EE46L, Power Electronics, DC-DC SEPIC Converter Version March 1, 01 Overview SEPIC converters make it possible to eiciently convert a DC voltage to either a lower or higher voltage. SEPIC converters are especially useul or PV maximum power tracking purposes, where the objective is to draw maximum possible power rom solar panels at all times, regardless o the load. Theory o Operation Relation Between V and V in in Continuous Conduction The idealized SEPIC converter circuit is shown below in Figure 1. Under normal operation, the circuit is in continuous conduction (i.e., i L1 and i L are always greater than zero). Variac (Optional, see Step ) I in v L1 i L1 v C1 i C1 i d I 10/5Vac Transormer DBR V in L1 C 1 L + v L i L C i C + V Remember never connect a variac directly to a DBR! Leave the 10µF cap across the input terminals 0.01Ω Figure 1. DC-DC SEPIC Converter The irst important relationship comes rom the act that capacitor C 1 should be large enough so that voltage v C1 has low ripple. Applying average KVL around the loop ormed by V in, L 1, C 1, and L, and recognizing that the average voltages across L 1 and L are each zero, yields v 1. (1) C V in The second important relationship comes by applying KCL in the average sense at the node atop L. Since the average currents in C 1 and C are both zero, then il avg idavg I. () With continuous conduction, the circuit has two states switch closed, and switch open. These states are shown in Figures a and b. Page 1 o 1
EE46L, Power Electronics, DC-DC SEPIC Converter Version March 1, 01 V in (V + V in ) + L 1 V in L C + C + 1 V L 1 charging C 1 discharging L charging C discharging Figure a. Switch Closed or DT Seconds V in L 1 V in + L 1 discharging C 1 L Figure b. Switch Open or (1-D)T Seconds C + V C 1 charging L discharging C charging When the switch is closed (Figure a), the diode is reverse biased and open, current i L1 increases at the rate o di L 1 Vin, t DT dt L1 0, () so that L 1 is charging. When the switch is open (Figure b), the diode is orward biased, and i L decreases at the rate o dil1 dt V L1, DT t T, (4) so that L 1 is discharging. The voltage across L 1 is shown in Figure. V in 0 V Figure. Inductor L 1 Voltage in Continuous Conduction Because o the steady-state inductor principle, the average voltage across L 1 is zero. Since v L1 has two states, both having constant voltage, the average value o v L1 is Page o 1
EE46L, Power Electronics, DC-DC SEPIC Converter Version March 1, 01 Vin DT ( V )(1 D) T T 0, so that Vin D V V D 0. (5) Simpliying the above yields the inal input-put voltage expression V DVin. (6) 1 D Thus, the converter is in buck mode or D < 0.5, and in boost mode or D > 0.5. The assumption o a lossless circuit requires input power to equal put power, so I D Iin 1. (7) D Inductor Currents in Continuous Conduction The graph o i L1 is shown in Figure 4. For PV applications, it is obviously desirable to have low ripple in i L1 to keep the solar panel operating at the peak o its maximum power curve. I 1 T il1max il1avg il1 avg Iin il1min il1avg I 1 I 1 DT (1 D)T Figure 4. Inductor L 1 Current Waveorm or Continuous Conduction From Figure 4 and Equation (), when the switch is open (i.e., L 1 is discharging ), dil1 dt V, L1 so that Page o 1
EE46L, Power Electronics, DC-DC SEPIC Converter Version March 1, 01 V V D D 1 I1 1 T, (8) L1 L1 where is the switching requency. The boundary o continuous conduction or L 1 is when T i L1 min = 0, as shown in Figure 5. I 1 il1 max I L 1avg il1 avg Iin i L1 min 0 DT (1 D)T Figure 5. Inductor L1 Current at the Boundary o Continuous Conduction Thus, at the boundary, I in V 1 D, (9) L 1boundary so that 1 D DV 1 D V in DV in L1boundary. (10) Iin 1 D Iin Iin As D approaches unity, Vin L1 Iin (11) will guarantee continuous conduction. Note in (10) and (11) that continuous conduction can be achieved more easily when I in and are large. Page 4 o 1
EE46L, Power Electronics, DC-DC SEPIC Converter Version March 1, 01 The graph o i L is shown in Figure 6. I T il max ilavg il avg I il min ilavg I I DT (1 D)T Figure 6. Inductor L Current Waveorm or Continuous Conduction From Figures b and 6, when the switch is open (i.e., L is discharging ), dil V I dt L 1 DT, so that 1 DT V 1 D V I, (1) L L where is the switching requency. The boundary o continuous conduction or L is when T i L min = 0, as shown in Figure 7. I il max I L avg il avg I i L min 0 DT (1 D)T Figure 7. Inductor L Current at the Boundary o Continuous Conduction Thus, at the boundary, I V 1 D, (1) Lboundary Page 5 o 1
EE46L, Power Electronics, DC-DC SEPIC Converter Version March 1, 01 so that Lboundary V 1 D. (14) I Since the maximum value o (14) occurs at D 0, V L (15) I will guarantee continuous conduction or L or all D. Note in (14) and (15) that continuous conduction can be achieved more easily when I and are large. Current Ratings or Continuous Conduction Operation Continuous current waveorms or the MOSFET, the capacitors, and the diode in continuous conduction are shown in Figure 8 on the ollowing page. Corresponding waveorms or the inductors were shown previously in Figures 4 and 6. Following the same ormulas and reasoning used or the buck converter, conservative current ratings or components L1, L, the MOSFET, and the diode ollow. For L1, using Figure 5, 1 1 I L1, rms,max Iin Iin Iin 1, 1 so that I L I 1, rms,max in. (16) Similarly, or L, using Figure 7, I L I, rms,max. (17) Page 6 o 1
EE46L, Power Electronics, DC-DC SEPIC Converter Version March 1, 01 il1 il MOSFET I1 I Iin I 0 DT i L1 C 1 I 1 I in 0 I I i L il1 il Diode I1 I Iin I 0 i L 1 il I C I1 I I in 0 Figure 8. Current Waveorms or MOSFET, Capacitors, and Diode in Continuous Conduction I Page 7 o 1
EE46L, Power Electronics, DC-DC SEPIC Converter Version March 1, 01 For the MOSFET and diode, assuming large worst-case D, and using Figure 8, I I MOSFET, rms,max Iin I, (18) Diode, rms,max Iin I. (19) For C1 and C, using Figure 8, I C I I 1, rms,max in or, whichever is larger. (0) I C I, rms,max in or I, whichever is larger. (1) Voltage Ratings or Continuous Conduction Operation Reerring to Figure b, when the MOSFET is open, it is subjected to (Vin + V). Because o the usual double-voltage switching transients, the MOSFET should thereore be rated (Vin+V). Reerring to Figure a, when the MOSFET is closed, the diode is subjected to (Vin + V). The diode should be rated at (Vin+V). Note sti voltages across capacitors C1 and C will help hold down overshoots on the MOSFET and diode in this circuit. Output Capacitor Voltage Ripple The maximum ripple voltage calculation or put capacitor C ollows rom Figure 8 and is the same as or the boost converter, namely Q I DT I D V. C C C The maximum peak-to-peak ripple thus occurs as D 1 and is I V max. () C Comparing the current graphs or C 1 and C in Figure 8 during the DT switch closed period, it can be seen graphically that the ripple voltage on C 1 and C are the same, i.e. Equation (). Page 8 o 1
EE46L, Power Electronics, DC-DC SEPIC Converter Version March 1, 01 The Experiment Important to avoid excessive put voltages, always keep a load attached to the converter when it is operating. Do not exceed 90V on the converter put. 1. Reconigure the buck or boost components according to Figure 1 in this document. Secure new components C 1 and L. Make all connections. Capacitor C 1 is bipolar (i.e., not polarized).. Connect the MOSFET Firing Circuit to your converter, using short leads. The iring circuit is the same as or the Boost Converter. Double check your range o D.. Beore connecting power, make sure that a 5Ω ceramic power resistor is connected as a load. View V GS on Channel #1, adjust D to the minimum setting, and F to approximately 90kHz. Connect Channel # to view V DS. Set the trigger or Channel #1. Important Note: the irst time you energize your converter, eed the 10/5V transormer through a variac, so that you can SLOWLY increase the voltage rom zero and read the variac ammeter to detect short circuits beore they become serious. A common problem is to 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 your circuit is working correctly, the variac is then optional. Remember your boost converter requires DC input power rom a DBR. Does your circuit have a short? I so, do the ollowing: 1. Make sure that your MOSFET is not connected backwards.. Observe VGS on the MOSFET as you vary D and F. Does the waveorm look correct?. Unplug the wall wart. Does the short circuit go away? I not, your MOSFET may be shorted so, disconnect the MOSFET rom the converter, and perorm the voltagecontrolled resistance test on the MOSFET. 4. Connect a 5Vac transormer to a DBR. Connect the DBR to your SEPIC converter, keeping the wires short (i.e., or less). Then, energize the 5Vac transormer and DBR. I using a variac, adjust the variac so that Vac o the transormer is approximately 7-8V. 5. With F 90kHz, slowly increase D rom its smallest value to obtain V = 10, 0 (within ±V), while recording D, Vin, V, Iin, I. Note by viewing V DS whether or not the circuit is in continuous current operation. For the 0V condition, compute input and put powers and eiciency. Do not go above 0V with the 5Ω load. Page 9 o 1
EE46L, Power Electronics, DC-DC SEPIC Converter Version March 1, 01 6. Turn o the DBR, and connect a 10Ω ceramic power resistor as a load. Continue the experiment as beore, adjusting D, and taking D, Vin, V, Iin, I readings with V = 0, 40V. Do not go above 40V with the 10Ω load. 7. Turn o the DBR, and connect a 10V, 150W light bulb as a load. Continue the experiment, adjusting D, taking D, Vin, V, Iin, I readings with V = 50, 60, 70, 80, 90V. For the 90V case, save a screen snapshot o VDS that shows the peak value. 8. For your report, compute converter eiciencies or the 0V, 40V, and 90V conditions. Also, plot actual and theoretical V/Vin versus D on one graph. The ollowing optional steps are to be perormed with solar panels as the power source and with good sun (i.e., panel short circuit current o.5a or more). The panel voltage that you measure should be at the panel (i.e., the let-most analog voltmeter) 9. Note the sky conditions. Connect a solar panel pair directly to a 10V, 150W light bulb. Measure panel voltage, panel current, and compute solar panel put power. 10. Next, insert the SEPIC converter between the panel pair and 10V light bulb. With F 90kHz, sweep D over its range to measure and plot the I-V and P-V characteristics o the panel pair. Record the maximum power value. Parts List Series capacitor, Xicon µf, 50V, high-requency bipolar (i.e., not polarized), rated 14A peak-to-peak ripple current (Mouser #140-BPHR50V) Second inductor like the one in the buck converter Second heat sink like the one in the buck converter Second nylon screw and lock nut like the one in the buck converter Two additional, -terminal, 0A terminal blocks (these may not be needed by students who are building minimum ootprint circuits) 8 nylon cable tie (in student parts bin) Extra parts For the student parts bin and screw cabinet, at least 5 o the 50V MOSFETs (individually bagged) 5 o the 00V, 16A ultraast rectiiers 5 o the DC jacks 5 o the 10kΩ audio taper and linear taper potentiometers 5 o the PWM modulator chips 5 o the inverting driver chips 5 o the 14-pin sockets 5 o the 8-pin DIP sockets 5 o the green plugs 10 o the #4-40 x 1 lat slotted nylon screws and lock nuts Page 10 o 1
EE46L, Power Electronics, DC-DC SEPIC Converter Version March 1, 01 Plastic bags or parts 6 x6, 4mil Page 11 o 1
EE46L, Power Electronics, DC-DC SEPIC Converter Version March 1, 01 Appendix Converter Type Buck Boost SEPIC Worst-Case Component Ratings Comparisons or DC-DC Converters Output Input Inductor Capacitor Output Capacitor Diode and Current (Arms) Voltage Current (Arms) MOSFET Voltage 1.5V I 1 V I in 1.5V I I V in 1.5V I V in V in max I in, I Diode and MOSFET Current (Arms) I I in Iin I Series Capacitor Voltage 1.5V in Additional Components or SEPIC Converter Series Capacitor Series Capacitor (C 1 ) (C 1 ) Ripple Current (Arms) Voltage (peak-topeak) I max I in, I C1 Comparisons o Output Capacitor Ripple Voltage Converter Type Volts (peak-to-peak) Buck I 4C Boost I C SEPIC I C Second Inductor (L ) Current (Arms) I Page 1 o 1
EE46L, Power Electronics, DC-DC SEPIC Converter Version March 1, 01 Minimum Inductance Values Needed to Guarantee Continuous Current Converter Type For Continuous Current in the Input Inductor For Continuous Current in L Buck V L I Boost Vin L Iin SEPIC Vin L1 V L I I in Page 1 o 1