Z-Parameter Of Two Port Network

In this article we will study about Z Parameter of two port network.

Z-Parameter is also called "Open Circuit Parameter" and "Impedance Parameter".
In Z-Parameter, the input and output voltage are function of input and output current.
( V1 , V2 ) = f ( I1 , I2 )
It can also be written as:
[V] = [Z][I]
Where Z represents Impedance Matrix.
In matrix form
[V1] =    [Z11  Z12]   [I1]
[V2] =    [Z21  Z22]   [I2]
Writing it in equation,
V1 = Z11* I1 + Z12* I2 .........eq1
V2 = Z21* I1 + Z22* I2 .........eq2
CASE-1 OPEN CIRCUITING THE OUTPUT PORT
If the Output port of the two port network is open circuited then the output current is zero, i.e. I2 = 0.

Now, equation 1 and 2 will be reduced to :
V1 = Z11* I1
V2 = Z21* I1
So, Z11 = V1/ I1    ( keeping I2 = 0 )
Z21 = V2/ I1  ( keeping I2 = 0 )
CASE-2 OPEN CIRCUITING THE INPUT PORT
If the Input port of the two port network is open circuited then the input current is zero, i.e. I1 = 0.

Now, equation 1 and 2 will be reduced to :
V1 = Z12* I2
V2 = Z22* I2
So, Z12 = V1/ I2    ( keeping I1 = 0 )
Z22 = V2/ I2  ( keeping I1 = 0 )
Z11 is called input driving point Impedance
Z12 is called forward transfer Impedance
Z21 is called reverse transfer Impedance
Z22 is called output driving point Impedance.
For a network to be symmetrical , Z11 = Z22
For a network to be reciprocal, Z12 = Z21
EQUIVALENT CIRCUIT OF Z-PARAMETER