Page 1 of 70
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`PHILIPS EXHIBIT 2009
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`WAC V. PHILIPS
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`IPR2015-01292
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`Page 1 of 70
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`PHILIPS EXHIBIT 2009
`WAC v. PHILIPS
`IPR2015-01292
`
`

`
`Fundamentals of
`Power Electronics
`SECOND EDITION
`
`
`Page 2 of 70
`
`

`
`eBook ISBN:
`Print ISBN:
`
`0-306-48048-4
`0-7923-7270-0
`
`©2004 Kluwer Academic Publishers
`New York, Boston, Dordrecht, London, Moscow
`
`Print ©2001 Kluwer Academic/Plenum Publishers
`New York
`
`All rights reserved
`
`No part of this eBook may be reproduced or transmitted in any form or by any means, electronic,
`mechanical, recording , or otherwise, without written consent from the Publisher
`
`Created in the United States of America
`
`Visit Kluwer Online at:
`and Kluwer's eBookstore at:
`
`http://kluweronline.com
`http://ebooks.kluweronline.com
`
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`1
`Introduction
`
`1.1
`
`INTRODUCTION TO POWER PROCESSING
`
`The field of power electronics is concerned with the processing of electrical power using electronic
`devices [1–7]. The key element is the
`
`switching converter, illustrated in Fig. 1.1. In general, a switching
`converter contains power input and control input ports, and a power output port. The raw input power is
`processed as specified by the control input, yielding the conditioned output power. One of several basic
`functions can be performed [2]. In a
`
`dc–dc converter, the dc input voltage is converted to a dc output
`voltage having a larger or smaller magnitude, possibly with opposite polarity or with isolation of the
`input and output ground references. In an ac–dc
`
`rectifier, an ac input voltage is rectified, producing a dc
`output voltage. The dc output voltage and/or ac input current waveform may be controlled. The inverse
`
`inversion, involves transforming a dc input voltage into an ac output voltage of controlla-
`process, dc–ac
`ble magnitude and frequency. Ac–ac
`
`cycloconversion involves converting an ac input voltage to a given
`ac output voltage of controllable magnitude and frequency.
`Control is invariably required. It is nearly always desired to produce a well-regulated output
`
`Fig. 1.1 The switching converter, a basic
`power processing block.
`
`Power
`input
`
`Switching
`converter
`
`Power
`output
`
`Control
`input
`
`1
`
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`2
`
`Introduction
`
`Fig. 1.2 A controller is generally required.
`
`Power
`input
`
`Switching
`converter
`
`Power
`output
`
`Control
`input
`
`Feedforward
`
`Feedback
`
`Controller
`
`Reference
`
`voltage, in the presence of variations in the input voltage and load current. As illustrated in Fig. 1.2, a
`controller block is an integral part of any power processing system.
`High efficiency is essential in any power processing application. The primary reason for this is
`usually not the desire to save money on one’s electric bills, nor to conserve energy, in spite of the nobility
`of such pursuits. Rather, high efficiency converters are necessary because construction of low-efficiency
`converters, producing substantial output power, is impractical. The efficiency of a converter having out-
`
` and input power P
` is
`put power
`P
`out
`
`in
`
`η =
`
`Pout
`Pin
`
`η
`
`1
`
`0.8
`
`0.6
`
`0.4
`
`0.2
`
`0
`
`(1.1)
`
`0.5
`
`1
`
`1.5
`
`Ploss / Pout
`Fig. 1.3 Converter power loss vs. efficiency.
`
`The power lost in the converter is
`
`(1.2)
`
`– 1
`
`1η
`
`Ploss = Pin – Pout = Pout
`
`Equation (1.2) is plotted in Fig. 1.3. In a con-
`verter that has an efficiency of 50%, power
` is dissipated by the converter elements
`P
`loss
`and this is equal to the output power,
`.
`P
`out
`This power is converted into heat, which
`must be removed from the converter. If the
`output power is substantial, then so is the
`loss power. This leads to a large and expen-
`sive cooling system, it causes the electronic
`elements within the converter to operate at
`high temperature, and it reduces the system
`reliability. Indeed, at high output powers, it
`may be impossible to adequately cool the
`converter elements using current technology.
`Increasing the efficiency is the key
`to obtaining higher output powers. For exam-
`ple, if the converter efficiency is 90%, then
`the converter loss power is equal to only 11%
`
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`1.1 Introduction to Power Processing
`
`3
`
`Pin
`
`Converter
`
`Pout
`
`Fig. 1.4 A goal of current converter technology is to construct converters of small size and weight, which process
`substantial power at high efficiency.
`
`of the output power. Efficiency is a good measure of the success of a given converter technology. Figure
`1.4 illustrates a converter that processes a large amount of power, with very high efficiency. Since very
`little power is lost, the converter elements can be packaged with high density, leading to a converter of
`small size and weight, and of low temperature rise.
`How can we build a circuit that changes the voltage, yet dissipates negligible power? The vari-
`ous conventional circuit elements are illustrated in Fig. 1.5. The available circuit elements fall broadly
`into the classes of resistive elements, capacitive elements, magnetic devices including inductors and
`transformers, semiconductor devices operated in the linear mode (for example, as class
` or class
`A
`B
`amplifiers), and semiconductor devices operated in the switched mode (such as in logic devices where
`transistors operate in either saturation or cutoff). In conventional signal processing applications, where
`efficiency is not the primary concern, magnetic devices are usually avoided wherever possible, because
`of their large size and the difficulty of incorporating them into integrated circuits. In contrast, capacitors
`and magnetic devices are important elements of switching converters, because ideally they do not con-
`sume power. It is the resistive element, as well as the linear-mode semiconductor device, that is avoided
`[2]. Switched-mode semiconductor devices are also employed. When a semiconductor device operates in
`the off state, its current is zero and hence its power dissipation is zero. When the semiconductor device
`operates in the on (saturated) state, its voltage drop is small and hence its power dissipation is also small.
`In either event, the power dissipated by the semiconductor device is low. So capacitive and inductive ele-
`ments, as well as switched-mode semiconductor devices, are available for synthesis of high-efficiency
`converters.
`Let us now consider how to construct the simple dc-dc converter example illustrated in Fig. 1.6.
` is 100 V. It is desired to supply 50 V to an effective 5
`The input voltage
` load, such that the dc load
`V
`Ω
`g
`current is 10 A.
`Introductory circuits textbooks describe a low-efficiency method to perform the required func-
`tion: the voltage divider circuit illustrated in Fig. 1.7(a). The dc–dc converter then consists simply of a
`
`+–
`
`DTs Ts
`Linear-
`mode
`Switched-mode
`Semiconductor devices
`
`Resistors Capacitors Magnetics
`
`Fig. 1.5 Devices available to the circuit designer [2].
`
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`4
`
`Introduction
`
`I
`10 A
`
`R
`5 Ω
`
`+
`
`V
`50 V
`
`–
`
`Dc-dc
`converter
`
`+–
`
`Vg
`100 V
`
`Fig. 1.6 A simple power processing example: construction of a 500 W dc–dc converter.
`
`+
`
`V
`50 V
`
`–
`
`I1
`
`0 A
`
`R
`5 Ω
`
`Pout = 500 W
`
`I1
`
`0 A
`
`Vref
`
`+–
`
`R
`5 Ω
`
`+
`
`V
`50 V
`
`–
`
`+ 50 V –
`
`Ploss = 500 W
`
`+ 50 V –
`
`Linear amplifier
`and base driver
`
`Ploss ≈ 500 W
`
`+–
`
`Vg
`100 V
`
`Pin = 1000 W
`
`+–
`
`Vg
`100 V
`
`(a)
`
`(b)
`
`Pin ≈ 1000 W
`Pout = 500 W
`Fig. 1.7 Changing the dc voltage via dissipative means: (a) voltage divider, (b) series pass regulator.
`variable resistor, whose value is adjusted such that the required output voltage is obtained. The load cur-
`
`rent flows through the variable resistor. For the specified voltage and current levels, the power P
` dissi-
`loss
`pated in the variable resistor equals the load power
` = 500 W. The source
` supplies power
`P
`V
`out
`g
` = 1000 W. Figure 1.7(b) illustrates a more practical implementation known as the linear series-pass
`P
`in
`regulator. The variable resistor of Fig. 1.7(a) is replaced by a linear-mode power transistor, whose base
`current is controlled by a feedback system such that the desired output voltage is obtained. The power
`dissipated by the linear-mode transistor of Fig. 1.7(b) is approximately the same as the 500 W lost by the
`variable resistor in Fig. 1.7(a). Series-pass linear regulators generally find modern application only at
`low power levels of a few watts.
`Figure 1.8 illustrates another approach. A single-pole double-throw (SPDT) switch is connected
`as shown. The switch output voltage
`(
`
`) is equal to the converter input voltage V
` when the switch is in
`v
`t
`s
`g
`position 1, and is equal to zero when the switch is in position 2. The switch position is varied periodi-
`cally, as illustrated in Fig. 1.9, such that
`
`(t
`) is a rectangular waveform having frequency
` and period
`v
`f
`s
`s
`
` = 1/f
`. The duty cycle
` is defined as the fraction of time in which the switch occupies position 1.
`T
`D
`s
`s
`
`
` D
` 1. In practice, the SPDT switch is realized using switched-mode semiconductor devices,
`Hence, 0
`≤
`≤
`
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`
`1.1 Introduction to Power Processing
`
`5
`
`+ v
`
`(t)
`50 V
`
`–
`
`I1
`
`0 A
`
`R
`
`1
`
`2
`
`+
`
`vs(t)
`
`–
`
`+–
`
`Vg
`100 V
`
`Fig. 1.8 Insertion of SPDT switch which changes the dc component of the voltage.
`
`vs(t)
`
`switch
`position:
`
`Vg
`
`DTs
`
`1
`
`Vs = DVg
`
`t
`
`1
`
`0
`(1 – D) Ts
`
`2
`
`Fig. 1.9 Switch output voltage waveform vs(t).
`which are controlled such that the SPDT switching function is attained.
`The switch changes the dc component of the voltage. Recall from Fourier analysis that the dc
`
`component of a periodic waveform is equal to its average value. Hence, the dc component of v
`(
`) is
`t
`s
`
`Vs = 1
`Ts
`
`Ts
`
`0
`
`vs(t)dt
`
`= DVg
`
`(1.3)
`
`. To convert the input volt-
`Thus, the switch changes the dc voltage, by a factor equal to the duty cycle
`D
`
` = 100 V into the desired output voltage of V
`
`
` = 50 V, a duty cycle of D = 0.5 is required.
`age
`V
`g
`Again, the power dissipated by the switch is ideally zero. When the switch contacts are closed,
`then their voltage is zero and hence the power dissipation is zero. When the switch contacts are open,
`then the current is zero and again the power dissipation is zero. So we have succeeded in changing the dc
`voltage component, using a device that is ideally lossless.
`) also con-
`(t
`
`
`In addition to the desired dc component V
`, the switch output voltage waveform
`v
`s
`s
`tains undesirable harmonics of the switching frequency. In most applications, these harmonics must be
`
`removed, such that the output voltage v
`(
`
`
`t) is essentially equal to the dc component V
`
` = V
`. A low-pass fil-
`s
`
`
`ter can be employed for this purpose. Figure 1.10 illustrates the introduction of a single-section L–C low-
`pass filter. If the filter corner frequency
` is sufficiently less than the switching frequency
`, then the fil-
`f
`f
`0
`s
`(
`). To the extent that the switch, inductor, and capacitor
`
`ter essentially passes only the dc component of v
`t
`s
`elements are ideal, the efficiency of this dc–dc converter can approach 100%.
`In Fig. 1.11, a control system is introduced for regulation of the output voltage. Since the output
`voltage is a function of the switch duty cycle, a control system can be constructed that varies the duty
`cycle to cause the output voltage to follow a given reference. Figure 1.11 also illustrates a typical way in
`which the SPDT switch is realized using switched-mode semiconductor devices. The converter power
`
`
`stage developed in Figs. 1.8 to 1.11 is called the buck converter, because it reduces the dc voltage.
`Converters can be constructed that perform other power processing functions. For example, Fig.
`
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`Page 8 of 70
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`

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`
`
`+ V –
`
`6
`
`Introduction
`
`+ v
`
`(t)
`
`–
`
`i(t)
`
`C
`
`R
`
`1
`
`2
`
`L
`
`+
`
`vs(t)
`
`–
`
`+–
`
`Vg
`100 V
`
`Pin ≈ 500 W
`
`Ploss small
`Fig. 1.10 Addition of L–C low-pass filter, for removal of switching harmonics.
`
`Pout = 500 W
`
`H(s)
`
`Sensor
`gain
`
`Load
`
`i
`
`+ v –
`
`Switching converter
`
`Power
`input
`
`+–
`
`vg
`
`Transistor
`gate driver
`
`δ(t)
`
`δ
`
`Pulse-width
`modulator
`
`Error
`signal
`ve
`
`–+
`
`vc
`
`Gc(s)
`Compensator
`
`dTs
`Ts
`t
`Fig. 1.11 Addition of control system to regulate the output voltage.
`
`Reference
`input
`
`vref
`
`(a)
`
`Hv
`
`2
`
`L
`
`1
`
`C
`
`R
`
`+–
`
`Vg
`
`Fig. 1.12 The boost converter:
`(a) ideal converter circuit, (b) output
`voltage V vs. transistor duty cycle D.
`
`(b)
`
`V
`
`5Vg
`4Vg
`3Vg
`2Vg
`Vg
`0
`
`0
`
`0.2
`
`0.4
`
`0.6
`
`0.8
`
`1
`
`D
`
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`Page 9 of 70
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`1.2 Several Applications of Power Electronics
`
`7
`
`2 1
`
`–
`
`vs(t)
`
`+ v(t) –
`
`Load
`
`t
`
`+
`
`1 2
`
`+–
`
`Vg
`
`(a)
`
`(b)
`
`vs(t)
`
`Fig. 1.13 A bridge-type dc-1øac inverter: (a) ideal inverter circuit, (b) typical pulse-width-modulated switch volt-
`age waveform vs(t), and its low-frequency component.
`boost converter, in which the positions of the inductor and SPDT
`1.12 illustrates a circuit known as the
`
`switch are interchanged. This converter is capable of producing output voltages that are greater in magni-
`tude than the input voltage. In general, any given input voltage can be converted into any desired output
`voltage, using a converter containing switching devices embedded within a network of reactive elements.
`Figure 1.13(a) illustrates a simple dc–1øac inverter circuit. As illustrated in Fig. 1.13(b), the
`
`switch duty cycle is modulated sinusoidally. This causes the switch output voltage v
`(
`) to contain a low-
`t
`s
`
`L–C filter cutoff frequency
` is selected to pass the desired low-
`frequency sinusoidal component. The
`f
`0
`frequency components of vs(t), but to attenuate the high-frequency switching harmonics. The controller
`modulates the duty cycle such that the desired output frequency and voltage magnitude are obtained.
`
`1.2
`
`SEVERAL APPLICATIONS OF POWER ELECTRONICS
`
`The power levels encountered in high-efficiency switching converters range from (1) less than one watt,
`in dc–dc converters within battery-operated portable equipment, to (2) tens, hundreds, or thousands of
`watts in power supplies for computers and office equipment, to (3) kilowatts to Megawatts, in variable-
`speed motor drives, to (4) roughly 1000 Megawatts in the rectifiers and inverters that interface dc trans-
`mission lines to the ac utility power system. The converter systems of several applications are illustrated
`in this section.
`A power supply system for a laptop computer is illustrated in Fig. 1.14. A lithium battery pow-
`ers the system, and several dc–dc converters change the battery voltage into the voltages required by the
`loads. A buck converter produces the low-voltage dc required by the microprocessor. A boost converter
`increases the battery voltage to the level needed by the disk drive. An inverter produces high-voltage
`high-frequency ac to drive lamps that light the display. A charger with transformer isolation converts the
`ac line voltage into dc to charge the battery. The converter switching frequencies are typically in the
`vicinity of several hundred kilohertz; this leads to substantial reductions in the size and weight of the
`reactive elements. Power management is used, to control sleep modes in which power consumption is
`reduced and battery life is extended. In a distributed power system, an intermediate dc voltage appears at
`the computer backplane. Each printed circuit card contains high-density dc–dc converters that produce
`
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`Page 10 of 70
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`

`
`8
`
`Introduction
`
`iac(t)
`
`Charger
`
`PWM
`Rectifier
`
`vac(t)
`
`Inverter
`
`Display
`backlighting
`
`Buck
`converter
`
`Microprocessor
`
`Power
`management
`
`ac line input
`85–265 Vrms
`
`Lithium
`battery
`
`Boost
`converter
`
`Disk
`drive
`
`Fig. 1.14 A laptop computer power supply system.
`
`locally-regulated low voltages. Commercial applications of power electronics include off-line power sys-
`tems for computers, office and laboratory equipment, uninterruptable ac power supplies, and electronic
`ballasts for gas discharge lighting.
`Figure 1.15 illustrates a power system of an earth-orbiting spacecraft. A solar array produces
`the main power bus voltage Vbus. DC–DC converters convert Vbus to the regulated voltages required by
`the spacecraft payloads. Battery charge/discharge controllers interface the main power bus to batteries;
`these controllers may also contain dc–dc converters. Aerospace applications of power electronics include
`the power systems of aircraft, spacecraft, and other aerospace vehicles.
`Figure 1.16 illustrates an electric vehicle power and drive system. Batteries are charged by a
`converter that draws high power-factor sinusoidal current from a single-phase or three-phase ac line. The
`batteries supply power to variable-speed ac motors to propel the vehicle. The speeds of the ac motors are
`controlled by variation of the electrical input frequency. Inverters produce three-phase ac output voltages
`of variable frequency and variable magnitude, to control the speed of the ac motors and the vehicle. A
`dc–dc converter steps down the battery voltage to the lower dc levels required by the electronics of the
`system. Applications of motor drives include speed control of industrial processes, such as control of
`compressors, fans, and pumps; transportation applications such as electric vehicles, subways, and loco-
`motives; and motion control applications in areas such as computer peripherals and industrial robots.
`Power electronics also finds application in other diverse industries, including dc power supplies,
`
`Dissipative
`shunt regulator
`
`Solar
`array
`
`+
`
`vbus
`–
`
`Battery
`charge/discharge
`controllers
`
`Batteries
`
`Fig. 1.15 Power system of an earth-orbiting spacecraft.
`
`Dc-dc
`converter
`
`Dc-dc
`converter
`
`Payload
`
`Payload
`
`
`Page 11 of 70
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`

`
`1.3 Elements of Power Electronics
`
`9
`
`ac machine
`
`ac machine
`
`Inverter
`
`Inverter
`
`control bus
`
`(cid:181)P
`system
`controller
`
`Vehicle
`electronics
`
`DC-DC
`converter
`
`Low-voltage
`dc bus
`
`battery
`
`+ v
`
`b –
`
`3øac line
`
`50/60 Hz
`
`Battery
`charger
`
`Variable-frequency
`Variable-voltage ac
`
`Inverter
`
`Inverter
`
`ac machine
`
`ac machine
`
`Fig. 1.16 An electric vehicle power and drive system.
`
`uninterruptable power supplies, and battery chargers for the telecommunications industry; inverter sys-
`tems for renewable energy generation applications such as wind and photovoltaic power; and utility
`power systems applications including high-voltage dc transmission and static VAR (reactive volt-ampere)
`compensators.
`
`1.3
`
`ELEMENTS OF POWER ELECTRONICS
`
`One of the things that makes the power electronics field interesting is its incorporation of concepts from
`a diverse set of fields, including:
`•
`analog circuits
`•
`electronic devices
`•
`control systems
`•
`power systems
`• magnetics
`•
`electric machines
`•
`numerical simulation
`Thus, the practice of power electronics requires a broad electrical engineering background. In addition,
`there are fundamental concepts that are unique to the power electronics field, and that require specialized
`study.
`
`The presence of high-frequency switching makes the understanding of switched-mode convert-
`ers not straightforward. Hence, converter modeling is central to the study of power electronics. As intro-
`duced in Eq. (1.3), the dc component of a periodic waveform is equal to its average value. This ideal can
`
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`Page 12 of 70
`
`

`
`10
`
`Introduction
`
`be generalized, to predict the dc components of all converter waveforms via averaging. In Part I of this
`book, averaged equivalent circuit models of converters operating in steady state are derived. These mod-
`els not only predict the basic ideal behavior of switched-mode converters, but also model efficiency and
`losses. Realization of the switching elements, using power semiconductor devices, is also discussed.
`Design of the converter control system requires models of the converter dynamics. In Part II of
`this book, the averaging technique is extended, to describe low-frequency variations in the converter
`waveforms. Small-signal equivalent circuit models are developed, which predict the control-to-output
`and line-to-transfer functions, as well as other ac quantities of interest. These models are then employed
`to design converter control systems and to lend an understanding of the well-known current-programmed
`control technique.
`The magnetic elements are key components of any switching converter. The design of high-
`power high-frequency magnetic devices having high efficiency and small size and weight is central to
`most converter technologies. High-frequency power magnetics design is discussed in Part III.
`Pollution of the ac power system by rectifier harmonics is a growing problem. As a result, many
`converter systems now incorporate low-harmonic rectifiers, which draw sinusoidal currents from the util-
`ity system. These modern rectifiers are considerably more sophisticated than the conventional diode
`bridge: they may contain high-frequency switched-mode converters, with control systems that regulate
`the ac line current waveform. Modern rectifier technology is treated in Part IV.
`Resonant converters employ quasi-sinusoidal waveforms, as opposed to the rectangular wave-
`forms of the buck converter illustrated in Fig. 1.9. These resonant converters find application where high-
`frequency inverters and converters are needed. Resonant converters are modeled in Part V. Their loss
`mechanisms, including the processes of zero-voltage switching and zero-current switching, are dis-
`cussed.
`
`REFERENCES
`
`[1]
`
`[2]
`
`[3]
`
`[4]
`
`[5]
`
`[6]
`
`[7]
`
`W. E. NEWELL, “Power Electronics—Emerging from Limbo,” IEEE Power Electronics Specialists Confer-
`ence, 1973 Record, pp. 6-12.
`
`R. D. MIDDLEBROOK, “Power Electronics: An Emerging Discipline,” IEEE International Symposium on
`Circuits and Systems, 1981 Proceedings, April 1981.
`
`R. D. MIDDLEBROOK, “Power Electronics: Topologies, Modeling, and Measurement,” IEEE International
`Symposium on Circuits and Systems, 1981 Proceedings, April 1981.
`
`S. CUK, “Basics of Switched-Mode Power Conversion: Topologies, Magnetics, and Control,” in Advances
`in Switched-Mode Power Conversion, vol. 2, pp. 279--310, Irvine: Teslaco, 1981.
`
`N. MOHAN, “Power Electronics Circuits: An Overview,” IEEE IECON, 1988 Proceedings, pp. 522-527.
`
`B. K. BOSE, “Power Electronics—A Technology Review,” Proceedings of the IEEE, vol. 80, no. 8, August
`1992, pp. 1303-1334.
`
`M. NISHIHARA, “Power Electronics Diversity,” International Power Electronics Conference (Tokyo), 1990
`Proceedings, pp. 21-28.
`
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`Ch6.fm Page 131 Wednesday, May 9, 2001 10:49 AM
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`6
`Converter Circuits
`
`We have already analyzed the operation of a number of different types of converters: buck, boost,
`C
`uk, voltage-source inverter, etc. With these converters, a number of different functions can
`buck–boost,
`be performed: step-down of voltage, step-up, inversion of polarity, and conversion of dc to ac or vice-
`versa.
`
`It is natural to ask, Where do these converters come from? What other converters occur, and
`what other functions can be obtained? What are the basic relations between converters? In this chapter,
`several different circuit manipulations are explored, which explain the origins of the basic converters.
`Inversion of source and load transforms the buck converter into the boost converter. Cascade connection
`C
`of converters, and simplification of the resulting circuit, shows how the buck–boost and
`uk converters
`are based on the buck and the boost converters. Differential connection of the load between the outputs
`of two or more converters leads to a single-phase or polyphase inverter. A short list of some of the better
`known converter circuits follows this discussion.
`Transformer-isolated dc–dc converters are also covered in this chapter. Use of a transformer
`allows isolation and multiple outputs to be obtained in a dc-dc converter, and can lead to better converter
`optimization when a very large or very small conversion ratio is required. The transformer is modeled as
`a magnetizing inductance in parallel with an ideal transformer; this allows the analysis techniques of the
`previous chapters to be extended to cover converters containing transformers. A number of well-known
`isolated converters, based on the buck, boost, buck–boost, single-ended primary inductance converter
`C
`uk, are listed and discussed.
`(SEPIC), and
`Finally, the evaluation, selection, and design of converters to meet given requirements are con-
`sidered. Important performance-related attributes of transformer-isolated converters include: whether the
`transformer reset process imposes excessive voltage stress on the transistors, whether the converter can
`supply a high-current output without imposing excessive current stresses on the secondary-side compo-
`nents, and whether the converter can be well-optimized to operate with a wide range of operating points,
`
`131
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`+ V –
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`L
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`1
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`2
`
`C
`
`R
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`132
`
`Converter Circuits
`
`+–
`
`Vg
`
`Fig. 6.1 The basic buck converter.
`
`. Switch utilization is a simplified figure-of-merit that mea-
` and
`that is, with large tolerances in
`P
`V
`load
`g
`sures the ratio of the converter output power to the total transistor voltage and current stress. As the
`switch utilization increases, the converter efficiency increases while its cost decreases. Isolated convert-
`ers with large variations in operating point tend to utilize their power devices more poorly than noniso-
`lated converters which function at a single operating point. Computer spreadsheets are a good tool for
`optimization of power stage designs and for trade studies to select a converter topology for a given appli-
`cation.
`
`6.1
`
`CIRCUIT MANIPULATIONS
`
`The buck converter (Fig. 6.1) was developed in Chapter 1 using basic principles. The switch reduces the
`voltage dc component, and the low-pass filter removes the switching harmonics. In the continuous con-
`
`
`
`duction mode, the buck converter has a conversion ratio of M = D
`. The buck converter is the simplest and
`most basic circuit, from which we will derive other converters.
`
`6.1.1
`
`Inversion of Source and Load
`
`Let us consider first what happens when we interchange the power input and power output ports of a con-
`verter. In the buck converter of Fig. 6.2(a), voltage
`
` is applied at port 1, and voltage V
` appears at port
`V
`1
`2
`2. We know that
`
`V2 = DV1
`
`(6.1)
`
`This equation can be derived using the principle of inductor volt-second balance, with the assumption
`that the converter operates in the continuous conduction mode. Provided that the switch is realized such
`that this assumption holds, then Eq. (6.1) is true regardless of the direction of power flow.
`So let us interchange the power source and load, as in Fig. 6.2(b). The load, bypassed by the
`capacitor, is connected to converter port 1, while the power source is connected to converter port 2.
`Power now flows in the opposite direction through the converter. Equation (6.1) must still hold; by solv-
`
`ing for the load voltage V
`, one obtains
`1
`
`V1 = 1
`D V2
`
`(6.2)
`
`So the load voltage is greater than the source voltage. Figure 6.2(b) is a boost converter, drawn back-
`
`wards. Equation 6.2 nearly coincides with the familiar boost converter result, M
`
`(D
`
`) = 1/D
`
`, except that D
`
`is replaced by D
`.
`Since power flows in the opposite direction, the standard buck converter unidirectional switch
`
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`6.1 Circuit Manipulations
`
`133
`
`(a)
`
`Port 1
`
`1
`
`Port 2
`
`L
`
`+ V
`
`2
`
`–
`
`2
`
`+ V
`
`1
`
`–
`
`+–
`
`Power flow
`
`+–
`
`+–
`
`Port 2
`
`L
`
`+ V
`
`2
`
`–
`
` Port 2
`
`L
`
`+ V
`
`2
`
`–
`
`2
`
`Power flow
`
`Power flow
`
`Port 1
`
`1
`
`+ V
`
`1
`
`–
`
`Port 1
`
`+ V
`
`1
`
`–
`
`Fig. 6.2 Inversion of source and
`load transforms a buck converter
`into a boost converter: (a) buck con-
`verter, (b) inversion of source and
`load, (c) realization of switch.
`
`(b)
`
`(c)
`
`realization cannot be used with the circuit of Fig. 6.2(b). By following the discussion of Chapter 4, one
`finds that the switch can be realized by connecting a transistor between the inductor and ground, and a
`diode from the inductor to the load, as shown in Fig. 6.2(c). In consequence, the transistor duty cycle
`D
`becomes the fraction of time which the single-pole double-throw (SPDT) switch of Fig. 6.2(b) spends in
`
`
`
`position 2, rather than in position 1. So we should interchange D with its complement D
` in Eq. (6.2), and
`the conversion ratio of the converter of Fig. 6.2(c) is
`
`V1 = 1
`D' V2
`
`(6.3)
`
`Thus, the boost converter can be viewed as a buck converter having the source and load connections
`exchanged, and in which the switch is realized in a manner that allows reversal of the direction of power
`flow.
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`+ V –
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`Converter 2
`
`= M 2(D)
`
`VV
`
`1
`
`+ V
`
`1
`
`–
`
`D
`
`134
`
`Converter Circuits
`
`Converter 1
`
`V1
`Vg
`
`= M 1(D)
`
`+–
`
`Vg
`
`Fig. 6.3 Cascade connection of converters.
`
`6.1.2
`
`Cascade Connection of Converters
`
`Converters can also be connected in cascade, as illustrated in Fig. 6.3 [1,2]. Converter 1 has conversion
`ratio
`(
`
`), such that its output voltage V
` is
`M
`D
`1
`1
`
`V1 = M 1(D)Vg
`
`(6.4)
`
`This voltage is applied to the input of the second converter. Let us assume that converter 2 is driven with
`the same duty cycle
` applied to converter 1. If converter 2 has conversion ratio
`
`
`(D), then the output
`D
`M
`2
`voltage
` is
`V
`
`(6.5)
`
`(6.6)
`
`Substitution of Eq. (6.4) into Eq. (6.5) yields
`
`V = M 2(D)V1
`
`= M(D) = M 1(D)M 2(D)
`
`VV
`
`g
`
`Hence, the conversion ratio
`ratios
`
`(D
`
`) and M
`(
`).
`M
`D
`1
`2
`Let us consider the case where converter 1 is a buck converter, and converter 2 is a boost con-
`verter. The resulting circuit is illustrated in Fig. 6.4. The buck converter has conversion ratio
`
`) of the composite converter is the product of the individual conversion
`
`
`
`M(D
`
`
`
`(6.7)
`
`(6.8)
`
`V1
`Vg
`
`= D
`
`=
`
`1
`1 – D
`
`VV
`
`1
`
`The boost converter has conversion ratio
`
`So the composite conversion ratio is
`
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`6.1 Circuit Manipulations
`
`135
`
`+ V –
`
`+ V –
`
`L1
`
`L2
`
`2
`
`1
`
`C2
`
`R
`
`+ V
`
`1
`
`–
`
`C1
`
`1
`
`2
`
`+–
`
`Vg
`
`{{
`Buck converter
`Boost converter
`
`Fig. 6.4 Cascade connection of buck converter and boost converter.
`
`L1
`
`L2
`
`2
`
`1
`
`C2
`
`R
`
`1
`
`2
`
`+–
`
`Vg
`
`+ V –
`
`1
`
`L
`
`iL
`
`2
`
`2
`
`1
`
`+–
`
`Vg
`
`Fig. 6.5 Simplification of the cascaded buck and boost converter circuit of Fig. 6.4: (a) removal of capacitor C1,
`(b) combining of inductors L1 and L2.
`
`(6.9)
`
`= D
`1 – D
`
`VV
`
`g
`
`The composite converter has a noninverting buck–boost conversion ratio. The voltage is reduced when
`
` < 0.5, and increased when D
` > 0.5.
`D
`, along with
` and
`The circuit of Fig. 6.4 can be simplified considerably. Note that inductors L
`
`L
`2
`1
`, form a three-pole low-pass filter. The conversion ratio does not depend on the number of
`capacitor
`C
`1
`poles present in the low-pass filter, and so the same steady-state output voltage should be obtained when
`a simpler low-pass filter is used. In Fig. 6.5(a), capacitor
` is removed. Inductors
` and
` are now in
`C
`L
`L
`1
`1
`2
`series, and can be combined into a single inductor as shown in Fig. 6.5(b). This converter, the noninvert-
`ing buck–boost converter, continues to exhibit the conversion ratio given in Eq. (6.9).
`The switches of the converter of Fig. 6.5(b) can also be simplified, leading to a negative output
`voltage. When the switches are in position 1, the converter reduces to Fig. 6.6(a). The inductor is con-
`nected to the input source
`, and energy is transferred from the source to the inductor. When the
`V
`g
`
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`+ V –
`
`iL
`
`+–
`
`Vg
`
`(b)
`
`+ V –
`
`136
`
`Converter Circuits
`
`iL
`
`+–
`
`Vg
`
`(a)
`
`Fig. 6.6 Connections of the circuit of Fig. 6.5(b): (a) while the switches are in position 1, (b) while the switches
`are in position 2.
`
`+ V –
`
`(b)
`
`iL
`
`+–
`
`Vg
`
`+ V –
`
`iL
`
`+–
`
`Vg
`
`(a)
`
`Fig. 6.7 Reversal of the output voltage polarity, by reversing the inductor connections while the switches are in
`position 2: (a) connections with the switches in position 1, (b) connections with the switches in position 2.
`
`switches are in position 2, the converter reduces to Fig. 6.6(b). The inductor is then connected to the
`load, and energy is transferred from the inductor to the load. To obtain a negative output, we can simply
`reverse the polarity of the inductor during one of the subintervals (say, while the switches are in position
`2). The individual circuits o