Question

How can you calculate the voltage gain from Y-parameters?

Answer 1

To calculate the voltage gain from Y-parameters (also known as admittance parameters), you'll need to consider the Y-parameters of a two-port network. The Y-parameters describe the input admittance (Y11 and Y12) and output admittance (Y21 and Y22) of the network.

A two-port network is a circuit or device that has two ports: an input port and an output port. The voltage gain (Av) for a two-port network is defined as the ratio of output voltage (V2) to input voltage (V1) when the network is terminated in its output impedance (Z2), while the input port is driven by a source with a source impedance (Zs). Mathematically, the voltage gain is given by:

Av = V2 / V1

To calculate the voltage gain (Av) from Y-parameters, follow these steps:

Step 1: Find the output current (I2) flowing through the output port:
I2 = Y21 * V1 + Y22 * V2

Step 2: Find the output voltage (V2) in terms of the output current (I2) and output impedance (Z2):
V2 = I2 * Z2

Step 3: Substitute the value of I2 from Step 1 into Step 2:
V2 = (Y21 * V1 + Y22 * V2) * Z2

Step 4: Solve for V2 to get it on one side of the equation:
V2 - Y22 * V2 * Z2 = Y21 * V1 * Z2

Step 5: Factor out V2 on the left side of the equation:
V2 * (1 - Y22 * Z2) = Y21 * V1 * Z2

Step 6: Solve for V2:
V2 = (Y21 * V1 * Z2) / (1 - Y22 * Z2)

Step 7: Finally, calculate the voltage gain (Av) by dividing V2 by V1:
Av = V2 / V1 = (Y21 * Z2) / (1 - Y22 * Z2)

So, the voltage gain (Av) of the two-port network in terms of its Y-parameters (Y21 and Y22) and output impedance (Z2) is (Y21 * Z2) / (1 - Y22 * Z2).