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

AN1207The required inductor with the minimum input voltage isshown in Equation 38.EQUATION 38:An inductor of at least 42 µH will prevent the converterfrom going discontinuous over the full input voltagerange.In fact, if the smallest inductor, L = 26 µH is selected,the maximum input voltage (VDC = 15.5V) would resultin a current ripple of I2 - I1 = 0.85A. Conversely, theinductor L = 42 µH with an input voltage of 8.5V givesa current ripple of 0.17A. This means that any inductorgreater than 42 µH will fit.Output CapacitanceEquation 39 is supposing to select a capacitancehaving ESR = 30 mΩ.EQUATION 39:V DC– V OUT,------------------------------ V OUT 1------------- --------------8.5---------------– 5------5 1== ⋅ ⋅ ------------ = 26μH0.2 ⋅ 2 8.5 200KL O m0.2I O,av,nomV DCF PWMCΔI LD--------------------------------------------------------------------0.4 ⋅ 0.42= = -------------------------------------------------------------------------------F PWM[ V RIPPLE– R ESRΔI L]200K[ 50 ⋅ 10 – 3 – 30 ⋅ 10 – 3 = 22μF⋅ 0.4 ]Input CapacitorUsing the same approach to compute the outputcapacitance, the input capacitance is then calculatedusing Equation 40.EQUATION 40:CΔI LD--------------------------------------------------------------------0.4 ⋅ 0.42= = --------------------------------------------------------------F PWM[ V RIPPLE– R ESRΔI L]200K[ 0.2 – 30 ⋅10 3 = 4.5μF⋅ 0.4]Free-Wheeling Diode SelectionBased on Equation 21 (see also Figure 5(D)), the maximumreverse voltage on the diode during TON is thencalculated, as shown in Equation 41.EQUATION 41:V R, max= – V DC, max+ V Q on,≈ – 15.5VAccording to Equation 20, the average current in thediode is calculated, as shown in Equation 42.EQUATION 42:I D, av= I O av,nom,( 1 – D) = 2 ⋅ ( 1 – 0.42) = 1.16ADS01207B-page 12© 2009 Microchip Technology Inc.