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Small-signal analysis of naturally-sampled single-edge PWM control loops

Mouton, Toit; Cox, Stephen; McGrath, Brendan; Risbo, Lars; Putzeys, Bruno


Toit Mouton

Stephen Cox

Brendan McGrath

Lars Risbo

Bruno Putzeys


This paper presents a simple method to analyse the behaviour of feedback loops that contain a naturally-sampled single-edge pulse-width modulator. A small-signal model is derived by means of simple geometric arguments. It is shown how this small-signal model can be used to analyse the stability of the continuous-time pulse-width modulated feedback loop by using standard z-domain techniques. The strategy relies on familiar concepts like transfer functions and small-signal gains and does not require any in-depth knowledge of non-linear systems. A simple design process, where the continuous-time compensator is designed directly in the z-domain, is developed and detailed design equations are derived for a PI current regulator. It is shown how the proposed strategy can accurately predict instability that cannot be explained by means of the well-known average model of the pulse-width modulator. The theoretical analysis is confirmed by means of detailed timedomain simulations. The mechanisms that lead to instability are discussed and an equation for the critical loop gain is derived.


Mouton, T., Cox, S., McGrath, B., Risbo, L., & Putzeys, B. (2017). Small-signal analysis of naturally-sampled single-edge PWM control loops. IEEE Transactions on Power Electronics, 33(1), 51-64.

Journal Article Type Article
Acceptance Date Jan 4, 2017
Online Publication Date Feb 8, 2017
Publication Date Jan 1, 2017
Deposit Date May 9, 2017
Publicly Available Date May 9, 2017
Journal IEEE Transactions on Power Electronics
Print ISSN 0885-8993
Electronic ISSN 1941-0107
Publisher Institute of Electrical and Electronics Engineers
Peer Reviewed Peer Reviewed
Volume 33
Issue 1
Pages 51-64
Keywords Small-signal model, pulse-width modulation, stability, bifurcation
Public URL
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