The Designer's Guide Community
Forum
Welcome, Guest. Please Login or Register. Please follow the Forum guidelines.
Mar 29th, 2024, 2:47am
Pages: 1
Send Topic Print
Stable loop with -180 phase shift and gain higher than unity? (Read 1919 times)
Horror Vacui
Senior Member
****
Offline



Posts: 127
Dresden, Germany
Stable loop with -180 phase shift and gain higher than unity?
Nov 16th, 2017, 1:49pm
 
Hi Everyone,

I have read an interesting example, which baffles me. It was claimed that a loop can be stable even if the loop gain is higher than unity when the phase shift is -180deg. It makes no sense for me, because in that frequency the input voltage will be increased which increases the output voltage, which increases ... etc.

The example says that an amplifier with 100*(s+1)^2/s^3 transfer function in a unity gain feedback is stable. It has two zeros at -1rad/s, and two poles at -1.12 rad/s and -0.92 rad/s. I can imagine that these poles and zeros more or less cancel each other. But still I do not see how can a loop stable if a large signal in phase with the input is coupled to its input... Is there any flaw in this naiv, but so far fruitful way of thinking? What do you think in general?

PS: the transfer function of the closed loop system:
   100(s+1)^2                      100(s+1)^2
------------------------- =  -------------------------------------------
s^3+100(s+1)^2      s^3 + 100s^2 + 200s + 100
Back to top
 
 
View Profile   IP Logged
Frank_Heart
Junior Member
**
Offline



Posts: 29

Re: Stable loop with -180 phase shift and gain higher than unity?
Reply #1 - Nov 16th, 2017, 11:30pm
 
Back to top
 
 
View Profile   IP Logged
Horror Vacui
Senior Member
****
Offline



Posts: 127
Dresden, Germany
Re: Stable loop with -180 phase shift and gain higher than unity?
Reply #2 - Nov 19th, 2017, 7:30am
 
I know that we should not decide stability from a Bode plot in every cases and the Nyquist plot is the ultimate way to analyse stability. There are functional multistage amplifiers with a very steep roll-off after the passband.
What I was looking for is an explanation how is it possible for a linear circuit. What I see is that the input grows, what an increase in the output is to be followed, which is fed back to the input, etc. Where does this positive regeneration chain brake? In the previous topics I found no explanation, just the notion that Nyquist criteria has to be used.
Back to top
 
 
View Profile   IP Logged
Frank_Heart
Junior Member
**
Offline



Posts: 29

Re: Stable loop with -180 phase shift and gain higher than unity?
Reply #3 - Nov 19th, 2017, 10:12pm
 
Hi, Horror,

  My understanding is, to apply a conditional-stable amplifier for some applications, we shall make sure there is no fixed strong signal @ fx, where phase=-180 degree .  Like if you are modulating and demodulating the signal with a fixed carrier and it's better to make sure the carrier is not around fx.  

 In any case we got signals containing strong fx for some period, the loop will be saturated in any circuit due to Gain>1 @ fx. The loop shall have some recovery mechanism, such that once fx part is gone, the loop goes into recovery. During the recovery the fast path in the loop (which is usually the 1st order one, which gives you 20dB/dec cross dB=0 line in the bode plot)  shall take over and hopefully the loop goes back to stable.

 How we guarantee the stable recovery of the loop, like in many SDM? I have done several ones and the only way I use is to run simulations to check.

 Hope this helps.

Regards,
Frank
Back to top
 
 
View Profile   IP Logged
Pages: 1
Send Topic Print
Copyright 2002-2024 Designer’s Guide Consulting, Inc. Designer’s Guide® is a registered trademark of Designer’s Guide Consulting, Inc. All rights reserved. Send comments or questions to editor@designers-guide.org. Consider submitting a paper or model.