EE462L, Power Electronics, DC-DC Buck/Boost Converter ... - ECS

EE462L, Power Electronics, DC-DC Buck/Boost ConverterVersion Oct. 10, 2011OverviewBuck/Boost converters make it possible to efficiently convert a DC voltage to either a lower orhigher voltage. Buck/Boost converters are especially useful for PV maximum power trackingpurposes, where the objective is to draw maximum possible power from solar panels at all times,regardless of the load.Theory of OperationRelation Between V out and V in in Continuous ConductionThe idealized buck/boost converter circuit is shown below in Figure 1. Under normal operation,the circuit is in “continuous conduction” (i.e., i L1 and i L2 are always greater than zero).VariacI in+ v L1−i L1+ v C1−i C1i dI out120/25VacTransformer DBR V inL1C 1L 2+v L2–i L2Ci C+V out–Remember – never connect avariac directly to a DBR!Leave the 10µF cap acrossthe input terminals0.01ΩFigure 1. DC-DC Buck/Boost ConverterThe first important relationship comes from the fact that capacitor C 1 should be large enough sothat voltage v C1has low ripple. Applying average KVL around the loop formed by V in , L 1 , C 1 ,and L 2 , and recognizing that the average voltages across L 1 and L 2 are each zero, yieldsv C1 = V in . (1)The second important relationship comes by applying KCL in the average sense at the node atopL 2 . Since the average currents in C 1 and C are both zero, theni L avg = idavg= Iout2 . (2)With continuous conduction, the circuit has two states – switch closed, and switch open. Thesestates are shown in Figures 2a and 2b.Page 1 of 12

EE462L, Power Electronics, DC-DC Buck/Boost ConverterVersion Oct. 10, 2011V in(V out + V in )– – +L 1 V in L C +C 2+ 1V out–L 1 chargingC 1 dischargingL 2 chargingC dischargingFigure 2a. Switch Closed for DT SecondsV inL 1V in+ – L 1 dischargingC 1L 2Figure 2b. Switch Open for (1-D)T SecondsC+V out–C 1 chargingL 2 dischargingC chargingWhen the switch is closed (Figure 2a), the diode is reverse biased and open, current i L1increases at the rate ofdi L 1 Vin= , ≤ t ≤ DTdt L10 , (3)so that L 1 is “charging.” When the switch is open (Figure 2b), the diode is forward biased, andi L decreases at the rate ofdiL1dt−VoutL1= , DT < t < T , (4)so that L 1 is “discharging.” The voltage across L 1 is shown in Figure 3.V in0− V outFigure 3. Inductor L 1 Voltage in Continuous ConductionBecause of the steady-state inductor principle, the average voltage across L 1 is zero. Since v L1has two states, both having constant voltage, the average value of v L1isPage 2 of 12

EE462L, Power Electronics, DC-DC Buck/Boost ConverterVersion Oct. 10, 2011( 1−D)VoutV( D)outΔ I1= • 1−T =, (8)L1L1fwhere f is the switching frequency.The boundary of continuous conduction for L 1 is whenTi L1 min = 0, as shown in Figure 5.Δ I 1iL1 max = 2I L 1avgi L1avg = Iini L1 min = 0DT(1–D)TFigure 5. Inductor L1 Current at the Boundary of Continuous ConductionThus, at the boundary,2Iin( 1−D)Vout= , (9)L f1boundaryso that( 1−D) DV ( 1−D)VoutinDV inL1 boundary = = • = . (10)2Iinf 1−D 2Iinf 2IinfAs D approaches unity,VinL1 > 2Iinf(11)will guarantee continuous conduction. Note in (10) and (11) that continuous conduction can beachieved more easily when I in and f are large.Page 4 of 12

EE462L, Power Electronics, DC-DC Buck/Boost ConverterVersion Oct. 10, 2011so thatL2boundary( 1−D)Vout= . (14)2IoutfSince the maximum value of (14) occurs at D → 0,VoutL2 > (15)2Ioutfwill guarantee continuous conduction for L2 for all D. Note in (14) and (15) that continuousconduction can be achieved more easily when I out and f are large.Current Ratings for Continuous Conduction OperationContinuous current waveforms for the MOSFET, the capacitors, and the diode in continuousconduction are shown in Figure 8 on the following page. Corresponding waveforms for theinductors were shown previously in Figures 4 and 6.Following the same formulas and reasoning used for the buck converter, conservative currentratings for components L1, L2, the MOSFET, and the diode follow.For L1, using Figure 5,2⎛ ⎞=2 1 +2 1I L1,rms,maxIin( 2Iin) = Iin2 ⎜1+ ⎟ ,12⎝ 3 ⎠so that2I L I31 , rms,max= in . (16)Similarly, for L2, using Figure 7,2I L I32 , rms,max= out . (17)Page 6 of 12

EE462L, Power Electronics, DC-DC Buck/Boost ConverterVersion Oct. 10, 2011i L1 + iL2MOSFETΔ I1 + ΔI 2I in + I out0DTi L1C 1Δ I 1I in0Δ I 2out− I− i L2i L1 + iL2DiodeΔ I1 + ΔI 2I in + Iout0iL 1 + iL2− IoutCΔ I1 + ΔI 2I in0−Figure 8. Current Waveforms for MOSFET, Capacitors, and Diode in Continuous ConductionI outPage 7 of 12

EE462L, Power Electronics, DC-DC Buck/Boost ConverterVersion Oct. 10, 2011For the MOSFET and diode, assuming large worst-case D, and using Figure 8,2I = +32I = +3( I I )MOSFET , rms,maxin out , (18)( I I )Diode, rms,maxin out . (19)For C1 and C, using Figure 8,2I C I32I31 , rms,max= in or out, whichever is larger. (20)2I C I3, rms,max= in or outI , whichever is larger. (21)Voltage Ratings for Continuous Conduction OperationReferring to Figure 2b, when the MOSFET is open, it is subjected to (Vin + Vout). Because ofthe usual double-voltage switching transients, the MOSFET should therefore be rated2(Vin+Vout).Referring to Figure 2a, when the MOSFET is closed, the diode is subjected to (Vin + Vout). Thediode should be rated at 2(Vin+Vout).Note – “stiff” voltages across capacitors C1 and C will help hold down overshoots on theMOSFET and diode in this circuit.Output Capacitor Voltage RippleThe maximum ripple voltage calculation for output capacitor C follows from Figure 8 and is thesame as for the boost converter, namelyΔQIoutDT IoutDΔ V = = = .C C CfThe maximum peak-to-peak ripple thus occurs as D → 1 and isIoutΔVmax = . (22)CfComparing the current graphs for C 1 and C in Figure 8 during the DT “switch closed” period, itcan be seen graphically that the ripple voltage on C 1 and C are the same, i.e. Equation (22).Page 8 of 12

EE462L, Power Electronics, DC-DC Buck/Boost ConverterVersion Oct. 10, 2011The ExperimentImportant – to avoid excessive output voltages, always keep a load attached to theconverter when it is operating. Do not exceed 90V on the converter output.1. Reconfigure the buck or boost components according to Figure 1 in this document.Secure new components C 1 and L 2 . Make all connections. Capacitor C 1 is bipolar (i.e.,not polarized).2. Connect the MOSFET Firing Circuit to your converter, using short leads. The firingcircuit is the same as for the Boost Converter. Double check your range of D.3. Before connecting power, make sure that a 5Ω ceramic power resistor is connected asa load. View V GS on Channel #1, adjust D to the minimum setting, and F toapproximately 100kHz. Connect Channel #2 to view V DS . Set the trigger for Channel#1.Important Note: the first time you energize your converter, feed the 120/25V transformerthrough a variac, so that you can SLOWLY increase the voltage from zero and read thevariac ammeter to detect short circuits before they become serious. A common problem isto have the MOSFET in backward, so that its internal antiparallel diode creates a short circuit.The ammeter on the variac is an excellent diagnostic tool. Once you are convinced that yourcircuit is working correctly, the variac is then optional. Remember – your boost converterrequires DC input power from a DBR.Does your circuit have a short? If so, do the following:1. Make sure that your MOSFET is not connected backwards.2. Observe VGS on the MOSFET as you vary D and F. Does the waveform look correct?3. Unplug the wall wart. Does the short circuit go away? If not, your MOSFET may beshorted – so, disconnect the MOSFET from the converter, and perform the voltagecontrolledresistance test on the MOSFET.4. Connect a 25Vac transformer to a DBR. Connect the DBR to your buck/boost converter,keeping the wires short (i.e., 3” or less). Then, use a variac to energize the 25Vactransformer and DBR. Raise the variac until Vac of the transformer is approximately 27-28V.5. Use a 5Ω ceramic power resistor as a load. With F ≈ 100kHz, slowly increase D fromits smallest value to obtain V out = 10, 20 (within ±2V), while recording D, Vin , Vout,Iin , Iout. Note by viewing V DS whether or not the circuit is in continuous currentoperation. For the 20V condition, compute input and output powers and efficiency. Donot go above 20V with the 5Ω load.Page 9 of 12

EE462L, Power Electronics, DC-DC Buck/Boost ConverterVersion Oct. 10, 2011AppendixConverterTypeBuckBoostBuck/BoostWorst-Case Component Ratings Comparisons for DC-DC ConvertersOutputInput Inductor Capacitor Output Capacitor Diode andCurrent (Arms) Voltage Current (Arms) MOSFET Voltage2 1.5VI out1 2VoutI inout332 1.5V I outI out2Voutin32 1.5VI out ⎛ 2 ⎞ 2 ( V in + V )inmax ⎜ I in , I ⎟out3out⎝ 3 ⎠Diode andMOSFETCurrent (Arms)2I out32I in323( I in + I out )Series CapacitorVoltage1.5VinAdditional Components for Buck/Boost ConverterSeries CapacitorSeries Capacitor (C 1 ) (C 1 ) RippleCurrent (Arms) Voltage (peak-topeak)⎛ 2 2 ⎞ Imax ⎜ I in , I out ⎟out⎝ 3 3 ⎠ C1fComparisons of Output Capacitor Ripple VoltageConverter TypeVolts (peak-to-peak)BuckI out4CfBoostI outCfBuck/BoostI outCfSecond Inductor(L 2 ) Current(Arms)23I outPage 11 of 12

EE462L, Power Electronics, DC-DC Buck/Boost ConverterVersion Oct. 10, 2011Minimum Inductance Values Needed to Guarantee Continuous CurrentConverter Type For Continuous Currentin the Input InductorFor ContinuousCurrent in L2BuckVoutL >2Ioutf–BoostVinL >2Iinf–Buck/BoostVinL1 VoutL2 2If2IfinoutPage 12 of 12