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Of Poles and Zeros and Phase Shifts, Oh My...

I just managed to crawl back up out of the rabbit hole I fell down concerning the SMPS design.

I've been reading Pressman's book on the subject. And dealing with the data sheets of related PWMs.

I had to read Pressman's chapter on stabilizing feedback loops about five times before I began to understand it.

So following the tennents of the chapter, I drew out the transfer function for the error amplifier. I'm simulating an UC3842 style device in a double ended flyback converter at the moment.

So for 100Khz switching frequency I chose 20kHz for the cress-over frequency, 2kHz for the zero, and 200kHz for the pole.

A plastic cap was employed for the filter cap so the esr zero was our around 10MHz or so. Accordingly I decided to make the gain curve of the error amplifier have a slope of zero between the zero and the pole in order to give the over all gain a slope of -1 as it passed through Fco.

At this point I felt rather pleased with my self for apparently being so smart, and moved on to simulate my newly worked out feed back loop.

Well, it worked. Worked terribly that is. :|

After an unsatisfying call to the chip manufactor. I put myself to ponder why the data sheet compensation network looked different from what was detailed in Pressman's book for a type 2 error amplifier.

Seeing that in the data sheet just a parallel RC was connected between the EA input and output pins, I tried that with various vales till I found some that worked well. This is without the input resistor as shown in the book.

So, I got the thing apparently working well, although I am clueless to why. I have come to the conclusion that the resistor divider for the feedback loop is the input resistor and it value is the Thevenin equivalent for that.

In one of the PWM data sheets I read it briefly mentioned that the Thevenin equivalent for the divider for that particular device should be around 3k to provide that best current cancellation, although omitted and further elaboration about that.

So I have a couple of questions. Why does the zero made seemingly so important in Pressman's book cause a bit of wobble in the error correction action. It less than sustained oscillation, but it does cause a few rebounds before settling down after a transient with the zero present.

With just the pole at 200kHz the error amp works great. Is there some reference that covers this in detail like Pressman's book?

I suppose I could try to derive how to calculate the phase margin of just the parallel RC error amp network with or without the Thevenin equivalent for the input impedance, although it sure would be convenient if someone has already explained how to do so properly.

And by the way what is a type 1 error amplifier?

Also If anyone could send me a copy of the Venable paper from the eighties referred to practically everywhere I would appreciate it. I've scoured the web in vain looking for one.

Fred

Reply to
Fred
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Your goals are narrow and the explanation would be broad. A university education is broad enough to answer all of your question.

Reply to
Globemaker

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I think I can get by without all the toxic crap they spew at our corrupted institutions of "higher" learning these days, thank you.

Since I have my own company, I lack a need to put bury myself in debt just in order to secure "Credentials" to maybe get a job with some exploitative corporation owned by some demonic banker, thank you again.

All I need to know is how to stabilize the control loops in the SMPS for the amplifiers I build. Thank you yet one more time.

Oh yeah, and as if you knew the answer anyway...

I found the Venable paper. It was on the Veneble website under a different title. That paper was more informative than Pressmans treatment of the subject.

So what I learned by just spending some time and effort is that a Type

1 error amplifier is this:

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It has one degree of freedom, which is the value of Cpole to locate where the EA gain curve cross unity.

And a type 2 error amplifier is this:

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It has three degree of freedom, which are to set the mid gain, and the frequencies of the zero and the pole.

What the data sheet for the device I'm simming showed for loop compensation with out any further explanation is some thing I have dubbed the "Type 1.5" error amplifier:

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This type, all else remaining the same, has two degrees of freedom. The low frequency gain and the frequency of the pole.

With the proper values this type of error amplifier works as well as I could want:

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Yellow is the EA output. Green is the output voltage. The transient is from minimal load to full load then back. Maximum load is about five times the minimum.

The EA correction is wonderful, quickly affected without any rebounding at all.

In this case the EA has a flat gain to the pole located at 200kHz. The cross over frequency ends up between 600Hz and 1kHz depending on the load. The switching frequency is 100kHz. I have yet to determine the phase margin, although I expect is rather large.

So, was all that to do about setting the phase margin around 45 degrees or so just hog wash?

When I sim the type two EA I get 3-4 rebound at each transition before it settles down.

In any case I seem to have answered my own question. However I still am wondering why the type 1.5 error amplifier seems to work so much better then the traditional type 2, and why is there an absence of any explainable of this anywhere?

Fred

Reply to
Fred

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Hey Fred,

The answer to your wondering is that the simple parallel RC between the input and output of the error amp is for current mode PWMs.

The error amplifier types detailed in the Pressman book and the Venable paper are for voltage mode PWMs.

The current mode makes things easier, just swap out value in the feedback network and watch the response on transients. When you find values that work well you done.

With current mode you can forget about all those zeros and poles and phase shifts.

Cheers,

Fred

Reply to
Fred

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Hey Fred,

I noticed that too after digging through thirty years of app notes and data sheets.

Some times those college educated jokers can be a real pain in the ass when it comes down to providing a simple answer to a simple question.

Cheers,

Fred

Reply to
Fred

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