TWO-PORT NETWORKSTWO-PORT NETWORKS

One-port network

- One pair of terminal

- Current entering the port = current leaving the port

A port : an access to a network and consists of two terminals

TWO-PORT NETWORK- Definition

+V

I

Linear network

I

+V1

I1

Linear network

+V2

I2

I2I1

Two-port network

- Two pairs of terminal : two-port

- Current entering a port = current leaving a port

TWO-PORT NETWORK- Definition

- V1,V2, I1 and I2 are related using two-port network parameters

- In SEE 1023 we will study on four sets of these parameters

Impedance parameters

Hybrid parameters

Admittance parameters

Transmission parameters

Output portInput port

TWO-PORT NETWORK

- Typically found in communications, control systems, electronics

- used in modeling, designing and analysis

- Know how to model two-port network will help in the analysis of larger network

- two-port network treated as ‘black box’

Why ?

TWO-PORT NETWORK

Impedance parameters (z parameters)

2

1

2221

1211

2

1

I

I

zz

zz

V

V

Parameters can be determined by calculations or measurement

2121111 IzIzV

2221212 IzIzV

TWO-PORT NETWORK

Impedance parameters (z parameters)

z11 and z21

+

V2

I2

V1

I1

Output port : openI2 = 0

Input port : Apply voltage source

2121111 IzIzV

2221212 IzIzV

1111 IzV 0I1

111

2I

Vz

1212 IzV 0I1

221

2I

Vz

TWO-PORT NETWORK

Impedance parameters (z parameters)

z12 and z22

V1

Input port : openedI1 = 0

Output port : Apply voltage source

2121111 IzIzV

2221212 IzIzV

2121 IzV 0I2

112

1I

Vz

2222 IzV 0I2

222

1I

Vz

V2

I2I1=0

+

V1

TWO-PORT NETWORK

Impedance parameters (z parameters)

2121111 IzIzV

2221212 IzIzV

Equivalent circuit based on these equations:

+

V1

+

V1

I1I2

11z 22z

211zI+

+

122zI

TWO-PORT NETWORK

Impedance parameters (z parameters)

2121111 IzIzV

2221212 IzIzV

Linear network with NO dependent sources: RECIPROCALRECIPROCAL

ammeter

AVI

Reciprocalnetwork A

V

IReciprocal

network

• Voltage source and ideal ammeter connected to the ports are interchangeable

TWO-PORT NETWORK

Impedance parameters (z parameters)

2121111 IzIzV

2221212 IzIzV

Linear network with NO dependent sources: RECIPROCALRECIPROCAL

• Voltage source and ideal ammeter connected to the ports are interchangeable

• z12 = z21

• Can be replaced with T-equivalent circuit:

Z11-z12 Z22-z12

Z12

+V1

+V2

TWO-PORT NETWORK

Impedance parameters (z parameters)

2121111 IzIzV

2221212 IzIzV

Linear network with NO dependent sources: RECIPROCALRECIPROCAL

Network with mirror-like symmetry: SYMMETRICALSYMMETRICAL

z11 = z22

TWO-PORT NETWORK

Impedance parameters (z parameters)

2121111 IzIzV

2221212 IzIzV

Linear network with NO dependent sources: RECIPROCALRECIPROCAL

Network with mirror-like symmetry: SYMMETRICALSYMMETRICAL

If the two-port network is reciprocal and symmetrical, only 2 parameters need to be determined

TWO-PORT NETWORK

Admittance parameters (y parameters)

2

1

2221

1211

2

1

V

V

yy

yy

I

I

2121111 VyVyI

2221212 VyVyI

Parameters can be determined by calculations or measurement

TWO-PORT NETWORK

Admittance parameters (y parameters)

y11 and y21

Output port : shortedV2 = 0

Input port : Apply current source

1111 VyI 0V1

111

2V

Iy

1212 VyI 0V1

221

2V

Iy

2121111 VyVyI

2221212 VyVyI

+

V1

+

V2 = 0

I2I1

TWO-PORT NETWORK

Admittance parameters (y parameters)

y12 and y22

Input port : shortedV1 = 0

Output port : Apply current source

2121 VyI 0V2

112

1V

Iy

2222 VyI 0V2

222

1V

Iy

2121111 VyVyI

2221212 VyVyI

+

V1=0

+

V2

I2I1

TWO-PORT NETWORK

Admittance parameters (y parameters)

Equivalent circuit based on these equations:

2121111 VyVyI

2221212 VyVyI

+

V1

+

V2

I1 I2

11y 22y212Vy 121Vy

TWO-PORT NETWORK

Admittance parameters (y parameters)

Linear network with NO dependent sources: RECIPROCALRECIPROCAL

• Current source and ideal voltmeter connected to the ports are interchangeable

• yy1212 = y = y2121

• Can be replaced with -equivalent circuit:

y11+ y12 y22+ y12

-y12

+V1

+V2

2121111 VyVyI

2221212 VyVyI

TWO-PORT NETWORK

Admittance parameters (y parameters)

2121111 VyVyI

2221212 VyVyI

Network with mirror-like symmetry: SYMMETRICAL :SYMMETRICAL :

yy1111 = y = y2222

TWO-PORT NETWORK

Hybrid parameters (h parameters)

2

1

2221

1211

2

1

V

I

hh

hh

I

V

2121111 VhIhV

2221212 VhIhI

Some two port network cannot be expressed in terms z or y parameters but can be expressed in terms of h parameters

Parameters can be determined by calculations or measurement

TWO-PORT NETWORK

h11 and h21

Output port : shortedV2 = 0

Input port : Apply current source

1111 IhV 0V1

111

2I

Vh

1212 IhI 0V1

221

2I

Ih

Hybrid parameters (h parameters)

2121111 VhIhV

2221212 VhIhI

()

+

V1

+

V2 = 0

I2I1

TWO-PORT NETWORK

h12 and h22

Input port : openedI1 = 0

Output port : Apply voltage source

2121 VhV 0I2

112

1V

Vh

2222 VhI 0I2

222

1V

Ih

Hybrid parameters (h parameters)

2121111 VhIhV

2221212 VhIhI

V2

I2I1=0

+

V1

(S)

TWO-PORT NETWORK

Equivalent circuit based on these equations:

Hybrid parameters (h parameters)

2121111 VhIhV

2221212 VhIhI

+

+

V1

I1 I2

+

V2

h11

h11V2 h21I1

h22

TWO-PORT NETWORK

Linear network with NO dependent sources: RECIPROCALRECIPROCAL

• Current source and ideal voltmeter connected to the ports are interchangeable

• hh1212 = -h = -h2121

Hybrid parameters (h parameters)

2121111 VhIhV

2221212 VhIhI

TWO-PORT NETWORK

Hybrid parameters (h parameters)

2121111 VhIhV

2221212 VhIhI

Network with mirror-like symmetry: SYMMETRICAL :SYMMETRICAL :

hh1111hh2222 – h – h1212hh2121 = 1 = 1

TWO-PORT NETWORK

Transmission parameters (t parameters)

2

2

1

1

I

V

DC

BA

I

V

221 BIAVV

221 DICVI

Used to express the sending end voltage an current in terms of receiving end voltage and current

+V1

I1

Linear network

+V2

-I2

I2I1

receiving endsending end

TWO-PORT NETWORK

Output port : opened I2 = 0

21 AVV 21 CVI

Transmission parameters (h parameters)

221 BIAVV

221 DICVI

0I2

1

2V

VA

0I2

1

2V

IC

Output port : shorted V2 = 0

21 BIV 21 DII 0V2

1

2I

VB

0V2

1

2I

ID

For RECIPROCALRECIPROCAL network, AD – BC = 1

For SYMMETRICALSYMMETRICAL network, A = D

TWO-PORT NETWORK

Relationships between parameters

If a two-port network can be presented by different set of parameters, then there exists relationships between parameters.

e.g. relationships between z and y parameters:

2

1

2221

1211

2

1

I

I

zz

zz

V

V

2

1

1

2221

1211

2

1

V

V

zz

zz

I

I

We know that

2

1

2221

1211

2

1

V

V

yy

yy

I

I

Therefore

1

2221

1211

2221

1211

zz

zz

yy

yy

TWO-PORT NETWORK

Relationships between parameters

1

2221

1211

zz

zz

z

1121

1222

zz

zz

where 21122211z zzzz

Therefore, z

2211

zy

z

1212

zy

z

2121

zy

z

1122

zy

The conversion formulae can be obtained from the conversion table

e.g. on page 869 of Alexander/Sadiku

TWO-PORT NETWORK

Relationships between parameters

TWO-PORT NETWORK

Interconnection of networks

Complex large network can be modeled with interconnected two-port networks

• Simplify the analysis /synthesis

• Simplify the design

Parameters of interconnected two-port networks can be obtained easily: depending on the type of parameters and type of connections:

• Series: z parameters

• Parallel: y parameters

• Cascade: transmission parameters

TWO-PORT NETWORK

Interconnection of networks

Series: z parameters

[z] = [za] + [zb]

I1a

I1b

I2a

I2b

+V1b

+V1a

+V2a

+V2b

+

V1

+

V2

za

zb

z+V2

+V1

I1 I2

TWO-PORT NETWORK

Interconnection of networks

Parallel: y parameters

[y] = [ya] + [yb]

y+V2

+V1

I1 I2

I1a I2a

+V1b

+V1a

+V2a

+V2b

+V1

+V2

ya

yb

I1 I2

I1b I2b

TWO-PORT NETWORK

Interconnection of networks

Cascade: t parameters

[t] = [ta][tb]

t+V2

+V1

I1 -I2

I1a -I2a

+V1b

+V1a

+V2b

+V1

+V2

ta tb

I1 I1b -I2b

+V2a

-I2