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

AN1207TRANSFORMER: PRIMARY, WIRE SIZEAs shown in Figure 22(G) the total current flowing intothe primary has two contributions: the magnetizing current(Equation 67) and the load current (Equation 72)reflected back into the primary, resulting inEquation 88.EQUATION 88:------ ( VV DC– V Q,onN SN DC– V Q,on)– V D, on– V OUT,------------------------------t ------ P=+ ---------------------------------------------------------------------------------tI P totalL MN PN SL OThe primary wire size can then be computed by firstreferring to Figure 22(G), and then replacing the realcurrent waveform with a pulse having a square shapedwaveform, with the same width and whose amplitude isthe value in the middle of the ramp (IQ, mr). The currentis expressed as a function of known (designrequirements) data.Note that in these computations, magnetizing current isneglected since the transformer is designed to make itabout one-tenth of the load reflected current.Therefore, the input power PI equals Equation 89.EQUATION 89:P IThe output power is shown in Equation 90.EQUATION 90:Solving Equation 90 results in Equation 91.EQUATION 91:This is the equivalent current flowing in the primarywires when TON is at its maximum allowed value. Therms value is computed in Equation 92.EQUATION 92:=V DC, minI Q, mrD maxP O= ηP I= ηV DC minwhere η is the converter efficiencyI Q, rmsI Q mr,I Q, mrD max1 PI Q, mr-- O=V DC,minD max⎛--------------------⎞ 1------------η⎝⎠P O1= ,D max= -- ⎛--------------------⎞----------------η⎝⎠V DC,minD maxD maxTRANSFORMER: SECONDARY, WIRE SIZEAs shown in Figure 24(C), the secondary currentequals the inductor current (IO, av) during TON.Again, as for the primary current, the actual currentwaveform is replaced with a current pulse having asquare shaped wave form whose amplitude equalsthe mid-ramp inductor current in the up-slope, IO, av,nom.Therefore, the secondary average current is equal toEquation 93.EQUATION 93:The rms value is computed as Equation 94.EQUATION 94:TRANSFORMER: RESET WINDING, WIRESIZEThe reset winding is not involved in carrying any currentreflected back into the primary from the secondary.The only current it has to carry is the magnetizing current,which is plotted in Figure 22(C). The magnetizingpeak current computed in Equation 67 is shown inEquation 95.EQUATION 95:I Sav ,= I O,av,nomI Srms ,= I O, av,nomD max–--------------------------------------------T ONV DCmin ( , )V Q,onI M, pk=L MThe rms value is the peak value multiplied by thesquare root of the duty cycle and divided by radix 3, asshown in Equation 96.The correct AWG (wire size) can be determinedaccordingly.DS01207B-page 26© 2009 Microchip Technology Inc.