1
C H A P T E R 1
Extraction of Small-Signal
Transfer Functions Using
PLECS
®
and MATLAB
®
1.1 INTRODUCTION
Switch-mode converters are widely used today to provide power processing for applications
ranging from computing and communications to medical electronics, appliance control, trans-
portation, and high-power transmission. eir high efficiency, small size, low weight, and re-
duced cost make them a good alternative for conventional linear power supplies, even at low
power levels.
Switched DC-DC converters are nonlinear variable structure systems. e nonlinearities
arise primarily due to switching, power devices, and passive components, such as inductors.
Various techniques can be found in the literature to obtain a Linear Time Invariant (LTI) model
of a switched DC-DC converter. e most well-known methods are [Ericson and Maksimovic,
2001]: Circuit averaging (CA) and State Space Averaging (SSA).
CA replaces the semiconductor switches (nonlinear part of the converter) with an (aver-
aged) equivalent linear circuit. In this method manipulations are carried out based on a circuit
diagram [Akbarabadi et al., 2013].
SSA uses the duty cycle as a weighting factor and combines the state equations into a single
averaged state equation.e procedure of state space averaging is explained in detail in Asadi and
Eguchi [2018] and Suntio [2009].
SSA has a number of advantages over circuit averaging technique. ese include:
• the ability to obtain more transfer functions than was possible using circuit averaging tech-
nique; and
• the ability to more easily obtain both DC and AC transfer functions.
Foundation of SSA was laid down in Middlebrook and Cuk [1977] and later extended
in Tymerski and Vorperian [1986], Chen and Ngo [2001], Sun et al. [2001], as well as many
other publications. e first attempt to model Discontinuous Conduction Mode (DCM) is pre-
sented in Cuk and Middlebrook [1977]. A unified SSA-based method to develop both Con-
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