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If the S-matrix is well defined , how the Zo is not defined ?
Zo is the characteristic impedance of the measurement system. It can be 50 Ohm or 75 Ohm smt..
By definition of S parameters , a Zo must be defined to measure or simulate them..
My idea of the question is:
saryee KNOWS that the Sparameter set represents a transmission line, and he wants to know what is the char imp of this line.
theorically the answer is simple, it's just to do a small mathematic.
Or, using a simulator, U can optimize Z0, attenuation and electrical length of an ideal transmission line in order to have the same S-parameter.
Oh my ***!
People!?
Don't you see the difference between the Zo of the measurement system, including Analyzer ports and cables and the Zc of the DUT?
Zo is usually impedance of normalization (reference), that is suggested to be impedance of ports and cables. So, 50Ohm (or 75, if you are into television)
Zc is the impedance of the *PASSIVE* DUT (2-port transmission line of the Unknown property)
Therefore, from the DUT point of view, Zo is a LOAD, not a characteristic impedance.
S-parameters&2 Loads are complete system. As well as ABCD parameters.
When you are calibrating your analyzer - you EXCLUDE ports and cables from equations by default. You don't need to know them - only the port impedance is enough.
Now, using normalization, you can convert S&Load->ABCD and *ESTIMATE* U/I form ABCD as SQRT(B/C)
The problem is, the load impedance is not always Real. So, you can only guess, is it 50Ohm, or X+jY, where X just MAY be something close to 48+- Ohm.
Use V.F.Fusco book, it is simpler.
And use passive calibrations kits! Calibrate with THRU of the same electrical length as both connectors.
Clean the kit with tools and alcohol before use. Automatic calibrators are useless for such kind of things, the phase error is horrible.
This works even in HFSS, but you must disable port renormalization, simulate 50Ohm input and output connector-structures alone and extract them from ABCD first (ABCDport^-1 x ABCD x ABCDport^-1).
Simple equation can be used on well calibrated Agilent PNAs in REAL TIME (unfortunately, with bad precision)
This doesn't work well on ferrite phase shifters because the phase shift could be >100pi and the errors are considerable. SQRT(B/C) also doesn't work here well, see Collin.
I've seen, there are more precise ways of extracting the impedance basing on knowledge of reciprocal matrices. I just didn't figure them out. One guy was reciprocally fixing symmetry in matrices before excluding port's ABCD^-1, so impedance was smooth and precise in the 2-20Gh band without waves with all singularities.
So, if you have an Idea how to make it more precise, please share the method here.
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