EE462L, Fall 2011 DC − DC Buck Converter
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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 highfrequency switching, the load voltage ripple can be reduced to a small value.lossless

Cs and Ls operating in periodic steadystateExamine the current passing through a capacitor that is operating in periodic steady state. The governing equation is
which leads to
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
which leads to
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 steadystateSince 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 DCDC 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 DCDC 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

Worstcase 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 peaktopeak 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 switchopen 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, attachIV 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 ripplefree 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 highfrequency bipolar (unpolarized) capacitor

BUCK DESIGN
WorstCase Component Ratings Comparisons
for DCDC 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
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10A1500F50kHzBUCK DESIGN
Comparisons of Output Capacitor Ripple Voltage
Converter Type
Volts (peaktopeak)
Buck
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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
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