TITLE:
Exact Dynamic Modeling of PWM DC-to-DC Power Converters—Part II: Discontinuous Conduction Mode
AUTHORS:
Justin Simmons, Richard Tymerski
KEYWORDS:
Describing Function, DC-to-DC Switching Power Converter, Small-Signal Modeling, Frequency Response
JOURNAL NAME:
Journal of Power and Energy Engineering,
Vol.9 No.5,
May
22,
2021
ABSTRACT: This paper follows on from the first paper, Part I, where a general
formulation of a describing function approach to frequency response
determination of switched linear networks, such as PWM converters, was
simplified and updated. The models assume a piecewise linear state space
equation description of the system and results in a closed form solution for
the sought after frequency response. In Part I, model derivation was
demonstrated for the case of PWM converters operating in the continuous
conduction mode (CCM). This operating mode does not feature any state dependent
switching times. In this paper, Part II, frequency response models for any
transfer function for PWM converters operating in discontinuous conduction mode
(DCM) are derived based on the theory presented in Part I. This operating model
features state dependent switching times. The describing function models
developed are exact and therefore, in terms of accuracy, are to be preferred
over averaged models which are widely used. The example of a boost dc-to-dc
converter operating in DCM is simulated to obtain the control to output and
input to output frequency responses and are compared with the models derived
here. Excellent agreement between the simulated and model responses was found.
Matlab code implementing the analytical models is also presented which the user
can adapt for any other PWM converter topology. The models derived here may be
used as a basis from which simplified models may be derived while still
preserving required accuracy.