Solving the RHPZ problem of boost converter using Fixed Off-time PWM Control

Hey guys, I've read this pdf file which I saw in one thread here.
https://www.venable.biz/uploads/files/05-Technical-Paper-Current-Mode-Control.pdf

It discusses about minimizing the RHPZ effects with the use of Fixed off-time control. It discusses it based on a time-domain figure which looks plausible but it goes on to say that it increases the frequency of the RHPZ in other words, it moves farther into the frequency domain. Is there any truth to this? The choice of the off-time seems to have no effect on my simulations for the frequency domain loop gain of the converter. In other words, it really doesn't show any help to the RHPZ problem. The RHPZ also doesn't seem to respond to choice of offtime. Also, based from the equation omega = (Vout*(1-D)^2)/(Iout*L), the location of the RHPZ, it clearly shows that the location of the zero is independent of the off-time, it's only the duty cycle that matters, or the percentage of the offtime with the whole period.

clearly you are correct, with constant off time converters, the rhpz is at a much higher frequency than for constant frequency converters.

However, virtually all the app notes get this wrong...and they give the same equation for rhpz in constant off time converters as for constant frequency converters...eg

Page 10 of this:-
**broken link removed**

page 17 of this:-
http://www.ti.com/lit/ds/symlink/lm3421.pdf

..it just goes to show, that few engineers in the world can calculate what the rhpz frequency is in c.o.t. converters.

I worked for a huge phone company once, and one time we had an unstable loop on an smps, we were then all told to go away and calculate bode plots for the loop....We all just number crunched the equations in the Basso book,....but the Chief Engineer came up with something different, telling us all that he had calculated it all out from first principles, so as to be sure that his work was correct.
He chided us for number crunching equations without knowing the basis behind them.

The following day, we found an onsemi app note and noted that he had copied it virtually word for word.
I am now very suspicious when someone declares themselves a control expert.
I think I'd rather blow the dust off the gain_phase analyser and take a measurement.

Actually, I think I bear responsibility for this misconception, since I used to post that same paper. But since then I've become convinced that that particular point is not true, and the RHPZ is not at all affected by constant off time control (or any type of modulation, for that matter).

Consider it this way: both constant frequency and fixed off time modulation work by varying the duty cycle of the converter. In the small-signal sense, changes in operating frequency are irrelevant (this is one of the fundamental assumptions of state-space averaging methods), and therefore frequency modulation won't affect your transfer function, only duty cycle will. If you want a quick demonstration, go ahead and make a transient simulation of two identical boost converters. Start out with them biased in CCM, lets say with fsw=100KHz and D=0.25 (so ton=2.5us, toff=7.5us). Then give them both a step response which is identical in duty cycle, but with a different modulation type. For example, change one to fsw=100KHz and D=0.4 (ton=4us, toff=6us, so constant f modulation) and the other to fsw=80KHz and D=0.4 (ton=5us, toff=7.5us, so constant off time modulation). What you should see is that both converters show the exact same transient small signal (that is, neglecting ripple) response. I've attached a simulation to demonstrate this.

Doing that simulation initially convinced me that the article was wrong, and since then I went and manually did the SSA calculations and found that, indeed, the results are exactly the same regardless of whether you modulate on-time, off-time, or both. It all comes down to what your duty cycle is doing.

This doesn't mean that constant off time modulation has no benefits. As the article says, it doesn't require slope compensation when used in CMC, and this can be the case because subharmonic instability is not something that can be derived from state space averaging in the first place.

yes you have proved it for that idealised controller case.
But I conjecture , as you know, in a real fixed frequency controller, the off-time will get compressed and constricted far more quickly with a constant frequency controller than a C.O.T. controller?
In the fixed frequency controller, there is nothing to stop that off time being compressed to the tiniest time interval, wheras with c.o.t, you arealways guaranteed that off time "slice".

I always imagine a fireman repeatedly filling and emptying a bucket of water from a tank into a reservoir.....then imagine it with constant emptying time, and constant bucket replenishment time.....as analogies, -you can kind of get the feel that the constant emptying time guy will keep filling the reservoir more smoothly and effectively.
The one who has the constant replenishment rate, and who just has to fill the bucket more, isn't going to get enough time to empty out the water each cycle.

treez said:

yes you have proved it for that idealised controller case.
But I conjecture , as you know, in a real fixed frequency controller, the off-time will get compressed and constricted far more quickly with a constant frequency controller than a C.O.T. controller?
In the fixed frequency controller, there is nothing to stop that off time being compressed to the tiniest time interval, wheras with c.o.t, you arealways guaranteed that off time "slice".

I always imagine a fireman repeatedly filling and emptying a bucket of water from a tank into a reservoir.....then imagine it with constant emptying time, and constant bucket replenishment time.....as analogies, -you can kind of get the feel that the constant emptying time guy will keep filling the reservoir more smoothly and effectively.
The one who has the constant replenishment rate, and who just has to fill the bucket more, isn't going to get enough time to empty out the water each cycle.

Click to expand...

What you're describing doesn't have anything to due with the duty cycle to output frequency response though. It's just a different method of changing the duty cycle. It might affect things like achievable duty cycle range, but that has nothing to due with the AC transfer function.