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I’m studying averaged switch modeling (specifically Section 14.1 in Fundamentals of Power Electronics by Robert W. Erickson).

The author states that once you derive an averaged switch model for a transistor–diode “switch network,” you can insert it into various converter configurations without having to rederive it for each topology.

My confusion is that during derivation, it is the switch network terminal waveforms from CCM SEPIC(Fig. 14.3) from the Schematic of the SEPIC shown in Fig. 14.2 that were used to express the average values of the switch net-work terminal waveforms in terms of the independent inputs and the state variables i.e equations (14.1), (14.2), (14.3) and (14.4). which were manipulated to yield averaged switch network models represented by equations (14.7) and (14.8).

I reason that if we change to another topology (say, a boost converter), those waveforms would be different because the surrounding circuit changes. How is it possible for the same transistor–diode averaged model to remain valid across topologies if the surrounding converter changes the waveforms?

This is the statement the author wrote for which I'm confused: "The switch network of Fig. 14.4a can be identified in any two-switch converter, such as the buck, boost, buck–boost, SEPIC, or Ćuk. If the converter operates in continuous con- In the derivation mode, the derivation of the averaged switch model follows the same steps, and the result shown in Fig. 14.4c is the same for all of these converter topologies. This means that the model of Fig. 14.4c can be used as a general large-signal averaged switch model for all two-switch converters operating in CCM" Below are the relevant Schematics and equations I'm referring to.

[Fig. 14.2: Schematic of the SEPIC,1 Fig. 14.3: Switch network terminal waveforms in the CCM SEPIC

14.1.2 Circuit Averaging: (14.1), (14.2), (14.3) and (14.4) equations (14.7) and (14.8) and the author's claim

averaged switch model

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    \$\begingroup\$ There is a restriction, that the switch operates in CCM. The word 'significantly' is doing all the heavy lifting that's needed after that. \$\endgroup\$ Commented Aug 13 at 10:37

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There are two important terms to understand when it comes down to modeling: averaged and invariant.

Averaged means that you want to look at the voltage and current waveforms across the switch and the diode then average them along a switching cycle. You obtain a nonlinear expression that will need to be later linearized (or SPICE will do it for you). You can linearize by inserting a small-signal perturbation (as in the text) but I prefer resorting to partial differentiation as I can automate the process (and you don't have to sort out ac and dc terms, neglecting cross-products)

If you now look at these voltage-current couples in different structures - say the basic switching cells - you will see that they are identical: the equations describing the switch/diode signals in a buck, boost or buck-boost remain the same - like the song ^_^ and are said to be invariant.

The first one to introduce this concept, was Dr. Vatché Vorpérian through a first publication he made in 1986, Simplified Analysis of PWM Converters using Model of PWM Switch, and you have two parts covering CCM and DCM. At the same time, Larry Meares, founder of Intusoft, did propose the same concept, covering CCM alone in New Simulation Techniques using SPICE.

enter image description here

The above picture is an excerpt of my APEC 2013 seminar where I described all these principles. In the below illustration, you can see how the same 2-switch model fits the basic cells by simply rotating the symbol, exactly as with the linear model of a bipolar transistor: common-base, -collector or -emitter configuration, same model, but different orientation for respecting the bce pins.

enter image description here

The CoPEC folks did not revolutionize the principle but did separate the switches while they are bonded at the c (common) node in the PWM switch model. This surely eases the model insertion in the converter but the basic principles remains the same.

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