Op-amp (or any feedback amplifier) stability and source impedance

[MarcelvdG]

A step response anomaly may be obvious on an oscilloscope but invisible in a response chart. 1% overshoot is easily visible on an oscilloscope but is only 0.1db. If an amp has a gain of 40 but rises to 41 at 100KHz, you may see overshoot on the step response but it might not look bad on the response chart.

Similarly, even though the effect of input impedance is usually tiny, if your goal is perfect square waves then this might actually become an issue. Whether that is audible is someone else's call, but if your amp only has overshoot when there is a high or mild source impedance, this is worth looking at if it means you don't have to overcompensate the amplifier.

The kind of artefact we were discussing was not quite that subtle: a big bang in the loudspeaker when the muting switch of the turntable closed 😉

 

[MarcelvdG]

I agree with your point that the input network is part of the feedback due to the capacitance between the differential inputs.

I'm glad to read that.

My Dual turntable has a shorting switch. My experience is that the switch opening/closing being audible is usually caused by DC across the cartridge. Also, the Dual's motor damping capacitor is prone to failure, which leads to a loud pop when the power switch opens.
Ed

In this case, the op-amp's bias current was specified as max. 20 pA. Across a 1 kohm or so cartridge resistance, that causes a 20 nV voltage drop. With 1000 times DC gain, 20 uV at the output, still much too small to cause a big bang. Besides, an RC series network from the input to ground helped.

 

[MarcelvdG]

The feedback to an LTP sees the positive input transistor as a common base stage, so the impedance connected to the base is part of the ~pole of that stage. I have seen an "input filter" effect the stability of an amplifier in simulation.

Yes, that's another way to analyse it.

 

[keantoken]

I think this is the resonance of the 47 kohm with the frequency-dependent negative resistance of the op-amp. The frequency should be proportional to 1/√R, so you get twice the frequency with a four times smaller resistance. A bit of shunt capacitance can damp it.

The RC shunt is the optimal solution and results in the smallest capacitance.

All currents and impedances are conduction loops, and when the total loop resistance is negative, the loop is unstable (passive components are always lossy therefore have impedance phase within +-90 degrees, whereas impedances with negative resistance always have a phase of more than +-90 degrees and net positive power gain). The only way to guarantee unconditional stability of the source impedance loop is to eliminate all negative input resistance. Otherwise, there will always be some value of passive source impedance which will lead to oscillation.

You can add an input capacitor and keep making it bigger and bigger, but there will always be some overshoot due to the loss cancellation occurring with the negative resistance. Most of the time the proper way to deal with negative resistance whether frequency dependent or not, is to cancel and swamp it with an equivalent positive resistance.

The issue here is that we have frequency dependent negative resistance as a result of gyrating a capacitor by 90 degrees. The impedance falls at twice the rate of a capacitor with frequency and has a phase of 180 degrees. This seems difficult to deal with until you realize that the effective parallel resistance of an RC shunt network, happens to be a positive resistance that falls with frequency at the same rate as the negative resistance of the input stage. With an RC shunt network, our input capacitance becomes constant with frequency again and we are able to achieve a perfect step response, with a small value of input capacitance not much exceeding the open-loop capacitance of the input stage. After compensation, the input capacitance is restored to what it would be without gyration. The positive resistance of the RC network is shunted by the negative resistance of the input stage and cancels to a perfect input capacitance.

The RC can be seen as a Zobel network for impedance equalization, but with the axes flipped.

I was writing an article about this phenomenon for Linear Audio years ago which is close to finished, but Linear Audio closed down and it ended up shelved indefinitely. It provides a complete and intuitive explanation (minimal math) for why amplifiers oscillate into capacitive loads and what we can do about it. Understanding negative resistance could lead to a small revolution in how we design amplifiers. Perhaps someone can help me edit and proofread the paper, preferably someone who has strengths to cover my weaknesses, for instance my sloppy math.