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1 EE462L, Fall 2011 DC−DC Buck Converter
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EE462L, Fall 2011 DC − DC Buck Converter. Objective – to efficiently reduce DC voltage. The DC equivalent of an AC transformer. I in. I out. DC − DC Buck Converter. + V in −. + V out −. Lossless objective: P in = P out , which means that V in I in = V out I out and. R 1. + V in - PowerPoint PPT Presentation

### Transcript of EE462L, Fall 2011 DC − DC Buck Converter

• EE462L, Fall 2011DCDC Buck Converter

• Objective to efficiently reduce DC voltage

DCDC Buck Converter

+Vin+VoutIoutIinLossless objective: Pin = Pout, which means that VinIin = VoutIout andThe DC equivalent of an AC transformer

• Here is an example of an inefficient DCDC converterIf Vin = 39V, and Vout = 13V, efficiency is only 0.33The loadUnacceptable except in very low power applications

• Another method lossless conversion of 39Vdc to average 13VdcIf the duty cycle D of the switch is 0.33, then the average voltage to the expensive car stereo is 39 0.33 = 13Vdc. This is lossless conversion, but is it acceptable?

• Convert 39Vdc to 13Vdc, cont.Try adding a large C in parallel with the load to control ripple. But if the C has 13Vdc, then when the switch closes, the source current spikes to a huge value and burns out the switch.Try adding an L to prevent the huge current spike. But now, if the L has current when the switch attempts to open, the inductors current momentum and resulting Ldi/dt burns out the switch.By adding a free wheeling diode, the switch can open and the inductor current can continue to flow. With high-frequency switching, the load voltage ripple can be reduced to a small value.lossless

• Cs and Ls operating in periodic steady-stateExamine the current passing through a capacitor that is operating in periodic steady state. The governing equation is

Since the capacitor is in periodic steady state, then the voltage at time to is the same as the voltage one period T later, so

The conclusion is that

or

the average current through a capacitor operating in periodic steady state is zerowhich means thatTaken from Waveforms and Definitions PPT

• Now, an inductorExamine the voltage across an inductor that is operating in periodic steady state. The governing equation is

Since the inductor is in periodic steady state, then the voltage at time to is the same as the voltage one period T later, so

The conclusion is that

or

the average voltage across an inductor operating in periodic steady state is zerowhich means thatTaken from Waveforms and Definitions PPT

• KVL and KCL in periodic steady-stateSince KVL and KCL apply at any instance, then they must also be valid in averages. Consider KVL,The same reasoning applies to KCLKVL applies in the average senseKCL applies in the average senseTaken from Waveforms and Definitions PPT

• Vin + Vout iL LC iC Iout iinBuck converter + vL Vin + Vout LC Iout iin+ 0 V What do we learn from inductor voltage and capacitor current in the average sense?Iout0 AAssume large C so that Vout has very low ripple

Since Vout has very low ripple, then assume Iout has very low ripple

• The input/output equation for DC-DC converters usually comes by examining inductor voltagesfor DT secondsNote if the switch stays closed, then Vout = VinSwitch closed for DT seconds

• Vin + Vout LC Iout Vout +iL(iL Iout)Switch open for (1 D)T seconds iL continues to flow, thus the diode is closed. This is the assumption of continuous conduction in the inductor which is the normal operating condition.for (1D)T seconds

• Since the average voltage across L is zeroFrom power balance,, soThe input/output equation becomesNote even though iin is not constant (i.e., iin has harmonics), the input power is still simply Vin Iin because Vin has no harmonics

• Examine the inductor currentSwitch closed,Switch open,DT(1 D)TTImaxIminIavg = IoutFrom geometry, Iavg = Iout is halfway between Imax and IminIiLPeriodic finishes a period where it started

• Effect of raising and lowering Iout while holding Vin, Vout, f, and L constantiLII is unchangedLowering Iout (and, therefore, Pout ) moves the circuit toward discontinuous operation

• Effect of raising and lowering f while holding Vin, Vout, Iout, and L constantiLRaise fLower fSlopes of iL are unchangedLowering f increases I and moves the circuit toward discontinuous operation

• iLEffect of raising and lowering L while holding Vin, Vout, Iout and f constantRaise LLower LLowering L increases I and moves the circuit toward discontinuous operation

• RMS of common periodic waveforms, cont. TV

0SawtoothTaken from Waveforms and Definitions PPT

• RMS of common periodic waveforms, cont. Using the power concept, it is easy to reason that the following waveforms would all produce the same average power to a resistor, and thus their rms values are identical and equal to the previous exampleTaken from Waveforms and Definitions PPT

• RMS of common periodic waveforms, cont. Now, consider a useful example, based upon a waveform that is often seen in DC-DC converter currents. Decompose the waveform into its ripple, plus its minimum value.Taken from Waveforms and Definitions PPT

• RMS of common periodic waveforms, cont.DefineTaken from Waveforms and Definitions PPT

• RMS of common periodic waveforms, cont.Recognize thatTaken from Waveforms and Definitions PPT

• Inductor current ratingMax impact of I on the rms current occurs at the boundary of continuous/discontinuous conduction, where I =2Iout2Iout0Iavg = IoutIiLUse max

• Capacitor current and current rating iL LC Iout (iL Iout)IoutIout0IMax rms current occurs at the boundary of continuous/discontinuous conduction, where I =2IoutUse maxiC = (iL Iout)

Note raising f or L, which lowers I, reduces the capacitor current

• MOSFET and diode currents and current ratings iL LC Iout (iL Iout)Use max2Iout0Ioutiin 2Iout0IoutTake worst case D for each

• Worst-case load ripple voltageIoutIout0T/2C chargingiC = (iL Iout)

During the charging period, the C voltage moves from the min to the max. The area of the triangle shown above gives the peak-to-peak ripple voltage.Raising f or L reduces the load voltage ripple

• Vin + Vout iL LC iC Iout Vin + Vout iL LC iC Iout iin Voltage ratingsDiode sees VinMOSFET sees VinC sees VoutDiode and MOSFET, use 2VinCapacitor, use 1.5VoutSwitch ClosedSwitch Open

• There is a 3rd state discontinuous Vin + Vout LC Iout Occurs for light loads, or low operating frequencies, where the inductor current eventually hits zero during the switch-open stateThe diode opens to prevent backward current flow The small capacitances of the MOSFET and diode, acting in parallel with each other as a net parasitic capacitance, interact with L to produce an oscillationThe output C is in series with the net parasitic capacitance, but C is so large that it can be ignored in the oscillation phenomenonIout

• Inductor voltage showing oscillation during discontinuous current operation 650kHz. With L = 100H, this corresponds to net parasitic C = 0.6nFvL = (Vin Vout)vL = VoutSwitch openSwitch closed

• Onset of the discontinuous state2Iout0Iavg = IoutiL(1 D)Tguarantees continuous conductionuse maxuse minThen, considering the worst case (i.e., D 0),

• Impedance matching

DCDC Buck Converter

+Vin+Vout = DVinIout = Iin / DIin+VinIinEquivalent from source perspectiveSourceSo, the buck converter makes the load resistance look larger to the source

• Example of drawing maximum power from solar panelIscVocPmax is approx. 130W (occurs at 29V, 4.5A)For max power from panels at this solar intensity level, attachI-V characteristic of 6.44 resistorBut as the sun conditions change, the max power resistance must also change

• Connect a 2 resistor directly, extract only 55W130W6.44 resistor2 resistor55WTo draw maximum power (130W), connect a buck converter between the panel and the load resistor, and use D to modify the equivalent load resistance seen by the source so that maximum power is transferred

• Vpanel + Vout iL LC iC Iout ipanelBuck converter for solar applications+ vL Put a capacitor here to provide the ripple current required by the opening and closing of the MOSFETThe panel needs a ripple-free current to stay on the max power point. Wiring inductance reacts to the current switching with large voltage spikes.In that way, the panel current can be ripple free and the voltage spikes can be controlledWe use a 10F, 50V, 10A high-frequency bipolar (unpolarized) capacitor

• BUCK DESIGN

Worst-Case Component Ratings Comparisons

for DC-DC Converters

Converter Type

Input Inductor Current (Arms)

Output Capacitor Voltage

Output Capacitor Current (Arms)

Diode and MOSFET Voltage

Diode and MOSFET Current (Arms)

Buck

1.5

2

_1150520754.unknown

_1150520756.unknown

_1221540160.unknown

_1150520755.unknown

_1150520753.unknown

• 10A1500F50kHzBUCK DESIGN

Comparisons of Output Capacitor Ripple Voltage

Converter Type

Volts (peak-to-peak)

Buck

_1191253542.unknown

• 40V2A50kHz200HBUCK DESIGN

Minimum Inductance Values Needed to

Guarantee Continuous Current

Converter Type

For Continuous Current in the Input Inductor

For Continuous Current in L2

Buck

_1221729697.unknown