Explain step-network correction in feedback amplifiers

[Radio Wrangler]

THe word 'Step' may be causing you to think that things happen abruptly. The phase transitions are of 90 degrees for each pole and for each frequency. At the frequency of a pole or zero, the phase shift due to that singularity is 45 degrees. Only half way there considering how far it's going to eventually get. It's asymptotic so the full shift is only reached at zero or infinite frequency.

The 180 degree lag point for the WHOLE loop is where trouble is likely to start.

If you measure and plot, and there is a pole even quite far-looking above where you expect the instability condition to be met, there can still be enough phase shift to eat your phase margin down at the frequency you're thinking of. But if you scan no further up, you may not see the risk. scan to far above what you think is necessary. Trash poles will be much clearer as you scan across their centre frequency.

What you didn't see can hurt you.

David

[trobbins]

The start frequency of the ideal shelf relates to the anode load resistance of 100k. However that 100k is shunted by the internal pentode anode resistance, and in the 5-20 there is also the 1Meg shunt from the phase splitter.

The 47pF shelf capacitor is also influenced more by parasitic capacitances than say the 200pF part that Williamson used.

[daviddeakin]

[QUOTE=kalee20;1724240]

Originally Posted by daviddeakin

Well no - a circuit doesn't oscillate at the gain crossover frequency, it oscillates (or at least, commences to oscillate) at the frequency where overall phase shift is 0°.

OK I suppose it must commence oscillating there, but it will sustain oscillation at the frequency where the loop gain is unity, which is basically the gain crossover point. So I think that's splitting hairs.

[John_BS]

It starts when the overall phase shift is 0 degrees: the amplitude builds up until something starts to saturate/clip to the point that the overall loop gain is reduced to exactly unity.
As has been said earlier by both David and kalee20, the purpose of the network is to shed gain well before the frequency where the open loop gain falls to unity, without introducing additional phase shift up at that frequency. I employed just this technique when at college - designing a solid-state amplifier to drive electrostatic headphones, having first measured the gain/phase response without feedback.

[Radio Wrangler]

Quite common in planning the loop gain/phase response for a PLL, two poles are used to bring the gain crashing down, and produce a phase plot which goes asymptotic to 180 degrees. but as the next feature at higher frequency is a zero, the phase peels away, further from the 180 degree line, to give a bump before later poles bring it across the 180 degree line. The loop gain is planned to cross unity within the phase margin created by the bump.

The common realisation of this system uses one pole at zero hertz created by the relationship between phase and frequency itself (The PLL has a VCO which is a voltage to frequency converter, but has a phase detector which converts PHASE to voltage) the second low frequency pole is created by having an integrator for a loop amplifier. maybe a capacitor driven by a charge pump, or it may be an opamp with only AC feedback around it - the rest of the PLL is effectively DC feedback for the opamp.

With both these poles at zero and almost zero frequency, their phase shift comes out as 180 degrees in a simple analysis and all hell ought to break out, but as a zero comes before we get to the frequencies of any more poles, we can prove that although the phase margin is infinitesimal, the zero peels the phase plot away from 180 degrees ON THE SAFE SIDE and we can prove that the phase plot never crosses the line until the zero has done its thing and the loop gain has come down to and below unity at a carefully controlled frequency within the phase bump.

The common PLL loop circuit really is splitting a hair, but has highly reliable stability because of just that.

Two successive poles will take you asymptotically close to instability, but you need three successive poles to cross it. Having a zero breaks the chain of succession.

David

[daviddeakin]

Originally Posted by John_BS

As has been said earlier by both David and kalee20, the purpose of the network is to shed gain well before the frequency where the open loop gain falls to unity

That makes sense. In which case the Mullard step network is abnormal. Maybe the designer just tried different values with a substitution box and that combination happened to work, for whatever reason.

[lesmw0sec]

Originally Posted by daviddeakin

That makes sense. In which case the Mullard step network is abnormal. Maybe the designer just tried different values with a substitution box and that combination happened to work, for whatever reason.

I'd reckon that is often the case! Working systems using a mathematical approach is obviously best, but that always assumes that you know all of the relevant parameters to begin with, otherwise you could end up with some nice sums which don't help.

[Radio Wrangler]

It fits the old analogy of skating on a frozen pond. You reached the other side and you're still alive! Congratulations. Therefore the ice was thick enough. What you don't know is what the safety margin was, nor did you know before you committed your life to it.

Things can be improved using these sorts of networks and fiddling with values, but unless you get a lot more involved and explore the stability margins, or do the maths, you don't know what your margins are. There was a lack of people who could or would work to this level of care, so there are plenty of iffy designs out there. The folk at Mullard will have done a good job on their published design examples. Arthur Bailey at Radford was fully competent and Harold Leak seemed to have done a thorough job. Peter Walker had Peter Baxendall backing him up. Some of the other manufacturers followed Mullard's lead, but may not have understood how changing gains or feedback fractions a bit can affect stability margin. Some of the modern boutique amplifiers contain evidence of a lack of awareness and guesswork.

David

I've just noticed, two Peters at Quad, two Arthurs at Radford.

[kalee20]

Originally Posted by John_BS

As has been said earlier by both David and kalee20, the purpose of the network is to shed gain well before the frequency where the open loop gain falls to unity, without introducing additional phase shift up at that frequency.

I got a bit confused reading this - let's take it bit by bit.

Originally Posted by John_BS

As has been said earlier by both David and kalee20, the purpose of the network is to shed gain well before the frequency where the open loop gain falls to unity,

I'd phrase it as, "the purpose of the network is to shed gain well before the frequency where the open loop phase shift falls to zero"

Because once we have zero overall phase shift, oscillation is possible.

Now comes the awkward part:

Originally Posted by John_BS

without introducing additional phase shift up at that frequency.

Unfortunately, if the gain is changing with frequency (whether rising or falling), there is unavoidably a phase shift introduced.

A multi-stage amplifier will always have several high-frequency roll-offs, caused by the output transformer; wiring capacitance; stray capacitance - which stops the frequency response extending up to light or X-rays.

One roll-off results in an ultimate phase-shift of 90 degrees; two roll-offs 180 degrees; three 270 degrees. It doesn't take much to realise that with three rolloffs, oscillation is possible. And if you have done a good job with making the output transformer, and you've used low-capacitance wiring, and good circuit techniques, the rolloffs won't start to bite until above the highest audio frequency.

Add some feedback, and you've made yourself an ultrasonic oscillator.

So the cure is to arrange for one of the rolloffs to kick in at a significantly lower frequency than the others. That will get the gain decreasing at a rate of 6db per octave. By the time the frequency has risen such that the remaining roll-offs become significant, the gain will have dropped to below unity. The phase shift then will be 90 degrees (from the dominant rolloff) plus just a bit more (from the others).

You can connect feedback, and it will be stable. This technique always works. It's often implemented by a shunt capacitor across the anode load in an early stage.

The down side is, the capacitor has to be a bit large because you have to make the dominant rolloff happen at a sufficiently low frequency for the remaining rolloffs to not matter. And although we've got a good output transformer etc, it's still not going to me flat into the MHz region. So the dominant rolloff has to happen at a few kHz - good enough for entertainment material, but it won't win the point in the Top Trumps of Hi-Fi Specmanship.

Fortunately, help is at hand. By adding a resistor in series with the capacitor, a high-frequency zero is introduced which reduces the phase shift caused by the dominant pole. It levels off the frequency response, sure, but to a considerably lower gain. So now the remaining high-frequency rolloffs can add their phase shift - and it will now take more of it to cause trouble, and there's less gain anyway. Because of this, we can afford to use a smaller capacitor in our dominant roll-off, and the flatness extends to perhaps the tens of kHz. The overall performance of the amplifier is improved.

[John_BS]

I'd phrase it as, "the purpose of the network is to shed gain well before the frequency where the open loop phase shift falls to zero"

Yes, agreed, my lack of precision!