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  1. #1
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    state space averaging

    usually to analyze a switched mode dc-dc converter we need to average the equations across the 2 states(ON and OFF). now my doubt is why must we linearize it(by perturbation) after averaging??

    does not averaging itself linearize the switched circuit, as the only nonlinear element was the switch??

    thank you,

    •   Alt30th December 2008, 11:23

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    state-space average nonlinear waveform converter

    i have not heard of this method of which you speak...

    if you google "feedback compensation"

    and

    "type 3 compensation networks"
    (also 1 and 2)

    you'll get some ideas...but i have never heard of your methods of averaging on/off etc.

    Lloyd dixon does some good notes for googling.



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    dynamic model dc dc converters

    Also try the patents on http://www.google.com/patents you will find the modern methods



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    dc-dc converter state space

    i am not talking about the compensation scheme. the averaging and linearization i mentioned was that pertaining to the small-signal representation of the switching converters.



    •   Alt31st December 2008, 16:25

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  5. #5
    ycj
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    average model dcdc converter

    The averaging only screen out the effect of switching. The average model still be a non-linear model. Linearization is necessary to apply linear control theory.



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    FvM
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    averaging state space dc dc converter

    I think there are different aspects involved with your question, and there is possibly no simple yes or no answer. You're talking of a small-signal equivalent ciruit, which is a usual method for modelling of switching circuits, I think. By definition, it's linear but valid for a particular operation point only. If your analysis also implies larger variations of the operation point, the linear model is more-or-less incorrect. You have to find out, if it can give meaningful results though.

    Because of this basic limitation, I'm not sure if it's of much use, to perform an accurate averaging of equations. Personally, I prefer simple equivalent circuits, that represent the basic properties of the circuit. For some circuits, that have a basical nonlinear behaviour, e. g. a buck converter in non-continuous mode, you may be able to define an equivalent circuit composed of a linear term and operation point dependant gain. But I don't think, there's a general numerical method, it's rather a matter of intuitive understanding.



    •   Alt4th January 2009, 08:52

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    linear state feedback boost converter

    @FVM

    as far as switching circuits are concerned averaging is basically done to remove the switch and decompose the switched circuit into a continuous time equivalent circuit model. this decomposed model has only resistors, capacitors and inductors. so it is a completely linear circuit. (we don't do small signal analysis for completely passive networks).

    but, still all the text books carry on the step of linearization after averaging. why is that so? am i missing out on anything?



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    FvM
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    reference model of dc dc converter

    You may want to give an example or a literature reference to make "linearization after averaging" understandable. As you said, a linear cicrcuit can't be linearized anymore.



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    ycj
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    state space model of dc dc converter

    To amriths04,
    IT IS A NON-LINEAR MODEL! if you took the duty ratio as a state variable. You CANNOT took the duty ratio as a constant in deriving the dynamic model of the system.



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    averaging in power electronic

    @FvM,
    fundamentals of power electronics by robert erickson and any TI manual dealing with small-signal analysis on buck design.

    @ycj.
    after averaging we might have controlled sources dependent on duty ratio in our circuit. but how do you say it is non-linear? could you please elaborate this one out?



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    ycj
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    average model of dc-dc converter

    Quote Originally Posted by amriths04
    @FvM,
    fundamentals of power electronics by robert erickson and any TI manual dealing with small-signal analysis on buck design.

    @ycj.
    after averaging we might have controlled sources dependent on duty ratio in our circuit. but how do you say it is non-linear? could you please elaborate this one out?
    To amriths04,
    I do not like to involve too much math here, so I just give some hints and you find out the rest yourself.
    I think you already have the book "Fundamental of Power Electronics" by Robert Erickson, so you have the state-space averaging model of one of the DC-DC converters. Now I tell you that the duty ratio is a state variable as the cap voltage and inductor current. Take a look of the model, you will find that the product term of the duty ratio and the other state variables make it non-linear. So IT IS A NON-LINEAR MODEL.



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    robert erickson dc dc converter

    I am currently studying this book for my MSEE. My understanding is that we use inductor volt-second balance and Capacitor Charge balance andt eh small-ripple approximation to eliminate the hassle in using long mathematical equations. Therefore the book focuses on steady-state and at the same time neglecting the ripple effect seen on the DC output. When we do this and look at the waveform in steady state we see a linear response in a buck boost converter etc.



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    non linear buck converter circuit

    if you take the duty cycle ratio as input variable; you will see that duty cycle cannot be greater than 1(%100) as its definition. (for full bridge it swings between +1 and -1)
    So there is a saturation effect..
    So there comes nonlinearity..



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    Re: state space averaging

    Quote Originally Posted by amriths04 View Post
    usually to analyze a switched mode dc-dc converter we need to average the equations across the 2 states(ON and OFF). now my doubt is why must we linearize it(by perturbation) after averaging??

    does not averaging itself linearize the switched circuit, as the only nonlinear element was the switch??

    thank you,
    averaging does not linearize the model, rather averaging is done to cancel off the switching harmonics brought about by the switch... i think u got the logic wrong... go backto erickson and check again...



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