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Flyback Converter Crossover Frequency, Sorted?

Discussion in 'Electronic Design' started by Marcus, Oct 2, 2003.

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  1. Marcus

    Marcus Guest

    Thanks to those who responded to my previous question.

    I think I've figured out what is going on and the result, if correct, might
    be of interest to others.

    I was trying to determine the maximum crossover frequency of a flyback
    converter operating in the discontinuous mode. I had derived an equation for
    the power circuit gain using peak current mode control and set up a linear
    model in Spice. I used this to verify stability.

    In doing so I determined a maximum gain for the error amplifier on the basis
    of how the output of this amplifier matched the sensed inductor current at
    the inputs to the current limit comparator. In particular, when the primary
    side switch is turned on there is no current flowing in the output. VOUT is
    discharged by the load current as a linear ramp. This is amplified through
    the error amplifier and compared to the current sense signal.

    If gain in the amplifier is set such that the upslope of this ramp matches
    the upslope of the current sense signal then switch turn on coincides with
    the point where the amplifier is demanding zero current and the comparator
    immediately terminates the pulse. Obviously not a good thing so I halved the

    When I transferred the results to a Spice switching model the result was
    kind of stable but it still showed some vestiges of instability. I had
    ensured that the converter would not enter continuous mode operation and
    clamped the error amplifier to prevent overshoot and recovery problems.
    Also, although it looked similar to sub-harmonic oscillation, the waveforms
    contained other artifacts that indicated it wasn't.

    Well, I believe my switching model so the blame was with the linear model. I
    didn't want to just reduce the gain until things worked without having a
    'valid' reason for the behaviour so I started to think about what might be
    missing from the linear model. This is what I came up with/guessed at.

    In magamp controllers there is an additional phase/time delay that arises
    because reset is applied during the period when no power is being
    transferred from the transformer. I wondered if I could apply a similar
    argument to a flyback converter. In a flyback converter the transformer is
    being set when no power is being delivered to the output....... sounds

    OK, so I tried this in my linear model. I added a time delay to the loop and
    tried out three cases.

    1) Delay time equivalent to the switching period T.
    2) Delay time equivalent to the duty cycle, D/Fs.
    3) Delay time equivalent to (1 - D)/Fs

    In 1) the phase at crossover was -31 degrees which should have been
    hopelessy unstable.
    In 2) the phase at crossover was +35 degrees which should have been
    eminently stable.
    In 3) the phase at crossover was +10 degrees which would be marginal.

    Now I realise that I've not proved things analytically but the argument and
    results seem to bear things out. I'm suggesting that in a flyback converter
    (continuous or discontinuous operation) there is an additional time delay
    equivalent to (1 - D)/Fs resulting in an additional phase shift which must
    be accounted for in any linear model.

    I've not seen this reported in the literature I have read to date, the stuff
    I have access to anyway.

    Does it seem reasonable or valid?


  2. R.Legg

    R.Legg Guest

    Now I realise that I've not proved things analytically but the argument and
    If the conversion frequency is constant, and the duty doesn't vary
    appreciably between periods (ie steady-state), the delay is always
    equal to 1/Fs.

  3. Marcus

    Marcus Guest

    Thanks for the reply.

    It doesn't quite agree with my results in that, as I mentioned, 1/Fs gives
    too much, D/Fs gives too little and (1 - D)/Fs give just about the right
    answer. Of course there is room for 'experimental' error and my original
    gain equation might be wrong. Mind you if it was I think I'd be looking at
    factors of 2, PI or 10. This doesn't seem to be the case.

    Although I haven't been able to get hold of a partial description of
    Vorperians work or a copy of the paper I understand his results predict an
    additional pole and a right half plane zero which don't seem consistant with
    what's being suggested here.

    As I said, this delay hasn't been mentioned in the literature I've read
    including Unitrodes seminars and application notes.

    Do you have a reference that confirms it?


  4. R.Legg

    R.Legg Guest

    Some models and spice libraries were offered in PESC'99,

    The tutorial by Erickson/Maksimovic from APEC'03 is pretty

    You can spend a lot of time modelling, but without putting a soldering
    iron to the breadboard, you may never get much of a feel practical
    stability concerns.

    Modeling is not my strength (or even very often a serious concern in
    smaller circuits that can be so easily breadboarded), so I suggest
    you contact the authors if you have any concerns. As educators, that
    is part of their business.

  5. Marcus

    Marcus Guest

    Thanks for the links. Time to do some more learning.

    Modelling isn't exactly my strength either but I've used it to learn quite a
    lot about some of the finer points and quirks of these things. There have
    been a number of times when sweating over a prototype has been going nowhere
    and I need to 'get away' from the physical thing, stop messing with it and
    start thinking about it.

    Modelling has given me the opportunity to focus on a particular aspect of
    the circuit by stripping out extraneous rubbish and seeing what might really
    be happening. It's an extremely useful way of gaining insight as to what
    might actually be happening and finding solutions. Less painful as well,
    sometimes. Great for documentation and training too.

    Each to their own, but I wouldn't be without it.

    Thanks again

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