Switch Mode Power Supply (SMPS) Topologies (Part II) - Microchip

AN1207FIGURE 8:DUTY CYCLE IN CONTINUOUS AND DISCONTINUOUS REGIONSD1VDC/VOUT = 1.25(A)VDC/VOUT = 2Discontinuous regionContinuous regionVDC/VOUT = 5.01IO/IO, limitAs shown in Figure 8, starting from the continuousregion and moving along line (A), where D = 0.5, assoon the boundary between continuous anddiscontinuous regions (dotted line) is crossed, to keepthe same output voltage (VDC/VOUT = 2), D changesaccording to the nonlinear relation in Equation 12.Design Equations and ComponentSelectionThis section determines the equations that enable thedesign of a Continuous mode Buck Converter.INDUCTORThe average minimum current (IO, av, min) is set as theaverage output current at the boundary of Discontinuousmode (Figure 7). This way, for any current largerthan IO, av, min, the system will operate in Continuousmode. Usually it is a percentage of IO, av, nom, wherea common value is 10%, as shown in Equation 13.EQUATION 13:1 ( V DC, nom– V OOUT)= ,= 0.1I o, av,nom= --I2 2= ------------------------------------------------- T2L ONOI o, av,minI O limitSolving Equation 13 with respect to LO results inEquation 14.EQUATION 14:L O5 ( V DC, nom– V )V OUT= --------------------------------------------------------------- OUTV DC, nomF PWMI O,av,nomwhere FPWM is the PWM frequency (FPWM =1/T)Power Losses In The InductorPower losses in the inductor are represented byEquation 15.EQUATION 15:P LOSS, inductor= I O,av,nom( ) 2 ESRwhere ESR is the equivalent inductor resistance© 2009 Microchip Technology Inc. DS01207B-page 7