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sushan

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Stability of -60dB/dec roll off system.
Aug 08^th, 2013, 6:07pm

Hi ,

Generally for PLL system the Roll off goes as -40dB or -60dB /dec from DC but when it crosses Wugb it does it with-20dB/dec for it to be stable using Barkhausen Criteria. So, generally the system is perfectly stable, but in time domain if I give a very low frequency sine wave with frequency falling under the -60dB/dec roll off analysis shows that it comes back with a magnified value with a phase shift. So, the system should eventually blow up. When analysed using the Nyquist or root locus we can conclude that the system to be conditionally stable, but in time domain the analysis shows the system will be unstable. Please help me in analyzing the system properly.

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nrk1

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Re: Stability of -60dB/dec roll off system.
Reply #1 - Aug 9^th, 2013, 7:28pm

The time domain analysis mentioned is incorrect. That kind of description implicitly assumes a delay in the system. The closed loop gain is ~ L/(1+L) and if L is large and negative (not equal to -1), you'll simply get a negative closed loop gain.

There are many references to this on the web(links from Kent Lundberg's page at http://web.mit.edu/klund/www/; lectures at http://nptel.iitm.ac.in/courses/117106030/ etc.)

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nrk1

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Re: Stability of -60dB/dec roll off system.
Reply #2 - Aug 9^th, 2013, 7:39pm

nrk1 wrote on Aug 9^th, 2013, 7:28pm:

The time domain analysis mentioned is incorrect. That kind of description implicitly assumes a delay in the system. The closed loop gain is ~ L/(1+L) and if L is large and negative (not equal to -1), you'll simply get a negative closed loop gain.

There are many references to this on the web(links from Kent Lundberg's page at http://web.mit.edu/klund/www/; lectures at http://nptel.iitm.ac.in/courses/117106030/ etc.)

One of the links: http://web.mit.edu/klund/www/weblatex/node4.html

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sushan

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Re: Stability of -60dB/dec roll off system.
Reply #3 - Aug 9^th, 2013, 10:19pm

Hi nkr1,
Thanks for your reply. I actually posted this thread when I was going through the lecture you have pointed out. But I don't understand when you say the "description assumes a implicit delay in the system". I understand somehow the time domain analysis is buggy, but it would be great if you could explain this.

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raja.cedt

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Re: Stability of -60dB/dec roll off system.
Reply #4 - Aug 9^th, 2013, 11:42pm

Dear Yuvan,
When you have a feedback system with let's say -180 phase at low frequency, you would think that feedback signal reached summing node and it will add in phase with the input signal and again it will be amplified by the amp an so on, so while explaining we explain in serial manner but every thing happen in parallel in reality.Bottom line is we have introduced some "Verbal delay" in the system. But please note that time domain has no bug. Why don't you take a system like K*(1+S^2/(S^3) , use RH criterion to find it's stability condition.

Thanks,
raj.

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sushan

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Re: Stability of -60dB/dec roll off system.
Reply #5 - Aug 9^th, 2013, 11:57pm

Hi Raja,

Now I understand, can we say like this: when we excite the system with some pulse then eventually the excitation frequency dies down, so even if the feedback comes back with some high magnitude with a phase shift we will not have any issues. Please correct me if I'm wrong.

Actually I meant the time domain which I did was buggy & not the original time domain analysis.

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raja.cedt

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Re: Stability of -60dB/dec roll off system.
Reply #6 - Aug 10^th, 2013, 12:19am

Hello,
You are wrong, In the attached fig With some finite vo, we say we will have some vfb and then it will add in phase with vin and sum of both will get amplified and so on...But till Vfb comes vin will not w8, this is what i mean by parallel.

Actually this kind of stuff little bit difficult to explain, so please spend some time to think. may be some experts can explain better...

Enjoy!!!!

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sushan Junior Member Offline Posts: 21	Re: Stability of -60dB/dec roll off system. Reply #7 - Aug 10^th, 2013, 12:31am Hi Raja, I guess I also meant the same. But thanks a lot for explaining.
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sushan Junior Member Offline Posts: 21	Re: Stability of -60dB/dec roll off system. Reply #8 - Aug 10^th, 2013, 8:59am Hi Raja, I worked out some examples, but I'm not quite sure on how to apply the same of unity gain. And having said that we can convince our self using Nyquist or root locus frequency domain methods.
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raja.cedt Senior Fellow Offline Posts: 1516 Germany	Re: Stability of -60dB/dec roll off system. Reply #9 - Aug 10^th, 2013, 9:18am hello, tell me which transfer function you have tried...First learn nyquist or RH criterion and then apply the same to chosen transfer function. You can read some more about this kind high low frequency phase systems in loop, please search motor boating in olden music instruments. Thanks, Raj.
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buddypoor

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Re: Stability of -60dB/dec roll off system.
Reply #10 - Aug 18^th, 2013, 6:25am

sushan wrote on Aug 8^th, 2013, 6:07pm:

............ but in time domain if I give a very low frequency sine wave with frequency falling under the -60dB/dec roll off analysis shows that it comes back with a magnified value with a phase shift.

...comes back with a phase shift...???
What does this mean?
Don`t you expect any amplification or phase shift at such a low frequency?

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LvW (buddypoor: In memory of the great late Buddy Rich)

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