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For channel modelling in high speed PCBs we always use S parameters. What is the specialty of S parameters for this purpose? Why we are not using Z, Y, h or any other parameter?

How do we determine passivity and and causality from S parameter data?

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    \$\begingroup\$ S-parameters for multiple elements are easy to cascade. \$\endgroup\$
    – SteveSh
    Oct 9, 2021 at 20:06
  • \$\begingroup\$ First of all you can quite easily go from and to the parameters set with formulas. Probably it's tradition and also it's mostly what the measurement bridge outputs \$\endgroup\$ Oct 18, 2021 at 7:01

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In order to define the parameters in a two port network using y, z, or h-parameters, you need to use short and open circuit conditions for the network. This is not ideal for transmission lines in general because the input impedance of a distributed parameter system is a function of length.

When you’re routing a PCB, you don’t want to be cornered into making all your traces an exact length. Although you may want to match the length of some traces, it’s usually important to have the flexibility of choosing what those lengths are.

If you present a load at the output of the transmission line that is perfectly matched to the characteristic impedance of the line, the input impedance will be the characteristic impedance, regardless of the length. This is important in high speed PCB design, and you will find that almost all high speed receivers have or should have a termination load that matches the trace impedance.

Since this is how these circuits are designed, it makes sense to characterize them using parameters that are calculated assuming the load is matched to the characteristic impedance of the network. This is what s-parameters are used for.

In reality, any mismatch in impedance with the load will also show up in the parameters, and using the parameters alone, you will not be able to tell if the associated reflections are caused by mismatched impedance or by components within the network.

Causality: Non-causal systems react to future inputs. I’ve never seen an actual system that does this on a PCB, so you can usually just assume that it’s causal.

Passivity: The purpose of a 2-port network is to characterize a “black box.” It doesn’t matter to the end user whether it’s active or passive, all they really care about is how it will respond to the inputs they give it. If you want to know whether the system is active or passive, then you will not be able to explicitly tell from the s-parameters. There’s a pretty good chance it is active however if the sum of all reflected powers is greater than the sum of incident powers (i.e. the gain is greater than 1). $$\sum{|b_n|^2} > \sum{|a_n|^2}$$

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  • \$\begingroup\$ Thanks Ryan.Very good explanation. \$\endgroup\$
    – Confused
    Oct 10, 2021 at 5:27
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Directly from Wikipedia:

... S+parameters differ from Z and Y in the sense that S-parameters do not use open or short circuit conditions to characterize a linear electrical network; instead, matched loads are used. These terminations are much easier to use at high signal frequencies than open-circuit and short-circuit terminations.

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