# Temperature modeling of S-parameters

Revised (yet again) for August 2020. Now we have a complete analysis of how we fit a real amplifier to perform over temperature. In this case we are looking at the AM1063 amplifier from Atlanta Micro.  It is a nice, broad-band low frequency amplifier that doesn't suffer the curse of huge gain-slope versus frequency that most cheap HBT parts do. However, you have to add your own bias network externally.  The manufacturer plotted gain at three temperatures, -40C, +25C and +85C. Note that you need to take gain/temperature data with a grain of salt, as it is hard to measure without errors of test cable temperature variation contributing to the overall effect. In this case the gain/temperature variation is pretty low, so we tend to believe it.

AM1063 GainTemp Data

Below is the manufacturer's data on noise figure over the same three temperatures.

AM1063 NF Temp Data

We set up our Microwave Office model of the AM1063 as a sub-circuit, with the variable "TempC" as a parameter.  This is an extra step, but it shows how the model would be used in a larger design, such as a receiver. The swept variable "SWPVAR" controls temperature. Using squiggly brackets allows you to enter a list of temperatures, in this case they are temperatures used in the data sheet.

Swept Temp Schematic

Here is the AM1063 sub-circuit.  It has four ideal amplifiers and four circulators, plus the AM1063 S-parameters. Ideal input amplifier U4 set the noise figure/temperature variation from the equation for G1 and ideal output amplifier U3 sets gain/temperature variation from the equation for G2. Note that G2 has G1 subtracted from it, which decouples the gain and noise figure temperature coefficients. Amplifiers U1 and U2 provide inverse gains at input (-G1)  and output (-G2), otherwise the reflection coefficients S11 and S22 would vary across temperature (which typically does not happen).

AM1063 with TempCo

Here's a closer look at the equation set, in case you can't read it from the schematic graphic.

Here, after some trial and error of adjusting TCGain (temperature coefficient of gain), gain at three temperatures are made to behave close to the data sheet.  Nothing in life is perfect, but this deemed good enough for a system design.

AM1063 Gain Temp Model

In order to have the noise figure predicted over temperature, there is an intermediate step.  You have to read the noise figure off the plot, and add it as text at the bottom of the S-parameter file. We have no idea why amplifier vendors refuse to do this.

Here is what we came up with, the frequency is in Hz because that is what Atlanta Micro used in the S2P file. The "0.2" is the noise resistance (not really important) and "0" is GammaOpt (assumed center of Smith chart). Learn more about faking noise parameters here.

! NF from data sheet at 25C
100000000   3.8  0.2  0 0
1000000000  3    0.2  0 0
2000000000  2.5  0.2  0 0
3000000000  2.1  0.2  0 0
4000000000  2    0.2  0 0
5000000000  2.3  0.2  0 0
6000000000  2.5  0.2  0 0
7000000000  2.8  0.2  0 0
8000000000  3.1  0.2  0 0
9000000000  3.3  0.2  0 0
10000000000  4.0 0.2  0 0

Finally, we used trial and error to find a value of TCNF (temperature coefficient of noise figure) to fit the measure performance.  Here is what we came up with.

AM1063 NF Temp Model

We didn't plot reflection coefficients S11 and S22 over temperature, you'll have to trust us that they don't vary if you do this correctly. Now that the model works, you can apply it to any temperature within reason (don't assume it is going to work at cryogenic temperatures!

Why not use attenuators to vary gain and NF? You could use attenuators for positive temperature excursions, but for low temperature it won't work. The Microwave Office attenuator model does not allow negative attenuation (in other words, it can't supply gain at low temperature).  Similarly, there is no way to express negative noise figure so you can't use an attenuator on the input if you expect to use the model to predict decreasing noise figure at cold temperatures

## Switch temperature model

Custom MMIC's CMD196 is a SPDT switch that works from DC to 26.5 GHz. It is currently the best switch for wide-band applications, the competitor's choices all suck.

The only S-parameter that CMD's datasheet shows temperature performance for is the low-loss state, shown below. However, you can rest assured that the isolation is also a function of temperature, even if we don't have data to show how much it varies. In any case, it is a high-isolation switch.

Custom MMIC does not offer three-port S-parameters of their switches, which are needed for switch matrices.  So you are on your own to gather that info.  We were able to obtain it by our awesome web of contacts throughout the industry (meaning we grabbed the data from our Day Job...)

Below is a three-port model of the switch that predicts performance over temperature. Port 1 is the common port, port 2 is isolated and port three is the through port. In this case we had to configure four amplifiers (and paired isolators) around the three-port network to make the magic happen.  Did someone say "magic?"  Take a break and hear Louis and Keely belt out Old Black Magic...

Note that there is no need for an amplifier pair on the common port, you can do all the dirty work on the other ports.  Further, note that the isolator pairs insert the ideal amplifiers in both directions so S21 varies the same as S12 and S31 varies the same as S13.  Further-further note that it was necessary to have temperature coefficients that change both the gain and the slope of the ideal amplifiers in order to fit the data.

Below is the best we could do to fit the temperature curves.  Oops, it sort of falls apart below 4 GHz, you will have to accept some error there if you want a good fit up at 26 GHz.  Also, the 25C loss seems higher at 30 GHz than the data sheet projects.  What can we say, these plots are based on data that was measured by the user, specifically to gather complete three-port de-embedded data. Up to 25 GHz the 25C data agrees pretty well with the data sheet. If you want a good SPDT switch at Ka-band, we suggest you pick a band-pass switch, it will have lower loss, better match and higher power handling.

What's up with the isolation curves?  If memory serves, the curves were fit to actual data, but we can't seem to find that right now so accept our apologies.

# Faking 3-port data for from two-port data

Here is a great topic to consider if you are designing switch matrices, switched filter banks, and time delay units. Go here....

Author : Unknown Editor