Darshan
Institute of Engineering & Technology
(Electrical Engineering Department)
Name of Topic:- “Two-Port Networks”
Enrollment No:- 130540109070
Subject Code:- 2130901
TWO-PORT NETWORKS
In many situations one is not interested in the internal organization of a
network. A description relating input and output variables may be sufficient
A two-port model is a description of a network that relates voltages and currents
at two pairs of terminals
LEARNING GOALS
Study the basic types of two-port models
Admittance parameters
Impedance parameters
Hybrid parameters
Transmission parameters
Understand how to convert one model into another
ADMITTANCE PARAMETERS
The network contains NO independent sources
The admittance parameters describe the currents in terms of the voltages
y21 determines the current
I1  y11V1  y12V2
The first subindex identifies
the output port. The second
the input port.
flowing into port 2 when the I 2  y21V1  y22V2
port is short - circuited and a
voltage is applied to port 1
The computation of the parameters follows directly from the definition
y11 
I1
V1 V
y12 
I2
V1 V
y22 
2 0
y21 
2 0
I1
V2 V 0
1
I2
V2 V 0
1
LEARNING EXAMPLE
Find the admittance parameters for the network
I1  y11V1  y12V2
I 2  y21V1  y22V2
Circuit used to determine y11, y21
 I2
Circuit used to determine y12 , y22
1
3
I1  (1  )V1  y11  [ S ]
2
2
1
1
1
 I2 
I1  I 2   V1  y21   [ S ]
1 2
2
2
5
 1 1
I 2    V2  y22  [ S ]
6
 2 3
3
3 5
1
 I1 
I2 
V2  y12  [ S ]
23
5 6
2
Next we show one use of this model
An application of the admittance parameters
Determine the current through the
4 Ohm resistor
I1  y11V1  y12V2
I 2  y21V1  y22V2
3
1
I1  V1  V2
2
2
1
5
I 2   V1  V2
2
6
1
I


V2
I1  2 A, V2  4 I 2 2
4
The model plus the conditions at the
ports are sufficient to determine the
other variables.
3
1
2  V1  V2
2
2
1
5 1
0   V1    V2
2
6 4
13
V2
6
8
V2  [V ]
11
2
I 2   [ A]
11
V1 
IMPEDANCE PARAMETERS
The network contains NO independent sources
V1  z11I1  z12 I 2
V2  z21I1  z22 I 2
The ‘z parameters’ can be derived in a manner similar to the Y parameters
z11 
V1
I1 I
z12 
V1
I2
z21 
2 0
V2
I1
z22 
I1 0
I 2 0
V2
I2
I1 0
HYBRID PARAMETERS
The network contains NO independent sources
V1  h11 I1  h12V2
I 2  h21 I1  h22V2
h11 
V1
I1 V
h21 
V1
V2
h22 
2 0
h12 
I1 0
I2
I1 V
h11  short - circuit input impedance
I2
V2
h21  short - circuit forward current gain
2 0
I1 0
h12  open - circuit reverse voltage gain
h22  open - circuit output admittance
These parameters are very common in modeling transistors
LEARNING EXAMPLE
I1
Find the hybrid parameters for the network
I2


V1
V2


V1  h11 I1  h12V2
I 2  h21 I1  h22V2
I2
I1

I2
V1

V1

V2  0
V1  (12  (6 || 3)) I1  h11  14
6
2
I2  
I1  h21  
3 6
3
I1  0

V2


V1 
6
2
V2  h12 
3 6
3
I2 
V2
1
 h22  [ S ]
9
9
TRANSMISSION PARAMETERS ABCD parameters
The network contains NO independent sources
V1  AV2  BI 2
I1  CV2  DI 2
A
V1
V2
B
C
I 2 0
V1
I2 V
2 0
I1
V2
D
A  open circuit voltage ratio
I 2 0
B  negative short - circuit transfer impedance
I1
I2 V
2 0
C  open - circuit transfer admittance
D  negative short - circuit current ratio
PARAMETER CONVERSIONS
If all parameters exist, they can be related by conventional algebraic manipulations.
As an example consider the relationship between Z and Y parameters
V1  z11I1  z12 I 2
V2  z21 I1  z22 I 2
V1   z11
V    z
 2   21
 y11
y
 21
1
z12   I1   I1   z11
 



z22   I 2   I 2   z21
y12   z11


y22   z21
z12 
z22 
1
1

Z
z12  V1   y11

z22  V2   y21
y12  V1 
y22  V2 
 z22  z12 
 z

 21 z11 
with  Z  z11z22  z21z12
In the following conversion table, the symbol  stands for the determinant of the
corresponding matrix
Z 
z11
z12
z21
z22
, Y 
y11
y12
y21
y22
, H 
h11
h12
h21 h22
, T 
A B
C
D