- 30th December 2008, 11:23 #1

- Join Date
- Jul 2006
- Posts
- 266
- Helped
- 23 / 23
- Points
- 3,089
- Level
- 13

## 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,

- 30th December 2008, 11:23

- 30th December 2008, 15:32 #2

- Join Date
- Jun 2008
- Posts
- 1,180
- Helped
- 35 / 35
- Points
- 8,202
- Level
- 21

## 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.

- 30th December 2008, 19:47 #3

- Join Date
- Dec 2006
- Location
- Malaysia
- Posts
- 1,143
- Helped
- 394 / 394
- Points
- 19,911
- Level
- 34

## dynamic model dc dc converters

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

- 31st December 2008, 16:25 #4

- Join Date
- Jul 2006
- Posts
- 266
- Helped
- 23 / 23
- Points
- 3,089
- Level
- 13

## 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.

- 31st December 2008, 16:25

- 4th January 2009, 07:25 #5

- Join Date
- Oct 2006
- Posts
- 50
- Helped
- 11 / 11
- Points
- 1,510
- Level
- 8

## 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.

- 4th January 2009, 08:52 #6

- Join Date
- Jan 2008
- Location
- Bochum, Germany
- Posts
- 27,774
- Helped
- 8760 / 8760
- Points
- 171,406
- Level
- 98

## 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.

- 4th January 2009, 08:52

- 4th January 2009, 11:51 #7

- Join Date
- Jul 2006
- Posts
- 266
- Helped
- 23 / 23
- Points
- 3,089
- Level
- 13

## 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?

- 4th January 2009, 13:55 #8

- Join Date
- Jan 2008
- Location
- Bochum, Germany
- Posts
- 27,774
- Helped
- 8760 / 8760
- Points
- 171,406
- Level
- 98

## 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.

- 5th January 2009, 06:46 #9

- Join Date
- Oct 2006
- Posts
- 50
- Helped
- 11 / 11
- Points
- 1,510
- Level
- 8

## 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.

- 5th January 2009, 12:13 #10

- Join Date
- Jul 2006
- Posts
- 266
- Helped
- 23 / 23
- Points
- 3,089
- Level
- 13

## 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?

- 8th January 2009, 05:47 #11

- Join Date
- Oct 2006
- Posts
- 50
- Helped
- 11 / 11
- Points
- 1,510
- Level
- 8

## average model of dc-dc converter

Originally Posted by**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.

- 8th January 2009, 21:01 #12

- Join Date
- Jan 2009
- Posts
- 7
- Helped
- 0 / 0
- Points
- 731
- Level
- 5

## 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.

- 14th January 2009, 16:33 #13

- Join Date
- Jan 2009
- Posts
- 1
- Helped
- 0 / 0
- Points
- 696
- Level
- 5

## 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..

- 27th June 2011, 10:50 #14

- Join Date
- Jun 2011
- Posts
- 1
- Helped
- 0 / 0
- Points
- 267
- Level
- 3