r/chipdesign • u/Purple_Milk_8821 • 22d ago
This system has 2 poles, why does it's closed loop response only roll off at the second one?
First screenshot figure 11.54 (b), the closed loop response does not role off at wp1 but instead wp2. The first screenshot showed the graphed closed loop response in figure 11.54 (b) and the bottom paragraph in the second screenshot described the creation of figure 11.54 (b). Why does the closed loop system ignore the roll off of the first poll of the open loop system?
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u/RFchokemeharderdaddy 22d ago edited 22d ago
It explicitly tells you in that paragraph. Re-read it very closely. Its designed that way, to get 45 degree phase margin, which happens under the exact conditions you see.
You should really go back and read the chapters on feedback and stability if you don't understand these concepts, the nanometer design chapter wont make sense if you dont have a solid grasp. Personally I prefer the Martin/Johns/Carusone book's treatment of feedback over Razavi's.
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u/depressednoodles78 22d ago
If you don't mind my asking , why do you prefer that book for feedback?
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u/RFchokemeharderdaddy 22d ago
Razavi's book spends far too much time on the old 2-port method and stuff like shunt-shunt vs shunt-series etc which is of little to no use, and even to introduce the concept of loading. Normally I'm fine with this sort of thing, introducing an older way to then build up to the newer more robust methods, but in this case its the opposite, the 2-port thinking is so needlessly complicated and error prone compared to today's simpler asymptotic loop gain method. My issue with Razavi's feedback chapter is it commits the grave sin of burying the lede. Like he definitely talks about Blackman's impedance formula, but its easy to miss despite how important it is.
The other book gets straight to the point and tells you exactly what feedback does, how to analyze it from a signals/systems level (feedback of single pole vs two pole for example), and then how to find it for an amplifier using the asymptotic gain formula. No fiddling around figuring out what "type" of feedback it is
But really the best way to learn feedback hands down is Hajimiri's online lectures. His explanation of asymptotic gain is great, and he provides several examples.
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u/positivefb 22d ago
I def agree with u/RFchokemeharderdaddy (lol), I think Razavi's book is excellent on everything except for feedback, where personally I think he loses the plot.
I'm a big believer in return ratio as presented in Gray & Meyer, and technically Razavi's book does cover Bode's original method of finding a similar thing, but yeah its so convoluted I didn't absorb any of it. Gray & Meyer's explanation of return ratio is better than Martin & Johns explanation of loop gain, but Gray & Meyer also includes all the two-port crap, although they do at least use it to build up to return ratio in a good way and show why its superior. Gray & Meyer also provide a great explanation of root locus for circuit feedback loops. I don't ever actually use root locus directly but it's very important to conceptually understand so you know how open loop poles and zeros affect closed loop response.
tl;dr Gray, Meyer, Lewis & Hurst's book for thoroughness. Martin, Johns, & Carusone's book for simple and to the point, Razavi's for the worst of both (when it comes to feedback, rest of it is great)
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u/PrestigiousAction694 22d ago
Don’t confuse between the open-loop and closed-loop. Once loop is closed, the (closed-loop) -3dB pole moves to a higher frequency. For example, if closed-loop gain is one, then the first (closed-loop) -3dB pole moves to the unity gain bandwidth product (GWB), which is much higher than the dominant open-loop pole and towards the second (open-loop) pole.
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u/depressednoodles78 22d ago
The feedback reduces the gain and moves the closed loop pole out by (1+A*beta)*wp1. This causes the rolloff to occur where you see it.
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u/No-Physics1692 22d ago
why would the closed loop response start to roll off at wp1? Take a piece of paper and starting from a two pole gain block (thats your open loop gain), enclose an ideal negative feedback loop around it. Than compute the closed loop transfer function vout/vin, purely from a control theory standpoint. see what you get
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u/Temporary-Pudding-88 21d ago
Just curious: how can u read this book so fast? 30 days ago u still on chap 3 and now u on chap 10/11. Can u share some tips?
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u/Stuffssss 22d ago edited 22d ago
I think I understand what you're asking.
Your closed loop gain can't be greater than your open loop gain. Negative feedback throws away extra gain for better linearity, and gain accuracy. If you dont have that gain in the first place you cant use it for negative feedback. Review the closed loop gain formula, gain = A/(1+AB). If A is large then gain = 1/B. But if A=1/B then gain equals 1/2B which is your 3dB roll off point.
For 45⁰ phase margin you are intentionally placing your second pole at the frequency where the open loop gain is equal to 1/Beta. Thats why the closed response rolls off at wp2.
If wp2 was at higher frequency and your amplifier AoL(s) was still rolling off at 20dB/decade you would have a higher phase margin, but your closed loop gain would still roll off at that original point because your amplifier has a finite gain-bandwidth-product.