ADS S-parameter and Z-parameter discrepancy - Page 1
Forum section: electronics / rf-microwave

author: szoftveres
author_rank: Regular Contributor
timestamp: March 02, 2023, 04:53:05 am
content: 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.

author: rf-messkopf
author_rank: Regular Contributor
timestamp: March 02, 2023, 09:28:11 am
content: Quote from: szoftveres on March 02, 2023, 04:53:05 amReviewthe definition of Z-parameters. \$Z_{11}\$ is defined as the quotient of the voltage at port 1 and the current into port 1under 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.

author: szoftveres
author_rank: Regular Contributor
timestamp: March 02, 2023, 05:25:31 pm
content: 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)

author: rf-messkopf
author_rank: Regular Contributor
timestamp: March 02, 2023, 08:02:37 pm
content: Quote from: szoftveres on March 02, 2023, 05:25:31 pmAs 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.Quote from: szoftveres on March 02, 2023, 05:25:31 pmNow, 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.

author: szoftveres
author_rank: Regular Contributor
timestamp: March 02, 2023, 09:03:02 pm
content: Totally clear - thanks!