INTEL 1325
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`CONTRIBUTED SHORT PAPERS
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`Efficient FDTD Analysis of Conductor-Backed CPW's with Reduced Leakage Loss
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`M. Harm. Y. Qian. and T. Ito/t
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`CALLS FOR PAPERS
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`Special Issue on Medical Applications and Biological Effects of RF/Microwaves ........................................
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`CONTRIBUTED PAPERS
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`that Uses a Heterojunction Bipolar
`An Experimental Study on a Self-Oscillating Optoelectronic Up-Converter
`Transistor ......................................................................................... H. Suwudu and N. lmui
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`Experimental Coupling Efficiency of Shaping Mirrors Matching a loll-CHI Gyrotron Output Wave to the HE“
`Mode .............................................................................................. Y. Hiram, M. Konmrr).
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`Y. Mirxmtuku. K. Huyashi. S. Sum/ti, Y. Kauai. S. Kit/)0. T. Shimmumu, M. Sam. Y. Takira. K. Oltkuhn. and T. Warari
`FDTD Computation of Temperature Rise in the Human Head for Portable Telephones .........1. Wang and 0. Fujiwara
`Analysis of Oscillators with External Feedback Loop for Improved Locking Range and Noise Reduction ...............
`............................................................. IL—C. Chang. A. Borgia/i. P. Yeh. and R. A. York
`Conformal Mapping of the Field and Charge Distributions in Multilayered Substrate CPW‘s ............................
`.............................................................................. E. Curisson and S. Get-orgian
`Theory of Digital Phase Shifters Based on High-T. Superconducting Films ...............................................
`................................................. l. B. l"r'ndik. 0. G. Vcndi/t. E. L. Kallberg. and V. 0. Sherman
`Silicon—Based Micromachined Packages for High-Frequency Applications ........ R. M. Henderson and L. P. B. Karehi
`TrapvRelated Gain/Phase Jump of HFET Power Amplifiers ............................... C.—./. Wet and J. C. M. Hwaug
`TemperaturcsCompcnsatcd Thermoplastic High Diclectric~Constant Microwave Laminates ............. L. M. Walpizu.
`M. R. AIIL’I'II, P. Chen. H. Goldberg, S. Hun/0y. W. M Plt’ban. S. Wain/my. C. Zipp. G. Adams. and Y. H. Wang
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`1588
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`IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 47, NO. 8, AUGUST 1999
`
`1471
`
`High-Efficiency Power Amplifier Using Dynamic
`Power-Supply Voltage for CDMA Applications
`
`Gary Hanington, Student Member, IEEE, Pin-Fan Chen, Student Member, IEEE, Peter M. Asbeck, Senior Member, IEEE,
`and Lawrence E. Larson, Senior Member, IEEE
`
`Abstract— Efficiency and linearity of the microwave power
`amplifier are critical elements for mobile communication systems.
`This paper discusses improvements in system efficiency that are
`obtainable when a dc–dc converter is used to convert available
`battery voltage to an optimal supply voltage for the output RF
`amplifier. A boost dc–dc converter with an operating frequency
`of 10 MHz is demonstrated using GaAs heterojunction bipolar
`transistors. Advantages of 10-MHz switching frequency and as-
`sociated loss mechanisms are described. For modulation formats
`with time-varying envelope, such as CDMA, the probability
`of power usage is described. Gains in power efficiency and
`battery lifetime are calculated. An envelope detector circuit with
`a fast feedback loop regulator is discussed. Effects of varying
`supply voltage with respect to distortion are examined along with
`methods to increase system linearity.
`Index Terms—Dynamic supply RF amplifier, envelope restora-
`tion amplifier, 10-MHz dc–dc converter.
`
`(a)
`
`I. INTRODUCTION
`
`RF POWER amplifiers used for wireless communications
`
`(b)
`Fig. 1. Power output probability distribution for CDMA modulation under:
`(a) short time variations and (b) long time variations.
`
`with spectrally efficient modulation formats require high
`linearity to preserve modulation accuracy and limit spectral
`regrowth. To minimize distortion, they are typically operated
`in Class-A or Class-AB mode. Unfortunately, the operation
`of Class-A or Class-AB RF amplifiers at
`less than their
`maximum output power leads to reduced power efficiency.
`For example, the power efficiency of a Class-A amplifier
`(relative to its peak value
`decreases with output power
`) in proportion to
`. Similarly, for a
`.
`Class-B amplifier, the efficiency varies as
`Class-AB amplifiers have output power variations intermediate
`between these values. Thus, there is customarily an inherent
`tradeoff between linearity and efficiency in the amplifier
`design.
`The dual requirements of high linearity and high efficiency
`have been under intense investigation recently for two reasons.
`First, the current trend is to operate portable wireless phones
`at only 3.5 V (corresponding to one Li-ion cell, whose voltage
`Manuscript received December 16, 1998. This work was supported by the
`Army Research Office under the Multidisciplinary Research Initiative “Low
`Power/Low Noise Electronics.”
`G. Hanington is with the University of California at San Diego, La Jolla,
`CA 92093-0407 USA, and also with American High Voltage, El Cajon, CA
`92020 USA.
`P.-F. Chen is with the University of California at San Diego, La Jolla,
`CA 92093-0407 USA, and also with Global Communication Semiconductors,
`Torrance, CA 90505 USA.
`P. M. Asbeck and L. E. Larson are with the University of California at San
`Diego, La Jolla, CA 92093-0407 USA.
`Publisher Item Identifier S 0018-9480(99)06082-2.
`
`drops to 3.2 V near end of life). Under these circumstances,
`nonlinearities associated with RF device saturation effects
`become prominent and efficiency drops. Second, to allow for
`the required variation of RF signal envelopes with modulation
`schemes such as QPSK or multicarrier signaling, amplifiers
`have to operate with large peak-to-average power outputs,
`usually of 5 dB or greater. Specifications such as IS-95 dictate
`finite distortion levels, limiting the adjacent channel power
`ratio (ACPR) measured in a 30-kHz bandwidth at 885 kHz
`from the center of the CDMA spectrum to be no more than
`26 dB relative to the average in-band power measured in the
`same bandwidth. Fig. 1(a) shows the probability distribution of
`the RF envelope power for a CDMA reverse link waveform
`(OQPSK modulation) on a time scale corresponding to the
`inverse of the modulation bandwidth (of order microseconds).
`Variations in output power also occur over a slower time
`scale for CDMA transmission (as well as for all most other
`cellular protocols) in order to accommodate variable distance
`between mobile and base, as well as multipath and shadow
`fading. In many wireless systems, an active feedback control
`is used to adjust the RF output from the portable transmitter
`to limit interference effects and save battery lifetime. Fig. 1(b)
`shows this slower probability distribution (or power usage
`0018–9480/99$10.00 © 1999 IEEE
`
`

`

`1472
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`IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 47, NO. 8, AUGUST 1999
`
`Fig. 2. Variation of efficiency with output power for various amplifier
`configurations. Also shown is the output power probability distribution for
`CDMA signals.
`
`Fig. 3. RF power amplifier transistor current versus voltage characteristics,
`illustrating representative RF load line and various dc-bias strategies. Point
`A is the quiescent bias point for Class-A amplifiers and point B for Class-B
`amplifier. Moving from V 1 to V 3 by varying supply voltage yields higher
`efficiency.
`
`profile) compiled from field tests on CDMA wireless trans-
`mission.1 In Fig. 2, the power usage profile is plotted together
`with the efficiency versus output power for various amplifier
`configurations. It is seen that even though the maximum output
`power capability of the amplifier is approximately 0.5 W,
`operation at this level occurs only a small fraction of the
`time. The most probable output power is only 1 mW. At this
`point, where most of the transmission takes place, a Class-A
`amplifier has only 0.1% efficiency, while a Class-AB amplifier
`is typically only 2% efficient.
`The variation of efficiency with output power for the ampli-
`fiers can be understood by considering the transistor biasing
`within the power amplifiers. Fig. 3 shows representative output
`current versus output voltage characteristics for the output
`transistor. In Class-A amplifiers, the dc current and voltage
`are kept constant as the output power varies. Consequently, the
`input dc power is constant, and the efficiency is proportional
`to RF output power. In the Class-B amplifier, the dc-current
`bias varies in proportion to the output RF current and, thus,
`changes according to the square root of output power. The
`corresponding voltage is kept constant. Another option is to
`vary the supply voltage in accordance with the output signal
`level. If both dc voltage and current are varied optimally, then
`the efficiency of the amplifier can, in principle, be kept high
`even as the output power decreases (as shown in Fig. 2 for the
`“variable bias” case). Amplifiers designed to accomplish have
`been called “envelope tracking” amplifiers.
`
`1Cellular Data Group Stage 4 System Performance Tests, San Jose, CA,
`July 1997.
`
`Fig. 4. Schematic diagram of RF amplifier system.
`
`To implement variable voltage bias, Buoli [1] developed
`supplied to
`a linear regulator power drive, whereby the
`a final MESFET amplifier varied with the RF envelope. To
`save power, this voltage was obtained from a dual source; a
`7 V was fed to the amplifier, which
`minimum voltage of
`could be overridden by a linearly controlled voltage between
`7–12 V, which followed the signal envelope. Although the
`higher voltage was provided by virtue of a relatively inefficient
`fast video-type amplifier controlling a linear-pass transistor,
`the savings in overall system power was up to 45%. Power
`was saved since, for small signals, the energy source was
`the 7-V supply (and not
`the 12-V supply). The dynamic
`7–12-V source was used to take care of the peaks required
`by the modulation format. A related technique for raising the
`efficiency, due to Raab [2], comprises a Class-S high-level
`amplitude-modulation scheme, where the modulator takes the
`form of a step-down buck regulator operating at 200 kHz. The
`signal input to the RF stage is hard-limited to preserve only
`the phase information. The envelope of the output signal is
`controlled by the varying dc supply voltage of the RF stage.
`This dc voltage is regulated by pulsewidth modulation of the
`buck regulator. In this system, the maximum frequency of
`modulation depends strongly on the switching frequency of the
`buck regulator. Sampling theory requires that this switching
`frequency be at least twice that of the highest modulation
`frequency required. In practice, it is usually seen that a factor
`of ten is required to minimize the effects of filter ripple
`components. With typical dc–dc converters,
`the switching
`frequency (usually below 1 MHz) is not high enough to allow
`rapid modulation of the supply voltage for many RF amplifier
`communication purposes.
`In this paper, we present a high-efficiency power-amplifier
`topology for use in a portable microwave communications
`system. Here, a boost dc–dc converter is used to provide the
`supply voltage to a MESFET power amplifier. The overall
`amplifier configuration is shown in Fig. 4. By sensing the RF
`envelope to be amplified, and providing a dynamically adjusted
`to the amplifier by means of the dc–dc converter, overall
`system efficiency may be increased. By using a boost converter
`operating at 10 MHz, two advantages are obtainable over
`a step-down approach. First, power amplifiers operate more
`
`

`

`HANINGTON et al.: POWER AMPLIFIER USING POWER-SUPPLY VOLTAGE FOR CDMA APPLICATIONS
`
`1473
`
`values due to the finite
`or
`efficiently with higher
`saturation voltage of the RF amplifier transistor. Secondly, as
`the input voltage drops, due to battery depletion, the required
`high-voltage level can still be maintained, even as the battery
`is running toward exhaustion. If a step-down converter is
`used,
`the highest voltage can only be that of the battery
`itself—limiting the available power output.
`The use of a switching frequency of 10 MHz has several
`benefits as well. First, all filter components may be reduced
`in value and size. This allows for inductors that contain few
`turns, thus reducing resistive losses. In addition, capacitors
`may be simple ceramic surface mount devices, easily located
`on the power circuit layout. This lends itself to miniaturization
`of the power converter. A second benefit of higher frequency
`switching is that the dynamic response of the power supply
`has greater bandwidth. An operating frequency of 10 MHz
`allows for less than 1- s transient response. This is required
`when attempting to follow a rapidly modulated envelope, as
`in CDMA modulation. For example, with IS-95 signals, the
`modulation bandwidth is 1.22 MHz.
`To properly gauge the effect of efficiency improvement, it is
`necessary to account for the probability distribution of power
`[4], [5]. As shown
`usage as a function of the output power
`of the power usage
`in Fig. 2, the probability density
`on a decibel scale is approximately Gaussian [6]. From this,
`the average input power consumed by the RF amplifier system
`(from the battery) can be calculated as
`
`Likewise, one may calculate the average RF output power
`obtained from the amplifier as
`
`(1)
`
`The average power-usage efficiency is defined here as
`
`(2)
`
`(3)
`
`This provides a numerical method for comparison of RF
`power systems, which corresponds directly with battery en-
`ergy consumption. It implicitly includes the power conversion
`efficiency of the dc–dc converter.
`
`Fig. 5. Schematic diagram of boost converter with driver.
`
`microwave diode. The output voltage of this detector followed
`the incoming RF envelope and yielded 2 V at full input power
`(15 dBm).
`
`III. DC–DC BOOST CONVERTER
`The boost or ringing-choke converter used is schematically
`shown in Fig. 5. Here, energy is stored in a magnetic field
`during the on-time of the switch. During the off-time, this
`energy is released and used to charge the output capacitor to
`the peak of the ring voltage and provide energy to the load.
`With the condition that the maximum ON time is 50% of the
`switching period, and that the operation of this converter is in
`the discontinuous mode, the maximum inductor value that can
`be used for energy storage is
`
`(4)
`
`Larger values limit the peak current and energy. This assumes
`a linear current ramp during the ON time and a rapid decreasing
`is the operating frequency and
`ramp in the OFF time. Here,
`is the maximum output power of the converter. It can
`be seen that by increasing the operating frequency, the value
`of inductance can be reduced. Moreover, the inductor value
`varies as the square of the input battery voltage. For single-
`cell operation, power output of 1 W, and operating at 10 MHz,
`inductor values may be as small as tens of nanohenries. Boost
`converters have a pole in their output transfer function, which
`limits dynamic response and is dependent on the value of the
`energy-storage output capacitor and the load resistance
`
`(5)
`
`II. MESFET AMPLIFIER AND ENVELOPE DETECTOR
`A GaAs power MESFET amplifier was constructed using
`hybrid microstrip techniques. The load impedance at the output
`. With
`of the MESFET was adjusted to approximately 50
`a maximum drain voltage peak-to-peak swing of 20 V, an
`output power of 1 W at 950 MHz could be obtained under
`continuous wave (CW) excitation. To achieve this, and stay
`within the specifications of IS-95, a maximum power-supply
`of 10 V was required. In addition, to increase the
`voltage
`linearity of the amplifier, a dynamically adjusted gate voltage
`was employed, which lowered the amplifier gain at higher
`power output. An envelope detector was constructed using
`an on-board directional coupler, which was terminated in a
`
`By raising the switching frequency, the output capacitance may
`be reduced for a fixed-output ripple magnitude, increasing the
`composite amplifier bandwidth.
`The power switch is the heart of the dc–dc converter. In
`this study, AlGaAs/GaAs heterojunction bipolar transistors
`(HBT’s) were used due to their ability to provide extremely
`fast switching at moderate power. The slowest transistors used
`greater than 1 GHz [7] and could switch 1 A with a
`had
`fall time of less than 2–4 ns.
`Boost regulators of this topology have efficiency largely
`limited by the voltage drops across their semiconducting
`elements. Power losses include several components:
`associated with voltage drops in the semiconductor devices and
`
`

`

`1474
`
`IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 47, NO. 8, AUGUST 1999
`
`associated with dynamic power dissipated in
`inductor,
`associated
`the switch during on-off transitions, and
`with the drive circuits.
`In summary, we have
`
`(6)
`
`(and the only one considered
`The largest contributor to
`was nearly
`here) is the HBT switch. In the devices used,
`0.8 V (a substantial portion of the incoming battery potential).
`represents the peak of the current ramp (nearly 1.4 A),
`If
`the conduction time of the power switch (50%
`and
`maximum), this loss is
`
`(7)
`
`Values of
`of 0.28 W were observed for 1-W output
`power. DC losses due to the inductor and conductor resistance
`were not considered in the analysis due to the relatively large
`conductors used. There are two main contributors to the ac
`switching loss. First, the ac switching loss in the transistor
`is the result of current still flowing through the collector as
`is rising above
`.
`the transistor is turning off and
`as the ring-up collector voltage peak,
`the
`Defining
`may be computed approximately by
`transistor ac loss
`[8]
`
`(8)
`
`In many conventional lower frequency power-supply designs,
`the ac transistor loss is comparable to the dc loss. With HBT
`power transistors, the ac loss is very small due to the fast
`rise and fall time. The maximum turn-off time associated with
`was estimated by oscilloscope
`the AlGaAs HBT
`measurements to be less than 3 ns, at a current peak of
`A. There is additional ac loss due to the charging
`and discharging of the Schottky rectifier capacitance and
`other stray capacitances located on the printed circuit board.
`Assuming that this total electrostatic energy is wasted every
`of
`cycle, we find a loss
`
`(9)
`
`Other sources of inefficiency stem from power consumed in
`the driver circuitry. The power HBT driver stage was required
`to provide over 35-mA input current to the drive switch due
`. With a driver voltage
`to its rather low current gain
`of 4 V, the power consumed is
`supply
`
`(10)
`
`or approximately 60 mW at full duty cycle.
`The measured efficiency of the dc–dc converter was found
`to be in the range of 65%–74% for output powers in the range
`of 0.2–1 W.
`
`IV. TOTAL SYSTEM AND FEEDBACK LOOP
`A one-pole filter with characteristic frequency of 1 MHz was
`used to provide a reference signal into an operational amplifier
`(LM301) that regulated the boost converter. By adjusting the
`feedback, the regulator provided the optimum voltage to the
`
`Fig. 6. Dynamic supply voltage and Vpeak swing of drain waveform versus
`Pout.
`
`RF amplifier. The correspondence between dc–dc converter
`supply) and RF power out is shown in Fig. 6.
`output (
`Also included is the peak swing of the drain voltage of the
`RF device. The amplifier was tuned so that 1-W CW output
`. The slope of
`was obtained with an input voltage of
`versus
`curve was set so that the ACPR level
`the
`was satisfied across the range of operation. The minimum
`output voltage from the converter was 3.0 V (battery voltage
`minus the Schottky diode drop), which was produced when
`the pulsewidth was reduced to zero.
`is a complete
`The drive circuitry, shown in Fig. 5,
`pulsewidth-modulated converter. A clock operating at 10 MHz
`and 50/50 duty cycle generates the frequency reference pulses
`by which the boost regulator is synchronized. To obtain the
`required base drive pulse, a high-speed CMOS digital inverter
`IC (MC74AC04N) was used. One inverter is used as a voltage
`comparator, while three others form the base drive to the main
`switching transistor. One feature of this circuit is that as the
`control voltage is raised, the time to achieve activation of
`the inverter is shortened, thereby increasing the ON time of
`the power switch. The clock output “low” truncates the drive
`pulse.
`limiting resistor with
`The base is driven through a 50-
`a diode shunt across to provide charge removal during the
`falling edge of the drive pulse. To improve speed and raise
`system efficiency, the inverter was run from a 4-V source.
`This can be derived as a bootstrapped supply via a tap off
`the boost inductor. The entire apparatus was constructed on
`a simple G-10 backside-grounded printed circuit board. Not
`included in the block diagram of Fig. 4 is the operational
`. A simple
`amplifier circuitry used to provide the varying
`summing amplifier was used, which converted the positive-
`going envelope detector waveforms to a negative voltage,
`2.4 V as the
`voltage varied
`which varied from 2.1 to
`from 3 to 10 V. This reduction of gain as a function of
`voltage improved system linearity and limited distortion over
`the full range of the amplifier [9], [10]. The measured RF
`gain is shown in Fig. 7.
`Efficiency tests were made on the complete RF system.
`Fig. 8 compares the dc power efficiency between an amplifier
`supply voltage (10 V) and one with
`with constant
`voltages. From (3), the long-term
`dynamic
`
`and
`
`

`

`HANINGTON et al.: POWER AMPLIFIER USING POWER-SUPPLY VOLTAGE FOR CDMA APPLICATIONS
`
`1475
`
`Fig. 7. Measured RF gain of the system versus Pout for sinusoidal signals.
`
`Fig. 9. Measured dynamic response of dc–dc converter Top trace: Vout
`2 V/cm. Bottom trace: Vcontrol. Horizontal: 1 S/cm.
`
`Fig. 8. Measured efficiency versus output power for dynamic supply ampli-
`fier and for a comparable amplifier with fixed VDD.
`
`power usage efficiency is calculated to be
`V
`
`Fig. 10. Measured output spectrum with CDMA input signal at maximum
`power.
`
`The results correspond to an increase in power usage efficiency
`of a factor of 1.64 . A battery powering this amplifier would
`last 64% longer when used in conjunction with the dc–dc
`converter scheme. Other probability of use distributions may
`yield different average efficiencies and different efficiency
`gains from the use of the dc–dc converter.
`
`V. SYSTEM BANDWIDTH AND LINEARITY
`To avoid loss of modulation efficiency and spectral re-
`growth, the amplifier must exhibit adequate linearity. A re-
`supplied to the RF
`quirement for linearity is that the
`amplifier is in-phase with the envelope and of sufficient
`magnitude to prevent clipping. To achieve this, a fast loop
`response in the dc–dc control section is mandatory. The
`dynamic response of the dc–dc converter for a step change
`in control voltage is shown in Fig. 9. From this, it is evident
`that modulation up to 1 MHz is possible for moderate-output
`level changes. The rise time for this output voltage change is
`noticeably shorter than the fall time, consistent with the fact
`that the only sink mechanism for the output is due to the output
`load discharging the filter capacitor. Since the rise time of the
`step change depends on the energy storage in the inductor,
`it is not sensitive to output load values unless its maximum
`power capability is exceeded. In addition, as far as linearity
`voltage are acceptable at the
`is concerned, overshoots in
`expense of power dissipation.
`A frequency-domain view of the amplified CDMA wave-
`form is shown in Fig. 10. This output was recorded using a
`standardized resolution bandwidth of 30 kHz, consistent with
`specifications for IS-95. This waveform shows an ACPR of
`
`Fig. 11. RF output spectrum with sinusoidal input showing sidebands caused
`by 10-MHz ripple on VDD. Vertical: 10 dBm/cm. Horizontal: 1 S/cm.
`
`greater than 26 dB. One potential concern involved the ripple
`output of the 10-MHz converter. In order to increase response
`time, the output capacitor was reduced in size, which, in
`turn, increases the output ripple. It was found that very little
`amplitude to RF gain variation resulted.
`conversion of
`This is shown in Fig. 11 where CW spectrum is displayed
`along with the 10-MHz created sidebands. Each spur is less
`60 dBc.
`than
`
`VI. SUMMARY
`A highly efficient microwave power amplifier was imple-
`mented using a GaAs MESFET amplifier and dc–dc boost
`converter. By dynamically controlling the supply voltages,
`an efficiency increase of over 1.64 was achieved compared
`
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`

`1476
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`IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 47, NO. 8, AUGUST 1999
`
`with a constant voltage system. DC–DC converter switching
`operation at 10 MHz allowed wide-bandwidth and small-
`sized components. By utilizing a fast feedback loop regulation
`scheme and dynamic gate bias, the ability to meet CDMA
`IS-95 specifications for ACPR was realized.
`
`ACKNOWLEDGMENT
`The authors gratefully acknowledge extensive discussions
`with T. Itoh, W. Hooper, H. Finlay, and V. Radisic.
`
`REFERENCES
`
`[1] C. Buoli, A. Abbiati, and D. Riccardi, “Microwave power amplifier
`with ‘Envelope Controlled’ drain power supply,” in 25th European
`Microwave Conf., Sept. 1995, pp. 31–35.
`[2] F. Raab and D. Rupp, “Class-S high efficiency amplitude modulator,”
`RF Design, vol. 17, no. 5, pp. 70–74, May 1994.
`[3] F. H. Raab, B. E. Sigmon, R. G. Meyers, and R. M. Jackson, “High-
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`Dig., vol. 2, 1998, pp. 2220–2225.
`[4] P. M. Asbeck, T. Itoh, Y. Qian, M. F. Chang, L. Milstein, G. Han-
`ington, P. F. Chen, V. Schultz, D. W. Lee, and J. Arun, “Device and
`circuit approaches for improved linearity and efficiency in microwave
`transmitters,” in IEEE MTT-S Tech. Dig., 1998, pp. 327–330.
`[5] G. Hanington, P. F. Chen, V. Radisic, T. Itoh, and P. M. Asbeck,
`“Microwave power amplifier efficiency improvement with a 10 MHz
`HBT dc–dc converter,” in IEEE MTT-S Tech. Dig., 1998, pp. 589–592.
`[6] J. F. Sevic, “Statistical characterization of RF power amplifier efficiency
`for CDMA wireless communication systems,” in Wireless Commun.
`Conf., Boulder, CO, Aug. 1997, pp. 110–113.
`[7] W. Hooper, private communication.
`[8] A. Pressman, Switching Power Supply Design. New York: McGraw-
`Hill, 1991.
`[9] R. K. Gupta, P. A. Goud, and C. G. Engefield, “Improvement of
`intermodulation distortion in microwave MESFET amplifiers using gate-
`bias compensation,” Electron. Lett,, vol. 15, no. 23, pp. 741–742, Nov.
`1979.
`
`[10] A. A. M. Saleh and D. C. Cox, “Improving the power-added efficiency
`of FET amplifiers operating with varying-envelope signals,” IEEE Trans.
`Microwave Theory Tech., vol. MTT-31, pp. 51–56, Jan. 1983.
`
`Gary Hanington (S’94) received the B.S. and M.S.
`degrees in electrical engineering and materials sci-
`ence from the State University of New York at
`Stony Brook, in 1974 and 1977, respectively, and
`is currently working toward the Ph.D. degree at the
`University of California at San Diego, where his
`work is focused on VHF dc–dc power converters
`and their applications.
`He is the founder and Chief Financial Officer
`of American High Voltage, El Cajon, CA. His
`interests include microwave circuits and miniature
`high-voltage power supplies for display applications.
`
`Pin-Fan Chen (S’93), for photograph and biography, see this issue, p. 1437.
`
`Peter M. Asbeck (M’75–SM’97), for photograph and biography, see this
`issue, p. 1437.
`
`Lawrence E. Larson (S’82-M’82-SM’90), for photograph and biography,
`see this issue, p. 1403.
`
`