An Educational Moment in Amplifier Stability

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Joined Jul 24, 2018
This was an educational experience, and also kind of dumb (so it was the best kind of educational experience). Because of that, I figured I'd share it.
I was designing a 2-stage RF amplifier today for something at work, and was pleasantly surprised when the gain I was getting in simulation for the input/output-matched amplifier was higher than the load-pull simulations on the unmatched system were predicting - almost 33% higher! I was about to start designing layout when I looked at my stability simulations. To my frustration, it was unstable (source, load, and Rollet stability weren't just <1 - they were <-35!). So, I sat there, trying to figure out why the single-stage version was stable, but the two-stage one was not, and so extremely unstable. I eventually figured out why, almost an hour later. This is representative of the original circuit (obviously not the actual system - it's about as vague as possible - not even drawn in the same tool!):
Can you spot the issue? What was causing the instability? Assume the wires can be replaced with transmission lines/microstrip lines.
The instability comes from the biasing network. What I have has a simple way to bias both transistors using only 1 inductor for the gate and one for the drain in an attempt to minimize the number of inductors and shrink the overall layout, due to limited floorspace. HOWEVER, it also forms a nice feedback loop: output of the second amplifier feeding back into its input, which, after passing through a decoupling capacitor, feeds back into the first stage's input. Anywhere I have gain > 0 dB, I'll have an instability. Not good. This is also why my gain was almost 33% higher than expected.

The fix to this issue is simple, but also mildly annoying. By moving the resistor on the gate bias into one of the branches and adding a copy into the other, and by moving the inductor in the drain bias into the branch and adding another, I can resolve the instability (with some match-tweaking required), like so:
Unfortunately, it also increases layout space by a decent amount (because inductor). Alternatively, I could have left it at 2 inductors like before and put resistors in the drain bias - that was actually the first thing I tried. The problem with that is that the DC power consumption goes up, and the drain voltage is no longer the full VDD it needs to be. Because the gate draws almost no DC current, it's fine to use resistors there instead.

The lesson learned: remember to pay attention to unwanted feedback loops, and don't try to cut corners on biasing, even if doing so causes more space to be used.