Topswitch feedback loop equation is incorrect?

Do you agree that equation 25 (page 14) of AN-57 by power integrations is missing factors of “2.pi”?

(It’s the equation for the error amplifier and modulator of a flyback power supply controlled by Topswitch.)

AN-57
https://ac-dc.power.com/sites/default/files/product-docs/an57.pdf

Maybe I am wrong, but this is what they say:

ok, thanks, you're right, that pole and zero do pretty much cancel each other, to give equation 25....but that isn't related to this question. This question concerns the missing "2 * pi" expressions in equation 25.

the missing "2 * pi" expressions in equation 25.

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missing where? I can't relate the equation to the schematic at first sight, e.g. where is RF1? But it looks like a plausible RC circuit transfer characteristic in s domain. You'll rarely find factor 2pi therein.

There should be a “2.pi” in all the little quotients…..eg “2.pi.RF2.CF1” and “2.pi.KT.RF2.CF1”.
..There is one quotient where they did actually put in the “2.pi”, it says “2.pi.f(topswitch)”
..So this is an equation where we expect “2.pi”, as it is not using the ‘omega’ thing (2.pi.f)

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As you know, "RF1" is not supposed to be in there, as RF1 is the lower divider resistor, and has only a DC setting purpose.

There should be a “2.pi” in all the little quotients

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No. Compare with s-domain transfer characteristics of simple RC filter circuits.

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No. Compare with s-domain transfer characteristics of simple RC filter circuits.

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...so why is there actually one "2.pi" expression in equation 25 then?

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Also, there is another problem relating to equation 25's use of the open loop gain of the TL431.......
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Equation 25, page 14 of AN-57 (attached) shows the feedback loop transfer function for the controller of a Flyback SMPS using the topswitch controller. It concerns the common TL431/Opto configuration.
Why does this equation involve the open lop gain of the TL431?
No other author includes the open loop gain of the TL431 in this transfer function , so why does AN-57 include it in its equation 25?

For example, a similar equation is derived by Fairchildsemi in their AN4150 document (Equation 39, page 12), but their equation does not include the TL431’s open loop gain.

Also, Equation 3-66, page 292, of Basso’s book “switch mode power supplies” does not include the TL431’s open loop gain.
Why does AN-57 include the TL431 open loop gain?

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Also, there is another problem relating to equation 25's use of the open loop gain of the TL431.......
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Also, Equation 25, page 14 of AN-57 has a parameter called the K(TOP), which is the gain of the topswitch.
What number should one insert for this?
Page 14 says that the topswitch gain is 0.4/mA
…so in thar case, should we put in “0.4”, or “400” to the equation 25?


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Also, there is another problem relating to Topswitch...
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Topswitch is the world's best monolithic flyback controller, so why are the full feedback loop calculations for it in an £86 book by Dr Basso? ("Designing control loops for linear and switching power supplies").
Surely this is I.P. belonging to Power Integrations?, why is this info not in the Power Integrations applications notes.?
When will Power Integrations take back their I.P.?

AN-4150
https://www.fairchildsemi.com/application-notes/AN/AN-4150.pdf

AN-57
https://ac-dc.power.com/sites/default/files/product-docs/an57.pdf

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Also there is another problem relating to the Topswitch Flyback Controller..
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Dr Ray Ridley is undoubtedly the best SMPS writer of today in terms of the quality & clarity” of his literature.
The Ridley gain phase analyser also looks excellent.

But why is Dr Ridley being unfair to Power Integrations Topswitch flyback controller as follows….
In Dr Ridley’s document called “Loop Gain Measurement”, on page three, Dr Ridley states….

As we mentioned earlier, the TOPSwitchTM is a
convenient component that requires only a handful
of parts around it to complete a power supply, but it creates
a complex feedback system.

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..surely the Topswitch feedback loop system is not much more (if any more) complicated than what you get with the feedback loop for any other flyback controller?
The problem is that the main brunt of the calculations are contained in an £86 book by Dr Basso, instead of being on the Power Integrations website (“Designing control loops for linear and switching power supplies”)

...so why is there actually one "2.pi" expression in equation 25 then?

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It's used with a frequency parameter, not RC values. But as said, I have difficulties to relate the calculated TL431 transfer function to the result of an exact circuit analysis. I consider the possibility the application note calculation might be wrong.

Open loop gain will of course appear in an exact transfer function, similar to an OP circuit transfer function, but can be usually ignored in an approximate analysis.

treez said:

Also, Equation 25, page 14 of AN-57 has a parameter called the K(TOP), which is the gain of the topswitch.
What number should one insert for this?
Page 14 says that the topswitch gain is 0.4/mA
…so in thar case, should we put in “0.4”, or “400” to the equation 25?

Click to expand...

I think you can insert whatever number you want as long as you insert coherent units for the others parameters in order to get controller's gain dimensionless.

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If you are not sure, and in case equation is correct, then place everything in SI units and you will have no problem. Always SI units work.

putting in "0.4" gives more sensible values of phase margin and crossover. Putting in 400, gives ridiculous crossover frequency of 47khz. So i guess its 0.4

And regarding "2.pi", it doesnt make much difference to the bode plots whether or not its included.

Worrying though is that the PI Expert software gives a topswitch design which becomes CCM at min vin. When you calculate the phase margin for this region of operation using their equations in AN-57, the phase margin comes out as just 20 degrees, (the crossover was 1400hz)