Journal of Computer and Communications, 2014, 2, 41-48

Published Online November 2014 in SciRes. http://www.scirp.org/journal/jcc

http://dx.doi.org/10.4236/jcc.2014.213006

How to cite this paper: Espinosa, C.A.L. (2014) State Variable Model for Considering the Parasitic Inductor Resistance on

the Open Loop Performance of DC to DC Converters. Journal of Computer and Communications, 2, 41-48.

http://dx.doi.org/10.4236/jcc.2014.213006

State Variable Model for Considering the

Parasitic Inductor Resistance on the Open

Loop Performance of DC to DC Converters

Carlos Alberto Lozano Espinosa

Pontificia Universidad Javeriana, Santiago de Cali, Colombia

Email: carlosal@javerianacali.edu.co

Received 17 October 2014

Abstract

This paper shows DC and small-signal circuit models for the PWM DC to DC bu c k, bo ost and back/

boost con ver te rs wi th the equivalent series resistance of the inductor. The DC voltage transfer

function and the efficiency of the converter are derived from the DC model. Small-signal open-loop

characteristics are derived from the small-signal model based on a state variable model. A design

example proves the performance of the circuit and verification of the model.

Keywords

DC to DC Con verte r, Parasitic Resistance of Inductor, Small Signal Analysis, Bu ck Conv erter , Boos t

Converter, Buck-Boost Conver ter

1. Introduction

Many papers about small signal analysis of a DC to DC b uc k-boost converter can be found in literature that in-

clude parasitic resistances in inductor and capacitors and voltage drop in power switch and diode [1]-[5]. Usual-

ly, the signal model representation is obtained from an equivalent circuit [4], or in other cases, using a state va-

riable model [3]. Any model can be calculated based on the continuous conduction mode or a non-continuous

conduction mode but have different results because the former has control over the duty cycle and the latter has

control over the frequency.

The objectives of this paper are: to obtain a DC and small-signal linear circuit models of PWM buc k, boost

and buck/boost DC-DC converter, taking into account parasitic resistance of the inductor; to derive the DC vol-

tage transfer function and efficiency; to derive small-signal open-loop input-to-output transfer function using a

state variable model; and to demonstrate, by a design consideration, the performance of a real circuit.

2. Work Description

In anon ideal DC to DC converter, it is necessary to consider power losses from parasitic resistance of the in-

ductor, parasitic resistance of capacitors and power losses in semiconductor switch and diode. Figure 1 shows

some real DC to DC converters with parasitic resistance in inductor.