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S paremter of cascaded system


Mar 30, 2024
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First, sorry for my bad English,
I have a question about the s parameter of the cascades system.
Assuming that there are two system A,B as shown in the figure and each has an s-parameter measured at 50ohm port,
I understand that the s-parameter of the A,B cascaded system can be calculated by signal flow graph analysis using the s-parameter of A and B.

However the s-parameter of system A,B are obtained with 50ohm port impedance attached to the system.
Why can I ignore this 50ohm port impedance when A and B are cascaded?
S-parameter is a value obtained when port impedance is attached in parallel to the port,
it is confusing because it seems to be used as if it is a response characteristics between port and port without port impedance.

The termination impedances are not part of the networks defined by the S-parameters, they are external to them. So, when you cascade these networks, you wouldn't include them in the cascade, only append them at the edges.
Check this article:

My understanding is that measurement devices like VNA are dealing with signal voltage and phase. Firmware contains constants for input/output impedance (Zport=50 Ohm) and some formulas to convert voltage/phase to S-parameters/point on a Smith Chart/VSWR etc.

Another way to think about it: assume we converted S-parameters to impedance and it is purely real, e.g., 133 Ohm at some frequency band. This means that it acts as a 133 Ohm resistor. We can put these 133 Ohm resistor in series and it doesn't matter if measurement device port impedance was 50 Ohm. Hope this makes sense.

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