`
`IE‘EE‘ TRAN SACTI D N S I N
`
`
`
`A PUBLICATION OF THE IEEE INDUSTRIAL ELECTRONICS SOCIETY
`
`FEBRUARY 1997
`
`VOLUME 44
`
`NUMBER 1
`
`ITIEDB
`
`(ISSN 0278—0046)
`
`SPECIAL SECTION ON ELECTRIC VEHICLE TECHNOLOGY
`
`Guest Editorial ................................................................................................... C. C. Chan
`An Overview of Power Electronics in Electric Vehicles ...................................... C. C. Chan. and K. T. Chan
`
`Advanced Concepts in Electric Vehicle Design ........... H. Shimiza, J. Harada, C. Bland, K. Kawakami, and L. Chan
`Propulsion System Design of Electric and Hybrid Vehicles ................ M. Ehsam', K. M. Rahman, and H. A. Toliyat
`Novel Motors and Controllers for HighuPerformance Electric Vehicle with Four In—Wheel Motors ......................
`.................................... 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. Tencom’
`A Permanent Magnet Hysteresis Hybrid Synchronous Motor for Electric Vehicles ............ M. A. Rahmah and R. Qin
`A Torque Controller Suitable for Electric Vehicles ......................................................................... ,
`.................................................. N. Matoh, S. Kane/<0, T. Miyazaki, R. Masalci, and S. Obara
`
`Analysis of Anti-Directional—Twin—Rotary Motor Drive Characteristics for Electric Vehicles .............................
`............................................... A. Kawamura, N. Hashi, T. W. Kim, T. Yokoyama, and T. Kame
`
`Resonant Snubber—Based Soft-Switching Inverters for Electric Propulsion Drives ................................ J.-S. Lai
`Design of Interface Circuits With Electrical Battery Models .................................... Y.-H. Kim and H. -D. Ha
`
`REGULAR PAPERS
`
`Improved Modulation Techniques for PWMwVSI Drives ............... F. Blaabjerg, J. K. Pedersen, and P. Thoegersen
`Optimal Control of ThreeLevel PWM Inverters .............................. S Halasz, A. A. M. Hassan, and B. T. Huu
`A New N— Level High Voltage Inversion System ............................................... B -.S Sah and D. S Hyrm
`Basic Considerations and Topologies of SwitchedMode Assisted Linear Power Amplifiers ..............................
`........................................................................ H Ertl J. W K01ar,aadF C Zach
`
`Robust Temperature Control for Microwave Heating of Ceramics ............................................ G 0 Beale
`
`LETTERS TO THE EDITOR
`
`Automatic Color G1ading of Ceramic Tiles Using Machine Vision ........................................................
`.......................................................... C. Boakouvalas, J. Kittler R. Marik andM. Petma
`
`Application of a PLL and ALL Noise Reduction Process in Optical Sensing Systems ....................................
`................................................................................. D. F. Clark and T. J. Moir
`
`Analysis of Unlocked and Acquisition Operation of a Phase—Locked Speed Control System .............................
`...... ..................................... CA.KarybakasandT.L.Laopoalos
`A Programmable Cascaded Low—Pass Filter—Based Flux Synthesis for a Stator Flux—Oriented Vector—Controlled Induction
`Motor Drive
`.............................................................. B. K. Bose andN. R. Patel
`
`1
`3
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`39
`46
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`54
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`64
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`71
`8]
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`87
`96
`107
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`ll6
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`124
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`132
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`136
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`138
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`140
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`i
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`INTEL 1216
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`INTEL 1216
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`

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`IEEE INDUSTRIAL ELECTRONICS SOCIETY
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`IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS
`EditOI‘nifl-Cllief
`JOACHIM HOLTz
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`University of Wuppertal
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`ii
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`

`

`IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 44, NO, 1, FEBRUARY 1997
`
`1
`
`Guest Editorial
`
`Special Section on Electric Vehicle Technology
`
`
`AM VERY GLAD to be able to present a Special Sec—
`
`5
`tion on Electric Vehicle Technology in this issue of our
`TRANSACTIONS. On the eve of going to press with this special
`section, I 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 demands of 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 philosophies of 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 for electric vehicles. The sixth paper, by Rahrnan
`and Qin, presents the design, analysis, and PWM vector control
`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 motor drive as
`anew power train for electric vehicles. The ninth paper, by Lai,
`presents resonant snubber-based soft—switching inverters for
`electric propulsion drives, which have superior performance in
`efficiency improvement, EMI reduction, and d’U/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 components in electric vehicle
`development, namely system design philosophy, various op—
`tions of electric motor drives and energy management. These
`are challenges for our profession. The 2lst 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 IEEE
`
`iii
`
`

`

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

`

`ERTL er (1].: BASIC CONSIDERATIONS AND TOPOLOGIES OF SWITCHED-MODE ASSISTED LINEAR POWER AMPLIFIERS
`
`ll7
`
`
`SWITCHED—MODE CURRENT DUMPING SYSTEM
`
`| l
`
`LINEAR AMPLIFIER
`
`
`IN
`
`
`
`
`
`
`in
`
`| l l
`
`I
`
`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) output filter 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.
`
`11. 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
`71) and actual
`value (class D stage output current isw), the calculation of
`the controlling quantity can be done in an implicit manner
`by direct measurement of the linear stage output current
`iLIN. 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 linear amplifier stage shall
`be calculated for the case that a hysteresis current controller
`with a constant tolerance band AI is applied. It is assumed that
`the load current 2' and the output voltage a can be treated as
`constant within the switching interval T, or that there exists
`a sufficient signal-to-switching frequency ratio, respectively
`(Fig. 3). Furthermore, the power transistors are assumed to be
`ideal (neglection of delay times, on—state voltages, etc). Also,
`dc supply voltage variations are neglected.
`Switching Frequency: With the assumptions given above,
`the output voltage u (averaged within a pulse interval T) is
`determined by the duty cycle 6. If we apply the definition m =
`u/ U for normalizing the output voltage (m = *~—l
`-
`-
`- +1), we
`get
`
`6
`
`_1+’LL/U_ l+m
`2
`2
`
`'(1)
`
`According to UL = L disw/dt,
`f6 = 1 /T can be calculated
`
`the switching frequency
`
`fS
`
`=
`
`fs,
`
`h
`max' 1— 2
`( m) Wlt
`
`U
`max: _....___..__
`2LvAI
`
`f5,
`
`(2)
`
`Power Losses: The power losses of the linear stage depend
`on its operating mode, where one has to distinguish between
`class A (linear amplifier with quiescent current eliminating
`crossover distortions) 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 lower transistor TL'of the linear stage, where it
`is assumed that for class A mode the quiescent current is as
`small as possible (IQ = IQ’min : AI/4) (see Fig. 3(e)).
`For IQ = AI/4, the class A mode losses are twice the
`losses of the class B mode. The total
`transistor losses pT
`are not dependent on the modulation index m and, therefore,
`the local transistor losses pT also represent the global losses
`(i.e., the losses averaged within the fundamental period of the
`amplified signal) pT : PT.
`
`

`

`118
`
`IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 44, NO. 1, FEBRUARY 1997
`
`amplitude AI. However, for a defined maximum switching
`frequency fsflmx,
`this would result
`in the usage of a high
`value of the inductance L. On the other hand, a higher value
`
`of L reduces the power bandwidth f3 of the switched-mode
`current dumping stage. If we normalize AI with respect to the
`value U/ R (maximum load current, resistive load ZL 2R
`assumed), i.e., 1% = AI/(U/R), we receive from (3):
`
`(4)
`
`1
`U2
`=—'~kn
`R 4
`
` 4
`
`U-AI
`
`PT:
`
`. normalized ripple amplitude).
`-
`for a class B linear stage (kA -
`The power bandwidth of the current dumping stage can be
`defined as f3 : R/(27rL) (if full output voltage utilization
`has to be achieved without overmodulation). Using (2), this
`leads to
`
`
`f3,max
`f3
`
`7"——
`_ kn.
`
`5
`U
`
`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 power losses) are fixed. However, there are some
`possibilities to overcome this fundamental limitation: (l) 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
`manner or application of a three-level topology (simultaneous
`reduction of L and of AI); and (3) higher order-type coupling
`impedance of 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 of the
`whole amplifier system whose dynamic response (especially
`the slew rate) is determined by the linear stage. (Full power
`operation of the amplifier above f3, however, can cause a
`thermal overload of the linear stage.)
`
`III. DIMENSIONING EXAMPLE—SIMULATION RESULTS
`
`In the following, a prototype system of a l-kVA switched—
`mode assisted amplifier system with the nominal values U =
`i 80 V, R = 2.5 Q (resistive load _Z_L = R; RMS value of
`the sinusoidalroutput voltage: 50 V), f3 = 10 kHz, f5,max =
`200 kHz shall be calculated briefly.
`
`Fig. 3. Voltage and current waveforms of a switched—mode assisted 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 mode of the linear amplifier part. (c) Currents for Class A mode.
`
`According to (5), we receive [CA 20157, Le, a current
`ripple of AI : 5 .A and a total power loss PT m 100/200
`Influence of the Switching Frequency 0n 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,
`power losses of the proposed system are far beneath the losses
`the demand for low power losses implies a small ripple
`
`
`class B
`class A
`
`
`iTU,avg = ’iTL,avg =
`§AI
`fiAI
`
`pTU = (U — u) - 23mm =
`UAI- gr — m)
`UAI- in _ m)
`timid-rm)
`mug—(1+...)
`PTL=(U+u)-z'TL,avg=
`Pr;P1jU+PTL=
`i
`UAIvfi
`UAI-%
`
`
`
`(3)
`
`
`
`
`
`
`
`
`
`
`
`
`/\
`
`. —-AI
`”LA 2
`
`4
`
`10+ZAI
`/
`J-
`,iTL’\
`//\ iTu
`~;— ———— "jwiow >
`-
`
`
`(a)
`
`(b)
`
`(C)
`
`(d)
`
`(e)
`
`

`

`ERTL er al.: BASIC CONSIDERATIONS AND TOPOLOGIES OF SWITCHED-MODE ASSISTED LINEAR POWER AMPLIFIERS
`
`ll9
`
`—
`
`+40A
`
`0
`
`—20A
`
`-40A—r“
`0
`
`l
`50,113
`
`1
`100Ms
`
`I
`150p;
`
`r
`ZOOus
`
`ZSOus
`
`(a)
`
`
`+4OA
`
`+20A
`
`+20A~
`
` *4OA
`
`
`
`
`
`0.25
`
`
`0.00
`
`
`
`
`
`
`
`
`
`
`
`
`:0
`
`u/zL
`
`1.25
`
`1.00
`
`0.75
`
`0.50
`
`O
`
`50,u.s
`
`100,113
`
`150m;
`
`(b)
`
`[
`20011.5
`
`250;“
`
`Fig. 5. Simulated current wave shapes of a 1 kW switched—mode assisted
`linear power amplifier (a) Sine wave response. (b) Pulse response (parameters:
`U = :l:80 V, R = 2.50, fig =10 kHz, f5)“,ax = 200 kHz, AI : 5 A).
`
`(b)
`
`(a) MOSFET UDs /ID—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 = U/U) and different load cunent displacement
`factors cos (,9. (The losses are normalized to U2/ ZL, U . .. supply voltage,
`Z L -
`.
`- 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 PT m 1 kW for M : l and coscp : 0.5).
`However, it has to be admitted that the losses shown in 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 iLiN not only has to compensate the ripple of the
`switching state, but also has to take over the dynamic current
`peaks (iLIN,
`therefore, cannot be' guided completely within
`
`the tolerance band AI). 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 AI of the switching stage
`generates a noise voltage Z - AI. If we strive for an SNR of,
`e. g., 280 dB, for the system simulated in the previous section
`an output impedance of Z s 2U/(AI-IOSNR/20) % 3 mt? 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 MOSFET source 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—0pm loop: Z w 0.8 Q for the assumed
`maximum switching frequency fS,rnztx : 200 kHz). Actually,
`
`

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`120
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`IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS. VOL. 44, NO.
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`1. FEBRUARY 997
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`(21) Equivalent circuit. (b)
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`Fig. 7. Output impedance of the linear amplifier stage.
`
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`
`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 loop gain to z 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 other side,
`
`is high enough to use a conventional op—amp as feedback
`amplifier (output voltage swing i7 V). This op-amp is used
`as a PI-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
`ampiifiers. Fig. 9(a) shows a topology for reduction of the
`linear stage power losses by ripple cancellation using, e.g.,
`four switching stages arranged 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 haveto 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 switching transistors {12].
`The primary advantage of this structure is that the worse
`
`

`

`ERTL BI (1].: 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 z33% due to the triangular
`current waveform and the resistive on—state characteristic of
`
`power MOSFET’s.
`Contrary to the parallel converter branches discussed before,
`a ripple reduction also can be achieved using a switching
`stage of multilevel structure (e.g., shown in Fig. 9(b), the well-
`known three—level converter) which is of interest especially for
`high output voltages because switching power transistors with
`lower rated 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.e., 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 bythe 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 phasewshifted 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 power supply for generating the dc
`supply voltage :tU being isolated from the mains). An isou
`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 an active “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
`dc~dc 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
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`IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 44, NO,
`
`I, FEBRUARY l997
`
`
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`Fig. 9. Further topologies of switched-mode assisted linear power amplifiers. (a) Ripple reduction by multiple bridge legs operated with a phase shift. (b)
`Ripple reduction using a three—level topology. (0) Avoiding the p-channel MOSFET of the linear stage (high-voltage applications). ((1) Ripple reduction using
`two parallel branches with explicit freewheeling diodes (e.g., Schottky—diodes). (e) Isolated topology using bidirectional 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, alaboratoryvmodel of the system
`Which iS described and simulated in Section IV is realized.
`Measuring results, and experiences taken from the practical
`.
`.
`.
`.
`.
`‘
`.
`realization, Will be p