Question

Derive the formulas to convert Z-parameters to Y-parameters.

Answer 1

To convert Z-parameters (impedance parameters) to Y-parameters (admittance parameters), you can follow these steps. First, let's define the Z-parameters and Y-parameters for a two-port network:

Z-parameters (Z11, Z12, Z21, Z22):
Z11 = Input impedance at Port 1 with Port 2 open-circuited.
Z12 = Input impedance at Port 1 with Port 2 short-circuited.
Z21 = Input impedance at Port 2 with Port 1 open-circuited.
Z22 = Input impedance at Port 2 with Port 1 short-circuited.

Y-parameters (Y11, Y12, Y21, Y22):
Y11 = Admittance looking into Port 1 with Port 2 open-circuited.
Y12 = Admittance from Port 2 to Port 1 with Port 1 short-circuited.
Y21 = Admittance from Port 1 to Port 2 with Port 2 short-circuited.
Y22 = Admittance looking into Port 2 with Port 1 open-circuited.

To convert Z-parameters to Y-parameters, use the following formulas:

Calculate the determinant of the Z-parameter matrix:
D = Z11 * Z22 - Z12 * Z21

Calculate the individual Y-parameters:
Y11 = Z22 / D
Y12 = -Z12 / D
Y21 = -Z21 / D
Y22 = Z11 / D

So, the conversion formulas are:

Y11 = Z22 / (Z11 * Z22 - Z12 * Z21)
Y12 = -Z12 / (Z11 * Z22 - Z12 * Z21)
Y21 = -Z21 / (Z11 * Z22 - Z12 * Z21)
Y22 = Z11 / (Z11 * Z22 - Z12 * Z21)

Remember that Z-parameters and Y-parameters are used to characterize two-port networks, and they provide different representations of the network's behavior. Converting between them can be useful in various circuit analysis and design scenarios.