Question

How do you convert Y-parameters to S-parameters?

Answer 1

Converting Y-parameters (admittance parameters) to S-parameters (scattering parameters) is a common task in microwave engineering and network analysis. This conversion is essential when working with different types of network representations. The process involves using mathematical formulas to transform one parameter set into the other. Here's how you can convert Y-parameters to S-parameters:

Y-parameters represent the relationship between voltage and current at the input and output ports of a two-port network. They are represented as a 2x2 matrix:

css
Copy code
[ I1 ]   [ Y11  Y12 ]   [ V1 ]
[    ] = [          ] * [    ]
[ I2 ]   [ Y21  Y22 ]   [ V2 ]


Where:

I1 and I2 are the input currents at ports 1 and 2, respectively.
V1 and V2 are the input voltages at ports 1 and 2, respectively.
Y11, Y12, Y21, and Y22 are the Y-parameters of the network.

S-parameters, on the other hand, represent the relationship between incident and reflected waves at the input and output ports of a two-port network. They are also represented as a 2x2 matrix:

css
Copy code
[ V1 ]   [ S11  S12 ]   [ V1' ]
[    ] = [          ] * [     ]
[ V2 ]   [ S21  S22 ]   [ V2' ]


Where:

V1 and V2 are the incident voltages at ports 1 and 2, respectively.
V1' and V2' are the reflected voltages at ports 1 and 2, respectively.
S11, S12, S21, and S22 are the S-parameters of the network.

To convert Y-parameters to S-parameters, you can use the following formulas:

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


Here, Y21 must not be zero for the conversion to be valid.

It's important to note that both Y-parameters and S-parameters are frequency-dependent, so the conversion is valid only for a specific frequency or frequency range. If you need to convert Y-parameters for a wide frequency range, you'll have to repeat this process for each frequency point of interest.