Page - 229 - in Emerging Technologies for Electric and Hybrid Vehicles

Energies 2016,9, 410 Figure14.Boundary inductances invariouspowerconditions. 3.5. SelectionConsiderationsofCharge-PumpCapacitor For theproposedBDCinchargestateoperation, theripplevoltageof thecharge-pumpcapacitor CB canbeobtainedas follows: ΔVCB “ 1CB ż t1 t0 iCBptqdt“ ILtDd2CBfsw – ILDd 4CBfsw (25) where: iCBptq“ IL4 ´ Δiripple 2 ` 0.5VH´2VL Lsfsw pt´ t0q (26) Δiripple “ 0.5VH´2VLLsfsw pt1´ t0q,t1 “DdTsw` t0 (27) FromEquation (25), it is known that although a capacitorwith low capacitance is used for charge-pumpcapacitorCB, thevoltageripplecanbereducedbyincreasingtheswitchingfrequency. Therootmeansquare (RMS)valueof thecurrent throughthecharge-pumpcapacitor is ICBpRMSq “ d 2 fsw ż t1 t0 i2CBptqdt– IL 4 a 2Dd (28) 3.6. Summaries ofComponentStressandLoss Forstressandlossanalysis, it isassumedthatthestudiedBDCoperateswithDd<0.5andDb>0.5 for chargeanddischargemodes, respectively. The resultsof component stress canbesummarized as inTable1. Furthermore, equations for loss analysis canbe summarizedas inTable2,whereQg represents theMOSFETtotalgatecharge; tr is rise time, it’s theperiodafter thevGS reaches threshold voltagevGS(th) to complete the transientMOSFETgatecharge; tf is fall time, it’s the timewhere the gatevoltagereaches the thresholdvoltagevGS(th) afterMOSFETturn-offdelay time[26]. 229