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Design >> Analog Design >> stability analysis in active-RC polyphase filter
https://designers-guide.org/forum/YaBB.pl?num=1355301449

Message started by CMChan on Dec 12^th, 2012, 12:37am

Title: stability analysis in active-RC polyphase filter
Post by CMChan on Dec 12^th, 2012, 12:37am

I am currently working on a polyphase filter, which is implemented using opamp-RC. The op-amp is written using veriloga with a DC gain of 50 dB and unity gain frequency of 500 MHz. The schematic is shown in Fig. 1.

A cmdmprobe is added in the feedback path of the in-phase opamp and the value of cmdm is set to -1. The obtained loop response is shown in Fig. 2. We can see that when the loop gain phase is 0 at 14.04 MHz, the loop gain is 20.99 dB. It implies an oscillation condition.

The in-phase opamp has a differential feedback loop gain response shown in Fig. 3, when the cross-coupling resistors between I and Q are removed. This loop gain response is easy to understand.

To verify the stability, I added a voltage impulse in one feedback path, shown in Fig. 4. The voltage impulse has both rising and falling slope as 10mV/5ns. The resulted transient response is shown in Fig. 5. We can see that the loop is actually stable.

This design has actually been fabricated and measured. Indeed, there is no oscillation. My question is that why the stability analysis shows that oscillation is possible at 14.04 MHz (zero loop phase and greater than unity loop gain)? Any comment/discussion is appreciated.

Title: Re: stability analysis in active-RC polyphase filter
Post by Frank Wiedmann on Dec 12^th, 2012, 1:09am

First of all, the cmdmprobe is obsolete and does not work well if a circuit is not completely symmetric. You should use the diffstbprobe instead.

To simulate the loop gains in this circuit, I would probably first simulate the feedback amplifiers by themselves and verify their stability (as you did).

To examine the complete circuit, I would then place the diffstbprobe in the global feedback path between the amplifiers (in series with the resistors). This treats the amplifiers together with their local feedback as "feedback amplifier units" (that have already been verified for stability).

By putting the probes in the local feedback path while the global feedback is active, you combine the effects from both loops so that the results are very difficult to interpret.

Title: Re: stability analysis in active-RC polyphase filter
Post by CMChan on Dec 12^th, 2012, 1:56am

Hi Frank, thanks for your quick comment.

Frank Wiedmann wrote on Dec 12^th, 2012, 1:09am:

First of all, the cmdmprobe is obsolete and does not work well if a circuit is not completely symmetric. You should use the diffstbprobe instead.

diffstbprobe was introduced in MMSIM10.1. Currently I only have access to MMSIM06.21.431_LNX86, where there is only cmdmprobe.

Frank Wiedmann wrote on Dec 12^th, 2012, 1:09am:

To simulate the loop gains in this circuit, I would probably first simulate the feedback amplifiers by themselves and verify their stability (as you did).

The amplifier in in-phase path without I/Q cross-coupling has no stability problem, as shown in Fig. 3. Thanks.

Frank Wiedmann wrote on Dec 12^th, 2012, 1:09am:

To examine the complete circuit, I would then place the diffstbprobe in the global feedback path between the amplifiers (in series with the resistors). This treats the amplifiers together with their local feedback as "feedback amplifier units" (that have already been verified for stability).

By putting the probes in the local feedback path while the global feedback is active, you combine the effects from both loops so that the results are very difficult to interpret.

Please see Fig. B1 and Fig. B2 for the "global feedback" loop response, where the cmdmprobe was added in the coupling path from I to Q. We can see that the global feedback is stable, as suggested by the PM of 30 deg and GM of 35 dB. So my doubt is that when the global feedback is stable, shall we care about the "local feedback" stability as shown in Fig. 2? Are we supposed to have "absolute" stability in every feedback loop? The simulation of the "local feedback" loop response should be correct. I derived the local feedback loop response and obtained the bode plot using matlab, which is close to Cadence stability results.

Is the "local feedback instability" a special phenomenon for polyphase filter and can be ignored?

Thank you.

Title: Re: stability analysis in active-RC polyphase filter
Post by Frank Wiedmann on Dec 12^th, 2012, 6:59am

When the global feedback is active, what you call local feedback is really a combination of local and global feedback. This often gives rather unusual results for the loop gain which can no longer be analyzed with the simplified rules of phase margin or gain margin. You can find a discussion about the significance of phase margin at http://groups.yahoo.com/group/Design-Oriented_Analysis_D-OA/message/45 (you probably should read the entire thread to understand the context).

Instead, you should examine your loop gain from Fig. 2 with the Nyquist stability criterion (see http://en.wikipedia.org/wiki/Nyquist_stability_criterion) that is valid in all cases. According to this criterion, your circuit must be stable. Please also note that the loop gain phase reported by the stb analysis has a difference of 180 degrees with respect to most other definitions (see http://www.designers-guide.org/Forum/YaBB.pl?num=1124688329).

However, I believe that the approach I described in my last response is sufficient and that you don't really need to examine the loop gain from Fig. 2.

Title: Re: stability analysis in active-RC polyphase filter
Post by nrk1 on Dec 12^th, 2012, 7:52am

CMChan wrote on Dec 12^th, 2012, 12:37am:

I am that oscillation is possible at 14.04 MHz (zero loop phase and greater than unity loop gain)? Any comment/discussion is appreciated.

Zero loop gain phase and greater than unity loop gain magnitude does not mean instability. That would be true where the loop gain has only poles and no zeros.

Title: Re: stability analysis in active-RC polyphase filter
Post by CMChan on Dec 12^th, 2012, 7:40pm

Frank Wiedmann wrote on Dec 12^th, 2012, 6:59am:

Thanks for the info. Yes, I agree that the "local feedback" I referred is actually a combined effect of local and global feedback. I will go through the detail regarding the stability margin and run the simulation using LT-spice.

Frank Wiedmann wrote on Dec 12^th, 2012, 6:59am:

Instead, you should examine your loop gain from Fig. 2 with the Nyquist stability criterion (see http://en.wikipedia.org/wiki/Nyquist_stability_criterion) that is valid in all cases. According to this criterion, your circuit must be stable.

I will check using Nyquist stability criterion as well.

Frank Wiedmann wrote on Dec 12^th, 2012, 6:59am:

Please also note that the loop gain phase reported by the stb analysis has a difference of 180 degrees with respect to most other definitions (see http://www.designers-guide.org/Forum/YaBB.pl?num=1124688329).

Assuming feed forward transfer function as A and feedback as B, the Cadence calculate -AB as the loop gain response. The minus sign stems from the negative feedback.

Title: Re: stability analysis in active-RC polyphase filter
Post by CMChan on Dec 12^th, 2012, 7:46pm

nrk1 wrote on Dec 12^th, 2012, 7:52am:

Zero loop gain phase and greater than unity loop gain magnitude does not mean instability. That would be true where the loop gain has only poles and no zeros.

Assuming the op-amp differential feedback resistor as Rlp and differential feedback capacitor as Clp. There are two zeros at low frequencies: one at 1/(2*pi*Rlp*Clp) and another is close to the first one. Due to negative feedback, the loop gain phase increases from -180 deg. Yes, the point at 14.04 MHz in Fig. 2 is mostly contributed by the two zeros. Thanks.

Title: Re: stability analysis in active-RC polyphase filter
Post by Frank Wiedmann on Dec 13^th, 2012, 12:58am

And just in case you have not already discovered it: you can find very extensive information about loop gain simulation in general on my webpage https://sites.google.com/site/frankwiedmann/loopgain.