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**EE462L, Spring 2014 DC−DC SEPIC (Converter)**

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**! Boost converter SEPIC converter i I + L1 V V C – i I + L1 C1 V V C**

+ v L1 – i I in out L1 C + V V in out – SEPIC converter V in i L1 + v L1 – + v L2 – C1 + v C1 – L2 + V out – I C + v L2 – C1 + v C1 – L2

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**! SEPIC converter SEPIC = single ended primary inductor converter**

+ v L1 – + v L2 – C1 + v C1 – L2 + V out – I C SEPIC = single ended primary inductor converter This circuit is more unforgiving than the boost converter, because the MOSFET and diode voltages and currents are higher Before applying power, make sure that your D is at the minimum, and that a load is solidly connected Limit your output voltage to 90V

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**KVL and KCL in the average sense**

+ Vin – + 0 – I I I in out out L1 + – + C1 I V out V in out I C L2 in – KVL shows that VC1 = Vin Interestingly, no average current passes from the source side, through C1, to the load side, and yet this is a “DC - DC” converter

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**Switch closed i I + L1 C1 V V C L2 – i I + L1 C1 V V C I L2 –**

assume constant + Vin – + Vin – + v D – i + V out – I C in L1 + v L2 – C1 V in L2 KVL shows that vD = −(Vin + Vout), so the diode is open Thus, C is providing the load power when the switch is closed + Vin – – (Vin + Vout) + + Vin – i I in out L1 – Vin + + C1 V V in out C L2 I out – iL1 and iL2 are ramping up (charging). C1 is charging L2 (so C1 is discharging). C is also discharging.

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**Switch open (assume the diode is conducting because, otherwise, the circuit cannot work)**

! assume constant + Vin – – Vout + i I in out L1 + + C1 V V V in out out C L2 – – C1 and C are charging. L1 and L2 are discharging. KVL shows that VL1 = −Vout The input/output equation comes from recognizing that the average voltage across L1 is zero Voltage can be stepped-up or stepped-down

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**The buck-boost converter**

! The buck-boost converter Inverse polarity with respect to input + V in – out i L C I d Compared with SEPIC: + Fewer energy storage components + Capacitor does not carry load current + In both converters isolation can be easily implemented - Polarity is reversed Voltage can be stepped-up or stepped-down

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**Inductor L1 current rating**

During the “on” state, L1 operates under the same conditions as the boost converter L, so the results are the same Use max

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**Inductor L2 current rating**

Average values + Vin – + 0 – I I I in out out L1 + – + C1 I V out V in out I C in L2 – iL2 2Iout Iavg = Iout ΔI Use max

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**MOSFET and diode currents and current ratings**

+ v L2 – C1 + v C1 – L2 + v L1 – i I in out L1 + V V in out C – iL1 + iL2 MOSFET Diode iL1 + iL2 2(Iin + Iout) 2(Iin + Iout) switch closed switch open Take worst case D for each Use max

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**Output capacitor C current and current rating**

iC = (iD – Iout) 2Iin + Iout −Iout switch closed switch open As D → 1, Iin >> Iout , so As D → 0, Iin << Iout , so

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**Series capacitor C1 current and current rating**

+ Vin – – (Vin + Vout) + + Vin – i I in out L1 – Vin + + C1 V V in out C L2 I out – + Vin – – Vout + i I in out L1 + + C1 V V V in out out C L2 – – Switch closed, IC1 = −IL2 Switch open, IC1 = IL1

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**Series capacitor C1 current and current rating**

! Series capacitor C1 current and current rating iC1 Switch closed, IC1 = −IL2 Switch open, IC1 = IL1 2Iin switch closed switch open −2Iout As D → 1, Iin >> Iout , so As D → 0, Iin << Iout , so The high capacitor current rating is a disadvantage of this converter

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**Worst-case load ripple voltage**

iC = (iD – Iout) −Iout The worst case is where D → 1, where output capacitor C provides Iout for most of the period. Then,

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**Worst case ripple voltage on series capacitor C1**

iC1 switch open 2Iin −2Iout switch closed Then, considering the worst case (i.e., D = 1)

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**Voltage ratings + L1 C1 V V C L2 – + L1 C1 V V C L2 – + Vin –**

– (Vin + Vout) + L1 + C1 V V in out C L2 – MOSFET and diode see (Vin + Vout) + Vin – – Vout + L1 + C1 V V in out C L2 – Diode and MOSFET, use 2(Vin + Vout) Capacitor C1, use 1.5Vin Capacitor C, use 1.5Vout

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**Continuous current in L1**

iL 2Iin Iavg = Iin (1 − D)T Then, considering the worst case (i.e., D → 1), use max guarantees continuous conduction use min

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**Continuous current in L2**

iL 2Iout Iavg = Iout (1 − D)T Then, considering the worst case (i.e., D → 0), use max guarantees continuous conduction use min

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**Impedance matching Iin DC−DC Boost Converter + + Vin − − Source Iin +**

Equivalent from source perspective

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! Impedance matching For any Rload, as D → 0, then Requiv → ∞ (i.e., an open circuit) For any Rload, as D → 1, then Requiv → 0 (i.e., a short circuit) Thus, the SEPIC converter can sweep the entire I-V curve of a solar panel

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**Example - connect a 100Ω load resistor**

2Ω equiv. 6.44Ω equiv. D = 0.50 100Ω equiv. With a 100Ω load resistor attached, raising D from 0 to 1 moves the solar panel load from the open circuit condition to the short circuit condition

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**Example - connect a 5Ω load resistor**

2Ω equiv. 6.44Ω equiv. D = 0.18 100Ω equiv.

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**Likely worst-case SEPIC situation**

SEPIC DESIGN 5.66A p-p 200V, 250V 16A, 20A Our components 9A 250V 10A, 5A 10A 90V 40V, 90V Likely worst-case SEPIC situation 10A, 5A MOSFET M. 250V, 20A L1. 100µH, 9A C. 1500µF, 250V, 5.66A p-p Diode D. 200V, 16A L2. 100µH, 9A C1. 33µF, 50V, 14A p-p

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**SEPIC DESIGN 5A 0.067V 1500µF 50kHz L1. 100µH, 9A L2. 100µH, 9A**

C. 1500µF, 250V, 5.66A p-p C1. 33µF, 50V, 14A p-p Diode D. 200V, 16A MOSFET M. 250V, 20A

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**SEPIC DESIGN 40V 90V 200µH 450µH 2A 50kHz 2A 50kHz L1. 100µH, 9A**

C. 1500µF, 250V, 5.66A p-p C1. 33µF, 50V, 14A p-p Diode D. 200V, 16A MOSFET M. 250V, 20A

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**Likely worst-case SEPIC situation**

SEPIC DESIGN SEPIC converter Our components 9A 14A p-p 50V 10A A 40V Likely worst-case SEPIC situation 5A 33µF 50kHz 3.0V L1. 100µH, 9A L2. 100µH, 9A C. 1500µF, 250V, 5.66A p-p C1. 33µF, 50V, 14A p-p Diode D. 200V, 16A Conclusion - 50kHz may be too low for SEPIC converter MOSFET M. 250V, 20A

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