Topics: Bode plots for constant on time converters
on General Discussion
Bode plots for constant on time converters
So for a pure hysteretic converter, we can probably agree that a Bode plot isn't possible. It's a large signal control scheme and there's no small-signal linear system analysis or measurement possible (?). However, there are some control schemes like TI's DCAP constant-on time control that uses the ESR of the output caps as current feedback. If you use a very small signal disturbance you can measure a Bode plot with these devices, where the crossover usually measures around 300kHz (!). My question is what does this Bode plot mean with this topology? I think it may by valid for small disturbances, but I don't think it will say anything about the response of the converter to large load steps and releases where the converter will be more like a pure hysteretic controller.
Any feedback on this or the general subject of Bode plots on these kinds of controllers would be appreciated.
09-10-2013 06:04 AM
I think we need to split this question into three parts.
Constant on-time converters in general are measurable and can have a valid small-signal model. The on time is constant, as the name says, but a variable width drive is derived from an error signal.
The hysteretic controllers can also be split - you can have hysteretic current mode where the current signal is constrained between two references. The current loop cannot be measured, but once the current loop is closed, you have a system that looks like a current source feeding the load cap and resistor. That part of the system can be measured and it is valuable to do so.
Then there is hysteretic control of the output directly. This type of control scheme has been around much longer than PWM controllers. The switch is controlled by the output bouncing between two references, and there is no meaningful measurement of the loop, but you can of course measure things like output impedance.
This type of hysteretic control didn't last long since it is too noise sensitive. Cherry Semiconductor came out with some specific controller for the hysteretic current mode, but it was really a niche part for the automotive industry. The technique does resurface now and then, but has noise issue for higher power levels.
09-10-2013 06:05 AM
Thanks Ray- I know constant on time converters in general can have a valid small-signal model. I was more interested in DCAP type architectures specifically where there is no error amp in the loop, only a comparator. The comparator uses the output ripple to trigger Ton when the ripple falls below Vref. (Ton is pre-set to give the target steady-state frequency based on Vin and Vout.)
So intuitively I think that for disturbances that don't cause the output to go out of the range of the output ripple there is still kind of a finite gain modulator action and a Bode plot can be measured and some sort of small-signal model can be derived.
However, once the output leaves the vicinity of the ripple magnitude for significant time, (due to a load transient for example) there's only an infinite gain comparator in the loop, no further change in the output can affect the loop. At that point it's purely hysteretic and the small signal model no longer predicts behavior.
So the Bode plot can predict stability in the steady state, and you have to use some sort of large signal analysis/simulation to predict stability for large transients?
I get asked about this a lot, and there is a lot of discussion and argument about it, but I have never seen a formal analysis.
09-10-2013 06:05 AM
There is no formal analysis available of the hysteretic part. Never really has been any.
This situation doesn't bother me too much because it's a bounded problem, and the only stability trouble you can get into is with noise, rather than small-signal. I don't really care for the hysteretic controllers because the noise is what determines operation, but there probably isn't any real need for a model.
I'm much more concerned about the burst-mode converters that are so popular these days at low power. The are only bounded on one side, and oscillations are possible, but measurements and the usual design tools are not. But perhaps that would merit a different topic of discussion.
At low power, it doesn't matter too much, but as power levels creep up it can be a problem.
09-10-2013 06:08 AM
There was a lot of work by Bose and Froeschle starting back in the 60's. See US Patent 3294981, 4,456,872, There are some great equations that give good insight into the stability issue in 5345165 from 1985.
09-10-2013 06:09 AM
Wow, thanks for all the great comments everyone- The third type of COT converter that Richard mentions is the one I'm most interested in.
"The third version is where the off-time is terminated when the output voltage (or a fraction of it) goes below the reference voltage. This control belongs to the family of ripple-based controls and it cannot be characterized with the usual averaging-based control-to-output frequency response, for the reason that the gain is affected by the output ripple voltage itself."
I agree with all the comments so far- What I'm trying to get to is a way to satisfy customers that they will not have stability or transient response problems with this type of controller. We can take a control to output response with a network analyzer if the disturbance signal is small enough, but I'm guessing that it only means anything right around the operating point where the plot was taken. Quoting a "phase margin" based on that information is probably of limited use. Transient response testing is helpful, but doesn't lead to a stability metric.
In practice, there are no problems, assuming enough output ESR to keep the phase node jitter down, and simulations (with SIMPLIS for example) correlate to actual performance, but there are still always questions about quantifying stability. Some customers prefer traditional current or voltage mode control and give up some of the advantages of these control schemes just because the traditional controls are easier to analyze.
I'll check out the references everyone provided so I can learn more.
09-10-2013 06:10 AM
Others may have different definitions, but to me, hysteretic control is a system where the controlled variable bounces between an upper and lower reference. The first converters used to do this, and they were called ripple regulators. They didn't last too long since they are noise-sensitive, but they are being discussed again as the digital controller people sometimes think this might be a good idea.
Hysteretic current mode was where the inductor current bounced between an upper and lower reference, but the references were controlled with a conventional feedback system. This still finds some application.
Burst mode is like hysteretic, but there is no upper limit, only a lower limit. When the output drops below a certain value, the converter switches for a number of cycles, then it stops when it goes above the value again. It's basically chaotic operation, and unbounded on the upper side.
The burst mode usually works OK at low power levels, and is the approach used by Power Integrations, and others, for many of their controllers.
09-10-2013 06:10 AM
THis is true,but not completely true.
The hysteretic control scheme is nonlinear by definition , so using the Bode plot to analyze the small signal behaviour is not straigh forward.If you are very familiar with analyzing linear systems what you can do is to try using the describing function method . It is widely used to " linearize " non linear systems , and therefore stability ,gain and phase margins and step respone can be approximated in that way.
It is not easy , but you may have a go.
09-10-2013 06:11 AM
This discussion has a somewhat academic perspective that is rife with errors.
I can tell you I have used hysteretic control in product application at over 10KW for precise medical MRI gradient amplifier control. Highly linear, less than 50ppm error over 97dB control range (2mA in 180A), stability better than 8uArms/sec in 15 minutes for arbitrary control, bandwidth DC to 30KHz.
There are over 18,000 units in the field in the past 10 years with no faults.
Think out of the box, guys!
As for small signal analysis, there are always small signals.
09-10-2013 06:12 AM
Some of my customers build well over 18,000 units per HOUR. Saying "trust me, I've built a lot of hysteretic (or DCAP or whatever) converters and never had a problem" doesn't cut it. They need some way to understand what kind of performance they can expect.
If you have any suggestions or can point out some of the errors in the discussion so far, please do so. Help us think out of the box here.
09-10-2013 06:12 AM
Medical MRI amplifiers are not commodities or pedestrian POL converters.
My comment earlier was to direct thinking towards what could be done, rather than encourage unfounded constraints.
Even the simplest regulators use more than one loop. Hysteretic operation can be modified in many ways to circumvent perceived shortcomings of the "pure" model.
Consider time domain or state-space modeling as it applies to a modified hysteretic control. Bode plots are not a complete tool.
09-10-2013 06:13 AM
Ray, something you mentioned about Burst Mode Operation confused me. There are some IC solutions which operates the burst-mode to keep the feedback voltage inside a range.(i.e. Infineon's ICE3BRXX series) That helps the designer to keep the converter output voltage ripple at a reasonable level at light load. But you are saying they are bounded on one side. Is there a point that I'm missing?
09-10-2013 06:16 AM
I agree with the definition by Ray, that "hysteretic control is a system where the controlled variable bounces between an upper and lower reference". As John wants to find the conditions to prove the stability of these controllers, it is interesting to define it in a control language. Then I would say that "hysteresis control is a system where a switching rule determines one switching variable based on the value of a single state variable or output." In other words, a hysteretic controller determines if one switch is ON or OFF, based on the value of only one measured variable (there can be no storage of information, as in the case of, say, a PI controller, only the present state of the system matters to the decision.).
The simplest example of hysteretic control that I can think of is the thermostat. In this case, the heater will be turned ON if the temperature below a set-point and turned OFF otherwise. The function of a hysteresis band is to limit the switching frequency.
Although very simple, this example shines some light on the conditions of stability. A hysteretic controller will only work if there is a simple relationship of the controlled variable with the switching action. In the example, the heater ON implies that the temperature will rise, while the heater OFF implies that the temperature will fall. Also, there is another condition for (asymptotic) stability: the set point must be in the range of temperatures that are achievable by the system. Once the basic conditions are satisfied, one can see that this control technique is very robust.
As Ray noted, you can use a hysteretic controller as internal current loop or to directly control the output voltage. But whether you can control a given variable depends on the structure of your circuit. Let me make this clear with an example:
=> For a BUCK converter, you can control the output voltage directly with a hysteretic controller, because there is a simple relationship (switch ON lets energy flow to the output, switch off reduces the energy stored in the output filter).
=> For a BOOST converter, it is clear that a hysteretic controller of the output voltage will never work. The more you keep the switch ON, trying to raise the output voltage, the more it will fall. There is no simple (i.e. 1-dimensional) relationship that you can use to implement a hysteretic controller. (It may be tempting to attribute this to a non-minimum phase effect, but it is neither necessary nor convenient to assume some linearization of the system).