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enter image description here

This image is from Christophe Basso presentation. It has been mentioned in the slide that average model can predict the transient response but I have one question when we say average model then it should not predict the any cycle variation or transient behavior. Is my understanding correct?

I can understand that an average model is a non linear model but how it is predicting the transient behavior that is not clear to me.

Document Link:http://powersimtof.com/Spice.htm

File Name: The PWM switch in transitioning models (Page: 3)

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  • \$\begingroup\$ Calling @VerbalKint :-) \$\endgroup\$
    – winny
    Commented Feb 19 at 12:06
  • \$\begingroup\$ Yes winny, coming up : ) Averaged models are created using nonlinear equations describing the average value of currents and voltages. You thus can use these models to determine a dc operating point for instance but you can also use them for simulating large-signal transient response. Very useful in PFC applications for instance since the switching component has gone, results are obtained in a very short time. And since SPICE is a linear solver, it will linearize the large-signal equations around a bias point and you can get an ac response. \$\endgroup\$
    – Verbal Kint
    Commented Feb 19 at 13:09
  • \$\begingroup\$ wow! direct answer from Christophe basso!! Many thanks Sir \$\endgroup\$
    – Power Path
    Commented Feb 19 at 15:49

2 Answers 2

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Question:

"When we say average model, should it not predict the any cycle variation or transient behavior?"

My simple answer:

Transient behavior of a voltage regulator can be seen by applying a step load and observing the output voltage response.

When we simulate an average model in the time domain, the response of the output voltage, when a load step is applied, should be matching that of the switching model. The average model does give results in the same time scale, but it is missing the higher order effects that are captured in the switching model (the effects of each switching cycle along with parasitics). The benefit of the average model is that it is faster to simulate.

When we simulate the average model in the frequency domain, we get the bode plot, which can also predict the transient behavior (response to step load).

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The simplest argument is thus:

When the system is linear with respect to switching frequency and harmonics, those harmonics don't affect the cycle-averaged / DC response.

That is, it obeys superposition.

Such a system can then be decomposed into the baseband / DC / cycle-averaged component, plus Fsw and harmonics.

The high-frequency content can further be ignored entirely, to focus on the baseband response.

Total linearity is not required, merely linearity with respect to the switching. For a typical square-pulse converter, this usually presumes CCM, so that the switch node always has a low impedance, always in the high or low state.

For more general use, some modifications are necessary, such as for DCM, accounting for the effective output resistance of the switches; but as long as the switching node behaves as expected for the approximation used (e.g. a square pulse approximation, with node returning to idle when inductor current falls to zero), this works.

The LC network between/after switches is generally a linear network, so can be cycle-averaged over. When it's also controlling power (resonant types), this gets more complicated, but can still be done.

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