Temperature modeling of S-parameters

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Updated May 2020

Have you ever had to predict performance of a microwave module over temperature and wished that you had a way to accurately vary the S-parameters of your components to any arbitrary temperature?  Below we will show you how to vary measured S-parameters over temperature inside of Microwave Office.  It helps to have some data over temperature that you can fit to, many data sheets provide curves at three temperatures.

Amplifier temperature model

 The CMD222 amplifier is a self-biased LNA that works well from 5 to 11 GHz.  The data sheet has temperature curves for gain and NF. at -55 and +85C. CMD makes some great products, be sure to check them out; if they don't have what you need they can design it fast and economically process it for you.

Below are gain curves at -55, +25 and +85C.

CMD222 Gain

And here are noise figure curves at the same temperature:


You can download the CMD222's S-parameters for 25C, and if you ask nicely, they will give you the S-parameters for the other temperatures.  But what if you are interested in 0C or 50C performance?

The temperature effect model below uses the 25C data (including NF which we typed into the S-parameter file). We put two ideal amplifiers before and after the amplifier S-parameter block and added temperature coefficients to their gain (TCGain) and noise figure (TCNF) in order to fit the curves. The four ideal circulators are needed in order to preserve the reflection coefficients and S12 of the amplifiers, as the ideal amps present perfect match and perfect reverse isolation. The two variables (shown in blue) that fit the measurements are "TCNF" and "TCGain", the temperature coefficients of noise figure and gain. Although we didn't make a zoomed-in plot of the exact fit to these data, trust us, they fit really well....

Note that we did not attempt to add a temperature coefficient to S12, but that would be possible by adding two more ideal amplifiers. Why bother, so long as you know the device is stable?

Notice that the ideal amplifier models include the possibility of a gain slope "S".  For this temperature model we did not use this option, but you might want to consider it. In the figure, although S=6 (6 dB/octave), F=0 essentially shuts off the slope.

New for May 2020: We improved the technique such that the temperature coefficinet of noise figure and gain are decoupled. Below is the original figure:

Amplifier temperature model

Here is the new figure.  Yes it is hard to read. But the only change is in the equation for G2.

Now we'll make it easier on your eyes with a blow-up of the equations for G1 and G2.  G1 directly affects noise figure (versus temperature) as it applies to the amplifier on the input. G2 applies to the amplifier on the output. Here we subtract G1 in the G2 equation, which decouples the two equations, and G2 only affects gain versus temperature:

Say, why not use attenuators to vary the gain and NF? You could use an 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

Below are gain and NF swept from -65 to +85C in 30C steps.  Note that the 25C data is plotted in red and is identical to the temperature model at 25C. Now you can input any temperature you like and get fairly accurate S-parameters. If you want perfection, you will have to characterize the amplifier at the temperature you are interested in. Don't waste your time, this is good enough for Government Work. (not the slang type, real government work!)  Feel free to compare our temperature curves to the plot with the data sheet, print them out and get a magnifying glass if you like.

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.

CMD196 Loss

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.

Switch temperature model

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.

Switch temperature prediction

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