Analog electronics
2. Two – Port Network
2.1. Impedance parameters
A linear two port network represented by black box is considered, having I1 and I2 as independent variables and V1 and V2 as dependent variables.
V1 = f1 ( I1, I2 )
V2 = f2 ( I1, I2 ) ------ (2.1)
The changes in the dependent variables may be given by:
∂V ∂V
dV 1dI 1dI 2 ∂I ∂I
|
dV 2 |
= |
|
dI 1 + |
|
dI 2 ------ (2.2) |
The partial derivatives in these equations become constant with operation over linear region of the device curve with constant slope.
The equations may, therefore, be written as:
V 1 = Z 11 I 1 + Z 12 I 2
V 2 = Z 21 I 1 + Z 22 I 2 ------ (2.3)
In the matrix form it is given by:
V1 Z 11 Z 12 I 1
=
------ (2.4)
V 2 Z 21 Z 22 I 2
Where Z’s are the impedance (resistance for d. c.) parameters, which may be defined as:
Z 11 =, is the input impedance when output is open
I 2 = 0
circuited or open- circuit input impedance.
Z 12 = , is the reverse transfer impedance when
I 1 = 0
input is open circuited or open circuit reverse transfer impedance.
Z 21 =, is the forward transfer impedance when
I 2 = 0
output is open circuited or open circuit forward transfer impedance. and Z 22 =, is the output impedance when input is open
I 1 = 0
circuited or open circuit output impedance.
These Z parameters also known as open circuit parameters, since in these parameters either input or output is open circuited. The equivalent circuit of the network using Z- parameters may be drawn as given below: