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The Designer's Guide Community Forum
https://designers-guide.org/forum/YaBB.pl Design >> Analog Design >> Gain and phase margin https://designers-guide.org/forum/YaBB.pl?num=1327149668 Message started by sapna on Jan 21st, 2012, 4:41am |
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Title: Gain and phase margin Post by sapna on Jan 21st, 2012, 4:41am How can we derive gain and phase margin for a ciruit? |
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Title: Re: Gain and phase margin Post by raja.cedt on Jan 21st, 2012, 5:00am hello, Seems you are a beginner in ckt design, so please refer razaavi analog integrated ckt book or any electronics book. Take a circuit and Draw small signal picture, now write expression for Phase and gain corresponding to the whichever Transfer function you are interested. And then find the frequency where gain equal to 1 and find the Phase corresponding to this Frequency. Find 180-phase, this is Phase margin. Thanks, Raj. |
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Title: Re: Gain and phase margin Post by buddypoor on Jan 21st, 2012, 5:05am raja.cedt wrote on Jan 21st, 2012, 5:00am:
Gain and phase margin are defined and can be identified for one single transfer function only: The transfer function of the (open) loop ("loop gain"). |
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Title: Re: Gain and phase margin Post by AnilReddy on Jan 21st, 2012, 5:29am hi, please read "Frequency Compensation" chapter of analog circuit design book by razavi. It has a very good explanation about stability, phase-margin, gain-margin..etc... Thanks Anil |
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Title: Re: Gain and phase margin Post by sapna on Jan 21st, 2012, 5:37am i have to check the stability of circuit in closed loop configuration. should i consider the transfer function in closed loop configuration to find the gain and phase margins? |
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Title: Re: Gain and phase margin Post by raja.cedt on Jan 21st, 2012, 6:04am hello, Please note that Gain and margins are the indicative of the how stable the system if you close the loop. So you have to find for the open loop and that gives indication of stability. Otherwise let us say you have system and you want to know about the stability, just find the poles and check if they are in LHP and bit far from the jw axis, you are done. But this tedious many times and need to estimate all kinds of feedback factors Thanks, Raj. |
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Title: Re: Gain and phase margin Post by buddypoor on Jan 21st, 2012, 1:54pm sapna wrote on Jan 21st, 2012, 5:37am:
Of course, you can chec0k if the system is stable or not in a closed-loop configuration - for example by applying a step at he input and watch the output. For a stable system the ouput must within a limited time period return to the quiescent condition. However, in general it is not possible to assess the phase or gain margin. For this purpose you must perform open-loop measurements resp. simulations. Exception: For a 2nd order system the gain peaking in the frequency domain or the overshoot in the time domain is a measure of the phase margin. For this purpose, some curves for evaluation are available. |
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Title: Re: Gain and phase margin Post by sapna on Jan 22nd, 2012, 2:36am i will derive the gain and phase margin in open loop configuration and look at its stability .i hope this is the correct method. |
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Title: Re: Gain and phase margin Post by buddypoor on Jan 22nd, 2012, 3:34am sapna wrote on Jan 22nd, 2012, 2:36am:
It is the correct PRINCIPLE. If the applied method is correct depends.... You should know that opening of a feedback loop may cause problems (bias point lost, loading condtions altered). For this purpose, some specific methods have been proposed (Middlebrook method, series injection,..) |
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Title: Re: Gain and phase margin Post by sapna on Jan 23rd, 2012, 2:17am i know that the system is stable in open loop configuration .. and unstable once i close the loop.should i find gain margin n phase margin keeping loop open and what should be the values of gain and phase margin to show that the system is unstable ? In simulations I see the phase going to 180 degree when i close th eloop .does that mean system is unstable ? In calculations should i get phase margin around 180 degree to prove its unstable_? |
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Title: Re: Gain and phase margin Post by raja.cedt on Jan 23rd, 2012, 2:29am hello sapna, You are wrong, any system can be unstable weather it could be open loop or closed loop. While calculating you have to take loop gain (means simply open loop gain*feedback factor). To prove your system unstable phase has to tough 180 in theory (but if it is near to 135 or 140, practically it is useless) Thanks, Raj. |
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Title: Re: Gain and phase margin Post by sapna on Jan 23rd, 2012, 2:34am i am getting phase margin close to 180 degree.what about the gain margin in theory? |
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Title: Re: Gain and phase margin Post by sapna on Jan 23rd, 2012, 2:42am i get phase angle for open loop transfer function at gain cross over freq as 57 degree .. so that means my phase margin will be 180+57 ? |
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Title: Re: Gain and phase margin Post by raja.cedt on Jan 23rd, 2012, 3:38am hello, why don't you upload the phase plot..it is not even basic level of discussion. If you get your Phase 57 deg means -123, so Phase margin is 180-123=57. Thanks, raj. |
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Title: Re: Gain and phase margin Post by sapna on Jan 23rd, 2012, 4:48am this is the gain and phase plot i am looking at |
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Title: Re: Gain and phase margin Post by raja.cedt on Jan 23rd, 2012, 5:46am hello, you don't even have 57 Phase Margin, In-fact here Phase margin won't give good picture due to lack of monotonicity ALWAYS USE MONOTONIC BODE PLOT. OTHERWISE GO FOR NYQUiST. Thanks, raj. |
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Title: Re: Gain and phase margin Post by buddypoor on Jan 23rd, 2012, 6:34am sapna wrote on Jan 23rd, 2012, 4:48am:
According to your gain/phase plot the phase margin is only approx. 20 deg. and the gain margin is approx. 25 dB |
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Title: Re: Gain and phase margin Post by SoliS on Feb 2nd, 2012, 7:19am Your gain drops to 0 dB at about 5x10^6 Hz. If we look at the same frequency on the phase plot, we see that the phase is about 20 degrees there. Thus, your phase margin is 20 degrees. |
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