To calculate the input impedance of a network using its S-parameters, you need to convert the S-parameters to impedance parameters. For a two-port network, S-parameters (Scattering parameters) are given as S11, S12, S21, and S22, which represent the voltage waves incident and reflected at each port.
The impedance parameters are represented by Z11, Z12, Z21, and Z22, which relate the voltage and current waves at each port. For the purpose of calculating the input impedance, we are interested in Z11.
To convert S-parameters to impedance parameters, you can use the following equations:
Z11 = Z0 * ((1 + S11) * (1 - S22) + S12 * S21) / ((1 - S11) * (1 - S22) - S12 * S21)
where:
Z11 is the input impedance of the network.
S11, S12, S21, and S22 are the S-parameters.
Z0 is the characteristic impedance of the network, usually 50 ohms for most RF systems.
Keep in mind that the above formula assumes a two-port network. If you have a multi-port network, the conversion becomes more complex as you will have multiple impedance parameters. The formula above holds only for a single-ended network.
Once you have calculated Z11, it represents the input impedance of the network as seen at Port 1. If you are interested in the input impedance seen at Port 2, you would need to swap the corresponding S-parameters and perform the calculation again.