IEEE TRANSACT|
`
`MICROWAVE
`AND TECHNIQ
`
`A PUBLICATION OF THE IEEE MICROWAVE THEORY AND TECHNIQUES SOCIETY
`
`AUGUST1999
`
`VOLUME 47
`
`RR.
`
`NUMBER8
`
`IETMAB
`
`(ISSN 0018-9480)
`
`MINI-SPECIAL ISSUE ON
`LOW-POWER/LOW-NOISE TECHNOLOGIES FOR MOBILE WIRELESS COMMUNICATIONS
`
`1401
`UKOGUCHON ear reir ce cite is ele Relate ck cant RON cantaretiotenearirgtea ee stad eereyranesnciacamen eae east OFJ. F. Harvey and R. J. Trew
`1403
`Gitest! Editors all saeco ts estes See Poet ee Ro ected RE Mee AN STONES CA UG tui eae Ci CRbees Thirds intern aeettv norte L. E. Larson
`
`MINI-SPECIAL ISSUE PAPERS
`
`INTEL 1325
`
`Ino.5(Al,Ga;—,)o.5P HEMT’s for High-Efficiency Low-Voltage Power Amplifiers: Design, Fabrication, and Device
`oy Bea ie cae tA DG ee at AU oon Goo? ene un Reet eciee aE Sa PE emer peTttT eA USIOCa arm GH EeareuLiNEaze ees Peartertictecne ee aoneseo
`Y.-C. Wang, J.-M. Kuo, F. Ren, J. R. Lothian, H.-S. Tsai, J. S. Weiner, H. Kuo, C.Lin,Y.-K. Chen. and W. E. May
`Teo lickerNoise GaN/AIGaN Heterostructure Field-Effect Transistors for Microwave Communications
`.............
`Pee eevee een este: A. Balandin, S. V. Morozov, S. Cai, R. Li, K. L. Wang, G. Wijeratne, and C. R. Viswanathan
`Integrated-Antenna Push—Pull Power Amplifiers................0ceeeeeeeeees W. R. Deal, V. Radisic, Y. Qian, and T. Itoh
`High-Efficiency Class-A Power Amplifiers with a Dual-Bias-Control Scheme ... K. Yang, G. 1. Haddad, and J. R. East
`Application of GalnP/GaAs DHBT’s to Power Amplifiers for Wireless Communications ..............-..-- P.-F. Chen,
`Y. T. Hsin, R. J. Welty, P.M. Asbeck, R.L. Pierson, P.J.Zampardi, W.-J. Ho, M.C.V. Ho, and M. F. Chang
`Push—Pull Circuits Using n-p-n and p-n-p InP-Based HBT’s for Power Amplification....... D. Sawdai andD. Pavlidis
`Power Performance of InP-Based Single and Double Heterojunction Bipolar Transistors ..............-----+..+.+.ss.ee0s
`:
`D. Sawdai, K. Yang, S. S.-H. Hsu, D. Pavlidis, and G.
`I. Haddad
`AcmlanamAn-Giuz C7 Powe4nr CONVENE sanuane este nner ner§. Djukié, D. Maksimovié, and Z. Popovié
`Nonlinear Amplifier Effects in Communications Systems .............. C.-P. Liang, J. Jong. W.
`E. Stark, andJ. R. East
`A Power Re-Use Technique for ImprovedEfficiency of Outphasing Microwave Power Amplifiers ...................+-.
`R. Langridge, T. Thornton, P. M. Asbeck, andL. E. Larson
`High-Efficiency Power Amplifier Using Dynamic Power-Supply Voltage for CDMA Applications .
`Bg eee eeu yith esne cee parttime Pan dG ea eee ee G. Hanington, P.-F. Chen, P. M. Asbeck, and L. E. Larson
`A Hich-Perlormance: Integrated -Ai- Band (Diplexenins.c-< 1c osses ee nessa sg cee A. R. Brown and G. M. Rebeiz
`Efficiency of Chip-Level Versus External Power Combining............... E.
`W. Bryerton, M. D. Weiss, and Z. Popovié
`Frequency-Selective MEMS for Miniaturized Low-Power Communication Devices (/nvited Paper) ... C. T.-C. Nguyen
`A ka-Band Micromachined Low-Phase-Noise Oscillator ............-0-002-s0secceece ress J 4. R. Brown and G. M. Rebeiz
`A Uniplanar Compact Photonic-Bandgap (UC-PBG) Structure and Its Applications for Microwave Circuits ............
`"...
`F-R. Yang, K.-P. Ma, Y. Qian, andT.Itoh
`
`1404
`
`1413
`1418
`1426
`
`1433
`1439
`
`1449
`1457
`1461
`
`1467
`
`1471
`1477
`1482
`1486
`1504
`
`1509
`
`(Contents Continued on Back Cover)
`
`INTEL 1325
`
`

`

`CONTRIBUTED SHORT PAPERS
`
`Efficient FDTD Analysis of Conductor-Backed CPW’s with Reduced Leakage Loss .... M. Hotta, Y. Qian, and T. Itoh
`
`CALLS FOR PAPERS
`
`Special Issue on Medical Applications and Biological Effects of RF/Microwaves ................122ssesecsssseces eee eeee
`
`(Contents Continued from Front Cover)
`
`CONTRIBUTED PAPERS
`
`that Uses a Heterojunction Bipolar
`An Experimental Study on a Self-Oscillating Optoelectronic Up-Converter
`sPFANSISLOM Yee hee sae eur ela oorma exe ian Wennet seas Auer mnt URRINE ctet cele a Oem ibrar aes H. Sawada andN. Imai
`
`Experimental Coupling Efficiency of Shaping Mirrors Matching a 168-GHz Gyrotron Output Wave to the HE,,
`WEP ey ener Re Preis 0s, Sl emia hae cn Na Nala Cyc rocrl
`a atti tape sa ae tg eee MN Ronen eee ie Y. Hirata, M. Komuro,
`Y. Mitsunaka, K. Hayashi, S. Sasaki, Y. Kanai, §. Kubo, T. Shimozuma, M. Sato, Y. Takita, K. Ohkubo, and T. Watari
`FDTD Computation of Temperature Rise in the Human Head for Portable Telephones.........J. Wang and O. Fujiwara
`Analysis of Oscillators with External Feedback Loop for Improved Locking Range and Noise Reduction...............
`poe ee ne ree yk. We ee er aeeek tt a RT ye Ne ce nar RT gh Re H.-C. Chang, A. Borgioli, P. Yeh, and R. A. York
`Conformal Mapping of the Field and Charge Distributions in Multilayered Substrate CPW’s ............0.ceeeeeeee eee es
`se eee Pee aac orate eet eeE Te ae NE ES aT eee eee E. Carlsson and S. Gevorgian
`Theory of Digital Phase ohitters:Based:on High=i.Superconducting Humsiscsc nim igecs seme aa idee seca ices
`Foe ee ora ete el a eet eer ra ata aero re RIPE toe I. B. Vendik, O. G. Vendik, E. L. Kollberg, and V. O. Sherman
`Silicon-Based Micromachined Packages for High-Frequency Applications ........ R. M. Hendersonand L. P. B. Katehi
`ilrap= Related: Gain/Phase Jump iol HREM: Power Amplifiers ce sae a econ tect ee nee C.-J. Wei and J, C. M. Hwang
`Temperature-Compensated Thermoplastic High Dielectric-Constant Microwave Laminates............. L. M. Walpita,
`M.R. Ahern, P. Chen, H. Goldberg, S. Hanley, W.M_ Pleban, §. Weinberg, C. Zipp, G. Adams, and Y. H. Wong
`
`1588
`
`

`

`IEEE MICROWAVE THEORY AND TECHNIQUES SOCIETY
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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
`
`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.
`
`1 Cellular 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
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`
`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
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`

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`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
`
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`HANINGTON et al.: POWER AMPLIFIER USING POWER-SUPPLY VOLTAGE FOR CDMA APPLICATIONS
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`1475
`
`Fig. 7. Measured RF gain of the system versus Pout for sinusoidal signals.
`
`Fig. 9. Measured dynamic resp