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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.

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Why can I ignore this 50ohm port impedance when A and B are cascaded?

It's not being ignored in the mathematics. It is already part of the S-parameter measurements made in the original 50Ω system.

You'll notice that when you cascade the networks, using Mason's Non-Touching Loops rule, or by first principles from the signal flow graph, or by converting them to ABCD matrices and multiplying, you are not simply multiplying A_S21 by B_S21 to get AB_S21. There are also terms in there which account for the gain round (for instance) the A_S22 and B_S11 loop. This accounts for the fact that A is now connected to B_S11 rather than 50 Ω. Just in case you were leaping to conclusions, this doesn't mean that A is now terminated in B_S11, it's terminated in B's 50 Ω termination as modified by all the S-parameters of B.

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Neither the 50 ohm source nor the 50 load are part of the system defined by the S-parameters.

The S-parameters describe block "A" and block "B." I think your confusion might be that the S-parameters are defined for a 50 ohm system (in this case).

More practically, you can think of the source impedance as port 1 of a network analyzer and the load impedance as port 2 of the network analyzer. They're needed to measure the block but they are not part of the blocks themselves.

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