Question

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

Answer 1

Converting S-parameters (Scattering parameters) to Z-parameters (Impedance parameters) involves a mathematical transformation. S-parameters describe the relationship between the incident and reflected waves at each port of a multi-port network, while Z-parameters represent the impedances seen at each port when the other ports are terminated with their characteristic impedances.

For a 2-port network, the conversion equations are as follows:

Z11 = (1 + S11)(1 - S22) / (S11 - S22 + S21 + S12)
Z12 = 2 * sqrt(Z11 * Z22) * S12 / (S11 - S22 + S21 + S12)
Z21 = 2 * sqrt(Z11 * Z22) * S21 / (S11 - S22 + S21 + S12)
Z22 = (1 - S11)(1 + S22) / (S11 - S22 + S21 + S12)

Where:

S11, S12, S21, and S22 are the S-parameters of the 2-port network.
Z11 and Z22 are the Z-parameters corresponding to the input and output impedance at Port 1 and Port 2, respectively.
Z12 and Z21 are the cross-impedances between Port 1 and Port 2.

Here are the steps to convert S-parameters to Z-parameters for a 2-port network:

Obtain the S-parameters: Measure or obtain the S-parameters of the 2-port network. These parameters are typically provided in the form of a matrix or data table.

Calculate the Z-parameters: Use the conversion equations mentioned above to calculate the Z-parameters (Z11, Z12, Z21, and Z22) based on the given S-parameters.

Validate the result: Check if the converted Z-parameters are physically meaningful. For example, Z11 and Z22 should have positive real values (impedance values), and Z12 and Z21 should have real and imaginary parts (reflecting coupling between ports).

Note that the conversion from S-parameters to Z-parameters may not always be straightforward, especially for higher-order networks. In such cases, it is common to use specialized software tools that can perform the conversion accurately. Many simulation and design software packages offer this functionality to facilitate RF and microwave circuit analysis and design.