Sparameters

Hello to all,

Can any person tell me the diffrence between computing the gain of an
RF circuit with a Sparam simulation and an AC simulation?

NB: I find always a diffrence between S21 and the gain obtained by an
AC simulation.

Thank you.

 

Hi,

AC simulation considers voltages and currents whereas s-parameter
considers incident and reflected power waves.

Let's say you have a quadripole Q with voltage v1 and current i1 at
the inputs and v2, i2 at the output (current going into Q).

In S-parameters you would define an incident power wave a1 and
reflected one b1 at the input, and alike a2, b2 at the output.
The S-parameters are defined as:
S11= b1/a1 @a2=0, S22= b2/a2 @ a1=0, S21= b2/a1 @ a2=0 <- the
"gain", S12 = b1/a2 @ a1=0

I can be shown that you have:
v1 = sqrt(Zo) x ( a1 + b1)
and i1 = ( a1 - b1 ) / sqrt(Zo) at the input, where Zo is the
characteristic impedance (usually 50ohm)
same thing at the output w/ v2, i2, a2, b2 [ S-parameters are
always defined relative to a given Zo ].

If Q is made of an input impedance Ze, and a voltage-controlled
voltage source (controlled by the input voltage)
with gain G in series with impedance Zs at the output (unidirectional
quadripole), you get:

S11 = (Ze-Zo)/(Ze+Zo)
S22 = (Zs-Zo)/(Zs+Zo)

S21 = G/2 x (1+S11) x (1-S22).

Thus, if you define an AC-simulation gain as v2/v1 when Q is unloaded
and driven by an ideal voltage source, v2/v1=G, but S21 is not
equal to G.

Let's take the specific case where Q has infinite input impedance and
zero output impedance (simply a vcvs source in spectre) , the
AC-simulation voltage gain is G - whatever the load and source
impedances -, but the S-parameters give you:
S11= 1
S22= -1
S12= 0
S21= 2G !

AC voltage or power gains are linked to s-parameter S21 gain, but not
equal to it.

Actually you can find conversion tables betwen a S-parameter matrix
and h-parameter / y-parameter matrices defining the quadripole
propertiies.