?: S-parameters and Characteristic Impedance

[saryee]

Hello, there,

If the S-parameters of a two-port device are known, can the characteristic impedance be calculated? And how?

BR,

saryee

 

[flatulent]

yes

There are standard equations to convert between all of the two port parameter sets.

What do you mean by characteristic impedance?

 

[eltonjohn]

I THINK HE IS THINKING ABOUT .......

IT SEEMS THAT HE IS TALKING OF A TRANSMISSION LINE!

 

[maxwell2002]

I don't think that you could get Zc's, for given S-MAT.

 

[Nuj_am]

I guess it con not be caculate,Zc is also influenced by the other parameters,u must need lots of others to caculate.

 

[mImoto]

Hello,

You need to know rs or rl (reflexion coeficient at source or load)

rin=S11 + s12.s21.rl/(1-s22.rl)=(Zin-Zo)/(Zin + Zo)
rout=S22+s12.s21.rs/(1-s11.rs)=....

knowing the S parameters and rs or rl then you know rin or rout and with the formula of the reflexion coeficient you get Zo. Check Pozar book.

but I remenber that it is not so easy in the real life to get the Zo (you need rs or rl).

Best regards,

mimoto

 

[BigBoss]

What a strange question ?? :?

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..

unlogical question , nonsense.. :sm31:

 

[maxwell2002]

BigBoss is absolutely right. I agree with you.

 

[nickwang]

I agree with mImoto.
You could normally get S parameters but not
Zo, with network analyzer.
and with all S parameters available, you can
calculate Zo

 

[saryee]

There are standard equations to convert between all of the two port parameter sets.

What do you mean by characteristic impedance?

-- I don't mean to calculate the Z-parameters.

IT SEEMS THAT HE IS TALKING OF A TRANSMISSION LINE!

-- Yes.

I guess it con not be caculate,Zc is also influenced by the other parameters,u must need lots of others to caculate.

-- But after the physical dimensions of the TxL are determinded, I think, the characteristic impedance should be constant at a certain frequence.

Check Pozar book.
-- Which one?

Any way, thank you all. I'm just a newbie. Thanks for you help.

 

[Mazz]

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.

Bye
Mazz

 

[Andryuha]

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.