This is called "conditional stability" or "Nyquist stability", named after the first person to study how it was possible.
Internet search on these terms.
Best wishes
David
Hello again Catalin,
I will attempt to explain further.
What is important (for this system), is whether on a Nyquist plot, the -1,0 point is ENCIRCLED. If you were to do a Nyquist plot of this system, you would see that the -1,0 point is not encircled, since the loophase becomes +ve again before the loopgain reaches zero. I'm sorry to give such a poor explanation, I could do better with a diagram, but haven't currently got access to a scanner.
I will attempt to explain further.
What is important (for this system), is whether on a Nyquist plot, the -1,0 point is ENCIRCLED. If you were to do a Nyquist plot of this system, you would see that the -1,0 point is not encircled, since the loophase becomes +ve again before the loopgain reaches zero. I'm sorry to give such a poor explanation, I could do better with a diagram, but haven't currently got access to a scanner.
Hi David,
Two main reasons:
1. With my designs, I like to keep the dc offset <50mV, without having to match the input transistors or use an offset pot. This requires low value feedback resistors, (and also input bootstrapping to get a decent >10kohm input resistance).
2. In order make the pole formed at the inverting (feedback) input have as high a frequency as possible, it is wise to use low value resistors. I think Bob Cordell mentioned this in his book.
Of course, low value resistors create issues:
1. A large feedback cap is required (if a dc servo isn't used).
2. High power dissipation in the feedback resistor (a 3W part or 3x1W resistors in my designs).
Best wishes,
Ian
Nope. What is important is that the number of counter-clockwise encirclements must be equal to the number of RHP poles. By logical inference, any clockwise encirclements indicates that the system would not be stable if the loop were to be closed. That is, a RHP zero cannot be used to cancel out a RHP pole, since this does not remove the instability when the loop is closed.
Hi Catalin,
I have found a webpage for you that illustrates the point I was trying to make earlier.
control system - Conditional stability - Electrical Engineering Stack Exchange
Best wishes,
Ian
I have a series of posts showing this starting from about #82 including Nyquist pics. These are very close to 'real life' amps.
My small brain doubts if any practical (or impractical) 'real life' amps will demonstrate Waly's counter-clockwise encirclements but I'm willing to be proved wrong
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The Nyquist curve you show approaches the origin from the bottom so is likely to stay far from (-1,0) and be very stable. It's GM is essentially infinite.
However, I would really like to magnify the region near (-1,0) and the origin to check on this.
As with most things, it depends. Damir's example with infinite GM is straightforward. One number, the PM is sufficient.Dave Zan said:
But with many 'advanced' compensation schemes where the LG is kinked to avoid (-1,0) you may like to have a closer look. It's only 3 mouse clicks in LTspice from a Loop Gain plot.
Did you actually manage to dig a Nichols plot from LTspice?
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I have a series of posts showing this starting from about #82 including Nyquist pics. These are very close to 'real life' amps.
My small brain doubts if any practical (or impractical) 'real life' amps will demonstrate Waly's counter-clockwise encirclements but I'm willing to be proved wrong
Hi Richard,
Thanks for the link, I will study it in more detail tomorrow.
My small brain is also unaware of any practical amplifiers that contain anti-clockwise encirclements. I would be very interested to see the details of such a device.
Thanks and best wishes,
Ian
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Is this better? And it is not infinite GM, it is 21 dB. This is Nyquist curve from my 200 W CFB amp and it uses a kind of Cherry compensation(TPC but connected to the output not to the VAS/TIS).
Damir
Attachments
GM of 21dB is 'essentially infinite'. No sign of peaking at all and very stable at that frequency.
Draw a unit circle at the origin to find the PM, where it cuts the Nyquist. This is the ULGF so its about 30. You can probably adjust the compensation to get better PM (cut the unit circle further from (-1,0) and reduce some slight peaking at the ULGF.
Bode's 'recommendation' is PM 45. Sorry Dave for simplifying Guru Bode's recommendations!
Cordell shows some PM & GM numbers for peaking. These aren't exact (and can be very far out) ... but its a useful guide. If it's easy to adjust both PM & GM in your amp, you can try this and check (by plotting Close Loop response) how applicable his chart is to your design.
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Du.uuh! You can only estimate PM like this if the x & y scales on your Nyquist plot are the same. Your PM is actually quite good and much better than 30.
Sorry.
Try the attached Nyq.PLT. Rename it from Nyq.plt.txt
What you are using is a Two Pole Cherry Compensation. I've had good 'real life' results from this but prefer 'pure Cherry' these days cos easier to analyze. [deleted: 1 page of rant about TLA/FLA for this]
If this is Guru Zan's 'inner' Tian probe, don't forget to check it out using his 'outer' probe too.
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This is #262. More good stuff from #278. Please ignore the pseudo guru noise.
With good amps, making the 'inner' loop more stable makes the 'outer' loop more unstable, so my contention is that the 'outer' loop is the one to go unstable first. But the more people that look at both loops in their different designs, the better a handle we will get on this.
I also contend an unstable or wonky 'inner' loop will ALWAYS result in an unstable or wonky 'outer' loop but not the other way round .. but you should look at both.
With good amps, making the 'inner' loop more stable makes the 'outer' loop more unstable, so my contention is that the 'outer' loop is the one to go unstable first. But the more people that look at both loops in their different designs, the better a handle we will get on this.
I also contend an unstable or wonky 'inner' loop will ALWAYS result in an unstable or wonky 'outer' loop but not the other way round .. but you should look at both.
Du.uuh! You can only estimate PM like this if the x & y scales on your Nyquist plot are the same. Your PM is actually quite good and much better than 30.
Sorry.
Try the attached Nyq.PLT. Rename it from Nyq.plt.txt
What you are using is a Two Pole Cherry Compensation. I've had good 'real life' results from this but prefer 'pure Cherry' these days cos easier to analyze. [deleted: 1 page of rant about TLA/FLA for this]
If this is Guru Zan's 'inner' Tian probe, don't forget to check it out using his 'outer' probe too.
PM is 74 degree and I showed both "inner" and "outer" Tian probe in here http://www.diyaudio.com/forums/solid-state/243481-200w-mosfet-cfa-amp-17.html#post3675331.
Damir
Kinked yes, but once you zoom close to the critical point then it is reasonably smooth.
Continuous, smooth function, Taylor expansion is always close to quadratic, that sort of stuff.
In this case it's a complex, analytic function but same principle, even more constrained in fact.
So I don't think it's practical to follow the GM boundary and then suddenly "sharp 90 to the left" to follow the PM boundary.
That's why the usual analysis to calculate the overshoot as a function of PM and GM more or less assumes a 2nd order function in the area of interest.
Not yet. I need more information about LTSpice interfaces.
I may try to ask Mike Engelhardt.
Best wishes
David
Two Pole Cherry looks very attractive on theoretical principles.
I need to study this more.
I asked Damir to try an inner Tian probe (that shows total Return Ratio).
That's all he needs to prove stability.
The simulation result is excellent.
It has a 10 MHz unity frequency so the issue will be to make the simulation and reality match.
Best wishes
David
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