How to compute 2-port S-parameters if all V+,V- are measured?

[genxium]

https://en.wikipedia.org/wiki/Scattering_parameters , here in wikipedia, it's said that 2 port S-parameters are defined as:

\[b_1=S_{11}a_1+S_{12}a_2, b_2=S_{21}a_1+S_{22}a_2,\] I'm quite curious on 2 questions

(1)When we're measuring a port voltage, say \[V,\] I know that \[V=V_{+}+V_{-},\] but how could I know how large is \[V_{+},V_{-}\] respectively?

(2)Even if I've got \[V_{+},V_{-}\] separately, the definition equations of S-parameters are not enough to figure out \[S_{ij}\] from \[a_1,a_2,b_1,b_2.\]

Is there any one would explain the details? Any help will be appreciated ^_^

 

[FvM]

As explained in the article, the relation of Vn+/- and a/bn depends on the external termination. But if you have an and bn, the problem refers to a simple matrix equation, so it's surely solveable, if all an are non-zero.

 

[genxium]

Do you mean that if I wanna measure the S-parameters for a 2-port component, I should first terminate 1 of the ports?

 

[FvM]

Do you mean that if I wanna measure the S-parameters for a 2-port component, I should first terminate 1 of the ports?

A VNA does. You can use arbitrary termination, if you consider it in your calculation.

I'm not sure if you understand the meaning of Vn+ and Vn- terms correctly. These are still wave parameters rather than scalar voltages, different from an and bn only by a normalization factor √Z0.

 

[genxium]

If you mean the same concepts(instance, reflection) as what're introduced in transmission line, I've just learned the concepts, and not sure if I really understand that, say if I've terminated 1 port of a 2-port network,then I may measure the voltage of the open port, but it's only 1 real number I can get, say \[V,\] how can I divide this \[V\] into instance and reflected component? Is there any principle related to Z0(I suppose you mean the characteristic impedance)?

 

[FvM]

A VNA uses a directional coupler to measure the incident and reflected wave. If you assume ideal test generator and termination resistors, you can calculate it from voltage measurements. They are however complex voltages (magnitude and phase), referenced to the generator e.m.f. Reflected wave at the generator side can be determined as a complex difference between e.m.f. and terminal voltage.

In practice, this kind of voltage measurement gives rather poor results for RF.