Feedback compensation for current-mode switching power supplies

[Joel Kolstad]

I'm back to working on a power supply (a forward converter), and while I think
I know how to compensate the feedback loop, I did read one application note
(regarding the venerable UC3845) that goes through the process the same way I
would, except that they start with an equation for "control voltage (i.e.,
error voltage) to output voltage gain" that I'm unable to re-derive. This is
on page 5 of www.onsemi.com/pub/Collateral/AND8039-D.PDF:

Adc = [(Vin-Vout)^2/VinVe](Nsec/Npri)

....which I'm interpreting as...

Adc = (Vin-Vout)^2/(Vin*Ve)*(Nsec/Npri)

with:

Adc = DC gain from "control to output"
Vin = power supply input voltage, which they set as 140-200V; I figure 170V is
a good nominal value
Vout = output voltage, 28V in their design
Ve = Ummm... they don't say... I'm guessing reference voltage, 2.5V?
Nsec = number of turns on secondary, 21
Npri = number of turns on primary, 41

They calculate Adc= 13.5, but plugging in the numbers above doesn't facilitate
that. The closest I could get is to take Vin=170 and Ve=4.5 -- the the
equation does then work out.

But more importantly... does anyone recognize the form of this equation?
And know the derivation?

I'm also interested in pointers to other application notes discussing feedback
compensation for current-mode switchers. My main reference is Pressman's
book, but while he goes through voltage-mode compensation thoroughly, he
leaves current-mode compensation as an exercise for the reader... which, as I
say, I believe I've done correctly, but it never hurts to double-check before
throwing the power switch.

I probably ought to get a copy of Keith Billings' book one of these days, eh?

Thanks,
---Joel

 

[Genome]

I'm back to working on a power supply (a forward converter), and while I think
I know how to compensate the feedback loop, I did read one application note
(regarding the venerable UC3845) that goes through the process the same way I
would, except that they start with an equation for "control voltage (i.e.,
error voltage) to output voltage gain" that I'm unable to re-derive. This is
on page 5 ofwww.onsemi.com/pub/Collateral/AND8039-D.PDF:

Adc = [(Vin-Vout)^2/VinVe](Nsec/Npri)

...which I'm interpreting as...

Adc = (Vin-Vout)^2/(Vin*Ve)*(Nsec/Npri)

with:

Adc = DC gain from "control to output"
Vin = power supply input voltage, which they set as 140-200V; I figure 170V is
a good nominal value
Vout = output voltage, 28V in their design
Ve = Ummm... they don't say... I'm guessing reference voltage, 2.5V?
Nsec = number of turns on secondary, 21
Npri = number of turns on primary, 41

They calculate Adc= 13.5, but plugging in the numbers above doesn't facilitate
that. The closest I could get is to take Vin=170 and Ve=4.5 -- the the
equation does then work out.

But more importantly... does anyone recognize the form of this equation?
And know the derivation?

I'm also interested in pointers to other application notes discussing feedback
compensation for current-mode switchers. My main reference is Pressman's
book, but while he goes through voltage-mode compensation thoroughly, he
leaves current-mode compensation as an exercise for the reader... which, as I
say, I believe I've done correctly, but it never hurts to double-check before
throwing the power switch.

I probably ought to get a copy of Keith Billings' book one of these days, eh?

Thanks,
---Joel

That is so 'horrible' someone should be shot at dawn for it....

The closest I might care to guess is the 'idiot' what wrote it has
managed to derive an equation for a PWM gain in the current sense
section based on the level of ripple current in the output inductor
reflected to the primary as it appears across the current sense
resistor which ends up incorporating the other equations he has used
to calculate a value for the filter inductor with. Look at his Eq
4).........

Oh no....... In fact once upon a time I provided a similar derivation
but for a single switch flyback converter using a UC38xx type
controller in order to develop a linear model. It works and is
necessary there because of the way a flyback converter operates.

Ooooh dear..... you don't think someone read that and has applied it,
incorrectly, to a Forward Converter?

Perhaps that's why I recognised the possibility.

Arse

In fact, since it is now dawn here I shall go out and shoot myself.



DNA

 

[Tom Bruhns]

I'm back to working on a power supply (a forward converter), and while I think
I know how to compensate the feedback loop, I did read one application note
(regarding the venerable UC3845) that goes through the process the same way I
would, except that they start with an equation for "control voltage (i.e.,
error voltage) to output voltage gain" that I'm unable to re-derive. This is
on page 5 ofwww.onsemi.com/pub/Collateral/AND8039-D.PDF:

Adc = [(Vin-Vout)^2/VinVe](Nsec/Npri)

...which I'm interpreting as...

Adc = (Vin-Vout)^2/(Vin*Ve)*(Nsec/Npri)

with:

Adc = DC gain from "control to output"
Vin = power supply input voltage, which they set as 140-200V; I figure 170V is
a good nominal value
Vout = output voltage, 28V in their design
Ve = Ummm... they don't say... I'm guessing reference voltage, 2.5V?
Nsec = number of turns on secondary, 21
Npri = number of turns on primary, 41

They calculate Adc= 13.5, but plugging in the numbers above doesn't facilitate
that. The closest I could get is to take Vin=170 and Ve=4.5 -- the the
equation does then work out.

But more importantly... does anyone recognize the form of this equation?
And know the derivation?

I'm also interested in pointers to other application notes discussing feedback
compensation for current-mode switchers. My main reference is Pressman's
book, but while he goes through voltage-mode compensation thoroughly, he
leaves current-mode compensation as an exercise for the reader... which, as I
say, I believe I've done correctly, but it never hurts to double-check before
throwing the power switch.

I probably ought to get a copy of Keith Billings' book one of these days, eh?

Thanks,
---Joel

I'm sure some Googling will turn up various references for you. One
example is Unitrode's ap note U-97 (as slua101.pdf on the TI web
site).

Have you done a simulation of your circuit? That may lead to valuable
insights too.

Cheers,
Tom

 

[Joel Kolstad]

Hi Tom,

I'm sure some Googling will turn up various references for you. One
example is Unitrode's ap note U-97 (as slua101.pdf on the TI web
site).

Thanks, I'll check it out.

Have you done a simulation of your circuit? That may lead to valuable
insights too.

Happily I'm using a Linear Tech IC in my power supply so, yes, I have done a
simulation with LTspice. However, I'd prefer to work out some theoretical
values and then do tweaking in a simulator rather than trying to do the
"design" in a simulator and not really know what, e.g., the phase margin is
other than by inferring it from the step response.

Also, since simulating the switcher itself is a bit slow, I am in the process
of doing some simple linear (AC) simulations as well... but of course to do
that I have to be able to input models of the system, hence the desire to
derive that app note's equation for control to output gain.

Since last night I've found that equation pops up in Marty Brown's book as
well (not exactly in the same class as Pressman or Billing's books, but it is
still useful).

---Joel

 

[Fred Bloggs]

Adc = (Vin-Vout)^2/(Vin*Ve)*(Nsec/Npri)

yeah that's right

with:

Adc = DC gain from "control to output"
Vin = power supply input voltage, which they set as 140-200V; I figure 170V is
a good nominal value
Vout = output voltage, 28V in their design
Ve = Ummm... they don't say... I'm guessing reference voltage, 2.5V?
Nsec = number of turns on secondary, 21
Npri = number of turns on primary, 41

They calculate Adc= 13.5, but plugging in the numbers above doesn't facilitate
that. The closest I could get is to take Vin=170 and Ve=4.5 -- the the
equation does then work out.

But more importantly... does anyone recognize the form of this equation?
And know the derivation?

You obviously start with Vout=Vin x D x Ns/Np, then arrange that in
terms of the error input to the error amplifier and differentiate wrt
the error as an independent variable. That gets you the required gain
for compensation purposes. D=ton x Fsw, and ton is obviously derived
from Vin/Lpri x ton + Iload x Ns/Np = Vsense, start from there. Iload
has a ripple to it as function of (Ns/Np x Vin -Vout)/L's too.

 

[Joel Kolstad]

Responding to myself here...

According to Marty Brown's book (pg. 203), (Vin-Vout)^2/(Vin*Ve)*Ns/Np is the
control to output gain for a *flyback* power supply, whereas for a *forward*
converter the gain is still the usual Vin/Ve*Ns/Np.

I'm tempted to believe Marty since -- other than tacking on a few more
constants and bundling them into "Ve" -- my derivation shows the same result
for a forward converter. I suppose that if I get ambitious I should derive
the results for a flyback and check it, though.

---Joel