[SOLVED] Multi-Stage Amplifier Stability question.

There is lots of information available for design of a a single stage amplifier. We may have gain and noise circles on Smith charts, and make trade-offs with the matching circuits to get good noise figure with OK (ish) VSWR, all the while noting the stability conditions.

We have handy expressions to express stability, derived from the S-Parameters, Like the Rolletts Stability Factor (K), not enough on its own, but OK when combined with various others. Some, like MU(load), or just MU, are a sufficient condition.

My question is, what happens when we have (say) a two-stage amplifier. I mean a input matching, and a matching network between the stages, and a output matching, and possibly some source inductance in the (GaAs HEMT) devices. Can the S-Parameters for the whole thing combined, with only a source and load termination, still be used to check stability in this way?

Do we have to make each stage stable separately, with the matching network between the stages temporarily terminated somehow to represent the connection of the other stage ?

Can we just keep optimizing the combined networks until the stability factors are OK? Might there be situations where a stage with an unstable region can end up "stable" when in combination with a second stage?

Multistage RF amplifier stability issue is one of the most discussed subject.As you have said, stability criteria is valid for single stage amplifiers only but it gives an idea about entire stability of cascaded stages.However NDF ( Normalized Determinant Function) based on Nyquist stability crieteria is available in commerically available simulation softwares.

Another problem is the layout. The output can couple to the input if they are close together and there could be a common impedance in what you think is a 0 +j0 ohm ground.

Thanks for the replies.

BigBoss said:

As you have said, stability criteria is valid for single stage amplifiers only but it gives an idea about entire stability of cascaded stages.

Click to expand...

Not quite. It is the very question I was asking. I don't know that that is actually true. In the simulation softwares I have managed to get a look at, the S-Parameters of the matching sections, and the devices in between, are all cascaded to make an equivalent 2-Port network.

If it is OK to consider a "stage" as one device cascaded with two passive "stages", these being the matching sections, our "stage" is already a 3-stage thing. From there on, all the Nyquist based stability expressions are based on S11, S22, and their conjugates S11* and S22*, and we can have plots of K, or MU, and others, meaning the whole lot taken together!

It seems logical that the entire network, with 2 active devices between 3 passive sections is actually a 5-stage cascaded network presented as a 2-port equivalent. The criteria are labelled slightly differently in some available softwares, but they are all there. The simulation software will provide a plot of MU, regardless. Also, meddling with the components produces changes and optimizations that seem not confined to 1-stage setups.

Friendly and Unfriendly Terminations
Part-way through building up the stages, you might have a potentially unstable stage which goes stable if offered the right terminating impedance, coming from the next stage that is to be added on. More often, you work to make a stage stable, only to find it goes badly wrong when you add the next stage. The matching sections may be fine for the frequencies of interest, but make unfortunate things happen at other frequencies where the devices have a whole lot of (unwanted) gain that can give you trouble.

I am thinking the stability criteria are valid for the whole lot put together - but not having seen an example of stability plots applied to more than one stage, I am still not sure! We can all accept that if you have each stage unconditionally stable, then the stages joined together will also be. Some of this carries the suggestion that the matching network between the stages has to be an equivalent reworked from two, so you don't have to visit 50 Ohms in the middle. Here is where I noticed how a messed up stage could become stable when offered the input of the next stage with matching in between.

Hopefully, we can get a hint from a member who has wide experience with stable (or unstable!) designs.

Just to get back to the question..

So.. if we just keep tweaking the matching components around a couple of GaAs FETs until we see stability (based on S11 and S22 only), are we fooling ourselves?

Would we be we ignoring bad stuff that may be happening in between?

OK - finally I found it!

If there are two stages, you cannot take it for granted that the whole ensemble is stable just because the stability factors based on the S-Parameters of the input and output ports look satisfied.

Although they may indicate the amplifier is stable, it is still possible for the amplifier to be unstable because of oscillation conditions that may exist between the stages.

Getting the whole thing matched, and preserving noise, and gain et al, and keeping it stable is.. er.. "challenging" :|