The Designer's Guide Community Forum

The Designer's Guide Community Forum
https://designers-guide.org/forum/YaBB.pl
Design >> Analog Design >> miller compensation
https://designers-guide.org/forum/YaBB.pl?num=1314197543

Message started by jjv on Aug 24^th, 2011, 7:52am

Title: miller compensation
Post by jjv on Aug 24^th, 2011, 7:52am

In an uncompensated two stage opamp if load pole is dominant than
first stage pole will miller compensation help.

Won't it make the nondominant first stage more dominant.

Title: Re: miller compensation
Post by raja.cedt on Aug 24^th, 2011, 8:15am

hello be clear while asking you question. I think what you are asking if load pole is dominate than first stage o/p pole how miller compensation will help.

the answer for this question is what-ever the location before compensation, after that dominate becomes more dominate as well as non-dominate becomes more non-dominate.

Get back to me if you have any question.
Thanks.

Title: Re: miller compensation
Post by jjv on Aug 24^th, 2011, 8:35am

Hi raja,
You understood my question correctly. But how can the dominant become
more dominant and non dominant become more nondominant. The miller
multiplied cap is going to come at the first stage output making it dominant from non dominant condition.

Also output remain close to same. So both poles should come closer after compensation.

Am I right.

Thanks,
jjv.

Title: Re: miller compensation
Post by jjv on Aug 24^th, 2011, 8:38am

I meant

Also output pole remain close to same location before compensation.

So both poles should come closer after compensation.

Am I right.

Thanks,

Title: Re: miller compensation
Post by buddypoor on Aug 24^th, 2011, 8:55am

i jv,
do you know what it means when one pole is "dominant"?
Can you describe under which condition a pole is dominant? Only then you can find and understand the answer to your question.

Title: Re: miller compensation
Post by jjv on Aug 24^th, 2011, 9:05am

buddy,
A node is dominant when the RC product at that node is greater than
other nodes

Title: Re: miller compensation
Post by raja.cedt on Aug 24^th, 2011, 9:13am

hello,
first off all they don't approch each other. I can tell explain through graph. Think compensation cap is feedback around the opamp. So the resultant transferfunction is having well seperated poles (dominate becomes more dominate and non dominate as well). I can explain through some otherway (because this is a special case, i spend so much of time to found this. here you dont see miller multiplied cap however you will get miller multiplied resister) bit complicated to explain. But i am sure this fig gives very good explanation.

Hope it helps.

Title: Re: miller compensation
Post by Rakesh on Aug 24^th, 2011, 11:35am

Hi,
After miller compensation irrespective of the initial pole locations
Always the first stage pole will be dominant and the second stage pole will be non dominant.

Rakesh

Title: Re: miller compensation
Post by buddypoor on Aug 24^th, 2011, 12:10pm

jjv wrote on Aug 24^th, 2011, 9:05am:

buddy,
A node is dominant when the RC product at that node is greater than
other nodes

I suppose you mean "pole" (rather than "node")?
Or do you define dominant nodes?
Your explanation holds for real poles only.
A general definition is based on the pole location in the complex s-plane.

Title: Re: miller compensation
Post by Praveen K on Sep 26^th, 2011, 3:06am

hi jjv,

as far as i know, the miller compensation will be helpful only when the pole of first stage is dominant. In your case the pole at the second stage is dominant, which occurs when the load cap is huge.

In this case my suggestion is just leave output pole to be dominant and put a buffer in between the two stages, so that the resultant non dominant poles at the input and output of buffer are far away from dominant.

praveen

Title: Re: miller compensation
Post by raja.cedt on Sep 27^th, 2011, 6:06am

hello praveen,
miller compensation will be usefull irrespecive of the dominate poles location. I would say "miller capacitor makes dominate pole more dominate and non-dominate more non-dominate"

I didn't understand your 2nd point, could plz explain more....

Thanks,
Raj.

Title: Re: miller compensation
Post by Praveen K on Sep 27^th, 2011, 11:45pm

hi raj,

I'm attaching the STB analysis of a LDO driving a load of 10nF. The first stage is an high swing OTA, second stage is a PMOS of large size to drive the 10nF. In this case the dominate pole is the output pole and first non dominant is the gate of PMOS.

in the fig, (red--case with no compensation cap , green--with miller compensation of 100pf) you can see that adding a 100pF miller cap moved the nondominant pole(@ gate of PMOS) significantly to lesser frequency and doesn't help in anyway in PM. the dominant output pole remains almost same.

So i'm afraid i can't agree with what you say, cause miller cap can't help here. I agree with jjv, with his original argument.

Instead of this say we add a buffer stage in between the OTA and PMOS. here we will have three poles, dominant one again is the output pole, the two other non dominate poles( one at the output of OTA, another at the gate of PMOS) will be at a higher frequency because your buffer will have lesser input cap and low output impedence.

correct me if i'm wrong.

regards,
Praveen

Title: Re: miller compensation
Post by raja.cedt on Sep 28^th, 2011, 6:00am

hello praveen,
let me think about this, but mean while you can read this paper.
Re-examination of Pole Splitting of a Generic Single Stage Amplifier

Thanks,
raj.

Title: Re: miller compensation
Post by Praveen K on Sep 28^th, 2011, 6:54am

hi Raj,

I don't have access to IEEE transactions on circuit and systems. will be thankful, if possible you can post me that paper.

interested in reading it,
praveen

Title: Re: miller compensation
Post by raja.cedt on Sep 28^th, 2011, 7:33am

i can't. It's ieee, soplease give your mail id so i can send you.

Thanks.

Title: Re: miller compensation
Post by Praveen K on Sep 28^th, 2011, 8:19am

Hi Raj,
Please send it to kpraveenthomas@gmail.com

thank you,
k.praveen

Title: Re: miller compensation
Post by rajkumar palwai on Sep 29^th, 2011, 9:42am

Hey Raja,

I think i understand what praveen is explaining. First stage will see a miller multiplied cap only when there exists a gain for stage2 (Ceff~=Av2*Ccomp). But if the 2nd stage load cap is so high that pole2 becomes dominant and Av2 falls to below 0dB before pole1, then stage1 does not see any miller multiplied cap. Pole1 simply becomes ro1*(Cp1+Ccomp), where Cp1 is parasitic cap at stg1 o/p.

So. in this case put a buffer between stg1 and stg2 so that, pole1=ro1*Cp1 and this increases ur phase margin (dont forget that pole2 is dominant and pole1 has to be moved away from origin for better phase margin)

Correct me if i am wrong.

-Rajkumar

Title: Re: miller compensation
Post by raja.cedt on Oct 2^nd, 2011, 4:04am

hello rajkumar,
i am about to post ans for this query, but one question do you think miller fail in case of o/p pole dominate and first stage pole non-dominate?

Thanks,
raj.

Title: Re: miller compensation
Post by rajkumar palwai on Oct 3^rd, 2011, 6:32am

Hi Raja,

Yes miller will fail when the o/p pole is dominant.
Under normal conditions when p2>UGB, P2 equation comes like gm2/CL, where gm2 is stg2 trans-conductance. Here gm2 comes in the equation, because after UGB, the Cc (miller cap) impedance is so low that M2 tranr appears like diode connected.

All these are derived under some assumptions. Now if u start increasing the CL, then after some value the pole2 itself will not be equal to gm2/CL, since the M2 presents more o/p impedance than simple 1/gm2. And if u further increase the CL, than the p2 equation becomes 1/(ro2*CL). And if u make P2 dominant, then Av2 falls after P2 and the stg1 doesn't see the full miller cap.

Title: Re: miller compensation
Post by raja.cedt on Oct 3^rd, 2011, 7:02am

hello rajkumar,
you are worng, let me explain. If outpole dominate then entire explanation is wrong. Miller works in any case for your reference plz check this fig (http://www.designers-guide.org/Forum/YaBB.pl?num=1314197543). So from that fig you can say miller works in any case. Because when you have o/p pole dominates, then you will see miller multiplied resistance rather miller cap, which is very difficult to explain and unfortunatly i forgot where i read this. Plz belive me that miller works in either case.

Thanks,
Raj.

Title: Re: miller compensation
Post by rajkumar palwai on Oct 4^th, 2011, 2:16am

Hi raja
i am still unable to understand ur point intuitively. But, anyhow i will do the maths and then try to analyse it.

-Rajkumar

Title: Re: miller compensation
Post by Praveen K on Oct 4^th, 2011, 2:54am

Hi Raj, Thanks for sending me those papers. I'm going thru them and working on it. Let me see if i can convince myself on what you say, if not i'll post my arguments to you shortly.

hi Rajkumar, your perception of AV2 falling below 0db if output pole is dominant is new to me, i've never thought of it that way. let me verify this in simulation, then i think i can appreciate it well.

thanks,
Praveen

Title: Re: miller compensation
Post by raja.cedt on Oct 4^th, 2011, 3:11am

hello rajkumar,
please find the attached fig, please derive the impedance into the cap, you get at lower frequency miller cap but at some high frequency you get some resistance which is called miller resister (this is the resister responcible to make non dominate pole at firrt stage o/p more non dominate)

Thanks,
Raj.

Title: Re: miller compensation
Post by Praveen K on Oct 6^th, 2011, 5:29am

hi Raj,

In my simulation I posted before, the values for the two stages were,

GM1 = 9.5mS , R1 = 11.36K , C1 = 11pF
GM2 = 18.82mS, R2 = 1.15K (after loading of 1mA) , C2 = 10nF
miller Cc = 0pF , 100pF

I tried to find the poles and zeros of the whole transfer function Vout/Vin with small signal models for the two stages with miller cap across it, and as you know its a long expression.

then I plugged in the above values to that expression in octave and tried to see how the pole and zero moves with variation of miller cap Cc

for Cc = 0pF the Vout/vin =

1.626e+15
---------------------------------
(s + 8.737e+04) (s + 8.004e+06)

for Cc = 10pF the Vout/Vin =

8.534e+14 (s - 1.883e+09)
---------------------------------
(s + 7.172e+04) (s + 5.104e+06)

for Cc = 100pF the Vout/Vin =

1.631e+14 (s - 1.883e+08)
--------------------------------
(s + 2.71e+04) (s + 2.554e+06)

for Cc = 1nF the Vout/Vin =

1.958e+13 (s - 1.883e+07)
----------------------------
(s + 3727) (s + 2.039e+06)

you can see from above, increasing the miller Cc results in both the poles moving to lower frequencies and there is no pole splitting. The zero is again away from the two poles at a higher frequency.

So with no approximation to the transfer function, clearly when C2*R2 > C1*R1 , miller cap Cc doesn't pole split nor helps in PM???

or am i missing something in the above?

thanks,
Praveen

Title: Re: miller compensation
Post by raja.cedt on Oct 6^th, 2011, 6:36am

hello pravin,
let me look at this, but i did some some behaviour model simulation at 25n compensation cap i am getting some 55deg PM. Soon i will get back to you.

Thanks,
raj.

Title: Re: miller compensation
Post by raja.cedt on Oct 13^th, 2011, 7:33am

hello pravin,
have you got conclusion regarding this or still strugling? try the cap what i gave in the previous post check once, what i found is in the case of o/p pole dominate miller caps needs to be much higher... Hope some one who has good understanding will clarify further..

Thanks,
raj.

Title: Re: miller compensation
Post by Praveen K on Oct 14^th, 2011, 12:39am

Hi raj,

there is no conclusion yet. As far as i see with the miller cap both the poles move to lower frequency when output pole is dominant. Yes, you get some phase margin with a miller cap > 10nF. But do you think its worth to have a miller cap > load cap of that size, again, off chip!! :D

Praveen

Title: Re: miller compensation
Post by raja.cedt on Oct 14^th, 2011, 3:25am

yes praveen,
you are correct, i am also in confusion. But here miller still works but not worthy i guess. Did you try in your sim?

Thanks,
Raj.

Title: Re: miller compensation
Post by Praveen K on Oct 14^th, 2011, 4:06am

hi raj,
yes i tried in simulation. As i increase the miller cap more than 25nF i get some PM of 35deg.

One thing i observed is that the dominate (output) pole moves faster inwards than the non-dominant pole to lower frequency as you increase the miller cap.

Praveen

Title: Re: miller compensation
Post by thechopper on Oct 18^th, 2011, 6:46am

raja.cedt wrote on Oct 3^rd, 2011, 7:02am:

I partially agree with Raja. It is correct to say that Miller effect will always take place, regardless the value of CL, since such effect depends on the DC gain of the second stages. Thus CL does not play a role in such multiplication effect.
What it is also true that if the o/p pole is the dominant one then the expression for it is not 1/(gm2*R2*Cmiller*R01) anymore since now the contribution from CL has to be considered. In any case Miller capacitor will have to be very large in order to make the o/p pole non-dominant, since actually in that case the location of p1 and p2 will have to be actually inverted when considering the closeness to the imaginary axis.
But Miller effect will still be there anyways.

Best
Tosei

Title: Re: miller compensation
Post by analogbeginer on Dec 10^th, 2011, 6:28pm

I have a basic question. Can the miller cap be seen as small signal current path between 2-stages, where it steals the small signal current form the dominant pole side and gives the samll signal current to the non-dominant stage, which looks like pole splitting? (So, it doesnt matter which is dominant)

Title: Re: miller compensation
Post by raja.cedt on Dec 11^th, 2011, 7:25am

hello,
could you please explain in-detail, sounds interesting and i am the great fan of answering miller compensation Questions.

Thanks,
Raj.

Title: Re: miller compensation
Post by analogbeginer on Dec 11^th, 2011, 10:40pm

Basically, I was thinking, when pole starts its effect, it means the small signal current from the main branch, is stolen by the R-C combination, which forms the pole(Lets say X-Amps). So, if we introduce a small signal current branch (the miller cap), at a much earlier frequency itself we can see that X-Amps being stolen from the main branch(amp-branch), which suggest that the pole is appearing at a much low frequency. The same holds good for the non-dominant pole. This is my intutive way and please correct me if I'm wrong.

Title: Re: miller compensation
Post by Praveen K on Dec 11^th, 2011, 11:25pm

Hi analogbeginer,

when miller compensating, the non-dominant pole moves to a higher frequency because of the feedback at the second stage and NOT due to the current thru the miller cap.

if you consider, the indirect way of compensation thru a current buffer (ahuja compensation type) or thru a source follower, the feedward current ("where it steals the small signal current form the dominant pole side and gives the samll signal current to the non-dominant stage") is in fact blocked! to get rid of the zero.

I guess your intuition is wrong when you apply to pole splitting!

Your intuition is right when applied to creation of a pole in general.

and i think it does matters which pole is dominant, before using miller cap compensation!!!!

cheers,
Praveen

Title: Re: miller compensation
Post by raja.cedt on Dec 12^th, 2011, 12:52am

hello analogbigner,
i agree with praveen, what he is saying is correct, but still i didn't get your idea of steeling current (it would be great if you try to explain with some fig becaz for me it is very difficult to understand verbally).

Thanks,
Raj.

Title: Re: miller compensation
Post by thechopper on Dec 12^th, 2011, 6:38am

sushan wrote on Dec 11^th, 2011, 10:40pm:

Correct...current stealing at high impedance node means gain dropping -> roll off started -> pole effect is there.

sushan wrote on Dec 11^th, 2011, 10:40pm:

The same holds good for the non-dominant pole. This is my intutive way and please correct me if I'm wrong

Not correct: Miller cap adds (does not steal) current to the non-dominant pole node (output node). Thus "delays" the effect of this second pole (ie. moves it to higher frequency).

Best
Tosei

Title: Re: miller compensation
Post by analogbeginer on Dec 12^th, 2011, 10:02pm

@Praveen,
I agree with you. Yes feedback increase the cap on the dominant side, and alter the resistance on the non-dominant side(Since there is a phase change, by the time it sees the non-dominant pole). But, in the classical miller experiment with vacuum tubes, he observed, "when a cap is connected between a gain stage, cap takes in a large amount of small signal current, which looks like as though the cap is boosted". So can't this current be termed as the steeled current? Correct me if I'm wrong.

And as you correctly pointed out, this cannot be directly applicable to cascode compensation(Ahuja).

@the hopper,
Actually I was saying the same. I meant the small signal current is added to the non-dominant side -->which explains pole splitting(if current is stolen, it should be given to some other baranch, which is non-dominant part). Pls correct me if I'm wrong.

Title: Re: miller compensation
Post by Praveen K on Dec 12^th, 2011, 10:55pm

Hi analogbigner,

I agree with you on steeling current and boosting cap as a result of that. this intution will also hold good for creation of pole in general.

But I don't agree, when you say that the non-dominant pole is moved to a higher frequency because of addition of current that was stolen before from dominant pole.

Because of miller cap, a part of the output signal (capacitive division between miller cap and gate cap) will again appear at the gate of second stage, and because of this a significant amount of current will be added to the non-dominant node (thru gm2), which is the one actually moves it to a higher frequency. The stolen current added thru miller cap does nothing to do with nondominant pole moving away (which is proven by ahuja compensation). And in the unapproximated expression for output pole, miller cap (Cc) contribution is very negligent.

It seems like, this addition of the stolen current creates a RHP zero which is useless!!!! But I can't picture this in my mind, in terms of how an added current would make the amplitude response go up and phase response go down......... :o??????!!!!!

cheers,
k.praveen

Title: Re: miller compensation
Post by thechopper on Dec 13^th, 2011, 4:07am

Praveen K wrote on Dec 12^th, 2011, 10:55pm:

The stolen current added thru miller cap does nothing to do with nondominant pole moving away (which is proven by ahuja compensation). And in the unapproximated expression for output pole, miller cap (Cc) contribution is very negligent.

Not correct: the Miller cap creates a short at a certain frequency which lowers the impedance on the output -> this forces the non-dominant pole to move at higher frequencies. At such frequency, the "stolen" current is fully injected in the output: two ways of describing same thing.
Miller cap DOES affect the non-dominant pole moving away.

That is why Miller effect creates the pole splitting effect.

Tosei