Convert S11 INTO S21 graph for filter passband sweeps?

Convert S11 INTO S21 graph for filter passband sweeps?

Why would I want to do such a thing if I had a shiny new VNA? Because I don't have a shiny new VNA. I took a very early retirement from the Valley (burnout) and I only have a vector antenna analyzer (which is basically just a single port network analyzer). The reason why I think this is even possible is that I, and any other engineer (retired or not), can gauge the filter's passband by eye just by looking at its return loss. Is there a conversion program for this?

Am I barking up the wrong tree, or is a graphic conversion possible in, say, Excel?

(FYI: To obtain the S11 of a passive device with an antenna analyzer is somewhat similar to using a regular two-port VNA: attach the analyzer's (single) port to the filter's "input", and then terminate the filter's "output" (with either a 51 ohm resistor or a connectorized 50 ohm termination.)

Thank you,

-Andrea

Consider |s11|2 + |s21|2 = 1 in case of a lossless filter.

Thanks FvM. Then this means, unless I'm mistaken (been away from engineering for 8 years), that the square root of 1-s11^2 equals s21, which would mean that it would be quite easy to write an Excel formula to convert an entire table of s11 values directly into an s21 graph? (Or, again, have I missed something critical?)

-Andrea

Yes, "in case of lossless filter".
Unfortunately ALL the filters have loss and ripple, and the S11 cannot give any information about these parameters.
And I have doubts that give accurate information about out-of-band rejection either.

But vfone, if you took the s11's freq, mag, and angle from a real-life terminated filter sweep (as described above), why wouldn't the end result be a real-life s21 graph?

-Andrea

The initial question was asking for a method comparable to "gauge the filter's passband by eye just by looking at its return loss". That's what the "energy conversation" equation in post #2 does. Internal losses are turning it into an inequation, still giving some information about the pass band.

The practical question is about expectable losses and intended accuracy. S11 phase doesn't hold additional information unless you can make presumptions about the filter topology.