Question

How can you calculate the short-circuit current gain from Z-parameters?

Answer 1

To calculate the short-circuit current gain from Z-parameters (also known as impedance parameters or impedance matrix), you will need to determine the short-circuit current flowing into the output of a two-port network when the input is shorted. Z-parameters are a set of four complex numbers that describe the input and output impedance of a two-port network.

The Z-parameters are typically represented as follows:

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[Z11  Z12]
[Z21  Z22]


Where:

Z11 is the input impedance seen at Port 1 with Port 2 open-circuited.
Z12 is the input impedance seen at Port 1 with Port 2 short-circuited.
Z21 is the input impedance seen at Port 2 with Port 1 open-circuited.
Z22 is the input impedance seen at Port 2 with Port 1 short-circuited.

To calculate the short-circuit current gain (h21), follow these steps:

Step 1: Short-circuit the input of the two-port network (set V1 = 0).
Step 2: Measure the short-circuit current flowing into Port 2 (I2_short).
Step 3: Calculate the short-circuit current gain (h21) using the following formula:

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h21 = I2_short / Isc


where Isc is the short-circuit current on the input side.

To find Isc, you can use the Z-parameters:

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Isc = V2_short / Z22


where V2_short is the voltage at Port 2 with Port 1 short-circuited (V2_short = 0V).

So, the final expression for h21 becomes:

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h21 = I2_short / (V2_short / Z22)


Remember that Z22 should be the impedance at Port 2 with Port 1 short-circuited.

By measuring the appropriate voltages and currents and using the Z-parameters, you can calculate the short-circuit current gain (h21) of the two-port network.