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`ANKER 1017
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`1
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`Fundamentals of
`PowerElectronics
`
`Robert W. Erickson
`University of Colorado
`Boulder, CO
`
`CHAPMAN & HALL
`
`KTP International Thomson Publishing
`
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`Cover desgrr Carolyn Walsitis
`
`Copyright © 1997 by Chapman & Mall
`
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`123456789 10 XXX 010 9 38 97
`
`Library of Congress Catalogingin-Publication Data
`
`Erickson, Robert W. (Robert Warren),
`Fundamentals of power electronics/Robert W. Erickson.
`pP
`om
`Includes Bibbographical references and index.
`BBN (-412.0654L0 (alk paper)
`LPower electronics.
`L Title
`TRKTSSL I ETS)
`«1997
`62ST~<dicdD
`
`96-3847 a
`
`British Library Cataloguing in Publication Data available
`
`sechnically accurate and authoritative
`"Fudamentals of Power Electronics’ = imended 10
`editors, advisers, and contributors have
`information from highly regared sources. The
`made every reasona
`effort 10 ensure the accuracy ofthe information. but cannot assume
`responsibility for the accuracyof all information, or for the consequences of its use.
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`3
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`iM
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`The Discewwinnows Conduction Mode
`
`Thus, we have two unknowns, V and D,, and we have two equations. The first equation, Eq. (3.19),
`was obtained by inductor volt-second balance, while the second equation, Eq. (5.27), was obtained
`using capacitor charge balance. Elimination of D, from the two equations, and solution for the voltage
`conversion ratio M(D,, K)= V/V,, yields
`
`Eee
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`a / 1+ ax
`
`where
`
`K=2L/RT,
`
`(5.28)
`
`This is the solution of the buck converter operating in discontinuous conduction mode.
`The complete buck converter characteristics, including both continuous and discontinuous conduc-
`tion modes, are therefore
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`D
`
`for K > K..
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`M*=
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`for KK <K...
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`t+/ 1 +p
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`(5.29)
`
`where the transistor duty cycle D is identical to the subinterval | duty cycle D, of the above derivation.
`These characteristics are plotted in Fig. 5.11, for several values of K, It can be seen that the effect
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`06
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`0.2 0.0
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`04
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`0.0
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`02.
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`0.4
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`0.6
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`0.8
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`1.0
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`dD
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`Fig. $.11 Voltage conversion ratio M(D,K), buck converter,
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`4
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