The Designer's Guide Community Forum

The Designer's Guide Community Forum
https://designers-guide.org/forum/YaBB.pl
Design >> Analog Design >> uncompensated opamp - frequency of oscillation
https://designers-guide.org/forum/YaBB.pl?num=1316774247

Message started by Praveen K on Sep 23^rd, 2011, 3:37am

Title: uncompensated opamp - frequency of oscillation
Post by Praveen K on Sep 23^rd, 2011, 3:37am

Hi guys,

What would be the frequency and amplitude of oscillation of an uncompensated opamp?

I've attached a zip file with three waveforms. it is the simulation result of an uncompensated two stage opamp (PMOS input pair) in unity negative feedback configuration. I've shown the frequency response of STB analysis, transient response with VIN_P pulled slowly to 2V and then a fast jump to 3V and back. Third waveform is the zoomed version of the transient to show the frequency of oscillation.

As you can see the oscillation is at 153MHz with amplitude of 805mV. From frequency response, the frequency at which phase margin becomes zero is around 130Mhz,

1. so why is the oscillation is at 153Mhz instead of 130Mhz?

2. which factor decides the amplitude of oscillations?

Thanks to all the guys who post on this forum, i've learnt a lot from their posts.
especially the posts from VIVKR, raja.cedt, loose-electron, RobG where very informative and helpfull. Thank you guys :)

Praveen

Title: Re: uncompensated opamp - frequency of oscillation
Post by boe on Sep 23^rd, 2011, 4:24am

Hi Praveen,
For oscillation you need gain of 1; if you have gain > 1 (as you do at zero phase-margin frequency for uncompensated opamp), the signal amplitude will increase until large-signal behaviour of the opamp limits (gain and thus) amplitude.
In this mode, your opamp is non-linear, so you need more parameters than the small-signal frequency response to describe it.

B O E

Title: Re: uncompensated opamp - frequency of oscillation
Post by raja.cedt on Sep 23^rd, 2011, 6:08am

hello pravin,
Always try to post figs rather than giving some zip files, people may not have time to open.

Coming to your opamp, it has 5 deg PM so it will give damped oscilations and frequency of the opamp keep on changing because of damping. Aproximatly you can say frequency of oscilations is wn*sqrt(1-g^2) where g is damping factor. By the way have you verified how frequency is varing with time, i guess it will.

Idealy oscilations occur only at the frequency where gain=1 and Phase=180, but here it is not happening, eventually some non-linerities makes your gain lower or some thing, finally it will get a point where it can oscilate.

Please refere pg 491 in razaavi to get more info.

Thanks,
Raj.

Title: Re: uncompensated opamp - frequency of oscillation
Post by boe on Sep 23^rd, 2011, 7:29am

Hi,
Just to clarify, in my post I meant large-signal gain of 1 (see Razaavi as raja.cedt suggested).

@Raj: good points, although it is -5° PM, so I would expect not damping but increasing amplitude.
Also note that this is a higher-order system with zero(s), so the PM stability criterion needs to be taken with a pinch of salt.

B O E

Title: Re: uncompensated opamp - frequency of oscillation
Post by raja.cedt on Sep 23^rd, 2011, 8:42am

hello boe,
yes you are correct. It is very difficult to estimate every thing through bode because phase is no monotonic.

Thanks,
Raj.

Title: Re: uncompensated opamp - frequency of oscillation
Post by harpoon on Sep 23^rd, 2011, 8:47am

Here are my thoughts ...
a) Transient and AC simulations are different in real life ... Your transient sims is the large signal behaviour (certainly ~0.8V swings classify as large signal), while AC sims are purely small signal and indicative of the performance.
b) If you re-simulate your AC sims across the different DC operating points (i.e. where you see the transient oscillation), I think you will find that the osc freq is different (but close to 153MHz).
c) Another point to note is how you are breaking your AC loop. If not done correctly, the effects of loading may be ignored. My simulator implements Middlebrook's method.
d) Oscillation is bad in op-amps ... any hint of a possibility of oscillation has to be dealt with ... especially if you have differential outputs ... that common mode oscillation catches out even the most experienced designer.

let us know what you think and what you find ...

Title: Re: uncompensated opamp - frequency of oscillation
Post by Praveen K on Sep 23^rd, 2011, 11:31am

@BOE : you are right to note that at ~153Mhz the phase margin has already crossed 0deg and it has a margin of -5deg, why do you say that since its is -5deg, its amplitude should be increasing, could you please give me a reference for this reasoning?
If things are not deducible from PM plot, then nyquist plot is only other one, but how do i find my oscillating freq. from it? all i know is that it goes in circles around that (-1,0) :)

@raja.cedt : there was no provision for me to attach more than one file in a single post, that's why i had no choice but zip it.
how do i find this natural freq. Wn of this system?
I checked the transient (conservative) simulation, the freq doesn't change much it hovers around that 153MHz through out, in fact the amplitude is also the same through out. thanks for you reference at razavi, i'm reading it.

@harpoon: b) you are right, the osc freq hovers around 153Mhz
c) my loop break point is correct and i'm doing an STB analysis which actually does middlebrook's, so loading issues on both side taken care off.

As you all pointed out its a large signal behaviour, can i reason like this, when the sudden jump happens at VIN_P, the VIN_N tries to catch up but over shoots, once overshot little bit, that is amplified by the gain and the reponse comes after the delay of the first stage, then the second stage amplifies and the reponse comes after the delay of the second stage, by this time it has overshot in the other direction :D
so can i say the amplitude will depend on the delay in the two stages and its gain?

thank you Boe, Raja and harpoon for your precious time in replying,
thanks,
Praveen

Title: Re: uncompensated opamp - frequency of oscillation
Post by harpoon on Sep 23^rd, 2011, 1:46pm

Hi praveen, i am confused by your reply ...

does your ac sims at various dc operating points indicate that the osc frequency is at 153 MHz?

Another sim you can run is an AC in the middle of a transient to confirm that it does oscillate at 153mhz.

Title: Re: uncompensated opamp - frequency of oscillation
Post by buddypoor on Sep 24^th, 2011, 1:34am

Title: Re: uncompensated opamp - frequency of oscillation
Post by buddypoor on Sep 24^th, 2011, 7:40am

Question Praveen: so can i say the amplitude will depend on the delay in the two stages and its gain?

The delay around the loop is idebtical to a (frequency dependent) phase shift. Thus, the whole oscillation condition (i.e. frequency and amplitude characteristics) depend on this delay.
remark: In control systems very often there are (unwanted) delays that are called "dead time" - and they considerably can reduce the phase margin.

Title: Re: uncompensated opamp - frequency of oscillation
Post by Praveen K on Sep 26^th, 2011, 12:03am

@buddypoor: Thanks for your explanation, i understand the idea of increasing exponential in time when in negative phase margin.

@Harpoon: simulating the system at different DC points changes the gain a little bit, the oscillation freq. remains the same around 153Mhz.

@raja.cedt: why should the oscillations change with time? why should the oscillations be damped?

after some middling around with the output pole and the output stage, my conclusions are these,

1. The oscillation frequency: is around the freq where PM goes to 0 (and gain > 1dB) ( brokewson's criteria)

2. The amplitude of oscillation: ideally speaking it the supply limits, as its a growing exponential. But it depends on our output stage current capability, in the simulation shown in my first post, the output stage is just current source with common source stage (class A type), which obviously has very less current capability to pull the output to supply rails in that oscillating frequency, so the oscillations appeared damped but it is not. So if i had a class AB with high current output, then output amplitude is just the supply rails. The oscillations are never damped!!!

thanks,
Praveen

Title: Re: uncompensated opamp - frequency of oscillation
Post by buddypoor on Sep 26^th, 2011, 1:17am

Hi Praveen,

I am quite familiar with oscillation criteria but i never have heard about brokewson's criteria
Please, could you give me some information about that?
Thanks.

Title: Re: uncompensated opamp - frequency of oscillation
Post by Praveen K on Sep 26^th, 2011, 2:15am

hi buddypoor,

sorry about the spelling, its 'Barkhausen criteria' . you can google it.

typo in my reply---- it should be gain>1 not 1dB.

regards,
praveen

Title: Re: uncompensated opamp - frequency of oscillation
Post by buddypoor on Sep 26^th, 2011, 3:45am

ok, no problem. Such things happen from time to time.
But be aware that the Barkhausen criterion is only a necessary one - it is not sufficient to guarantee oscillations. For my opinion and knowledge, a sufficient oscillation criterion is still missing. But I am working on it.

Title: Re: uncompensated opamp - frequency of oscillation
Post by raja.cedt on Sep 26^th, 2011, 4:08am

hello buddypoor,
What i feel is if any system has clossed loop gain>1 and phase is 0, then it start blowing up and if there any non-linerity eventually it will make your gain =1 and this what i feel is criterion for oscilations. Please corect me if am wrong.

i didn't understand your post regaring some thing missing in Barkhausen criterion. Could you please explain this.

Thnaks,
Raj.

Title: Re: uncompensated opamp - frequency of oscillation
Post by harpoon on Sep 26^th, 2011, 4:55am

Hi praveen,

If your AC sims at different operating points indicate an osc of 153MHz, then why r u saying that it is 130MHz as in yr original post ?

Or are you saying your TRANSIENT sims at various dc operating points are around 153MHz ? If so, can you run an AC sim and determine the frequent when PM is 0?

... =)

Title: Re: uncompensated opamp - frequency of oscillation
Post by raja.cedt on Sep 26^th, 2011, 5:27am

hello harphon,

is it posb to find oscilation frequency of any REAL sytem with ac sim? Up to my knoledge only in case of two integrators in loop it's posible.

Thanks,
raj.

Title: Re: uncompensated opamp - frequency of oscillation
Post by buddypoor on Sep 26^th, 2011, 5:50am

Hi RAJ, regarding your last posting:

What i feel is if any system has clossed loop gain>1 and phase is 0, then it start blowing up and if there any non-linerity eventually it will make your gain =1 and this what i feel is criterion for oscilations. Please corect me if am wrong.

i didn't understand your post regaring some thing missing in Barkhausen criterion. Could you please explain this.

At first, two definitions (to refresh):
* If a circuit oscillates it is necessary that the loop gain T(s) is unity (T=1); that is the (necessary) Barkhausen condition;
* A sufficient condition for oscillation would be: A circuit always will oscillate and produce a sinusoidal output if ....? According to my knowledge such a condition has been not yet formulated.
_________
Correction (typing error?): The loop gain T(s) must be equal or larger than 1 (not the closed-loop gain) to start oscillations. What do you mean with "blowing up"?.

Regarding "your criterion" for oscillation: There are many loop gain expressions and also many circuits that exhibit a loop gain that is real and equals unity at one single frequency WITHOUT being able to oscillate.
Examples (counter example to the Barkhausen criterion):
1.) T(s)=-N(s)/D(s) with N(s)=9(26+2s+s^2) and N(s)=s(s+1)(s+2).
One can show that T(s)=1 at app. 0.7 Hz.
2.) Classical WIEN oscillator with exchanged opamp inputs (opamp ideal). The loop gain will still be T(s)=1, however, the circuit never will oscillate. Instead, the circuit will exhibit latch-up.
__________________________
One final question:
What is the meaning of your posting:
is it posb to find oscilation frequency of any REAL sytem with ac sim? Up to my knoledge only in case of two integrators in loop it's posible.

I don`t understand the restriction to two-integrator circuits.

Title: Re: uncompensated opamp - frequency of oscillation
Post by raja.cedt on Sep 26^th, 2011, 7:18am

hello buddypoor,
thanks for your reply. What you are saying there is sufficent condition for the sustained oscilation. What i feel is if you have gain>1, then it start increasing with time (exponentially this is what i mean blowing) and if you have sufficient non-linerity in the ckt then it will be oscilate. Any how i feel i don't have enough knoeledge to coment more thn this.

Coming to your example WIEN oscillator with exachanged opamp inputs, it can't oscilate because there is no DC -ve feedback, how it will get bised?

Thanks,
raj.

Title: Re: uncompensated opamp - frequency of oscillation
Post by buddypoor on Sep 26^th, 2011, 8:27am

hello RAJ,

What you are saying there is sufficent condition for the sustained oscilation. What i feel is if you have gain>1, then it start increasing with time [i](exponentially this is what i mean blowing) and if you have sufficient non-linerity in the ckt then it will be oscilate[/i].

No, that`s not the case. Although most of the circuits with loop gain T(s)=1 will behave like this, there are exceptions as given by me as counterexamples. Thus, this criterion is NOT sufficient. For example, the WIEN circuit with opamp inputs exchanged needs a RISING gain for rising amplitudes in order to bring the eigenvalue back to the LHP of the s-plane (stabilizatuion). But that is contradictory.

Coming to your example WIEN oscillator with exachanged opamp inputs, it can't oscilate because there is no DC -ve feedback, how it will get bised?
That`s the reason I mentioned the IDEAL opamp that needs no dc bias.
Nevertheless, it will not oscillate.

Finally, believe me, up to now there is no sufficient oscillation criterion.
If you have the opportunity to read "Analog Integrated Circuits and signal processing" you will find some recently published articles dealing with this subject.
Regards
buddypoor

Title: Re: uncompensated opamp - frequency of oscillation
Post by raja.cedt on Sep 26^th, 2011, 8:53am

hello buddypoor,
thanks for sharing knoledge. Could please tell me names of the authors for the book you mentioned.

Thanks.
Raj.

Title: Re: uncompensated opamp - frequency of oscillation
Post by buddypoor on Sep 26^th, 2011, 9:26am

Oh, sorry - I forgot to mention that
"Analog Integrated Circuits and signal processing"
is a monthly magazine (Springer.com).
It contains very interesting contributions from authors round the world.

I wonder, if any member of this forum knows something about a sufficient criterion for a harmonic oscillator

Thanks
buddypoor

Title: Re: uncompensated opamp - frequency of oscillation
Post by harpoon on Sep 26^th, 2011, 2:16pm

raja.cedt wrote on Sep 26^th, 2011, 5:27am:

hello harphon,

is it posb to find oscilation frequency of any REAL sytem with ac sim? Up to my knoledge only in case of two integrators in loop it's posible.

Thanks,
raj.

I think it will be very close. In case of crystal osc, the AC sim is bang on ... The q is very high.

Title: Re: uncompensated opamp - frequency of oscillation
Post by rajkumar palwai on Sep 29^th, 2011, 10:49am

Hi Raja,
i am not very clear about ur point saying "if u have 0 deg phase shift and gain >1, then the signal will blow up and finally the ckt non-linearities will limit". This means that even though the small signal gain is >1, the large signal gain will become one.

Can u explain what happens in PLL, where its low freq gain is >> 1 and phase shift is 0 deg, but it is not unstable. We only bother about the freq at which the loop gain goes exactly 0 deg and see if the phase margin is ok there.

Title: Re: uncompensated opamp - frequency of oscillation
Post by Alexandar on Sep 30^th, 2011, 12:35am

You should check on literature on moving poles.
If I recall correctly, the poles have a large excursion when you have a first order oscillator: the poles end up on the real axis, and move back and forth. The poles don't move a lot in case of a second order oscillator, and stay near the imaginary axis.

Title: Re: uncompensated opamp - frequency of oscillation
Post by raja.cedt on Sep 30^th, 2011, 4:18am

hello ,
PLL is diferent case.

let me explain two wings in stability discussion. I am talking about all pole system, for this if you have >1 gain and phase=180deg you would end up with blow but for a system which has zero's we could use nyquist (after all bode is one special result of nyquist plot ). Please find the attached fig for more details.

@rajkumar: for pll please draw nyquist or root locus, but forunatly bode is working.

Thanks,
Raj.

Title: Re: uncompensated opamp - frequency of oscillation
Post by raja.cedt on Sep 30^th, 2011, 4:21am

i forgot to ask...

@Alexandar: i didn't understand what you have written, may be because i am not that good in non-linear theory, so could please point me any basic book which gives me better knoledge on this.

Thanks.
Raj.

Title: Re: uncompensated opamp - frequency of oscillation
Post by buddypoor on Sep 30^th, 2011, 6:11am

Yes, I agree with raj.
The system belonging to the green curve will be stable after closing the loop - it is a system called "conditionally stable". It will become unstable if the gain falls below a certain limit.

Title: Re: uncompensated opamp - frequency of oscillation
Post by raja.cedt on Oct 1^st, 2011, 1:11am

hello rajkumar,
please try this TF with bode plot, you find 70deg PM and decent GM but check it's step responce it has lot of ringing.

0.38(s2 + 0.1s + 0.55)
----------------------------
s(s + 1)(s2 + 0.06s + 0.5)

Thanks,
raj.
.

Title: Re: uncompensated opamp - frequency of oscillation
Post by buddypoor on Oct 1^st, 2011, 1:33am

Hi RAJ,

I suppose, you mean that ringing occurs after closing the loop with a negative sign around the given TF? Correct?

This is another example that in some cases the concept of stability margin cannot be applied and the Nyquist plot must be used to decide stable/unstable.
Comment/Addendum:
For clarification - both margins are positive which means the loop will be stable after closing. However, the amount of phase margin gives not the correct picture about stability margin (the gain margin is very small). That means: The concept of stability margin can be applied to decide stable yes/not but the PM indicates a false safety.

Title: Re: uncompensated opamp - frequency of oscillation
Post by raja.cedt on Oct 1^st, 2011, 2:12am

hello buddypoor,
yes you are correct, but here PM and gain margin doesn't look good, infact stability margin (means how close your nyquist plot to (-1,0) point) would give better result.

Thanks.
Raj.

Title: Re: uncompensated opamp - frequency of oscillation
Post by buddypoor on Oct 1^st, 2011, 2:27am

Yes, I agree. I think, you are referring to the so called "vector margin" or "stability radius".

Title: Re: uncompensated opamp - frequency of oscillation
Post by buddypoor on Oct 1^st, 2011, 5:32am

Hi RAJ,

here is an additional information - perhaps it is new for you:

The mentioned vector margin (min. distance between T(s) and "1" in the Nyquist plane) can be easily found:

Display 1/abs(1-T(s)) and find the maximum of this curve.
The inverese of this maximum gives this stability measure.
In your example: margin app 1/3.85 which is rather poor.
(T(s) is the real loop gain - including sign inversion at the summing node).

Title: Re: uncompensated opamp - frequency of oscillation
Post by rajkumar palwai on Oct 1^st, 2011, 5:54am

Hi Raja, buddypoor

Thanks for the information. So i should use the bode only for all pole system and nyquist for systems with zero's.

i guess i need to study more about nyquist plots as I am not very comfortable with them.

-Rajkumar

Title: Re: uncompensated opamp - frequency of oscillation
Post by raja.cedt on Oct 1^st, 2011, 7:07am

hello rajkumar,
yes, for all pole systems (or monotonic mag and phase responce) you can apply bode with out any issue. You can refer this book for all the details "Feedback Systems: An Introduction for Scientists and Engineers ".

@buddypoor: do you know any simulator which can plot Nyquist plot, i know LTspice can.

Thanks,
Raj.

Title: Re: uncompensated opamp - frequency of oscillation
Post by buddypoor on Oct 1^st, 2011, 8:25am

@buddypoor: do you know any simulator which can plot Nyquist plot, i know LTspice can.

In most cases I work with PSPice - and, of course, it can display the Nyquist curve. Microcap and Simetrix as well.
I don`t like LTSpice to much because - for my opinion - it is not very convenient. I cannot play with parts and expressions and displays like PSPice allows.