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When the S-parameters of a 2-port device whose input and output impedance are different from 50 Ohm are calculated/measured in a 50-Ohm system, multiple reflections occur at port 1 and port 2.

Let's take the example of calculating/measuring S11:

When injecting a signal into port 1, part of it is reflected at the generator-port1 interface and the rest travels to port 2 where part of it is reflected at the port 2 load interface.

This partial reflection travels back, part of it goes into the generator impedance, the rest is re-reflected towards port 2, etc.

Is it correct to say that all these waves reflected back into the generator are summed up and therefore accounted for in the calculation/measurement of S11?

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Is it correct to say that all these waves reflected back into the generator are summed up and therefore accounted for in the calculation/measurement of S11?

Yes.

That's part of the beauty of S-parameters.

Perhaps it might help you believe that it works, and isn't magic, if we review what happens when you take two of these 2-port things you've just measured, and cascade them, with or without an intervening 50 ohm line.

Cascading involves use of Mason's Non-Touching Loops rule, aka Mason's Gain Formula to combine them. As well as a simple product of the S21s in the numerator that you'd expect, there's a tricky 1+/-loop_gains in the denominator that handles these multiple reflections.

If you do cascade the 2-ports via a piece of 50 ohm line, then you are cascading three sections, and although the middle one is 50 ohms so S11=S22=0, it's vital you include its electrical length in the phase of S21 and S12, so that the reflections add up correctly.

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