IEEE Power Electronics Magazine - September 2017 - 52

About the Author
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101 k 1 Meg

FIG 21 The DCM PWM switch and the CoPEC DCM model give
identical dynamic responses.

and
H 0 = Vin

1
2x L .

(51)

As a final check, we can compare the dynamic response
delivered by Mathcad and that of the SPICE simulation from
the Figure 11 large-signal model. As shown in Figure 19, the
curves are perfectly matching.
Another verification consists of simulating the same
SEPIC structure with a different average model whose
construction is detailed in [11]. This is also an autotoggling CCM-DCM model, but it is wired in a slightly different
way. Figure 20 shows both the average models in a similar
SEPIC configuration.
Figure 21 confirms that both ac responses in phase and
magnitude are perfectly identical.

Christophe Basso (christophe.basso@onsemi.com)
received his B.S.E.E. degree equivalent in electrical engineering from Montpellier University, France, and his
M.S.E.E. degree in electrical engineering from Institut
National Polytechnique of Toulouse, France. He is a technical fellow of ON Semiconductor, based in Toulouse,
where he leads an application research and development
team dedicated to developing new offline pulsewidth
modulation controller specifications. He has more than
20 years of power supply industry experience and has
originated numerous integrated circuits for ON Semiconductor, including the NCP120X series, which set new
standards for low standby power converters. He has published several books on switching power supplies; his latest is Linear Circuit Transfer Functions: An Introduction
to Fast Analytical Techniques. Prior to joining ON Semiconductor, he was an application engineer at Motorola
Semiconductor in Toulouse, France, and a power supply
designer at the European Synchrotron Radiation Facility
in Grenoble, France. He holds 17 patents on power conversion. He is a Senior Member of the IEEE.

References
[1] R. D. Middlebrook, "Methods of design-oriented analysis: Low-entropy
expressions," in Proc. 21st Annu. Frontiers Education Conf., Santa Barbara, CA, 1992.
[2] R. D. Middlebrook, "Null double injection and the extra element theorem," IEEE Trans. Edu., vol. 32, no. 3, pp. 167-180, Aug. 1989.
[3] V. Vorpérian, Fast Analytical Techniques for Electrical and Electronic
Circuits. Cambridge, U.K.: Cambridge Univ. Press, 2002.
[4] C. Basso, Linear Circuit Transfer Functions: An Introduction to Fast
Analytical Techniques. Hoboken, NJ: Wiley, 2016.
[5] V. Vorpérian, "Simplified analysis of PWM converters using the model of
the PWM switch, parts I and II," IEEE Trans. Aerosp. Electron. Syst., vol. 26,

Conclusions

no. 3, pp. 490-505, May 1990.

FACTs offer a fast and efficient method to derive the
transfer function of linear circuits. With passive networks, inspection is possible, and very often, a transfer
function can be obtained without writing a single line of
algebra. As circuits complicate and include active sources,
you have to resort to classical Kirchhoff's current law
and Kirchhoff's voltage law analyses. However, as you
determine individual polynomial factors in the numerator
and the denominator, it is easy to track errors and focus
only on the defective term, if any. The help of small
sketches and SPICE to that matter is invaluable with
complicated networks. Finally, the end result comes out
in a meaningful format and offers immediate insight on
where poles and zeros are located. This is of utmost
importance, as you must know where the offenders hide
in the transfer function. As a designer, you must neutralize them so that natural production spreads, or component changes do not jeopardize the stability of your
system during its operating life.

[6] D. Feucht. (2013, Jan. 6). Design-oriented circuit dynamics. EDN Net-

IEEE POWER ELECTRONICS MAGAZINE

z September 2017

work. [Online]. Available: http://www.edn.com/electronics-blogs/outside-thebox-/4404226/Design-oriented-circuit-dynamics
[7] D. Peter. (2007). We can do better: A proven, intuitive, efficient and
practical design-oriented circuit analysis paradigm is available, so why
aren't we using it to teach our students? ASEE 2007 Annu. Conf. Expo.
[Online]. Available: http://www.icee.usm.edu/ICEE/conferences/asee2007/
papers/1362_WE_CAN_DO_BETTER__A_PROVEN__INTUITIVE__E.pdf
[8] C. Basso, "Fast analytical techniques at work with small-signal modeling," presented at the Applied Power Electronics Conf. Expo., Long Beach,
CA, 2016.
[9] J. Betten. (2011). Benefits of a coupled-inductor SEPIC. Texas-Instruments. [Online]. Available: http://www.ti.com/lit/an/slyt411/slyt411.pdf
[10] C. Basso, Switch-Mode Power Supplies: SPICE Simulation and Practical Designs, 2nd ed. New York: McGraw-Hill, 2014.
[11] D. Maksimovic and R. Erickson, "Advances in averaged switch modeling and simulation," presented at the Power Electronics Specialists Conf.,
Charleston, NC, 1999.

http://www.edn.com/electronics-blogs/outside-the http://www.icee.usm.edu/ICEE/conferences/asee2007/ http://www.ti.com/lit/an/slyt411/slyt411.pdf

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