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

AN1207OUTPUT FILTER INDUCTORAs in all other topologies with an LC low-pass filter atthe output, the inductor is selected to not operate thesystem in Discontinuous mode. The inductor is calculatedjust at the edge between Continuous and Discontinuousmode (i.e., Critical mode), where the inductorcurrent starts from zero at the beginning of the PWMperiod and returns to zero before the PWM periodends. In this condition, the average current equals 0.5the peak current (or current ripple), as shown inFigure 23.FIGURE 23:INDUCTOR CURRENT: PEAK CURRENT, RIPPLE CURRENT AMPLITUDE ANDOUTPUT CURRENT AT THE EDGE OF DISCONTINUOUS MODEI InductorIO, PNIO, av, minIRIPPLETONTON + TRtIn Critical mode, the minimum acceptable outputcurrent (defined by design requirements) is madecoincident with the average current, as shown inEquation 99.EQUATION 99:Using Equation 72 to compute IO, ripple, results inEquation 100.EQUATION 100:L OOUTPUT CAPACITORI O, rippleI O, av,min= --------------------2N SN P------V DC, min– V OUT= ---------------------------------------------D2F PWMI maxO,av,minThe output voltage ripple is mainly due to the capacitorESR. The inductor current ripple flowing through it,determines a voltage drop. Therefore, a capacitor withan ESR equal to Equation 101 must be selected.EQUATION 101:The capacitor value itself can then be computed withEquation 102, which describes the value of the voltageripple taking into account all components.EQUATION 102:Neglecting ESL, since it is normally very small (at leastfor PWM frequencies less than 400 kHz), results inEquation 103.EQUATION 103:V OUT,rippleI O,rippleESR < ----------------------------where I O, ripple is computed as in Equation 98V rippleC OD maxESL ⋅ FI rippleESR ------------------PWM= ⎛ + + -----------------------------⎞⎝ F PWMC⎠I O, rippleD maxD max= ---------------------------------------------------------------------------------------F PWM( V OUT, ripple– I O, rippleESR)DS01207B-page 28© 2009 Microchip Technology Inc.