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SEE 4433Power Electronics
And Drives
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Chapter 3:
DC to DCConversion(Choppers)
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Overview
General Buck converter
Boost converter
Buck -Boost converter Switched-mode power supply (SMPS)
- fly back converter
- forward converter
- bridge converter
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DEFINITION :
Converting the unregulated DC input to a controlledDC output with a desired voltage level.
General block diagram:
DEFINITION
Applications:High-frequency switched-mode power supply(SMPS), DC motor control (traction, forklift, electric vehicles, trams,battery chargers, capacitor chargers)
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Linear Regulator
Transistor is operated in linear
(active) mode. Output voltage:
The transistor can be convenientlymodeled by an equivalent variableresistor, as shown.
Power loss is high at high currentdue to:
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Switching Regulator
Transistor is operated in switched-mode:Switch closed: Fully on (saturated)Switch opened: Fully off (cut-off)
When switch is open, no current flow in itWhen switch is closed no voltage drop
across it.
Since P=V.I, no losses occurs in theswitch.
Power is 100% transferred from
source to load.Power loss is zero (for ideal switch):
Switching regulator is the basis of allDC-DC converters
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Buck (Step-Down) Converter
Duty cycle D:0 D 1
complement D :D
= 1 - D
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Switch is turned on (closed)
Diode is reversed biased. Switch conducts inductor current This results in positive inductor voltage, i.e:
It causes linear increase in the
inductor current
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Switch turned off (opened)
Because of inductiveenergy storage, i L continues toflow. Diode is forward biased
Current now flows(freewheeling) through thediode. The inductor voltage can bederived as:
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Analysis
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Analysis
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Steady-state Operation
Realization using
power MOSFET
and diode +-
+ -
V L(t) ic(t)
V g
i L(t)
t DT s T s
+
L
D1 R
Unstable
Steady-state
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Average, Maximum andMinimum Inductor Current
Average inductor current = Average current in R L
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Continuous Current Mode (CCM)
From previous analysis,
For continuous operation,
This is the minimum inductor current to ensure continousmode of operation. Normally L ischosen to be >> L min
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Output Voltage Ripple
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Basic Design Procedures
Calculate D to obtain required output voltage. Select a particular switching frequency (f) and device
preferably f >20 kHz for negligible acoustic noise higher f s results in smaller L and C. But results in higher losses.Reduced efficiency, larger heat sink.
Possible devices: MOSFET, IGBT and BJT. Low power MOSFETcan reach MHz range.
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Calculate L min . Choose L >>10 L min Calculate C for ripple factor requirement.
Capacitor ratings: must withstand peak output voltage must carry required RMS current. Note RMS current for
triangular waveform is I p/3, where I p is the peak capacitor current given by i L/2.
Electrolytic Capacitors (E-CAPs) can be used. Wire size consideration:
Normally rated in RMS. But i L is known as peak. RMS valuefor iL is given as:
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Question 1.
A buck converter has an input voltage of 12 V. The required averageoutput voltage is 5 V and peak-to-peak output ripple voltage is 20 mV.The switching frequency is 25 kHz. If the peak-to-peak ripple currentof inductor is limited to 0.8 A, determine
i. duty ratio, Dii. filter inductance, Liii. output filter capacitor, C
Question 2. A buck converter is supplied from a 50V battery source. Given L = 400H, C=100 F, R=20 , f =20 kHz and D = 0.4. Calculate:
(a) output voltage(b) maximum and minimum inductor current,(c) output voltage ripple.
Examples
(0.42, 148 mH, 197 uF)
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Question 3.
A buck converter has an input voltage of 50V and output of 25 V.The switching frequency is 10KHz. The power output is 125 W.
(a) Determine the duty cycle,(b) value of L to limit the peak inductor current to 6.25 A,(c) value of capacitance to limit the output voltage ripple
factor to 0.5 %.
Question 4.Design a buck converter such that the output voltage is 28 V whenthe input is 48V. The load is 8 . Design the converter such that it willbe in continuous current mode.
The output voltage ripple must not be more than 0.5 %.Specify the frequency and the values of each component.Suggest the power switch also.
Examples
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Buck Converter Conclusion
The output voltage may be controlled by the duty -ratio, but cannot be larger than input voltage
The voltage conversion ratio depends solely on duty -ratio, and is independent of load condition The capacitor ripple current is independent of loadcurrent
The off -state voltage across device is supply voltage
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Boost (step-up) converter
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Boost Analysis: Switch Closed
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Boost Analysis: Switch Opened
UTM St d t t
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Steady-stateOperation
Boost converter produces output voltage that is greater or equalto the input voltage. Alternative explanation:
when switch is closed, diode is reversed. Thus output is
isolated. The input supplies energy to inductor. When switch is opened, the output stage receives energy fromthe input as well as from the inductor. Hence output is large.
Output voltage is maintained constant by virtue of large C. The off-state voltage impressed across power device is V o
UTM
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Average, Maximum, MinimumInductor Current
UTM
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L and CValues
UTM
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The output voltage is always greater or equal to theinput voltage The voltage conversion ratio depends solely on duty -ratio, and always greater than or equal to one
Theoretically the output voltage tends to infinity as Dtends to 1, but in practice the maximum output voltagewill be limited to conduction loss The capacitor ripple current is severe and dependsdirectly on the load current level The off -state voltage impressed across device isoutput voltage
Boost Converter Conclusion
UTM
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Example :
A boost converter has an input voltage of 5 V. The average
output voltage is 15 V and the average load current is 0.5 A. If fs = 25kHz, L = 150 H and C = 220 F, determine(a)duty cycle (b) inductor ripple current(c) inductor peak current (d) output ripple voltage
Design a boost converter to provide an output voltage of 36Vfrom a 24 V source. The load is 50 W. The voltage ripple factor must be less than 0.5%. Specify the duty cycle ratio, switchingfrequency, inductor and capacitor size, and power device.
The boost converter has the following parameters:Vd = 20V, D = 0.6, R = 12.5, L = 65 H, C = 200 F, f s= 40 kHz.Determine(a) output voltage, (b) average, maximum and minimuminductor current, (c) output voltage ripple.
UTM
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Buck-boost Converter
UTM
B k b A l i
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Buck-boost Analysis
UTM
B k b A l i
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Buck-boost Analysis
UTM
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Output Voltage
Steady state operation : NOTE :
Output of a buck-boostconverter either be higher or lower than input.
If D > 0.5, output is higher than input
If D < 0.5, output is lower input Output voltage is alwaysnegative.
Note that source is never directly connected to load. Energy is stored in inductor when switch is closed andtransferred to load when switch is opened. Off -state voltage across power switch is ( V d Vo )
UTM
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Average Inductor Current
Assuming no power loss in theconverter, power absorbed bythe load must equal power supplied the by source, i.e .
But average source current is relatedto average inductor current as :
Substituting for V o ,
UTM L and C
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L and Cvalues
Ripple Factor, r
UTM
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Example :
A buck-boost converter has input voltage of 12 V. The duty cycle
is 0.25 and the switching frequency is 25 kHz. L = 150 H andC = 220 F. The average load current is 1.25 A.Determine:(a)average output voltage
(b)peak-to-peak output voltage ripple(c)peak-to-peak inductor ripple current(d)peak current transistor (-4 V, 56.8 mV, 0.8 A, 2.07 A)
A buck-boost converter has the specification as follows:
Vd = 18 V, D = 0.6, f s = 40 kHz, R = 10 , L = 50 H, C = 200 FConsider all components are ideal, determine(a)output voltage(b)average, maximum, and minimum inductor current
(-27 V, 6.75 A, 9.45 A, 4.05 A)
UTM
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Buck-Boost Converter conclusion
The voltage conversion ratio depends solely on duty -ratio and less than unity for D < 0.5.
For D > 0.5, the conversion ratio greater than unity. Themaximum conversion ratio is limited in practice by circuitlosses
Similar to boost, the capacitor current ripple is severeand depends on load current
The off -state voltage impressed across the device is
the sum of supply and output voltage The average inductor current is the sum of averageinput and output current
UTM
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Converters in CCM: Summary
UTM
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Converters in CCM: Summary
UTM
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Converters in CCM: Summary
UTM Control of DC DC Converter:
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Control of DC-DC Converter:Pulse Width Modulation (PWM)
UTM
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DC-DC Converter Control
Purpose of control:To regulate theoutput voltage sothat it is
maintained withina specifiedtolerance band(e.g. 2% of outputDC voltage)
Basic blockdiagram for converter control
UTM
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Isolated DC-DC Converter
Isolated DC -DC requires isolation transformer
Two types: Linear and Switched -mode Power Supply ( SMPS ) Advantages of switched mode over linear power supply
-Efficient (70 95%)-Weight and size reduction
Disadvantages-Complex design-EMI problems
However above certain ratings, SMPS is the only feasible choice Types of SMPS
-Flyback-forward-Push-pull-Bridge (half and full)
UTM
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Linear and SMPS Block Diagram
UTM
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Linear and SMPS Block Diagram
UTM
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High Frequency Transformer
Basic function:
1) Input - output electrical isolation2) Step up/down time - varying voltageBasic input - output relationship
UTM Fl b k C
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Flyback Converter
UTM
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Operation: Switch Closed
Flyback Converter
UTM h l d
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Flyback Converter49
Operation: Switch Closed
UTM O i S i h O d
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Operation: Switch Opened
Current flows in different direction at the Primary..
Flyback Converter
UTM O i S i h O d
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Flyback Converter51
Operation: Switch Opened
UTM O V l
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Output Voltage
Input output relationship is similar to buck-boost converter.Output can be greater of less than input, depending upon D.
Additional term, i.e. transformer ratio is present.Positive output voltage polarity
Flyback Converter
UTM
Flyback Waveforms
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Flyback Waveforms
AverageInductor Current
UTM M Mi I d C
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Max., Min. Inductor Current
UTM M Mi I d C
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Max., Min. Inductor Current
UTM E l
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Example :
The Flyback converter has these specifications:
DC input voltage: 40 VOutput voltage: 25 VDuty cycle: 0.5Rated load: 62.5 WMax peak-peak inductor current ripple: 25 % of the
average inductor current.Maximum peak-peak output voltage: 0.1 VSwitching frequency: 75 kHz
Based on the abovementioned specifications, determinea) Transformer turns ratiob) Value of magnetizing inductor L m .c) Maximum and minimum inductor current.d) Value of capacitor C.
UTM E l
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Example :
The Flyback converter has the following:
Input voltage: 24 V DCOutput voltage: 5 VTransformer turn-ratio (N1/N2): 3Load resistance: 5Magnetising inductance: 500 HOutput capacitor: 200 FSwitching frequency: 40 kHz
Based on the abovementioned specifications, determinea) duty ratiob) average inductor current in L m .c) maximum and minimum inductor current.d) output voltage ripple.
0.39, 540 mA, 770 mA, 310 mA, 48 mV
UTM E l
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Example :
For a Flyback converter, consider all components are ideal.
The parameters are shown as follows:
Based on the abovementioned specifications, calculatea) The range of duty ratios, Db) The minimum value of Lm , to ensure continuous current if the input voltage varies from 10 V to 40 V.c) The required capacitor if output voltage ripple is 0.2 V p-p .
0.123
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Forward Converter Derived from Buck Converter, but D max = 0.5 Transformer magnetizing current must be taken into account Assume transformer ideal, when switch ON, D 1forward biased and D 2 reversed biased, V L positive and i Lincreases linearly
When switch OFF, D 1 reversed biased and i L circulatesthrough D 2 . VL negative and i L decreases linearly
UTM Forward Converter
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Equating the integral of inductor voltage over one time
period to zero,
It shows that the output voltage is proportional to the duty
ratio, D, similar to buck converter Practically transformer magnetization current must beconsidered in converter operation to avoid converter failuredue to energy stored in its core. A third/reset/demagnetizing winding is required so thatenergy in transformer core can be transferred back to thesupply when switched turned OFF.
Forward Converter
UTM Forward Converter
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Forward Converter
UTM
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UTM Forward Converter
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Forward Converter When switch ON,
UTM
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UTM Full bridge Converter
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Full-bridge Converter
UTM
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UTM Full Bridge: Basic Operation
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Full Bridge: Basic Operation
Switch pair: [S1 & S2]; [S3 & S4].
Each switch pair turn on at a time as shown. The other pair is off. AC voltage is developed across the primary. Thentransferred to secondary via high frequency transformers.
On secondary side, diode pair is high frequency full waverectification. The choke (L) and (C ) acts like the buck convertercircuit.
Output Voltage
UTM Half bridge Converter
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Half-bridge Converter
UTM
Half-bridge
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Converter
UTM Industry Favorites SMPS
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Industry Favorites SMPS
UTM Example :
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Q1 Referring to Figure Q1,a) Sketch the waveforms for the inductor voltage and current (per cycle) with f s = 25 k Hz. (5 marks)b) With the assumption that the switching device operates as a fixedfrequency switch with a duty ratio D and the inductor current iscontinuous, show that the output voltage V o = Vd / (1 D).
(10 marks)c) If the switching device operates at a duty ratio of 0.4, calculate theoutput voltage and the average inductor current when the inputvoltage is 60 V and the resistive load is 10 . Determine the inductor value such that peak to peak inductor ripple current is 4 A.
(10 marks)
Example :
Ans: 100 V, 16.67A, 240 u H
UTM
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Q2 Referring to Figure Q2, and assuming converter operates in CCMa) Sketch the waveforms for the inductor voltage ,inductor currentand capacitor current(per cycle).b) Prove that the peak-to-peak output voltage ripplec) The converter in Figure Q2 required to provide a 400Vregulated output from a variable DC source, ranges between 150V < Vd < 300 V. The output power varies over the range of 100 Wto 1 kW and the switching frequency is 50 kHz. If the converter operates in CCM,
i) Calculate the range of the duty ratio, Dii) Determine the capacitor value that results in the maximumpeak-to-peak ripple voltage of 3 Viii) Determine the minimum value of inductance to ensure CCMof current over all condition
Example :
Ans: 0.25
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Q2 (a)Draw and label a block diagram of a switched mode power supply(SMPS).Briefly state the function of each element in the diagram. (8 marks)
(b) Figure Q3 shows a boost converter with the inductor current waveform insteady state. The key quantities of the waveforms are labeled. The circuit usesa feedback controller to regulate the output voltage at 12V by varying the dutycycle, D. It was found that, for this condition, the peak-peak output voltageripple, vo, is 0.08V. Based on the circuit condition and its waveformdetermine:(i) The duty cycle D and the input voltage, Vs. (3 marks) (ii) The values of R, L and C. (6 marks) (iii) The maximum value of R to keep the converter operation in a continuousconduction mode. All other parameters are kept constant. (3 marks) (iv) Draw the voltages across MOSFET, vm and diode, vd. Suggest theminimum voltage rating for the diode and MOSFET. (3 marks)
Ans: i)0.4, 7.2V, ii)2.5 , 7.2u, 240uH, iii)10
p
UTM
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The End
of Chapter 3