Question about crossover frequency of flyback converter

[Marcus]

I have a 100W flyback converter operating in the discontinuous mode at
40KHz.

I've managed to work out a power circuit gain and end up with,

Gp = SQRT(2.Fs.Lpri/ROUT)/Rs

Where Fs is my switching frequency. Lpri is the transformer primary
inductance. ROUT is an equvalent maxim load and Rs is the current sense
resistor, it uses peak current mode control on the primary side. Gp is the
change in output current in response to a change in the error amplifier
output voltage.

I can add my output filter capacitance, along with its esr, and work out how
to compensate the thing with a pole zero network. The thing I haven't
managed to figure out is what the maximum allowable crossove frequency is.

Can anyone help or direct me to a suitable source that explains things. All
I've found on Google is various statements like 1/5 or 1/10 of the switching
frequency but I'd like to know an analytical answer.

TIA

Marcus

 

[Yzordderex]

-----Snip taken here-----

Can anyone help or direct me to a suitable source that explains things. All
I've found on Google is various statements like 1/5 or 1/10 of the switching
frequency but I'd like to know an analytical answer.

TIA

Marcus

Marcus,

This site should have all the info you need. I think to get into a
lengthy discussion would be pointless. From the tone of your post,
you shouldn't have any problem de-coding the info. An interesting
discussion should be found relating to the creation of bode plots by
measurement techniques. All that is needed is an old gain-phase
meter. Bought one for a couple hundred bucks and does a fine job.
With a little patience you could do as well a job with even a 2
channel scope.

I downloaded all of the app notes many years ago. Since then Dean has
deleted some of the info regarding the cheap methode of doing the job
- he is trying to sell an ultrasophisticated machine for an ungodly
amount of money to do the same thing.

regards,
Bob
N9NEO
http://www.venable.biz/

 

[Marcus]

"Marcus" <[email protected]> wrote in message

-----Snip taken here-----


Marcus,

This site should have all the info you need. I think to get into a
lengthy discussion would be pointless. From the tone of your post,
you shouldn't have any problem de-coding the info. An interesting
discussion should be found relating to the creation of bode plots by
measurement techniques. All that is needed is an old gain-phase
meter. Bought one for a couple hundred bucks and does a fine job.
With a little patience you could do as well a job with even a 2
channel scope.

I downloaded all of the app notes many years ago. Since then Dean has
deleted some of the info regarding the cheap methode of doing the job
- he is trying to sell an ultrasophisticated machine for an ungodly
amount of money to do the same thing.

regards,
Bob
N9NEO
http://www.venable.biz/

Thanks for the reply.

I've come across this one but it doesn't appear to provide any information
beyond the general concepts of closing a feedback loop. I'm fairly confident
about doing this. However I need to know some fixed starting point from
which the rest follows.

Switch mode power supplies behave in strange ways. Average current mode
control and slope matching (the limiting condition) was the best thing since
sliced bread for me. It's the first time I could read the words and then
make the leap to proving for myself that the sums were right. That turned
out to be simple algebra and a bit of implicit integration and that fixed
the crossover frequency.

I'm trying to find similar limiting conditions, perhaps different ones, for
a flyback converter operating in the discontinuous mode. My best 'guess' so
far is that it is,

Fcomax = Fs/4.PI.(1-D)

If I make the overall loop first order at crossover and out to the switching
frequency.

And that comes from messing about with values in SPICE, seeing what works
and trying some sums that 'might' fit on the basis of previous experience. I
hate doing that. Next thing I'll be selling network analysers.

It might be right but if I can't prove it in a simple understandable way
then it's worthless.

Regards

Marcus

 

[Yzordderex]

-----Snip taken there----
----Here a snip, there a snip, everywhere a snip snip-----

Fcomax = Fs/4.PI.(1-D)

If I make the overall loop first order at crossover and out to the switching
frequency.

And that comes from messing about with values in SPICE, seeing what works
and trying some sums that 'might' fit on the basis of previous experience. I
hate doing that. Next thing I'll be selling network analysers.

It might be right but if I can't prove it in a simple understandable way
then it's worthless.

Looks like a formula out of an old Unitrode handbook. What happens
when you increase Fco beyond your calculated Fcomax? Obviously it
wont do you any good to have Fco greater than Fs. How was this
formula derived?

regards,
Bob

 

[Marcus]

-----Snip taken there----
----Here a snip, there a snip, everywhere a snip snip-----

Looks like a formula out of an old Unitrode handbook. What happens
when you increase Fco beyond your calculated Fcomax? Obviously it
wont do you any good to have Fco greater than Fs. How was this
formula derived?

regards,
Bob

It's a mad guess. I've got the thing modelled in spice. One thing I have
done is look at how the output of the voltage error amplifier is related to
the current sense signal.

When the primary side switch turns on the main transformer is fully reset
with no current being delivered to the output. The output voltage therefore
drops due to current in the load. If I treat the maximum load as a current
source and assume an ideal output capacitor, no esr, then there is a linear
ramp on the output voltage.

dVOUT/dT = ILOAD/COUT

That gets amplified and inverted through the error amplifier as an upslope.

The current sense waveform on the primary has an upslope as well.

dVsns/dT = VIN/Lpri

If I set the two slopes to be the same by adjusting the error amplifier gain
then that, at the moment, is my first limiting point. Yes, it's along the
lines of the wisdom from Unitrode on average current mode control and slope
matching but I'm trying to bend the concept to work for this.

When I do that the voltage error amplifier output is demanding zero current
at the point when the primary side switch is turned on. This is bad news
because it gets turned off again pretty sharpish. (hope that makes sense) It
turns out that doing this places the crossover frequency at sort of half the
switching frequency....

As I say, that's the first limit I can place on the gain and hence crossover
frequency. After that all I have done is reduced the gain to half the
original guess with crossover occuring at about a quarter of the switching
frequency at which point the spice model is stable.

Then I took a mad guess at the appropriate sum.

Hope that made sense. If you've got some more insight then it would be
appreciated.

Regards

Marcus

 

[R.Legg]

Switch mode power supplies behave in strange ways. Average current mode
control and slope matching (the limiting condition) was the best thing since
sliced bread for me. It's the first time I could read the words and then
make the leap to proving for myself that the sums were right. That turned
out to be simple algebra and a bit of implicit integration and that fixed
the crossover frequency.

I'm trying to find similar limiting conditions, perhaps different ones, for
a flyback converter operating in the discontinuous mode. My best 'guess' so
far is that it is,

Fcomax = Fs/4.PI.(1-D)

If I make the overall loop first order at crossover and out to the switching
frequency.

Are you sure you are only interested in discontinous mode (ie

complete energy transfer)? I believe that DCM doesn't have the RHPZ in
it's response. Under transient conditions, continuous mode may occur,
but only temporarily.

You didn't mention whether you'd refered to the actual Unitrode notes.

Topology and Bode plot SEM300appendxC slup071, SEM300appendxB slup070.
Effective output filter SEM300appendxII slup074
150W DCM flyback example SEM400 topic6 slup078.
Flyback average current mode control is covered in SEM500topic5
slup082.
Discussion of Right Half-Plane Zero SEM500addenda slup084.
The control loop SEM800 topic7 slup098
Current mode models (Ridley) is SEM1300 topic1 slup080.
Testing feedback SEM1300appendxA-1 slup121

http://focus.ti.com/docs/training/c...egory.jhtml?templateId=5517&navigationId=8455

Transient load testing can give you a good idea as to the ruggedness
of the control loop. Just be sure to cover the design temperature
ranges, before you decide everything's perfect.

Line (input) transient immunity is pretty well compensated for by the
topology.

RL

 

[Marcus]

complete energy transfer)? I believe that DCM doesn't have the RHPZ in
it's response. Under transient conditions, continuous mode may occur,
but only temporarily.

You didn't mention whether you'd refered to the actual Unitrode notes.

Topology and Bode plot SEM300appendxC slup071, SEM300appendxB slup070.
Effective output filter SEM300appendxII slup074
150W DCM flyback example SEM400 topic6 slup078.
Flyback average current mode control is covered in SEM500topic5
slup082.
Discussion of Right Half-Plane Zero SEM500addenda slup084.
The control loop SEM800 topic7 slup098
Current mode models (Ridley) is SEM1300 topic1 slup080.
Testing feedback SEM1300appendxA-1 slup121

http://focus.ti.com/docs/training/catalog/events/eventsbycategory.jhtml?temp
lateId=5517&navigationId=8455

Transient load testing can give you a good idea as to the ruggedness
of the control loop. Just be sure to cover the design temperature
ranges, before you decide everything's perfect.

Line (input) transient immunity is pretty well compensated for by the
topology.

RL

Thanks for the reply,

I'll have to do some more reading. I have looked at this source of
information before (good stuff) but I'll grab hold of your suggestions
tomorrow. As far as I can remember none of the ones I've seen give a
specific analysis of 'why' there is a maximum gain that you can get from the
error amplifier in a discontinuous flyback converter, other than the case of
average current mode control. Slup082 sounds promising but I might be
dissapointed(?)

I knew about the RHPZ. It was only when one of Lloyd Dixons papers on the
SEPIC converter gave me the twig on state space averaging that I was able to
analyse things in more depth.. At least I think that's what I'm doing,
sometimes, almost, maybe, not. It's something like k(-jVIN/aXLPRI - IOUT)
Anyway I can use something like it to analyse circuits in the continuous
mode. As a result I think I can work out where the beasty lies and how it
moves about. In this case I had to resort to a bit of differentiation.

Yes, I am limiting myself to the discontinuous mode, although I do accept
that things are very likely to go out of bounds during transient events.
I've been bitten by large signal versus small signal behaviour before.

I've got to account for power circuit gain variations and adjust my zero
frequency accordingly so I'll certainly be looking at tolerances of
components. Ultimately I will probably aim for a gain response that is first
order over all, most, frequencies by adding a similar network on the input
to the error amplifier.

I've read some of Ridleys stuff, and tried to get hold of Vorperians.
Ultimately I sort of have to admit that I'm thick or certainly don't speak
the same language. If I can't understand it to a level that I can explain it
then I worry about it.

Oh well, I'll give it a look.

Thanks

Marcus