finding z12 and z22

Examples

(a) T equivalent circuit (for reciprocal case only), (b) general equivalent circuit

Admittance ParametersAdmittance or y parameters are defined by

2

1

2221

1211

2

1

V

V

yy

yy

I

I

2221212

2121111

VyVyI

VyVyI

admittance matrix Y

022

021

012

011

12

2

21

2

12

1

21

1

VVI

VVI

VVI

VVI

y

y

y

yShort-circuit input admittance.

Short-circuit transfer admittance from port 1 to port 2

Short-circuit transfer admittance from port 2 to port 1

Short-circuit output admittance.

22221212

12121111

sc

sc

IVyVyI

IVyVyI

Determination of the y parameters: (a) finding y11 and y21, (b) finding y12 and y22.

(a) -equivalent circuit (for reciprocal case only), (b) general equivalent circuit.

Hybrid ParametersHybrid or h parameters are defined by

2221212

2121111

VhIhI

VhIhV

hybrid matrix Z

022

021

012

011

12

2

21

2

12

1

21

1

IVI

VII

IVV

VIV

h

h

h

hShort-circuit input impedance.

Open-circuit reverse voltage gain

Short-circuit forward current gain

Open-circuit output admittance.

The h-parameter equivalent network of a two-port network

Inverse hybrid parameters (g parameters)

2221212

2121111

IgVgV

IgVgI

The g-parameter model of a two-port network

Transmission ParametersTransmission or T parameters are defined by

2

2

1

1

I

V

DC

BA

I

V

2222211

2122111

IaVaI

IaVaV

Transmission matrix T

0

0

0

0

22

1

22

1

22

1

22

1

VII

IVI

VIV

IVV

D

C

B

A Open-circuit voltage ratio

Negative short-circuit transfer impedance

Open-circuit transfer admittance

Negative short-circuit current ratio

Inverse transmission parameters

112

112

dIcVI

bIaVV

------------- linear and has no dependent source

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

1

1

21122112

2112

2112

bcadT

BCADT

gg

hh

yy

zz

Reciprocal Two-Port Circuits

Symmetric Two-Port CircuitA reciprocal two-port circuit is symmetric if its ports can be interchanged without disturbing the values of the terminal currents and voltages.If a two-port circuit is symmetric, the following relationships exist among the port parameters: (besides those exist in reciprocal)

da

DA

ggggg

hhhhh

yy

zz

1

1

21122211

21122211

2211

2211

Question: How many calculations or measurements are needed to determine a set of parameters of a two-port circuit?

For a general two-port with sources: 6

For a general linear two-port: 4

For a reciprocal two-port: 3

For a symmetric two-port: 2

Relationships between parameters

Example: z parameters y parameters

2221212

2121111

IzIzV

IzIzV

2221212

2121111

VyVyI

VyVyI

z

zy

z

zy

z

zy

z

zy

1122,

2121

,12

12,22

11

21122211 zzzzz

where

Interconnection of networksSeries connection of two two-port networks

ba ZZZ

Parallel connection of two two-port networks ba YYY

Cascade connection of two two-port networks ba TTT

Transistor amplifier with source and load resistance