Single transistor microwave amplifier matching process question

[szoftveres]

Hi All,

I'd like to figure out a "best practice" matching process for transistor amplifiers. The problem: when either the input or the output is matched individually, matching the other port always has an effect and "pulls"/ de-tunes the already matched port significantly, obviously due to the transistor internal (Miller) capacitance. Cascode largely solves this problem, however I'm still curious how it's done in general for just a single common-emitter/common-source gain blocks.

[TheUnnamedNewbie]

I work a lot with single-transistor amplifiers since cascodes don't work at very high frequencies. The truth? iteration. You go back and forth. Match output, then input, then output again, and so on untill it stays still. It gets harder if you have to do a power match.

But honestly, I can't remember the last time I manually did this - this kind of iterative optimization work is what we have optimization algorithms for.

[Odysseus]

FWIW, iteration/optimization isn't necessary to derive source and load reflection coefficients for a simultaneous two port match.
ADS provides the sm_gamma1(S) and sm_gamma2(S) functions for this exact purpose.
Similarly, the MATLAB RF Toolbox provides gammams and gammaml, where the underlying s-parameter equations are conveniently documented at the bottom of the page.

It should be noted that a perfect bilateral conjugate match is only possible if the amplifier is unconditionally stable.

[mtwieg]

FWIW, iteration/optimization isn't necessary to derive source and load reflection coefficients for a simultaneous two port match.
ADS provides the sm_gamma1(S) and sm_gamma2(S) functions for this exact purpose.
Similarly, the MATLAB RF Toolbox provides gammams and gammaml, where the underlying s-parameter equations are conveniently documented at the bottom of the page.

It should be noted that a perfect bilateral conjugate match is only possible if the amplifier is unconditionally stable.

I agree with all these points. If the S parameters of the DUT are known, and k>1, then exact input/output match circuits (or more specifically, their S parameters) can be derived analytically to give perfect input and output return. However this will only be at one frequency. When bandwidth requirements are factored in is when things get much more complicated, then it turns into a convex optimization problem with no unique solution... either use good software or crack open the dusty tomes...

Of course the physical implementation of the circuits can always turn out to be iterative, of course.

[BigBoss]

Search "Simultaneous Conjugate Matching Technique" in Textbooks or Internet.
You can achieve best available Reflection for a single frequency bot Input an Output Ports.
Iteration is not necessary,
http://em.emedu.org.tw/elec_sim/ElectromagnetismModule/Module4/Module4.html

[TheRuler8510]

I work a lot with single-transistor amplifiers since cascodes don't work at very high frequencies. The truth? iteration. You go back and forth. Match output, then input, then output again, and so on untill it stays still. It gets harder if you have to do a power match.

Cascodes do work at higher frequencies. I'm not sure why you would say that--maybe the way you are terminating the gate of the upper device? Using Casodes can increase your gain at higher frequencies.

[TheRuler8510]

I roughly design the in and out matching using iteration, then simultaneously optimize both input and output using simplex, gradient and random techniques. Once the topology is discovered this is easy to do. Must keep an eye on stability the whole time also.

[Georgy.Moshkin]

I only focused on stability. Instead of stability factor I used formulas for input & output stability circles, which give center, radius, and stable area (stable inside or outside). Then I had two distances from Smith chart center to unstable areas, e.g. if circle stable outside then distance to circle center minus circle radius gives distance between Smith chart center and circle outer boundary. I still have doubts why stability factor is used nowadays while stability circle formulas provide much better information, especially if you can't make it stable over wide bandwidth, with stability circles there is clear information on stability margin. I made several parallel feedback oscillators based on these calculations and all worked well, which makes me think I successfully avoided unwanted oscillations, and transistor worked as stable gain block. I had no chance to measure any of my prototypes using VNA or spectrum analyzer, because I don't have those for tenths of GHz frequencies. If you have an VNA i think next logical step would be measuring your amplifier.
For higher frequencies, it is worth investigating butterfly radial stubs for matching, e.g. sometimes you can increase stability margin alot when using 4 radial stubs (one butterflies on each source pin of fet transistor) instead of grounding through vias. And then tune rafius and offset of drain/gate radial butterflies for matching.

[LM21]

How about shorting output to ground with a capacitor when you measure and match input. Some parameters are measured that way anyway.

[szoftveres]

How about shorting output to ground with a capacitor when you measure and match input. Some parameters are measured that way anyway.

As soon as you un-short and try to match the output as well, the input parameters will change significantly enough to ruin your previous input match.

[Georgy.Moshkin]

From experience: I've used ne3210s01 as amplifier in parallel feedback oscillator. What I observed is that S21 phase given in datasheet for certain bias, frequency and terminations is more or less consistent. For the same conditions simulation would provide S parameters which sometime differ by a relatively big amount, e.g. phase and amplitude differs a lot: 30 degree vs 90 degree S21 phase, and sometimes it was almost the same. There are different simulators and different simulation approaches. Tools such ADS have a thing called "momentum", but there is also spice style simulation using building blocks, and result differ too. It is really interesting to hear true experts in this field, but before they arrive, I share some more thoughts. Maybe you can try some transient simulations and examine if there is some unexpected wiggling added to amplified frequency, see if transient S21 phase have an expected value.

What is always worried me was amplifier stability. I had no measurement equipment at all, and going through many papers I've got a feeling that the best way is to have a VNA and/or signal generator, feed ports of amplifier and measure what is coming back and coming through. Many old designs have very strange copper matching, which looks like initial design was tuned using large copper pieces and cutting, and then final design just copied this layout, especially designs from 20-30 years ago. All those frequency triplers and quadruplers, they are stable and have a lot of tuning copper areas which do not look like analytically calculated open/short stubs at certain offsets. I think many of such designs are made by prototype tuning (cutting/adding copper) and measurement.

There is a great article called "The oscillator as a reflection amplifier: an intuitive approach to oscillator design" by John W. Boyles. I recommend everyone interested in matching topic to read it, because it shows how the same matching at single frequency may have very different behavior when active device "travels" through it's S-parameter curve. It is about oscillators, but may help to understand how to make an opposite - a stable amplifier. It is 1986 and frequency was 3.8GHz, there is obviously some measurement equipment was used. And this article was written 37 years ago, very detailed. My opinion, you just need to match and measure it, and then maybe go through few iterations. Simulation may help, but at some point it may become an endless useless tuning of parameters.

In my case it was kind of simple: First, I designed amplifier which is very stable theoretically. All unstable regions are far away from Smith Chart center. Then I could terminate gate line with resistor and make it very stable at remaining unstable lower frequency band. Because my design was pretty narrow band and at high frequency, I just coupled signal by tightly coupled quarterwave lines when needed, or a microstrip ring / split ring resonator. When I used this approach, nothing was "beeping" at unwanted frequencies. But of course, only measurements would help to ensure if everything is ok.