impedance, s11, s21 relation

If you have a *.s2p file of a transistor,and you will know
S parameter.how to invert to Zin( Re,Im)
need equation?

input the s11(or s22) to the smithchat (smith_v191) , the Zin(or Zout) will appear on the bottlm of display when cursor moving to location! have a try!

In ADS a very useful function is zin(S(i,i),Z_ref) where i=1,2 depends if you want input impedence at port 1 or 2 and Z_ref is the reference impedence used to caculate the S parameters in the ADS simulation, typically 50 ohm.

Here is the formula, you can find in microwva books (Pozar,..)

Rin(reflexion coeficient at the input)
Rl(reflexion coef. at the load)
Rin=S11 + S12.S21.Rl/(1-S22.Rl)=(Zin-Zo)/(Zin + Zo)


Anyway, the practical way is to download an rf app.programme(I don't remenber the name from rfglobalnet.com there you can intro de s parameters in .s2p and you can see the Zin in SChart.

Best regards,

mimoto

The relationship between Z-matrix and S-matrix is this:
lets call n the characteristic impedance matrix of the lines (it is a diagonal matrix) then:
S = (Z-n)(Z+n)^(-1) S, Z, n are matrix and the one i indicate is a matrix relation and it is very general

bye

If you're 5yrs exp. RF designer (then I'm curious why u ask this), you are probably using some CAD as ADS or MWO. Then it's possible to import .s2p file and get graph of whatever you need (s-params, Z,Y...)
Regards,
Eirp

I am discussing a base knowledge about Zin and Sparameter.I have used motorola impedence matching program.
It wants to input zin,and then selects match circuit,and then you can see Z(matched )rotating with the value of component changing in smith chart.
In the middle of smith is a requirement RL circle,Within it everything is OK.
Where does S11 and S22 rotate to when Zin rotate in the RL circle?
And how to decide mini Q value simple from Sparameter?
I think it maybe easy for somebody,but don't laugh me for ask this question.
Unknown is possible for everypeople.
Xie Xie Ni

I was wondering too :)

Anyway, as others said above, and as found in text books:

Calculate your input reflection coff. first:
Gamma_i=S11 + S12.S21.Gamma_L/(1-S22.Gamma_L)
(where Gamma_L is your load reflection coff.)
then calculate Zin:
Zin=Z0*(1+Gamma_i)/(1-Gamma_i)
where Z0 is characteristic impedance (50ohms in most cases)..

All variables (S11, S12, S21, Gamma_i, Gamma_L, Zin) are complex numbers, so you need to convert the dB values usually found in *s2p files to ratios (antilog) first, then plug it in the above equations with its associated angles, then you get your Zin as a complex number also..

Alternatively, (and much quiker if you have a *s2p file), use any RF CAD tool to simulate your s-parameters block connected to your load and then use builtin CAD functions (like Zin(s,50) in A_D_S) to get your Zin...

Cheers...

For those of you who want to do such things in an automated way, adlab http://www.weberconnect.de/adlabp2.htm has a program called vierpol (two port in English) that will acclept s parameter files and calculate other parameters, impedances, gain, stability, etc. It works free for 20 times or so. The shareware fee is pretty low for what you get.

We are not laughing at you, but wondering only :)

Such questions will be easier for you to answer by refering to a basic RF book (like Pozar, or Gonzalez books), where you will find all the equations/relations between all those parameters (S11, Zin, Gamma-in ...etc), and I assume you already have one, or read one of those books before. It is always in my desk, b/c you never know when you gonna need it :)

Cheers....

It is very common for someone who is self studied on a topic and learn from their job experience to have some lack of knowledge that is taught in schools. How many of you who do complete communication systems know the relationship between autocorrelation and power spectral density? Or the analytical mathematical relationship between amplitude and phase in an analog filter?

I am clearly about some of it now.
I wanna to know
For Example:
Input matching,no considering S12 for simplizing,Zin=a+jb(at a freq),in somewhere one point in SmithChart and then add a series Capacitor for some value ,then it will turn clockwise alone G curve......so it can be changed to middle point of SmithChart by adding some LC.
I ask does S11 also in the middle of SmithChart when matched?
And another question is unmatched Zin is somewhere so we can decided the mini value of Q,
does S11 also can decide Q value ?

please Answer Ques first,and then wonder as much as you like

If 50 +j0 is what you want to end up with, the center of the chart is where to aim for.

In general, the ratio of the real parts of the start and end impedances set the Q (or bandwidth) of the matching circuit.

The general way to do a L network is to first notice if the real part is being transformed up or down. If up the first element is series, if down the first element is shunt. You then have the opposite (shunt or series) direction for the second element.

The best way to visualize the matching on the smith chart is to use one with two colours for the impedance lines and the admittance lines.

Here is an example to follow on such a chart. We will us the normailzed chart with 1.0 at the center. We want to end up with 2.0 as the impedance. You add a series +/- J1 to the 1.0 and then at the end of that you put a -/+ j1 in shunt. If you follow the lines on the chart you see that the two reactance lines running through 1 and 2 on the impedance colour and the admittance colour meet at a point.

Here is a chart to practice on.

Convert the S matrix into Y matrix. Zin = 1/Y11. Zout=1/Y22
You can also see from the smith chart.

No ! It's wrong. This is ONLY valid unilateral circuits. I mean if S12 is 0 , it can be applicable. Otherwise No..

Gamma(In)=S11+(S12*S21*Gamma(out))/(1-S22*Gamma(out))

Hereafter ,

Zin=Zo(1+Gamma)/(1-Gamma)

or on Smith Chart , could be found.