ADS S-parameter and Z-parameter discrepancy

[szoftveres]

I'm trying to match the input of a textbook bipolar NPN cascode, in ADS, on a single frequency (not needed for anything, just for my learning).

I've built up the model and attached a 50ohm port to the input. I biased the amplifier properly and verified the voltages and currents with DC simulation. I then selected the S-parameter simulation, and turned on the Z-parameters as well, so that I can directly plot the input impedances (real and imaginary parts) seen by the input port.

I then ran the S-parameter simulation, and got the Z-parameters. Then I built the input matching network at the frequency of interest, and ran the sims again. The input impedance seen by the port at the frequency of interest is 50+j0 after matching, but the S1,1 Smith chart shows a totally different story (capacitive).

Just for curiosity, I tried to model the input impedance of the transistor amplifier with discrete RC parts, and applied the matching network on it, and in that case both the Z-parameters and the S1,1 Smith chart agreed and showed perfect match.

I'm stuck, not knowing why the transistor input impedance is making the S-params and the Z-params look different, and don't know how to fix this. The amplifier is BTW making 12dB'ish of gain.

[rf-messkopf]

I'm stuck, not knowing why the transistor input impedance is making the S-params and the Z-params look different, and don't know how to fix this. The amplifier is BTW making 12dB'ish of gain.

Review the definition of Z-parameters. \$Z_{11}\$ is defined as the quotient of the voltage at port 1 and the current into port 1 under the condition that the current into port 2 is 0.

If you want to convert \$S_{11}\$ to impedance you have to do
\[Z_{\rm in}=Z_0\frac{1+S_{11}}{1-S_{11}},\]
where \$Z_0\$ is the reference impedance (usually 50 ohms). Unless \$S_{12}\$ or \$S_{21}\$ is zero, \$Z_{11}\$ for a two-port is different from \$Z_{\rm in}\$.

Addendum: If your two-port is not terminated with \$Z_0\$ at port 2, but with a load with reflection factor \$\Gamma_2\$, the reflection coefficient looking into the input is given by
\[\Gamma_1=S_{11}+S_{12}S_{21}\frac{\Gamma_2}{1-S_{22}\Gamma_2},\]
which determines the impedance looking into port 1.

[szoftveres]

Thanks, this is interesting.

I removed the 50ohm port from the output (see port 2 the drawing above) and substituted it with a 50ohm resistor (now I only have S1,1 and Z1,1), and re-matched the input.

Now both Z1,1 and S1,1 agree.

(I still wonder why port 2 impedance was not considered in the Z1,1 calculations, but at least I'm now unblocked)

[rf-messkopf]

(I still wonder why port 2 impedance was not considered in the Z1,1 calculations, but at least I'm now unblocked)

As I said, by definition, \$Z_{11}\$ is the quotient of the voltage at and the current into port 1, assuming that the current into port 2 is equal to zero, i.e., with port 2 open. When you convert \$S_{11}\$ to impedance by \$Z_0(1+S_{11})/(1-S_{11})\$, or equivalently by reading the real and complex part of the impedance from the curvilinear coordinate lines of the Smith chart, you are assuming that port 2 is terminated with an impedance of \$Z_0=50\,\Omega\$. This is how S-parameters are defined. Unless \$S_{21}=0\$ or \$S_{12}=0\$ (or both), these impedances are not the same. Check the transformation formulas between S-parameters and Z-parameters to verify this.

I removed the 50ohm port from the output (see port 2 the drawing above) and substituted it with a 50ohm resistor (now I only have S1,1 and Z1,1), and re-matched the input.

Now both Z1,1 and S1,1 agree.

Now, since you are dealing with a one-port, \$Z_0(1+S_{11})/(1-S_{11})\$ and \$Z_{11}\$ agree, and the impedance you are getting is the actual impedance looking into the input of your amplifier when the output is terminated by the 50 ohms resistor that you added.

[szoftveres]

Totally clear - thanks!