Evaluating S-Parameter when Not Match Terminated

[taik]

Hi all,

Normally when we are using a set of S-Parameter, we are told that it's matched terminated.

For e.g a 2-port parameters, it is S= [S11 S12;S21 S22]

Now if my output is connected to a load which is not matched terminated, for e.g R.

Is there any way to find my new S-parameters by making use of the S-parameters given above?

Thank you.

 

[eastern]

Dear Taik,
I suppose you have not got the meaning of S-parameters completely. When you terminate the output port of s 2-port network with a load you will end with a 1-port network. If the load does not changes the 2-port parametrs (I mean it does not load your previous network) you will be able to derive the S11 of the resulting 1-port network with simple mathematics.

[b2 b1]=S [a2 a1]
b2=f(a2)

=>

b1=g(a1)

 

[taik]

Hi Eastern,

Yup, I might not understand it fully.

Still trying to comprehend the whole thing.

But for my question, if I am given the S-Parameter of a 2-Port network and now a load of R is placed at port 2, how do I find the resulting s-parameter matrix?

Thank you

 

[eastern]

Hi Taik,

Lets suppose we have got a 2-port network described with S-parameters:

eq. 1: b2=s22*a2 + s21*a1
eq. 2: b1=s12*a2 + s11*a1

then we also suppose that the second port is terminated to R, and we denote the reference port impedances by R0. So we may easily write:

eq. 3: b2=G*a2
where
eq. 4: G=(R-R0)/(R+R0)

ommiting b2 and a2 from equations 1-3 yeilding:

eq. 5: b1=(s1 + s12*s21/(G-S22) )*a1

and this is the port parameter for the new 1-port circuit. obviously:

eq. 6: s11(new)=(s1 + s12*s21/(G-S22) )