FOUR TERMINAL NETWORKS TWO – PORT NETWORKS
Two – ports – are electric circuits with two input and two output
terminals as shown
I1
I2
V2
V1
Input Port
Output Port
In two – ports, the input voltage and current (V1 & I1) are related with the
output voltage and current (V2 & I2) by the following equations:V1 = Z11 I1 – Z12 I2
V2 = Z21 I1 – Z22 I2
Z – parameters
I1 = Y11 V1 – Y12 V2
I2 = Y21 V1 – Y22 V2
Y– parameters
V1 = h11 I1 – h12 V2
I2 = h21 I1 – h22 V2
h – parameters
V1 = A V2 + B I2
I1 = C V2 + D I2
ABCD
parameters
The coefficients of the current and/ or voltage on the right – hand side of
the above equations are called the parameters of the two-port circuit.
 If ports can be interchanged without disturbing the values of the
terminal currents and voltage then the two-port circuit is called
Symmetrical.
For Symmetrical two-ports:A=D
Also the ABCD parameters are related by the following equation:
AD-BC = 1.
A and D – no units, B in (ohm), C in (mho).
 We can find the ABCD parameters in terms of Z – parameters for
example as follows:V1 = Z11 I1 – Z12 I2 …………….1
V2 = Z21 I1 – Z22 I2 ……………………..2
From eq (2):
V
Z
I1  2  22 I 2 ……………3
Z 21 Z 21
Sub. for (I1) in eq (1) we get.
V

Z
V1  Z11  2  22 I 2   Z12 I 2
 Z 21 Z 21 
Z 
 Z Z  Z12 Z 21 
I 2
V1 =  11   V2   11 22
Z
Z
 21 


21
Since V1 = A V2 + B I2.
I1 = C V2 + D I2.
A 
C
Z11
Z Z  Z12 Z 21
& B  11 22
Z 21
Z 21
Z
1
& D  22
Z 21
Z 21
 When interchanging the places between the source and the load in
a two-port the following equations should be used:V2 = D V1+ BI1
I2 = C V1 + AI1
ABCD – parameters calculations
The ABCD parameters could be found by experiment as well as by
calculation when finding the ABCD parameters by calculation,
circuit components and their interconnection must be known.
For the experimental determination of the parameters we must
conduct – 3 – experiments (because we have only – 3 independent parameters). The simplest method used is by
conducting short and open circuit experiments.
Experiment No. 1
In this experiment the source is connected to the input terminals,
the output terminals are open – circuited.
I10
I20 =0
V20
V10
~
V10 = A V20
I10 = C V20

V10
A
 Z10 
I10
C
………………..1
Experiment No. 2
In this experiment the source is connected to the input terminals, the out
put is connected to the input terminals, the out put terminals are shortcircuited.
~
I1S
I2S
V1S
V2S
V2S = 0
V1S = B I2S
I1S = D I2S

VI S
B
Z


IS
I IS ……………………..2
D
Experiment No. 3
In this experiment the source is connected to the out put terminals, the
input terminals are short-circuited.
I1S
I2S
V1S = 0
V2S
V1S = 0
V2 =DV1 + BI1
I2 = CV1 + AI1
 V2S = BI1S
I2S = AI1S

V2S
B
 Z 2S 
I 2S
A
………………..3
~
Since we have: AD-BC = 1
1 

BC
1

AD AD
Z10  Z15
1

Z10
AD
1 
Z15
1

Z10 AD
…………………..4
Z 25 B D D
…………………..5
  
Z 25 A B A
Multiplying eq (4) By eq (5) we get
Z 25 Z10  Z15
1


Z15
Z10
A2

A
Z10 Z15
Z 25 Z10  Z15 
After finding A from eq (6), we can find (C) from eq (1), from eq (3) we
can find (B) then (D) can be find from eq (2).