Question

How do you find the input impedance of a network using Z-parameters?

Answer 1

To find the input impedance of a network using Z-parameters (impedance parameters or impedance matrix), you need to follow a specific set of steps. The Z-parameters represent the relationship between the voltage and current at the input and output ports of a linear network. For a two-port network, the Z-parameters can be represented as a 2x2 matrix:

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[ V1 ]   [ Z11 Z12 ] [ I1 ]
[    ] = [          ] [    ]
[ V2 ]   [ Z21 Z22 ] [ I2 ]


where:

V1 and V2 are the voltages at the input and output ports, respectively.
I1 and I2 are the currents at the input and output ports, respectively.
Z11, Z12, Z21, and Z22 are the elements of the Z-parameter matrix.

To find the input impedance (Zin), follow these steps:

Short-circuit the output port (V2 = 0). This means that the output port is replaced with a short circuit, effectively making V2 = 0.

Write the equations using the Z-parameters and the short-circuited condition:

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V1 = Z11 * I1 + Z12 * I2    (V2 = 0, so I2 = 0)

Solve for I1:
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I1 = V1 / Z11

The input impedance (Zin) is the ratio of the voltage to current at the input port (V1/I1):
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Zin = V1 / I1 = V1 / (V1 / Z11) = Z11


So, the input impedance (Zin) of the network is equal to the Z11 element of the Z-parameter matrix.

Keep in mind that this method assumes a linear network. If the network is non-linear, the concept of impedance parameters may not apply, and you might need to use other techniques for analysis.