Question

How do you find the transmission gain from Y-parameters?

Answer 1

To find the transmission gain from Y-parameters (also known as admittance parameters), you'll need to convert the Y-parameters into S-parameters (scattering parameters) first. Once you have the S-parameters, you can easily calculate the transmission gain.

The Y-parameters represent the relationship between the port currents (I) and the port voltages (V) of a two-port network. They are defined as follows for a two-port network:

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[ I1 ]   [ Y11  Y12 ] [ V1 ]
[    ] = [          ] [    ]
[ I2 ]   [ Y21  Y22 ] [ V2 ]


where:

Y11 is the admittance between port 1 current and port 1 voltage.
Y12 is the admittance between port 1 current and port 2 voltage.
Y21 is the admittance between port 2 current and port 1 voltage.
Y22 is the admittance between port 2 current and port 2 voltage.

To calculate the S-parameters, you can use the following equations:

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S11 = (Y21 * Y12 - Y11 * Y22) / (Y21)
S12 = -Y11 / Y21
S21 = 1 / Y21
S22 = -Y22 / Y21


Once you have the S-parameters, the transmission gain (also known as forward gain) can be obtained as follows:

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Transmission Gain = |S21|^2


The magnitude squared of S21 represents the power gain from input port 1 to output port 2.

Keep in mind that Y-parameters are more commonly used in certain situations, such as when dealing with devices that have parallel terminations. However, S-parameters are more prevalent in most RF and microwave engineering applications due to their ability to handle a wider range of impedance variations. If you are working with Y-parameters, you can convert them to S-parameters using the above equations before calculating the transmission gain.