# Why is it so important that an amplifier is unconditionally stable?

When studying microwave/milimeter wave amplifier design, one often finds discussions about stability. Stability means that the amplifier will not generate signals by itself (except for noise). As we often find in microwave amplifiers that there is always some form of feedback path that can lead to oscillations (in addition to input and output reflections), considering their effects is an important part of the design.

The definitions of the two types of stability are generally something along the lines of the following:

• Unconditional stability: The amplifier will be stable (= not oscillate) for any load and source connected, provided it does not have a reflection coefficient greater than one in magnitude ($|\Gamma_{L}|<1$ and $|\Gamma_{S}| <1$).
• Conditional stability: The amplifier is stable for certain, but not all load and source connections. This means that an amplifier that is stable when connected to a matched output might oscillate when mismatch occurs due to an open output. Sometimes also called "Potentially unstable".

We have mathematical techniques to determine stability, based on concepts such as the Rollett Stability Factor. From this we can determine if an amplifier is unconditionally stable. When designing amplifiers we put this unconditional stability as a requirement: We will only consider our design done once the amplifier is unconditionally stable. If it is not, we might use design techniques (such as adding gate resistance or such) to ensure that our amplifier is unconditionally stable.

Now to come to my question: Why? When one is designing an amplifier, I often know that impedance I am going to connect to. When building an amplifier for a radio system, I probably know what the impedance into my antenna is. If it's for distribution over cable networks, it will likely be 75 Ohm. When it's part of an ASIC, I will likely know exactly what the load impedance and source impedance are since I or my teammates will be designing the preceding and next stage, or the circuit board it is placed on! So then why would I sacrifice gain (as this is a result of many stabilizing techniques used), in order to ensure it is stable for all loads, when it will only be used with a single load impedance? Why not just ensure it is stable for that load impedance (well, the range of impedance we can expect due to production errors and such).

• Do you really have such faith in your modeling that you trust a design that is potentially unstable? Commented Oct 28, 2017 at 15:34
• @glen_geek We trust in the same software modelling programs that the amplifier will meet noise performance, have a sufficiently high IIP3 and has the bandwidth we need. If any of those is incorrectly modelled my chip might be useless. If we trust the tools to model that, why would this be any different? Commented Oct 28, 2017 at 15:55
• IIP3, noise, bandwidth are all parameters that might not meet your spec, but won't kill functionality. Oscillation will destroy functionality - its margin of safety must be higher. Commented Oct 28, 2017 at 22:24

We like to pretend that circuits such as amplifiers are essentially linear around some specific operating point, because that vastly simplifies their analysis. However, like many things in electronics, that is only an approximation.

That approximation fails to a certain extent with large input signals, and to a greater extent during transient events such as power-up and power-down, leading to undesired behavior in real-world circuits. Therefore, we use conservative margins in our designs, including such rules-of-thumb as requiring unconditional stability.

As always, the "principle of least surprise" applies for others who may need to deal with the circuit.

In addition to the previous answers, you have to guarantee the robustness of the design against a variety of factors outside of your control. These factors may include thermal variations, device ageing, unexpected ESD or even unintentional misuse by the end-user. These things sometimes lead to vary your input/output impedances which may cause oscillation if the design is not unconditionally stable.

Moreover, if your design is intended to be put on massive production, you'll find some device dispersion which may contribute to the aforementioned factors.

I asked this question to a few people that do designs of mm-wave amplifier ICs. Their response was along the following lines:

It is true that unconditional stability might be an excessive requirement. And sometimes, people do infact design and use amplifiers that are not unconditionally stable. The reason it's not common is two fold:

Even if you are designing all stages and hence have control over the source and load impedance, you still need to ensure that your design is stable for that specific load impedance. Often, the easiest way to do that is just to ensure that it is stable for all impedance. It is very possible that trying to get stability for a certain impedance will just result in you getting unconditional stability - meaning you can spend more time on optimizing other parameters of your amplifier such as linearity or PAE (power-added efficiency).

In addition, the gain benefit of allowing the amplifier to not be unconditionally stable is small. One designer told me that usually you see about 1dB of gain loss by going from conditionally stable amplifier with high confidence of stability for your load (with regards to fabrication variability) and the same amplifier with some stabilization such that it is unconditionally stable.

One designer also compared it to a similar specification often found in electronics design: Historically, almost nobody sold an operational amplifier that was not stable for unity-gain feedback (or so he says, I am not old enough to verify this). It was a sort of "requirement" that wasn't really a requirement. Nowadays, it is becoming more and more common to have opamps that are not unity-gain feedback stable. This can allow the designers freedom to focus on other specifications such as power.