2010 IEEE TRANSACTIONS ON MICROWAVE THEORY AND...

2010 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 60, NO. 6, JUNE 2012

Codesign of PA, Supply, and Signal Processing forLinear Supply-Modulated RF Transmitters

John Hoversten, Member, IEEE, Scott Schafer, Student Member, IEEE, Michael Roberg, Student Member, IEEE,Mark Norris, Student Member, IEEE, Dragan Maksimović, Member, IEEE, and Zoya Popović, Fellow, IEEE

Abstract—This paper presents a method for achieving high-ef-ficiency linear transmitters by codesign of the RF power ampli-fier (PA), dynamic supply, and signal processing. For varying am-plitude signals, the average efficiency of the PA is improved byadding a supply modulator with requirements derived from non-standardPAmodeling. The efficient PA and supplymodulator bothintroduce signal distortion. A targeted linearization procedure isdemonstrated with reduced complexity compared to standard dig-ital predistortion. Experimental results on a 2.14-GHz 81% effi-cient 40-W peak power GaN PA illustrate the codesign methodby achieving 52.5% composite power-added efficiency with highlinearity for a W-CDMA signal with a 23-MHz supply modulatorbandwidth.

Index Terms—Envelope elimination and restoration (EER),envelope tracking (ET), microwave power amplifiers (PAs), polartransmitter.

I. INTRODUCTION

M ODERN modulation schemes include amplitude- andphase-modulated signals with high peak-to-average

ratios (PARs) and bandwidths. In addition, in two-way commu-nications, the up- and down-link signals have different powerlevels and PARs. The main challenge in transmitter designis achieving simultaneous linearity and efficiency [1], andexisting solutions include outphasing [2], [3], different DohertyPA architectures (e.g., [4]–[6]) and various types of envelopetracking (ET) [7]–[9]. ET and polar split transmitters originatefrom envelope elimination and restoration (EER) pioneered inthe 1950s [10]. In this approach, signal amplification is doneby modulating both the RF power amplifier (RFPA) and itsdc supply with some prescribed dependence, which we refer

Manuscript received October 01, 2011; revised January 11, 2012; acceptedJanuary 12, 2012. Date of publication March 15, 2012; date of current ver-sion May 25, 2012. This work was supported by the National SemiconductorCorporation (now Texas Instruments Incorporated) through the Colorado PowerElectronics Center (CoPEC), Berrie Hill Research Corporation, by the U.S. AirForce under Contract FA8650-10-D-1746-0006, and by the Office of Naval Re-search under the Defense Advanced Research Projects Agency (DARPA) Mi-croscale Power Conversion (MPC) Program under Grant N00014-11-1-0931.J. Hoversten is with Texas Instruments Incorporated, Longmont, CO 80503-

7752 USA.S. Schafer, M. Roberg, D. Maksimović, and Z. Popović are with the De-

partment of Electrical, Computer and Energy Engineering, University of Col-orado at Boulder, Boulder, CO 80309-0425 USA (e-mail: [email protected]).M. Norris was with the Department of Electrical, Computer and Energy Engi-

neering, University of Colorado at Boulder, Boulder, CO 80309-0425 USA. Heis now with Texas Instruments Incorporated, Longmont, CO 80503-7752 USA.Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TMTT.2012.2187920

Fig. 1. Various input trajectories shown in the literature, defined as the gener-ally nonlinear dependence . A: Traditional linear PA with constant

. B: EER with constant and full supply modulation. C: ET. D: PDM.E: Partial supply modulation. F: Offset supply for minimum drive amplitude.G: Following best path for parameter (i.e., PAE, gain, linearity). The envelopevoltage PDF of a WCDMA signal preprocessed for a 7-dB PAR is also shown.

to as the “input trajectory.” Fig. 1 shows an illustrative plotof the supply voltage variation with input signal amplitude,

, where the analog input signal to be amplified isgiven by .In a standard linear amplifier, the supply is constant, as repre-

sented by line A in Fig. 1. EER, or full supplymodulation shownwith line B and first proposed by Kahn, implies a constant inputenvelope with the entire signal amplitude being modulated bythe supply. Other curves (C–F) show examples reported in theliterature, corresponding to transmitters that have been termedvarious names, such as ET, wideband ET (WBET), polar modu-lation, hybrid quadrature polar modulation (HQPM), EER, hy-brid EER (HEER), partial drivemodulation (PDM), and discretedynamic voltage biasing (DDVB). Table I gives examples ofvarious experimental input trajectories reported in the literaturealong with the stated PA classes of operation. Other trajectoryexamples obtained illustrated by simulation are given in [11].If the probability density function of the envelope voltage

is superimposed in Fig. 1 for a given signal, a designer has astarting point for the range of supply voltages that the supplymodulator needs to provide. This, however, does not give anyinformation about the signal bandwidth, which will determinehow fast the supply needs to be. The average transmitter effi-ciency for a signal with a known probability density function

can be calculated from [24]

(1)

0018-9480/$31.00 © 2012 IEEE

HOVERSTEN et al.: CODESIGN OF PA, SUPPLY, AND SIGNAL PROCESSING FOR LINEAR SUPPLY-MODULATED RF TRANSMITTERS 2011

TABLE IEXAMPLES OF TRANSMITTERS WITH SUPPLY MODULATION

and is obviously maximized when both the RFPA efficiency andthe supply modulator efficiency are maximized over all inputamplitudes.Referring to Fig. 1, for the linear amplifier case (A), the av-

erage efficiency is low, but the amplifier can be kept fairly linearand this has been standard practice. An EER transmitter, (B),can be very efficient provided the supply modulator is efficient,but the linearity will be poor. Full ET, (C), has a dynamic RFinput amplitude proportional to the signal envelope, giving thehighest PA efficiency, but making efficient supply modulator de-sign difficult. Partial supply or PDM can be achieved along dif-ferent nonlinear and possibly nonsmooth trajectories. One ex-ample of PDM, (D), has been reported in [24] where a minimalvalue is specified for the drive voltage, resulting in efficiencyimprovements for low signal amplitudes at the expense of lin-earity. Examples of partial supply modulation that have beenreported in the literature are given by E, F, and G. The curvefor E* in the table is similar in shape to E, but shifted near zerosupply voltage for low . The curved trajectory G trades PAefficiency, linearity, and supply modulator efficiency: at low en-velopes, the supply is held constant, and the curve exhibits asecond deflection point for higher input signal values.This paper develops a codesign method for determining

RFPA, supply-modulator and signal-processing requirementsunder given efficiency and linearity constraints, building oninitial simulation results first presented in [11]. The generalizedtransmitter block diagram is shown in Fig. 2, with the followingmain components:1) high-efficiency RFPA designed optimized for efficiencyover a range of envelopes;

2) efficient supply modulator;3) feedback circuit for calibration and linearization;4) digital control circuit, which includes the signal split andpredistortion.

The signals and are baseband (digital) signals. The ratioof signals and is referred to as the “signal split,” and thisratio is critical to achieving high overall average power-addedefficiency (PAE) of the system. The signal split applies a trans-formation to the desired signal envelope to produce the supply

Fig. 2. Block diagram of a general supply-modulated transmitter contains com-ponents at several frequency ranges: the RF portion with an upconverter, driverPA and high-efficiency PA optimized for efficiency over a range of envelopes;the signal envelope bandwidth supplymodulator circuit, which provides the biasto the RFPA in some relationship to the envelope of the signal; and the digitalportion, which performs the signal split and other processing necessary for lin-earization and control. We refer to the ratio of signals and as the “signalsplit,” and this parameter can be optimized for efficiency, linearity, etc. of theentire transmitter.

modulator digital input, and determines the weighting of thecomplex signal paths. A properly chosen vector of input base-band signals enables optimal efficiency and linearity for a spe-cific type of signal (PAR, PDF, bandwidth). This general supplymodulated PA can be configured to be an ET, EER, polar, partialdrive, or partial supply transmitter.The contributions of this paper are as follows.• Section II describes the modeling approach and presents acharacterization method for a high-efficiency PA designedfor the architecture in Fig. 2;

• Section III presents the method used to determine supplymodulator characteristics and the signal split ( );

• Section IV presents experimental results that demonstratethe approach, and describes sources of signal distortion.The final linearization approach is demonstrated on a mea-sured spectrum with reduced regrowth after each step ofthe targeted linearization method. The heat dissipation isdramatically reduced and distributed more uniformly be-tween system components.

II. PA MODELING AND CHARACTERIZATION

In this section, we present the basic measurement and simu-lation method required to characterize a PA for the architecturein Fig. 2. The method is first illustrated using simulated datafor a typical PA that would be suitable for such a transmitter,which needs to be designed to have high efficiency over a rangeof supply voltages. This means that no specific class of oper-ation will be appropriate, although a class is usually specifiedwhen discussing ET transmitters in [10]–[19]. For example, ina class-F PA, the harmonic terminations in the output networktake into account the output capacitance of the device. However,

changes with operating supply voltage so the terminationswill not satisfy class-F conditions for all envelope values. An-other example is a class-E power amplifier (PA) in which theoutput device capacitance is a part of a specific output compleximpedance that enables soft switching [1]; changing the supplyvoltage will change and modify the class-E impedance atthe fundamental.


Fig. 3. Static model of PA characterized for multiple supply voltages. This can be used as a static LUT for supply-modulated system simulation. From: (a) constantoutput RF voltage and (b) constant current contours, as the RF input voltage and supply voltage are varied, other parameters such as (c) gain and (d) PAE can becalculated. For these simulations, the RF load is kept fixed at 50 .

The simulations in this section are performedwith a nonlinearmodel for a Eudyna high-power GaN HEMT (EGN030MK)for a gate bias of 1 V and a drain bias from 0 to 35 V. ThePA design takes into account small-signal gain, efficiency, andoutput power over a range of supply voltages correspondingto an input envelope range of 15 V for a WCDMA down-link signal, resulting in class-AB operation. Once the PA isdesignedwith supplymodulation inmind, in addition to standardcharacterization ( , PAE versus ), the PA also needs tobe characterized as the bias is varied. First both andare varied and output voltage and drain current are measuredas shown in Fig. 3(a) and (b). From this data, relevant staticparameterized plots can be derived. The gain and PAE areplotted in Fig. 3(c) and (d), and other parameters such asinsertion phase can be obtained. This data serves as a static2-D lookup table (LUT) PA model for subsequent systemsimulations.From these figures, the following observations can be made.

Under pure drive modulation (horizontal blue line A in on-line version), gain decreases as the PA enters high-powerhigh-efficiency compressed operation, causing distortion of theoutput signal. This is the traditional PA driving method withno supply modulation. Under pure drain modulation (vertical

red line B in online version), efficiency remains high over alarger output power range. PA gain variation is much moresignificant in this case than under traditional drive modulation,requiring significant pre-correction of . Both A and B inputtrajectories intersect a wide range of drain currents and outputpowers. Other input trajectories from Fig. 1 trade efficiency andlinearity. An input trajectory that focuses on high efficiencyis shown in Fig. 3(d), which would require some type of lin-earization. One can also choose the trajectory to increase PAlinearity and reduce the amount of pre-distortion required, asshown by the trajectory in Fig. 3(c), which follows a constant12-dB gain curve. It is difficult to determine what the “best”trajectory is for the transmitter as a whole without additionalsystem specifications, such as supply modulator efficiency,overall size, or complexity of the digital processing.It is important to note that the data is static and should not

include dynamic effects. For example, it would be appropriateto measure the data under pulsed RF conditions where the pulseis shorter than the thermal time constant of the device. Unfor-tunately, PAs have dynamic effects at time constants around thesignal bandwidth due to, e.g., matching and bias lines, whichcan be accounted for by modeling the network as frequency de-pendent.


Fig. 4. Simulated data from Fig. 3(d), replotted in terms of output envelopevoltage , which takes the PA gain into account. This plot is used to definethree output trajectories discussed in the text.

III. SIGNAL SPLIT DESIGN

Although the input trajectory is a relevant starting pointfor supply-modulated PA design, an “output trajectory”

is a more practical representation since it in-cludes the PA gain and is the quantity of interest. Choosinga trajectory determines not only the gain and efficiency for avarying signal, but also requirements for the supply modulator:total voltage range, voltage slew rate, variation, and bandwidthof the PA acting as a load to the supply.

A. PA-Optimized Trajectory

Fig. 4 shows PAE contours derived from Fig. 3(c) and (d).Thus, if the goal of the transmitter design is to maximizeefficiency, the supply should follow the output envelope, asshown with curve T3, since it intersects the lower efficiencycontours over the smallest range of values. However, theknee voltage of the device limits PA performance at low supplyvoltages. As decreases, there is little room for the inputsignal before entering the knee voltage region, which leads toreduced gain and/or linearity.

B. Trajectory Implications on Supply Requirements

Caution should be used when choosing what appears to be the“best” trajectory for efficiency. Curve T3 optimizes RFPA effi-ciency, but clearly requires increased supply dynamic capabili-ties, which usually results in lower supply modulator efficiency,discussed for example, in [25]. An important parameter to con-sider for supply modulator design is the percentage change inoutput voltage that results from a 1% error in the supply voltage,which we define as “PA supply sensitivity” given by

(2)

This parameter, defined first in [11], is similar to the powersupply rejection ratio (PSRR) often considered in analog elec-tronics [26]. Contours of constant are shown in Fig. 5, and it is

Fig. 5. Simulated contours of constant supply sensitivity parameter with thethree trajectories from Fig. 4 provide information on the requirements for supplymodulator design.

clear that choosing the highest efficiency output trajectory (T3)implies the most challenging supply modulator requirements.In this case, the supply modulator needs to maintain the prede-termined supply voltage within 1% to prevent a 90% error inoutput envelope for V, which is a very difficultspecification for a practical supply. Trajectory T2 trades supplymodulator requirements for some PA efficiency resulting in aneasier system design.The supply modulator is responsible for amplifying the enve-

lope voltage waveform with the following requirements:1) certain minimum and maximum output voltage level;2) flat gain over a specified bandwidth;3) maximum slew rate for acceptable distortion;4) drive a time-varying load (the RFPA).The first two requirements are contradictory becausehigh-power devices that enable large voltage swings havelarge capacitance, limiting maximum speed. For a given dy-namic range, architecture may allow a dc offset to be appliedto the output voltage range to allow higher peak voltages atthe expense of higher minimum voltage. The maximum andminimum drain voltages impact RFPA efficiency.Bandwidth and frequency response are small-signal param-

eters, while slew rate describes large-signal performance andis the limiting factor for the supply modulator. For example,a fast voltage ramp across a low-impedance load may depletethe charge stored in supply modulator decoupling capacitors,causing the supply voltage rail to dip, with resulting outputsignal distortion due to inadequate slew-rate capability. Table IIshows simulated required bandwidths and slew rates, whichwould results in acceptable adjacent channel power ratio(ACPR) for a WCDMA down-link signal with 7-dB PAR, forthe three trajectories discussed throughout this section. Theanalysis used to produce these results involves simulation ofan idealized supply-modulated transmitter imposing bandwidthand slew rate limitations on the supply modulator, as discussedin [22]. T3 optimizes PA efficiency, but imposes yet anotherdifficult requirement on the supply modulator: a bandwidth of23 MHz with a slew rate of 230 V s and a voltage swing of27 V.


TABLE IISUPPLY MODULATOR REQUIREMENTS TO ACHIEVE

NEGLIGIBLE SYSTEM DISTORTION

Fig. 6. Simulated resistance seen by the supply modulator and drain currentthat supply modulator must supply as a function of to meet the three tra-jectories shown in Figs. 4 and 5. For signals with low envelope voltages, theresistance changes very rapidly, increasing the dynamic capability requirementof the supply modulator.

The load driven by the supply modulator () at the PA drain supply terminals is referred to

as the drain resistance. Note that this is not directly related tothe PA load line and is made constant over the RF cycle by theRF choke. varies with PA output power and efficiency as

and this variation is dependent upon design of the signal split,as shown in Fig. 6 for the three simulated trajectories. There-fore, the output impedance of the supply modulator should bekept low over a wide frequency range to limit errordue to voltage division between the supply modulator outputimpedance and load PA impedance. Fig. 6 also shows the simu-lated drain–current variation with output envelope for the threetrajectories, where T3 requires a maximum-to-minimum currentratio of 16, while the T1 ratio is only 4, significantly loweringthe burden on the supply modulator.

IV. EXPERIMENTAL RESULTS AND TARGETED LINEARIZATION

In this section, we present measured results produced usingthe method illustrated by simulations of Sections II and III. Notethat the PA is designed for supply modulation and based on aTriQuint Semiconductor GaN transistor with no available non-linear model. While the simulations in Section II are performedwith an existing nonlinear model for a Class AB PA, even thisavailable model would not be valid for an extremely saturatedclass-F experimental PA.The PA in the general supply-modulated transmitter needs to

be designed to have high efficiency over a range of supply volt-ages. This means that no specific class of operation will be ap-

Fig. 7. Measured load–pull data for a TriQuint Semiconductor TGF-2003–10GaN HEMT. The “class” of the amplifier is ambiguous because the operatingpoint will move with the supply bias. The goal is to optimize the operating pointover the supply modulator range of voltages for gain, power, and/or efficiency.Contours of constant measured power (at V), constant drain effi-ciency at 20, 28, and 36 V, and constant small-signal gain contour for a 12-Vsupply shown on a 10- Smith chart.

TABLE IIIPA HARMONIC TERMINATIONS AT THE VIRTUAL DRAIN OF THE TRANSISTOR

propriate, and the output impedance at the fundamental needsto be a tradeoff that optimizes power, low-voltage small-signalgain, midvoltage efficiency, and high peak power. As an illus-tration of the type of impedance tradeoff at the PA output, Fig. 7shows load–pull contours at the bond-wire plane of a TriQuintSemiconductor TGF-2003-10 discrete device for an examplehigh-efficiency PA design used in this work.In the final PA, the chip device is mounted on a 15-mil-thick

gold-plated CuMo pedestal using an eutectic die attach withAuSn performs, and wire bonded to the microstrip circuit(30-mil RO4350B substrate) with eight 1.25-mil-diameterwire bonds. The matching circuits present fundamental im-pedances of at the bond-wire planeand extracted at the virtual drain ofthe device. The harmonic terminations at the virtual drainwere designed for a class-F PA [27] at a midrange supplyvoltage of 28 V and given in Table III. The PA input matchingis accomplished with ATC600F capacitors, while the outputmicrostrip matching circuit has 0.27-dB insertion loss. Theoutput supply circuit is designed for pulsed RF measurementsto obtain the static nonlinear characteristics, as described inFig. 3. A photograph of the PA is shown in Fig. 8, alongwith measured and simulated fundamental, second, and thirdharmonic impedances listed in Table III. The PA gives 36-Wpulsed power with 81% drain efficiency and 14.5-dB gain (78%PAE) for a 28-V drain bias at 2.14 GHz.The PA is characterized following the method described

in Section II and the output results are shown in Fig. 9. Thetrajectory is chosen to trade off PA efficiency and linearity,taking into account supply modulator voltage range. The corre-sponding drive variation is plotted for completeness.


Fig. 8. Photograph of a high-efficiency PA implemented using theTGF-2003-10 discrete device and the load–pull data from Fig. 7 withsecond and third harmonic terminations [27].

Fig. 9. Measured and versus with contours of measured PAEshown in color (in online version). The trajectory chosen for further demonstra-tion is shown via the black solid line.

With the trajectory chosen and expected static performanceknown, dynamic effects can now be addressed.A linear supply modulator is next implemented as shown in

Fig. 10 to finalize obtaining specification parameters for thefinal supply modulator. Similar to the configuration describedin [28], the supply modulator is a parallel combination of awide-bandwidth high slew-rate linear amplifier and a standardsynchronous buck switcher that supplies a dc output current thatresults in the maximum efficiency for a given envelope signal[29]. Designed for laboratory testing purposes, this supplymodulator does not have final-solution efficiency or formfactor, but it does enable system characterization experiments.The linear amplifier stage consists of three voltage-gain stagesfollowed by a buffer consisting of 48 LM7372 op-amps inparallel, to obtain up to 7-A 30-V output capabilities with over100-MHz bandwidth and 3000-V s slew rate. Therange is 3–32 V with a supply rail ( ) of 36 V for the linearamplifier and switcher stage. Particular attention was given toop-amp frequency compensation, printed circuit board (PCB)layout, and dc supply decoupling to achieve stable wide-band-width operation and current sharing among buffer op-amps.To minimize the inductance and retain high signal bandwidthbetween the supply modulator and the PA, a 76.2-mm-wide

Fig. 10. Block diagram (left) of the supply modulator used for characterization,and photograph (right) of the linear amplifier. Gain peaking is applied to extendthe bandwidth beyond 70 MHz. V for both the linear amplifier andswitcher stage with the varying from 3 to 32 V.

dual-row 2.54-mm header connector was used with the top rowconnected to the modulator output and the bottom row to theground plane, as shown in Fig. 10.

A. Sources of Distortion

In the block diagram of Fig. 2, there are a number of distortionmechanisms, which can, in principle, be corrected by complexdigital predistortion (DPD). However, if the sources of distor-tion are identified and addressed one at a time using the simplestsolution, the complexity of the final DPD can be dramaticallyreduced. We consider four distinct mechanisms of distortion.• Supply modulator gain and phase distortion, due to the fre-quency response of the supply modulator path. This lineartime-varying mechanism can be corrected with a linearequalizer (digital filter).

• RFPA gain variation with . This nonlinear time-in-variant distortion can be corrected with standard AM–AMand AM–PM methods using LUT data.

• Path delay difference between the and paths inFig. 2 occurs when both and are changing overtime, which can be corrected by adding delay in thepath.

• Remaining nonlinear time-varying distortion, such as dy-namic memory effects in the PA, are corrected with poly-nomial-based DPD after all other simpler corrections havebeen made.

In this approach, the order of operations is important: if thepath is not equalized first, the linear time-varying dis-

tortion of the supply modulator will become nonlinear time-varying distortion at the RFPA output, resulting in much moredifficult required linearization. Section IV-B provides experi-mental results of this targeted linearization method.

B. Gain of Supply Modulator

The signal path may have several analog componentsthat have amplitude and phase response with frequency. Themeasured response for the supply modulator shown in Fig. 10 isshown via the red line (in online version) in Fig. 11(b). After ap-plying digital filtering, the corrected gain and delay frequency


Fig. 11. (a) Block diagram showing method to measure the broadband gainand delay characteristics of the supply modulator path using a repeated chirp(frequency-modulated) excitation and “demodulating” to obtain I and Q com-ponents. There is a tradeoff between the resolvable supply modulator frequencyresponse, length of the chirp, lower and upper chirp frequency, and the reso-lution of the capture instrument (oscilloscope). (b) Measured gain and delayresponse of the linear supply modulator from Fig. 10 before and after the cor-rection.

dependence are flat to 70MHz. Since without knowing the prop-erties of the particular signal that is amplified, there is no bench-mark for how much bandwidth the modulator needs to have,the measurements are in far excess of the supply modulatorbandwidth and RF bandwidth. The correction is not expectedto change over operating conditions. The frequency response ismeasured by driving the path with a logarithmic chirpfrom 1 to 110 MHz every 4 ms. The resulting signal is multi-plied by the original signal shifted by 90° and low-pass filtered.Equivalently, the process could be thought of “modulating” thesignal (chirp) and “mixing” the resulting signal with the orig-inal chirp [see Fig. 11(a)]. This results in an in-phase (I) andquadrature (Q) component of gain over frequency. The adjustedgain and delay correct the time-varying linear response so thatthe distortion introduced by the supply modulator does not gothrough the nonlinear distortion of the RFPA. This simple equal-ization is the initial step taken to reduce spectrum regrowth.

C. PA Gain Linearization

Measured PA gain and insertion phase vary withthrough the path. For example, for low expected outputpower, an increase of input power will be needed becauseof lower gain with smaller . The PA has a complexexpected gain . The signal split ( ) adjusts for theexpected gain to make the system linear. This procedure cannotbe done using the same method as in Section IV-B becausethe PA has a nonlinear response and depends on the operating

Fig. 12. Measured PA AM–AM and AM–PM correction through static adapta-tion. The red line (in online version) is the extracted trend of the measured datapoints.

conditions. Instead, the PA is “corrected” by implementing aclosed-loop adaptation ( in Fig. 2). The initial starting pointfor the coefficient is for all (linear transmitter)and has “converged” when the difference between two consec-utive iterations is negligible. Fig. 12 shows the extracted trendfrom the variation in the magnitude and phase of the RFPAgain parameter. This type of PA data is presented in many ofthe publications on this topic, e.g., [21] and [30]. This step ofthe targeted linearization iteratively corrects for AM–AM andAM–PM static PA nonlinearities.

D. Path Delay Correction

The relative delay between the supply modulator and PApaths is due to the fact that both the supply voltage and inputRF voltage are changing. The and signal pathsmust be aligned in time at the PA, otherwise some distortionwill be incurred at the output. There is no distortion when

is low because then (see Table II forvalues of corresponding to different trajectories). Delaydistortion is much more apparent when there are large changesin amplitude, as this causes the greatest amount of amplitudeerror for small differences in time (Fig. 13). This behaviorcauses amplitude/phase correlation methods to fail. Thoughthere are several options to correct for path delay, Fig. 14 showsthe results of a simple brute-force approach of measuring theadjacent channel power (ACP) at a certain frequency offset,and setting the additional delay at a value that produces theminimum ACP.

E. DPD for Final Correction

Digital pre-distortion is the last implemented targeted lin-earization step. It aims to create a digital “inverse” of the PAdistortion [31]. In contrast to the previous sections, whichimplemented adaptive static or linear time-invariant pre-dis-tortion, digital pre-distortion here refers to polynomial-basedtechniques, which aim to correct dynamic linear and non-linear distortion of the transmitter system. Polynomial-based


Fig. 13. Illustration of signal path delay causing gain error. Steeperslopes correspond to a greater gain error because of the larger difference (at thatinstant of time) between the expected signal and actual signal.

Fig. 14. Measured ACP at two offsets (5 and 10 MHz) as a function of signalpath delay difference between the and paths gives the delay neededto minimize distortion due to time misalignment.

techniques use weighted basis functions to account for staticnonlinearity ( ), linear frequency response ( ), anddynamic nonlinearity ( ). The series terms should bechosen carefully to avoid creating unnecessary computationalcomplexity or over-fitting the system. Two examples of expan-sion sets are memory polynomial [32] and dynamic deviationreduction (DDR) [33].The DDR DPD routine has three complexity control param-

eters. is the order of nonlinearity, and only odd orders areused here. is the maximummemory depth in number of sam-ples, implying that the sample rate is relevant. For our case, thesample rate was 1/2 of the signal sample rate, around 100 MHz.The final control parameter is order of the dynamics, where

is completely static, and as increases, the DPD ap-proaches the full Volterra model.For PAs that have a minimum , the designer

can make use of piecewise Volterra series, as in [34]. The dif-ferent modes of operation of the PA can be modeled separatelyand have different expansion functions to account for differenttypes of dynamic distortion. The first mode is the linear region( ) and the second is saturation ( ).For the measured spectrum shown in Fig. 15, the “two-level”DPD refers to two predistorters. One operates at low amplituderegions ( 14 V drain voltage) and the other at high amplitude

Fig. 15. Normalized measured spectrum of the supply-modulated transmitteramplifying a W-CDMA signal at 2.14 GHz at various stages of the targetedlinearization process.

TABLE IVMEASURED TX PERFORMANCE FOR TWO TRAJECTORIES

regions ( 14 V) with and ,respectively. The DPD is implemented only after the other tar-geted linearizations have been applied and the complexity isminimized. If DPD were to be performed first, a significantnumber of additional termswould be needed to achieve the samelinearity.

F. Measured Transmitter Results

The final measured results are summarized in Fig. 15 andTable IV. In the measured spectrum, several stages of targetedlinearization are shown. The “initial” spectrum includes onlysupply modulator frequency response equalization, and in-cludes an a priori estimated delay mismatch likely less than1 ns from optimal. The spectrum labeled “initial signal splitand time alignment” shows the result after the first iterationto correct the static AM/AM and AM/PM of the PA througha LUT, as well as the delay correction for minimal ACP. Thefinal signal split result is shown after the sixth iteration. The“two-level DDR DPD” is the resulting spectrum after fouriterations on the DPD coefficients. Note that iterations are notunusual in commercial DPD implementations, and some of theiterating and fine tuning can be done while the transmitter isactive.Table IV compares two trajectories on the same PA from

Fig. 8 and a custom-designed supply modulator [11]: drivemod-ulation (A in Fig. 1) with set to 32 V and the trajectory in


Fig. 9 with peak reaching 32 V. Note that the supply-mod-ulated trajectory results in a measured composite average trans-mitter PAE of 52.5% with 8-W average output power for a 7-dBPAR signal with 23-MHz supply modulator bandwidth. The lin-earity is met for W-CDMA downlink signals, with an errorvector magnitude (EVM) below 1%. To meet linearity, in thiscase, the PA average drain efficiency was 75.9% compared to30% for the drive modulated case.The efficiency measurements for the supply-modulated trans-

mitter are not straightforward since they include measurementsof both supply modulator and PA efficiencies. Briefly, first thesystem efficiency is calculated as the PA output power, ,divided by the supply modulator input power. is measuredby an average power meter with a low-impedance supply modu-lator-PA interconnect (Section IV). The second step is to replacethe low-impedance interconnect by a current probe, which de-grades linearity, but the system efficiency remains nearly un-changed. The final step is to find the component efficienciesusing the instantaneous voltage and current output of the supplymodulator captured by an oscilloscope. We believe these reflectthe actual component efficiencies, provided that their product isvery nearly equal to the system efficiency.An interesting conclusion from the results in Table IV can be

drawn by observing the dissipated heat for the two trajectories.When the optimized trajectory is compared to the flat trajectory(A), which corresponds to drive modulation, operating from abattery the supply-modulated transmitter would last 75% longer,and in a fixed installation consume 43% less power. PA dissipa-tion is reduced from 19.8 W to only 2.7 W, reducing the coolingrequirements. In the supply-modulated transmitter, 61% lessheatis produced, and more importantly, the transistor in the PA op-erates with 86% less heat. The power dissipation is reduced, butalso spread between the PA and supply modulator, reducing fur-ther heat sinking requirements and thermal device stress.

V. DISCUSSION

The general supply-modulated transmitter architecture fromFig. 2 introduces considerable complexity in order to improveoverall efficiency. An efficient dynamic supply is added to anefficient RFPA, and the supply introduces additional distortion.This paper shows how to characterize the PA in order to de-termine supply requirements, and then how to correct distor-tion using a simple targeted linearization process. The imple-mentation details of all the steps described here depend on thesignal characteristics, in particular on the signal envelope band-width, rather than the signal I and Q component bandwidth. Forexample, a Gaussian multiple shift keyed (GMSK) signal with4-MHz double-sided complex modulation bandwidth has a con-stant amplitude, with 0-Hz envelope bandwidth. In this case, nosupply modulator would be required ( ). Consider nextthe spectrum of a four-tone 4-MHz bandwidth [orthogonal fre-quency division multiplexing (OFDM)] signal shown in Fig. 16.Though the I and Q components are band-limited to 4 MHz, theamplitude of the signal has frequency components extending farbeyond 20 MHz. In this case, the supply modulator bandwidthchoice will determine the amount of distortion that has to bedealt with [22]. The signal split needs to be chosen tominimize distortion while maintaining high efficiency.

Fig. 16. Simulated four-tone spectrum showing the I, Q, and amplitude com-ponents of a signal. While the I and Q are well within a 5-MHz bandwidth, theamplitude (and therefore, the supply modulator) bandwidth has frequency com-ponents well beyond 20 MHz of the signal.

Increased instantaneous transmission bandwidth presentsa challenge to the supply-modulated transmitter technique,placing more demands on supply modulator bandwidth,PA-supply modulator interconnect, and signal timing accu-racy. As discussed previously, the linearity degradation canbe reduced by selecting a less aggressive signal split inexchange for PA efficiency. A second option is to design thesupply modulator, interconnect, and timing alignment mecha-nisms to meet the more stringent linearity requirements, thusdegrading system efficiency via supply modulator or digitalpower dissipation. codesign of the transmitter system allowsfor the best tradeoff of PA, supply modulator, and digital powerconsumption for highest overall system efficiency.In the general supply-modulated system from Fig. 2, the

average transmitter efficiency (1) strongly depends on theefficiency of the supply modulator, which, in turn, dependson the required supply modulator bandwidth and slew-raterequirements. A combination of a high-performance linearamplifier and a standard switched-mode power converter, asshown in Fig. 10, can serve laboratory testing and character-ization purposes for a range of signals, and for various polarsplit designs, but at the expense of reduced efficiency. To reachhigh-efficiency targets for the transmitter system, it is essentialto consider techniques to improve dynamic response capabili-ties of a high-efficiency switcher in the supply modulator. Forexample, an optimum signal split between the linear ampli-fier and the switcher has been considered in [35]. Multilevelswitcher configurations have been investigated in [36] and [37].An approach based on high-bandwidth multiphase concept [38]and soft-switching techniques [39] has recently demonstrateda switched-mode supply with 10-MHz large-signal trackingbandwidth, more than 200-V s slew-rate capability, togetherwith efficiency exceeding 90% [40]. Design, implementation,and integration of such more advanced supply modulatorsin vector-split polar transmitters remains an area of activeresearch.In summary, the general supply-modulated transmitter from

Fig. 2 has a digitally reconfigured signal split, which enablesany trajectory from Fig. 1, or even a combination of trajectoriesthat varies in time. Although specific versions of this approach


have been demonstrated in the literature with excellent results,to the best of our knowledge, a general approach to PA char-acterization, supply modulator requirement determination, andtargeted distortion correction is for the first time presented. Thespectrum in Fig. 15 and the experimental results in Table IV val-idate the approach on an example W-CDMA 40-W peak-power2.14-GHzGaNPAwith a 69.1% efficient supplymodulator. Thesupply modulated transmitter composite PAE is measured to be52.5% with 61.0% less heat produced than in the drive modu-lated linear amplifier. It is further shown that the heat dissipationis distributed between the system components reducing thermalstress on the RF transistor.

ACKNOWLEDGMENT

The authors are grateful to TriQuint Semiconductor,Richardson, TX, for generous device donations and helpwith packaging, and to R. Woolf , Texas Instruments Incorpo-rated, Longmont, CO, for many useful discussions.

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John Hoversten (S’03–M’11) received the B.S.degree from Embry-Riddle Aeronautical University,Prescott, AZ, in 2005, and the M.S. and Ph.D.degrees from the University of Colorado at Boulder,in 2008 and 2010, all in electrical engineering. Hisgraduate research concerned the area of high-ef-ficiency RF power amplification with a focus onharmonic-tuned PA design and ET techniques.Since 2008, he has been involved in research

efforts centered around RF front end efficiencyenhancement with Texas Instruments Incorporated

(formerly National Semiconductor). He is currently an RF/system DesignEngineer with Silicon Valley Laboratories, Texas Instruments Incorporated,Longmont, CO.

Scott Schafer (S’10) received the B.S. degree inengineering physics from the Colorado School ofMines, Golden, in 2010, and is currently working to-ward the Ph.D. degree at the University of Coloradoat Boulder.His research has included millimeter-wave

near-field probing. His current research interests in-clude GaN monolithic microwave integrated circuit(MMIC) microwave PA design and high-efficiencylinear transmitters.

Michael Roberg (S’09) received the B.S. degreein electrical engineering from Bucknell University,Lewisburg, PA, in 2003, the M.S.E.E. degree fromthe University of Pennsylvania, Philadelphia, in2006, and is currently working toward the Ph.D.degree at the University of Colorado at Boulder.From 2003 to 2009, he was an Engineer with Lock-

heed Martin–MS2, Moorestown, NJ, where he wasinvolved with advanced phased-array radar systems.His current research interests include microwave PAtheory and design and high-efficiency radar and com-

munication system transmitters.

Mark Norris (S’08) received the B.S. degree in elec-trical and computer engineering and Ph.D. degree inmultiphases tracking power supplies from the Uni-versity of Colorado at Boulder, in 1989 and 2012, re-spectively.For four years, he designed gas chromatography

equipment for Base Line Industries. He spentthe next two years implanting power supplies forsputtering equipment up to 30 kW. From 1995 to2005, he was Lead Electrical Engineer for pulseoximetry with Ohmeda–Datex Ohmeda–GE, where

he successfully applied multiplexing techniques from communications toenhance the cost and performance of pulse oximeters. He is currently withTexas Instruments Incorporated, Longmont, CO, where he designs integratedcircuits (ICs) for mobile power applications. He holds 19 patents. His researchhas focused on efficiently extending the large-signal bandwidth of multiphaseswitch-mode power supplies beyond 20 MHz for use in EER of RF transmittersin LTE cell-phone base stations.

Dragan Maksimović received the B.S. and M.S.degrees in electrical engineering from the Universityof Belgrade, Belgrade, Yugoslavia, in 1984 and1986, respectively, and the Ph.D. degree from theCalifornia Institute of Technology, Pasadena, in1989.From 1989 to 1992, he was with the University

of Belgrade. Since 1992, he has been with the De-partment of Electrical, Computer and Energy Engi-neering, University of Colorado at Boulder, wherehe is currently a Professor and Director of the Col-

orado Power Electronics Center (CoPEC). His current research interests includemixed-signal integrated-circuit design for control of power electronics and dig-ital control techniques, as well as energy efficiency and renewable energy ap-plications of power electronics.Prof. Maksimovic was the recipient of the 1997 National Science Foundation

(NSF) CAREERAward, the 1997 IEEE Power Electronics Society TransactionsPrize Paper Award, the 2009 and 2010 IEEE Power Electronics Society PrizeLetter Awards, the 2004 and 2011 Holland Excellence in Teaching Awards, andthe 2006 University of Colorado Inventor of the Year Award.

Zoya Popović (S’86–M’90–M’99–F’02) receivedthe Dipl.Ing. degree from the University of Belgrade,Belgrade, Serbia, Yugoslavia, in 1985, and the Ph.D.degree from the California Institute of Technology,Pasadena, in 1990.Since 1990, she has been with the University of

Colorado at Boulder, where she is currently a Distin-guished Professor and holds the Hudson Moore Jr.Chair with the Department of Electrical, Computerand Energy Engineering. In 2001, she was a VisitingProfessor with the Technical University of Munich,

Munich, Germany. Since 1991, she has graduated 44 Ph.D. students. Her re-search interests include high-efficiency, low-noise, and broadband microwaveand millimeter-wave circuits, quasi-optical millimeter-wave techniques, activeantenna arrays, and wireless powering for batteryless sensors.Prof. Popović was the recipient of the 1993 and 2006 Microwave Prizes pre-

sented by the IEEE Microwave Theory and Techniques Society (IEEE MTT-S)for the best journal papers and the 1996 URSI Issac Koga Gold Medal. In 1997,Eta Kappa Nu students chose her as a Professor of the Year. She was the re-cipient of a 2000 Humboldt Research Award for Senior U.S. Scientists of theGerman Alexander von Humboldt Stiftung. She was elected a Foreign Memberof the Serbian Academy of Sciences and Arts in 2006. She was also the recipientof the 2001Hewlett-Packard (HP)/American Society for Engineering Education(ASEE) Terman Medal for combined teaching and research excellence.

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