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1 EE462L, Fall 2011 DC − DC Buck/Boost Converter

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2 Boost converter + V out – I C V in i L1 + v L1 – Buck/Boost converter + v L2 – C1 + v C1 – L2 V in i L1 + v L1 – + v L2 – C1 + v C1 – L2 + V out – I C

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3 Buck/Boost 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 V in i L1 + v L1 – + v L2 – C1 + v C1 – L2 + V out – I C

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4 + V – I C V in I L1 + 0 – +0–+0– KVL and KCL in the average sense 0 0 I out I in C1 L2 I out + V in – KVL shows that V C1 = V in 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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5 Switch closed V in i L1 + V in – + v L2 – C1 + V in – L2 + V out – I C assume constant + v D – KVL shows that v D = −(V in + V out ), so the diode is open Thus, C is providing the load power when the switch is closed V in i L1 – V in + C1 + V in – L2 + V out – I C – (V in + V out ) + I out i L1 and i L2 are ramping up (charging). C1 is charging L2. C is discharging. + V in –

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6 Switch open (assume the diode is conducting because, otherwise, the circuit cannot work) V in i L1 – V out + C1 + V in – L2 + V out – I C C1 and C are charging. L1 and L2 are discharging. + V out – KVL shows that V L1 = −V out The input/output equation comes from recognizing that the average voltage across L1 is zero assume constant

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

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8 Inductor L2 current rating 2I out 0 I avg = I out ΔIΔI i L2 Use max + V out – I C V in I L1 + 0 – +0–+0– 0 0 I out I in C1 L2 I out + V in – Average values

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9 MOSFET and diode currents and current ratings 0 2(I in + I out ) 0 Take worst case D for each V in i L1 + v L1 – + v L2 – C1 + v C1 – L2 + V out – I C MOSFETDiodei L1 + i L2 Use max switch closed switch open 2(I in + I out ) i L1 + i L2

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10 Output capacitor C current and current rating 2I in + I out − I out 0 As D → 1, I in >> I out, so i C = (i D – I out ) As D → 0, I in << I out, so switch closed switch open

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11 Series capacitor C1 current and current rating Switch closed, I C1 = − I L2 V in i L1 – V in + C1 + V in – L2 + V out – I C – (V in + V out ) + I out + V in – V in i L1 – V out + C1 + V in – L2 + V out – I C + V – Switch open, I C1 = I L1

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12 Series capacitor C1 current and current rating 2I in −2 I out 0 As D → 1, I in >> I out, so i C1 As D → 0, I in << I out, so switch closed switch open Switch closed, I C1 = − I L2 Switch open, I C1 = I L1

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13 Worst-case load ripple voltage The worst case is where D → 1, where output capacitor C provides I out for most of the period. Then, − I out 0 i C = (i D – I out )

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14 Worst case ripple voltage on series capacitor C1 2I in −2 I out 0 i C1 switch closed switch open Then, considering the worst case (i.e., D = 1)

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

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16 Continuous current in L1 2I in 0 I avg = I in iLiL (1 − D)T guarantees continuous conduction Then, considering the worst case (i.e., D → 1), use max use min

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17 Continuous current in L2 2I out 0 I avg = I out iLiL (1 − D)T guarantees continuous conduction Then, considering the worst case (i.e., D → 0), use max use min

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18 Impedance matching DC − DC Boost Converter + V in − +−+− I in + V in − I in Equivalent from source perspective Source

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19 Impedance matching For any R load, as D → 0, then R equiv → ∞ (i.e., an open circuit) For any R load, as D → 1, then R equiv → 0 (i.e., a short circuit) Thus, the buck/boost converter can sweep the entire I-V curve of a solar panel

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20 Example - connect a 100Ω load resistor D = Ω equiv. 100Ω equiv. D = 0.50 D = Ω 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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21 Example - connect a 5Ω load resistor D = Ω equiv. 100Ω equiv. D = 0.18 D = Ω equiv.

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A p-p200V, 250V16A, 20A Our components 9A250V 10A, 5A10A90V40V, 90V Likely worst-case buck/boost 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 BUCK/BOOST DESIGN

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23 5A 1500µF 50kHz 0.067V 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 BUCK/BOOST DESIGN

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24 40V 2A50kHz 200µH 90V 2A50kHz 450µH 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 BUCK/BOOST DESIGN

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25 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 10A 5A40V Likely worst-case buck/boost situation 5A 33µF 50kHz 3.0V BUCK/BOOST DESIGN Our components9A14A p-p50V Conclusion - 50kHz may be too low for buck/boost converter

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