Re: PWM Amp Design

Larry Brasfield wrote: 
"Chris Carlen" <crcarleRemoveThis@xxxxxxxxxxxxxxx> wrote in message
news:d36fkj022dd@xxxxxxxxxxxxxxxxxxxx

I'm designing a PWM amp PCB module based on the Apex
Microtechnology SA60 chip.


Target specs are to be able to sustain 80V at up to 7.1A
continuously and 10A max. into a load of unspecified resistance.


Specifying at least a range would help a lot.  Does the load actually
change once a system is built?  Or do you just not know the load yet?

My idea was that since I had to build an amp for about 3.5A RMS into the load of 2.5ohm+250uH for a specific application in which the load will never change, that I might use the opportunity to make a somewhat more generalized hardware foundation which could be used for similar applications in the future with different loads. Hence the "unspecified" load. Reasonably speaking, we would be considering mostly slightly inductive loads such as motors and solenoids ranging from perhaps 0.5-20ohms, and 10-1000uH. I doubled the current capability from my application's 3.5A RMS (but must be able to deliver 10A peak currents anyway, so the filter inductors mustn't go flat at that current) to 7A just for flexibility.

That means for small load resistances, the output voltage might not
ever reach 80V, but for any load resistance, the output current
must be able to reach 7.1A continuously.


Is current limiting an issue?  (I would think so if the load is as
ill-behaved as you have allowed here.)

At this point, current limit isn't necessary. I don't like being unprotected from short circuit, but the complexity of implementing this vs. the timeframe for getting something running (this is an experimental lab apparatus application, not a commercial product) forces me to implement the simplest approach first. I can spend time on refinements later.

Current limiting would also be complicated by the fact that we need to be able to deliver accelerating currents of 10A to perhaps even the SA60's 15A peak capability, which the load coils can handle briefly, but not continuously. So a current limit designed to protect the load would have to allow short bursts of high current, but somehow take into account the average power limitations of the load as well as its transient thermal limitations.

Frequency response should be flat to -3dB at 10kHz or better. 

If phase delay up to 150 Hz is what you really care about, it would
be more useful to know that requirement.


2 degrees.

The PWM amp is closed loop with a differential output voltage sense
amp feeding into a simple integrating summing amp driving the PWM
control input, which also has the main input signal applied.  Note
that the output voltage sense is done prior to output filtering, so
that a simple integrator compensation is able to maintain control.


I suggest that, with an appropriate controller, it would be fine to
control the filter output instead.  That would likely simplify
getting the phase delay you want, by easing the derived and hence
subsidiary requirements.

The output is filtered with a differential LC Butterworth
arrangement, the LC values of course needing to be tuned to the
load resistance.


That makes me think the load may be knowable after all.

I have chosen a 125kHz switching frequency.  The output filter
cutoff will be 12.5kHz.

Is it a 2 pole LC LPF, nominally? 

Yes.

My present load will be a 2.5 ohm coil with 250uH of inductance.
Thus the LC filter elements are 22.5uH and 7.2uF.


Is there any reason you cannot adjust the controller response to
accomodate the load variation?

There is no load variation in this case. The response would have to be adjusted for different load applications.

The inductive load requires equalization to cancel its reactance or
else the LC filter for the PWM becomes resonant with the added load
inductance, resulting in freq. response peaking.


The controller could provide the damping without the necessity of
dissipation or extra HF output.


That would be cool (in more ways than one.)

To fix this, I have added a 2.5ohm resistor in series with a 40uF
capacitor across the load.

That is a hit with respect to ripple.

Huh? Wouldn't crossover of load current at high frequency to the capacitive branch actually reduce ripple? Oh wait, or does it modify the filter response so as to reduce the cutoff slope? No! That's the point of the equalization, to present to the filter an effective resistive load of 2.5 ohms at all frequencies. But from the real load's perspective...it sees its current dropping off as its own inductance kicks in. Actually, since the voltage across both the real load and the capacitive branch are the same, I don't think there is any effect on ripple. I'll have to check this.

This all works fine except for some drawbacks.  Obviously, at high
frequencies near and above the crossover frequency of the load RL
combination, the equalizer RC network begins to conduct substantial
current and dissipating massive power.  Up to about 115W at the
output specs mentioned.


EMI might suffer, too, depending on what the inductors really look
like.

Do you mean because they are having to conduct the full current expected from a resistive load at the cutoff freq. whereas if there was no capacitive equalizer, then their current thus radiated mag. field would drop off more quickly at HF?

I should point out that the application signal has an upper
bandwidth of only about 150Hz, so the 10kHz amplifier response is
way overkill. The point is that at 150Hz, I want very low phase
shift for a servo loop, so the wide band amp relative to the application is warranted. (Actually, perhaps only about 3kHz might
suffice). 

With a controller designed to bring the LC LPF poles where they would
help form a traditionally design, controlled phase-delay filter, I
expect the difference between your desired passband and the switching
frequency will make it an easy job.


Hmm.

However, for more academic purposes I am still curious about what
other approaches other than an equalizing network one might try to
solve the reactance problem? It seems to me that one approach
might be to try to sense the PWM output post-filter, and then compensate for the peaking within the PWM amplifier control loop. 

Glad you are open to this.

Is this typically done? 

I don't know about typical.  I've done exactly that for a system with
much less separation between the intended signal band and the
switching frequency.


That's a good sign.

I am as of yet unable to do this, because my AC model for the PWM
amp power train is inadequate. I am aware of the state space averaging and other models which correctly predict the presence of
a right plane zero in these circuits. 

The simple PWM with bridge does not have the RHP zero and its
response is quite consistent as long as the initial filter inductors
do saturate and the input supply is relatively stable.


Saturate?  Why would we want that?  Perhaps you mean "don't saturate?"

They will be designed to hold up at least 75% of their inductance to 10A.

I think I need to be able to understand this and be able to compute
the correct model for my PWM amp before I can attempt designing the
correct loop compensation.


The response is very simple.  The transfer function is a constant
once the switching frequency is taken out.  Write a few expressions
for the steady state DC output versus duty cycle and see for
yourself.

Yes, I have already done this. Quite a while ago I did a sim where it seemed things *didn't* work with this model, but did work in reality. Kind of backwards from what usually happens. I thought because my AC model was missing the RHP. Perhaps you are correct. Now the other day I discovered that maybe my model wasn't so broke after all. I haven't pursued it very thoroughly because I knew I could get away with a simple integrator and "turn the knobs until it works" design based on the simple topology in Apex's app note AN33. But I hate to design things that way. Like I said, we need a result and I have already gotten burned once in this project for spending too much time making sure things worked theoretically, while some other guy just empirically tinkered his way to a working result (that's referring to the outer control loop in which this amplifier will fit).

One possible advantage of post-filter PWM amp output voltage
sensing and control might be to eliminate the overshoot inherent in
 the output filter (or I suppose the filter might be damped down to
a Bessel response as well).


Yes.

It seems problematic that the output filters for a PWM amp must be
tuned to the load impedance, and if there is substantial load reactance, that additional compensating measures must be taken
which either waste power or complicate the compensation required. 

That would depend on how far the poles are moved by the controller
relative to the variation in their open loop positions due to load
variation.  I do not see an inherent problem, depending on your final
accuracy requirements.

I need to spend some more time with pencil and paper to understand how the controller can "move the poles" of the filter. I think you mean that the closed loop transfer function will have it's poles not in the same place as the open loop right? So far I haven't dealt with any cases of having complex poles in the open loop, so this is virgin territory.

Maybe linear amplifiers are not so bad after all.  I tend to prefer
them since they are ripple free, but in this case I opted for the
PWM amp because 4 channels must fit along with 1200W of power
supplies, and bunch of other CPU type electronics in a 7" high rack
chassis.  That just didn't seem feasible or power efficient with
linear amps.


Given your requirements, PWM with appropriate feedback and control
seems like a good choice.

Yes, a linear amp would have needed water cooling to fit in the desired package.

Thanks for the input.

Good day!


--
_____________________
Christopher R. Carlen
crobc@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx
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