`
`[EEE TRANSACTIONS ON
`
`
`
`A PUBLICATION OF THE IEEE INDUSTRIAL ELECTRONICS SOCIETY
`
`FEBRUARY 1997
`
`VOLUME 44
`
`NUMBER1
`
`ITIED6
`
`(ISSN 0278-0046)
`
`SPECIAL SECTION ON ELECTRIC VEHICLE TECHNOLOGY
`
`Guest Editorial 000...EEE ECE E EEE EEE EEE E CEE CEE EDEN EE DES ES EE EEE CLC. Chan
`An Overview of Power Electronics in Electric Vehicles ........ 0.0.0. c ccc ec ce eee eee ees C. C. Chan and K. T. Chau
`Advanced Concepts in Electric Vehicle Design ........... H. Shimizu, J. Harada, C. Bland, K. Kawakami, and L. Chan
`Propulsion System Design of Electric and Hybrid Vehicles ................ M. Ehsani, K. M. Rahman, and H. A. Toliyat
`Novel Motors and Controllers for High-Performance Electric Vehicle with Four In-Wheel Motors ...................++-
`beeen eee nett e bbe eee M. Terashima, T. Ashikaga, T. Mizuno, K. Natori, N. Fujiwara, and M. Yada
`Axial Flux Machines Drives: A New Viable Solution for Electric Cars ........... F. Profumo, Z. Zhang, and A. Tenconi
`A Permanent Magnet Hysteresis Hybrid Synchronous Motor for Electric Vehicles............ M,. A. Rahman and R. Qin
`A Torque Controller Suitable for Electric Vehicles 2.0.0.0... 0... ccc ce cece ee ee eennee nn eer ees
`Ln e eee bene bene e dense ete ene ben eee n en tnens N. Mutoh, S. Kaneko, T. Miyazaki, R. Masaki, and §. Obara
`Analysis of Anti-Directional-Twin-Rotary Motor Drive Characteristics for Electric Vehicles ................2..:eeeeee ees
`Leen eee eee ne deen ed eee eee tenn ee A. Kawamura, N. Hoshi, T. W. Kim, T. Yokoyama, and T. Kume
`Resonant Snubber-Based Soft-Switching Inverters for Electric Propulsion Drives............. 0... cc see c eee e eee J.-S, Lai
`Design of Interface Circuits With Electrical Battery Models ...............e ee ce eee een eee ees Y.-H. Kim and H.-D. Ha
`
`i
`3
`14
`19
`
`28
`39
`46
`
`54
`
`64
`71
`81
`
`REGULAR PAPERS
`
`87
`Improved Modulation Techniques for PWM—VSI Drives............666. F. Blaabjerg, J. K. Pedersen, and P. Thoegersen
`96
`Optimal Control of Three-Level PWM Inverters.......... 0.0... ee eres S. Haldsz, A. A. M. Hassan, and B. T. Huu
`A New A-Level High Voltage Inversion System ....... cc sce ee tence eee eet e tenn nee n tenes B.-S. Suh and D.-S. Hyun—107
`Basic Considerations and Topologies of Switched-Mode Assisted Linear Power Amplifiers .......0 00.0... 0c eee cere eee
`nee Ente n ee eee nae Eee H. Ertl, J. W. Kolar, and F.C. Zach=116
`Robust Temperature Control for Microwave Heating of Ceramics ......... 0600. c cece eect eens G. O. Beale
`124
`
`LETTERS TO THE EDITOR
`
`Automatic Color Grading of Ceramic Tiles Using Machine Vision ............ 0. cece ener eee nets
`CE EER REELED E NEED ren DEE ee a EEE EES C. Boukouvalas, J. Kittler, R. Marik, and M. Petrou
`Application of a PLL and ALL Noise Reduction Process in Optical Sensing Systems ............. 0... eeeee ee eeee eee
`LE REEL EERE Ren EEE EEE E ENED een nnn Eee eee e Eee D. F. Clark and T. J. Moir=136
`Analysis of Unlocked and Acquisition Operation of a Phase-Locked Speed Control System ............05:.s6ee scenes
`a C. A. Karybakas and T. L. Laopoulos—138
`A Programmable Cascaded Low-Pass Filter-Based Flux Synthesis for a Stator Flux-Oriented Vector-Controlled Induction
`Motor Drive... 00... ccc EERE EEE EEE EER nn EEE Een EES B. K. Bose and N. R. Patel
`
`140
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`132
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`INTEL 1216
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`INTEL 1216
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`E. J. KENNEDY
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`ii
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`

`

`IBEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL.44, NO. 1, FEBRUARY 1997
`
`l
`
`Guest Editorial
`Special Section on Electric Vehicle Technology
`
`
`rAM VERY GLAD to be able to present a Special Sec-
`
`tion on Electric Vehicle Technology in this issue of our
`TRANSACTIONS. Onthe eve of going to press with this special
`section, | was confronted by the following data. As recently as
`1950, there were only 53 million motor vehicles registered in
`the world, and their exhaust emissions could still be tolerated
`because of their relatively modest effects. In 1992, our planet
`had well over half a billion cars and trucks! By the year 2000,
`their number will exceed one billion! If they were all to be
`powered by gasoline and diesel oil, our world could not stand
`it. Therefore, one of the most pressing demandsof our time is
`an alternative clean, efficient, intelligent, and environmentally
`friendly urban transportation system. Electric vehicles offer
`a solution for improving air quality, reducing reliance on
`fossil fuels, and they are energy efficient. Furthermore, electric
`vehicles will be more intelligent
`to improve traffic safety
`and road utilization.
`In this special section,
`there are ten
`papers authored by researchers in academia and industry.
`These papers address the state of the art as well as some
`of the key issues and key technology of electric vehicles.
`The first paper, by Chan and Chau, provides an overview of
`current electric vehicle technology and the challenges ahead.
`The second paper, by Shimizu, Harada, Bland, Kawakami, and
`Chan, describes a unique ECO Vehicle Project in Japan with
`an in-wheel motor drive system, a hollow load floor which
`accommodates the batteries, and a new battery management
`system. The third paper, by Ehsani, Rahman, and Toliyat,
`addresses the system design philosophiesof electric and hybrid
`vehicle propulsion systems. The dynamics are studied .in
`an attempt
`to find an optimal
`torque-speed profile for the
`Publisher Item Identifier S 0278-0046(97)00066-X.
`
`electric propulsion. The fourth paper, by Terashima, Ashikaga,
`Mizuno, Natori, Fujiwara, and Yada, describes unique in-
`wheel motors for a high-performance experimental electric
`vehicle. The fifth paper, by Profumo, Zhang, and Tenconi,
`describes alternative axial flux induction or synchronous in-
`wheel motors forelectric vehicles. The sixth paper, by Rahman
`and Qin, presents the design, analysis, and PWMvectorcontrol
`of a hybrid permanent magnet hysteresis synchronous motor
`for electric vehicle application. The seventh paper, by Mutoh,
`Kaneko, Miyazaki, Masaki, and Obara, describes a torque
`controller which suits electric vehicle operating conditions.
`The eighth paper, by Kawamura, Hoshi, Kim, Yokoyama, and
`Kume, proposes an anti-directional-twin-rotary motordrive as
`anew powertrain for electric vehicles. The ninth paper, by Lai,
`presents resonant snubber-based soft-switching inverters for
`electric propulsion drives, which have superior performancein
`efficiency improvement, EMI reduction, and du/dt reduction.
`The last paper, by Kim and Ha, deals with the design of
`interface circuits with electrical battery models. On the whole,
`the above ten papers address important technology for the next
`century. They deal with the key componentsin electric vehicle
`development, namely system design philosophy, various op-
`tions of electric motor drives and energy management. These
`are challenges for our profession. The 21st century will be the
`environmental century, and electric vehicles will be the major
`means of urban transportation.
`
`C. C. CHAN, Guest Editor
`Dept. Electrical & Electronic Engineering
`University of Hong Kong
`Hong Kong
`
`
`
`0278-0046/97$10.00 © 1997 TEER
`
`iii
`
`

`

`This material may be protected by Copyright law (Title 17 U.S. Code)
`
`

`

`ERTL et al: BASIC CONSIDERATIONS AND TOPOLOGIES OF SWITCHED-MODE ASSISTED LINEAR POWER AMPLIFIERS
`
`117
`
`
`SWITCHED-MODE CURRENT DUMPING SYSTEM
`
`| |
`
`I | |
`
`
`
`ee
`
`LINEAR AMPLIFIER
`
`
`
`
`
`"
`
`Fig. 2. Circuit diagram of a switched-mode assisted linear power amplifier.
`
`the linear
`(current dumping). In the ideal (stationary) case,
`power amplifier only has to deliver the ripple of the class D
`stage which significantly reduces its power losses. Contrary to
`a (passive) outputfilter of a conventional switching amplifier,
`the linear amplifier of the proposed concept also reduces low-
`frequency distortions and subharmonic components. It has to
`be pointed out, however, that a very low output impedance of
`the linear system part is of paramount importance in order to
`get a high noise rejection. This circumstance has to be consid-
`ered by an appropriate design of the linear amplifier circuitry
`and feedback system. Furthermore, the switched-mode assisted
`linear amplifier only allows a significant reduction but not a
`complete loss elimination as an idealized class D amplifier.
`Therefore, considering the losses, the proposed system can be
`seen as an intermediate solution between pure linear and pure
`class D power amplifiers. As an advantage of the proposed
`system, it has to be mentioned that the dynamic response of the
`whole system is determined by the linear stage and, therefore,
`not influenced by an output filter.
`
`Il. SYSTEM CONTROL—CALCULATION OF POWER LOSSES
`
`The guidance of the class D part is realized by a current
`controller whose reference value is identical to the current
`through the load. Thus, only the control error and the ripple
`have to be delivered by the linear stage. Instead of an explicit
`subtraction of reference value (load current 7) and actual
`value (class D stage output current igw), the calculation of
`the controlling quantity can be done in an implicit manner
`by direct measurement of the linear stage output current
`tLIN- In the simplest case,
`the current controller can be a
`hysteresis controller (Fig. 2), which results in a nonconstant
`switching frequency within the fundamental period of the
`amplified signal. As an alternative, a pulse width modulator
`(PWM) with a superimposed linear current controller, or other
`types of current controllers being well-known from switched-
`mode power supplies (e.g., conductance control), can be
`applied. The usage of a PWM allows a switching frequency
`being constant which is, however, of not essential significance
`for this application, as stated before. An advantage of the
`hysteresis controller is its inherent overmodulation ability
`which yields a more efficient utilization of the dc supply
`
`voltage +U. On the other hand, PWM current controllers with
`their well-defined switching instants. allow an easier extension
`
`of the class D stage to a parallel arrangement being operated in
`an optimum phase-shifted manner, in order to reduce the total
`ripple current or increase the effective switching frequency,
`respectively. However,
`it should be mentioned that
`there
`exist solutions for two hysteresis-controlled converter branches
`(arranged in parallel) where a suboptimal phase shift can be
`achieved in a very simple way (Section V).
`- In the following, the losses of the lmear amplifier stage shall
`be calculated for the case that a hysteresis current controller
`with a constant tolerance band AI is applied. It is assumedthat
`the load current 2 and the output voltage wu can be treated as
`constant within the switching interval 7, or that there exists
`a sufficient signal-to-switching frequency ratio, respectively
`(Fig. 3). Furthermore, the powertransistors are assumed to be
`ideal (neglection of delay times, on-state voltages, etc.), Also,
`de supply voltage variations are neglected.
`Switching Frequency: With the assumptions given above,
`the output voltage « (averaged within a pulse interval 7’) ts
`determined by the duty cycle 6. If we apply the definition m =
`u/U for normalizing the output voltage (m= —1---+1), we
`get
`
`6
`
`—itu/U_ itm
`a ee
`
`a
`
`According to uy, = L digw/dt,
`fs = 1/T can be calculated
`
`the switching frequency
`
`fs = fs,max . (1 _ m?) with
`
`fs;max =
`
`U
`
`2L-Al
`
`(2)
`
`Power Losses: The powerlosses of the linear stage depend
`on its operating mode, where one has to distinguish between
`class A (linear amplifier with quiescent current eliminating
`crossoverdistortions) and class B (without quiescent current)
`mode. The following table gives the local losses (i.e., the losses
`averaged within a switching period T) of the upper transistor
`TU and the lowertransistor T'Z of the linear stage, where it
`is assumed that for class A mode the quiescent current is as
`small as possible (Iq = lg,min = AI/4) (see Fig. 3(e)).
`For fg = AI/4, the class A mode losses are twice the
`losses of the class B mode. Thetotal transistor losses pr
`are not dependent on the modulation index m and, therefore,
`the local transistor losses pr also represent the global losses
`(i.e., the losses averaged within the fundamental period of the
`amplified signal) pr = Pr.
`
`

`

`118
`
`IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 44, NO. 1, FEBRUARY 1997
`
`
`
`
`
`(a)
`
`(b)
`
` )
`
`—}al[~ Ly
`
`(d)
`
`wn
`
`—3al
`in 2
`
`aN
`
`amplitude A/. However, for a defined maximum switching
`frequency fsmax,
`this would result
`in the usage of a high
`value of the inductance ©. On the other hand, a higher value
`of E reduces the power bandwidth fp of the switched-mode
`current dumpingstage. If we normalize A/ with respectto the
`value U/ R (maximum load current, resistive load Z2,=R
`assumed), ie., ka = AI/(U/R), we receive from (3):
`
`U?
`1
`U-AT
`= Rh
`Pr=—7
`for a class B linearstage (ka --- normalized ripple amplitude).
`The power bandwidth of the current dumping stage can be
`defined as fg = R/(2xL) (if full output voltage utilization
`has to be achieved without overmodulation). Using (2), this
`leads to
`
`(4)
`
`fS,max nT
`I
`ka
`
`(5)
`
`This shows clearly that the switching frequency-to-band-
`width ratio is linked to the losses of the linear system. For a
`given maximum switching frequency and a required power
`bandwidth of the whole amplifier the current ripple (and,
`therefore, the powerlosses) are fixed. However, there are some
`possibilities to overcomethis fundamentallimitation: (1) usage
`of a higher supply voltage for the switching stage (reduced
`modulation index); (2) splitting up the current dumping stage
`into several parallel branches operated in a phase shifted
`manneror application of a three-level topology (simultaneous
`reduction of Z and of AJ); and (3) higher order-type coupling
`impedanceof the switching stage (e.g., L > LCL). However,
`it has to be noted that the described effect only limits the
`power bandwidth of the current dumping stage and not ofthe
`whole amplifier system whose dynamic response (especially
`the slew rate) is determined by the linear stage. (Full power
`operation of the amplifier above fp, however, can cause a
`thermal overload of the linear stage.)
`
`III. DIMENSIONING EXAMPLE—SIMULATION RESULTS
`
`In the following, a prototype system of a 1-kVA switched-
`mode assisted amplifier system with the nominal values U =
`+ 80 V, R = 2.5 Q (resistive load Z;, = R; RMS value of
`the sinusoidal. output voltage: 50 V), fg = 10 kHz, fs, max =
`200 kHz shall be calculated briefly.
`According to (5), we receive ka =0.157, ie., a current
`ripple of AJ = 5.A anda total power loss Py = 100/200
`Influence of the Switching Frequency on the Amplifier Band-
`W (class B/class A mode). As can be seen from Fig. 4(b), the
`width: According to (3), shown at the bottom of the page,
`powerlosses of the proposed system are far beneath the losses
`the demand for low power losses implies a small ripple
`
`
`Fig. 3. Voltage and current waveforms of a switched-modeassisted linear
`power amplifier. (a) Switching stage output voltage. (b) Output currents of
`the class D system and of the linear stage. (c) and (d) Transistor currents for
`class B modeofthe linear amplifier part. (e) Currents for class A mode.
`
`class B
`class A
`
`
`tTUavg = ITLavg =
`gAl
`$Al
`
`
`pru =(U-4)-iruavg=|UAT-3(L-m) UAL: 4}(1—m) (3)
`pre =(U +): trtavg =
`UAT-4(1+m)
`UAI-4(1+m)
`Pp = pru + prt =
`|
`UAI- 4
`UAI-4
`
`
`
`
`
` .
`
`plotaal
`.
`-
`TEN,
`© PachEK B
`
`a~ Slt
`
`

`

`ERTLet al: BASIC CONSIDERATIONS AND TOPOLOGIES OF SWITCHED-MODE ASSISTED LINEAR POWER AMPLIFIERS
`
`19
`
`
`+20A4
`+40A
`
`~
`
`+40A
`
`0
`
`—20A
`
`—40A—
`0
`
`T
`50us
`
`T
`100us
`
`T
`150us
`
`T
`200 us
`
`250 us
`
`(a)
`
`
`—40A
`
`0
`
`S0us
`
`100 us
`
`1
`150us
`
`F
`200 us
`
`250 us
`
`(b)
`
`Fig. 5. Simulated current wave shapes of a 1 kW switched-mode assisted
`linear poweramplifier (a) Sine wave response. (b) Pulse response (parameters:
`U = £80 V, R = 2.5Q, fg = 10 KHz, fs, max = 200 kHz, AI = 5 A).
`
`'p, tu
`
`UZ,
`
`'p,tL
`UZ
`
`
`
`1.25
`
`0.75
`
`0.50
`
`
`
`
`
`0.25
`
`
`0.00
`
`(a)
`
`
`
`
`
`
`
`
`
`
`(b)
`
`(a) MOSFET Ups /Ip-trajectories (load lines) and (b) power losses
`Fig. 4.
`of a conventional linear power amplifier and of a switched-mode assisted
`linear (SMAL) amplifier (both class B mode) for sinusoidal output voltage
`(normalized amplitude M = O/U) and different load current displacement
`factors cos y. (The losses are normalized to U?/ Z,, U ... supply voltage,
`Z 1,+++ magnitude of the complex load impedance).
`
`of conventional linear power amplifiers, especially for the case
`of nonresistive loads (e.g., the losses of a conventional linear
`amplifier would be Pp = 1 kW for M = 1 and cosy = 0.5).
`However, it has to be admitted that the losses shownin Fig. 4
`for the switched-mode assisted amplifier do not include the
`losses of the switching stage. On the other hand, the efficiency
`of switched-mode bridge topologies usually lies above 95%,
`so that the total losses of switched-mode assisted amplifiers
`would not be increased significantly.
`The current wave shapes of the simulated 1-kW amplifier
`system are shown in Fig. 5. There, the pulse response demon-
`strates the limited slew rate of the switched-mode current
`dumping system. In this case, the output current of the linear
`amplifier i,y~ not only has to compensate the ripple of the
`switching state, but also has to take over the dynamic current
`peaks (iin, therefore, cannot be’ guided completely within
`
`the tolerance band AJ). This effect results in increased power
`losses of the linear stage.
`
`IV. LINEAR STAGE DESIGN—OUTPUT IMPEDANCE
`
`A very low magnitude Z of the high-frequency output
`impedance Z of the linear stage is of fundamental importance
`for a high output voltage signal-to-noise ratio (SNR) of the
`system because the ripple current AJ of the switching stage
`generates a noise voltage Z - AI. If we strive for an SNR of,
`e.g., >80 dB, for the system simulated in the previous section
`an output impedance of Z < 2U/(AI-108N®/?°) = 3 mQ has
`to be guaranteed, which complicates the design of the linear
`stage.
`Today, the output stages of linear amplifiers usually are real-
`ized by using power MOSFETsource followers[6]. The output
`impedance of source followers is defined by the transconduc-
`tance gm of, e.g., the upper transistor and is also influenced
`by the output impedance R; of the driver stage (Fig. 6) in the
`upper frequency region.
`In general, the transconductance of power MOSFET’s is far
`too low to get an output impedance in the desired milliohms-
`range (Fig. 7—open loop: Z ~ 0.8 Q for the assumed
`maximum switching frequency fs,max = 200 kHz). Actually,
`
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`Frequency response.
`
`Fig. 7. Output impedance of the linear amplifier stage.
`
`————»
`
`f
`
`this fact is not of primary significance because the effective
`output impedance is reduced by the loop gain of the feedback
`system (introduced originally to improve the linearity of
`the amplifier). For the described system, we have to adjust
`the leop gain to ~ 50 dB at 200 kHz. A higher
`loop
`gain would allow to further increase the SNR, but would
`reduce the stability margin of the linear amplifier system.
`The frequency response of the amplifier mainly is determined
`by that of the voltage booster stage (Fig. 8) because the
`output current buffer usually shows a much higher bandwidth
`due to the application of MOSFET’s and a high-frequency
`driver stage using bipolar video transistors. Contrary to con-
`ventional
`linear power amplifiers,
`the frequency design of
`the voltage booster has to be performed not only regarding
`the power bandwidth, but also has to consider the switching
`frequency of the current dumping stage in order to get the
`described reduction of the output impedance. Therefore, we
`use a symmetric wide-band push-pull differential amplifier
`arrangement with a relatively low gain of 10 (defined by the
`internal current feedback resistors) which, on the otherside,
`is high enough to use a conventional op-amp as feedback
`amplifier (output voltage swing +7 V). This op-amp is used
`as a Pl-controller to increase the loop gain (and, therefore,
`reduce the switching frequency noise components)
`in the
`region of lower frequencies and to enhance the linearity of
`the system.
`A further improvement of the loop gain could be achieved
`by the well-known principle of splitting up the voltage booster
`into a low-frequency part with full output voltage swing (for
`amplification of the actual input signal) and a high-frequency
`small-signal path being arranged in parallel to increase the
`loop gain in the switching frequency region [7]. However,
`in any case,
`the design of the feedback loop has to be
`adopted if the load impedance shows a capacitive portion
`
`In this case,
`due to the then given additional phase shift.
`it would be more efficient
`to directly improve the output
`impedance of the current buffer stage using a feedforward
`compensation [8] or an inner feedback/feedforward corrector
`scheme as proposed in [9]. It has to be noted that, concerning
`the output
`impedance,
`the realization of the output stage
`using bipolar power transistors would probably be a better
`solution because of their higher transconductance as compared
`to MOSFET’s. On the other hand, power MOSFET’s have
`the advantage of a rectangular safe operating area which
`is of importance for the pulse response of the amplifier
`(Fig. 5(b)).
`
`-
`
`V. TOPOLOGY SURVEY
`
`Concluding the paper, we want to give a brief survey of
`further topologies of switched-mode assisted linear power
`amplifiers. Fig. 9(a}) shows a topology for reduction of the
`linear stage power losses by ripple cancellation using, e.g.,
`four switching stages atranged in parallel and operated in
`a phase-shifted manner. The-easiest way to obtain the op-
`timum phase shift
`is the application of an explicit PWM
`with a superimposed linear current controller instead of the
`hysteresis current controller described so far. In this case,
`however, special controller extensions have to be added to
`guarantee a uniform current sharing between the several con-
`verter branches [10]. But, also, if hysteresis current controllers
`are applied (quasi-) optimal phase-shifted output currents of
`the single converter branches can be realized using coupled
`(or partially common) output
`inductors [11].
`If the total
`ripple amplitude of each converter branch exceeds twice
`the average output current, soft-switching can be obtained
`by adding capacitors across the switchingtransistors [12].
`The primary advantage of this structure is that the worse
`
`120
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`IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 44, NO.
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`1, FEBRUARY 1997
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`ERTL et al: BASIC CONSIDERATIONS AND TOPOLOGIES OF SWITCHED-MODE ASSISTED LINEAR POWER AMPLIFIERS
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`Fig. 8. Schematic diagram of the linear amplifier stage.
`
`switching behavior of the MOSFET body diodes does not
`further contribute to the switching losses. However, the on-
`state losses are increased by 33% due to the triangular
`current waveform and the resistive on-state characteristic of
`power MOSFET’s.
`Contrary to the parallel converter branches discussedbefore,
`a ripple reduction also can be achieved using a switching
`stage of multilevel structure (e.g., shownin Fig. 9(b), the well-
`knownthree-level converter) whichis of interest especially for
`high output voltages because switching powertransistors with
`lowerrated voltage can be used (e.g., 500 V power MOSFET’s
`instead of 1000 V types which would lower the on-sate losses
`noticeably).
`Fig. 9(c) shows a modification which is also of interest
`in the higher voltage region. P-channel power MOSFET’s
`used in the linear amplifier stage usually are available only
`with rated voltages lower than 200-500 V.If the tolerance
`band of the hysteresis current controller is modified in that
`way, i.c., the linear stage only has to support positive output
`currents, the p-channel part can be omitted. However,in this
`case, the pulse response of the whole system is not uniform
`due to the different slew rates of the rising (defined by the
`linear stage) and the falling (defined by the switching stage)
`slope.
`A freewheeling action of the relatively slow internal body
`diodes of the power MOSFET’s can be avoided in the hard-
`switching mode by using the circuit
`topology shown in
`Fig. 9(d). There, explicit fast-recovery diodes can be used. The
`two branches of the system operate in. parallel only concerning
`
`the ripple currents. Contrary to the circuit of Fig. 9(a), a very
`simple phase-shifted PMW control scheme can be applied
`because no load sharing has to be provided.
`The presented fundamental operating principle of switched-
`mode assisted linear power amplifiers can also be extended
`to isolated converter structures which are of special interest
`because this solution avoids the explicit power supply unit
`(usually a switched-mode powersupply for generating the de
`supply voltage +U being isolated from the mains). An iso-
`lated switched-mode assisted linear amplifier can be realized
`by the application of a full-bridge switching converter and
`a high-frequency isolating transformer (Fig. 9(e)). However,
`for nonresistive amplifier loads, a bidirectional power flow
`capability has to be considered and anactive “rectifier” stage
`(four bidirectional switches at the secondary side of the high-
`frequency transformer) would be necessary [13],
`[14]. The
`switched-mode stage is supplied, for example, by the rectified
`ac mains voltage, whereas an additional dc-dc converter (not
`shown in Fig. 9(e))
`is required to generate the (isolated)
`supply voltage of the linear amplifier stage (realized here
`also using a full-bridge topology). The output power of the
`de-de converter is about in the range of the losses of the
`linear part and, therefore, relatively small as compared to the
`total output power of the amplifier. A further possibility for
`achieving an isolated current dumping stage would be the
`application of a class D amplifier based on a four-quadrant
`Cuk-converter as described in [15] (Fig. 9(f)), which would
`reduce the number of switching transistors significantly as
`compared to the topology of Fig. 9(e).
`
`

`

`122
`
`IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 44, NO. 1, FEBRUARY 1997
`
`
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`(c)
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`(c)
`
`(f)
`
`Fig. 9. Further topologies of switched-modeassisted linear power amplifiers. (a) Ripple reduction by multiple bridge legs operated with a phase shift. (b)
`Ripple reduction using a three-level topology. (c) Avoiding the p-channel MOSFETofthelinearstage (high-voltage applications). (d) Ripple reduction using
`two parallel branches with explicit freewheeling diodes (e.g., Schottky-diodes). (e) Isolated topology using bidirectidnal rectification and a linear amplifier
`in full-bridge configuration. (f) Isolated topology using a four-quadrant Cuk-converter.
`
`the basic relationships of combining linear
`In this paper,
`power amplifiers with current-dumping switching amplifiers
`has been presented. Presently, a laboratorymodel of the system
`which is described and simulated in Section IV is realized.
`Measuring results, and experiences taken from the practical
`realization, will be presented in a future paper. Furthermore,
`the analysis of an extension of the proposed system applying
`a Capacitive coupling of the linear stage to the switching stage
`for a further improvement of the system efficiency is under
`preparation.
`Ts
`
`REFERENCES
`
`F. H. Raab, “Average efficiency of class-g power amplifiers,” JEEE
`Trans. ConsumerElectron., vol. 32, no. 2, pp. 145-150, 1991.
`R. W. Erickson and R. D. Middlebrook, “Origin of harmonic distortion
`in switching amplifiers,” in Proc. 4th