# Can I get the S21 parameter from a one-port open, short and load reading?

I am currently working with a custom rectangular waveguide, which has one port abled to connect to a VNA,(call it port a) but the other side cannot, (its part of a bigger system but for now its only important to know that it cannot connect to a VNA & we'll call it port b.) I need to find the S21 parameter at port a, and I have a custom-made match, short, and open for port b. So the question is: Can I convert S11 to S21 if I have one-port S11 open, short, and load readings? Thank you very much.

• Is there any reason to think the waveguide is not reciprocal ($S_{12}=S_{21}$)? Is there a mode conversion involved in the transition from port a to b, and if so are the feeds long enough to assume any evanescent waves have decayed before reaching the ports? – The Photon Jan 28 at 20:42

Your device under test has four complex unknowns, S11, S22, S21, S12.

You have three complex knowns with which to terminate the far end, short, open and match.

Four unknowns, three equations, no, it cannot be done without further information or further measurements.

Where can you get extra information from?

a) Is the waveguide reversible? Can you remove it from the system and connect the second port to the analyser, and terminate the first port. Six measurements, four unknowns. You can now find all the unknowns, if you can assume that S11 and S22 stay constant as you disconnect and reconnect, so keep those mating surfaces clean and undamaged. The extra two equations will get you an estimate of your measurement errors as well.

b) Can you assume S11=S22, or S12=S21? That would reduce the number of unknowns, assuming either gets you to the right number of equations. If you assume both, you'll get an estimate of your errors as well.

c) Do you have another section of identical waveguide, which can be cascaded with the first? This offsets the loads, to give you more equations, making the assumption that they're identical. Swap them over if you can, the extra equations will let you test that assumption.

• @JacobGiese, if you can't connect anything to the far end, then where are you connecting your open, short, and match terminations? – The Photon Jan 28 at 21:03
• @Neil_UK Thank you so much answer Ill reply to each point: A) Unfortunately I cannot connect anything to the far end. This far end, is basically just a cut waveguide antenna. So reversibility is not possible B) I have waveguide that is assumable identical to the DUT, which is able to be fully tested. I found that this waveguide showed S12=S21 but not S11=S22. So for the DUT I don’t want to assume S11=S22 C) Yes, I have waveguides that are very similar to the DUT and for all intends and purposes they’re equal. In regards to cascading, there is no possible way to connect anything to the far end. – Jacob Giese Jan 28 at 21:45
• @The Photon My apologies for the confusion, the far end is a cut waveguide antenna, and I have a custom made short, open, and match which are just applied to the opening of the far end (I.e the match is just applied to the opening). If that makes sense? When I say nothing can connect, I mean that nothing can screw into the far end for a secure connection – Jacob Giese Jan 28 at 21:46