785

Class-E Power Amplifier in a Polar EDGE Transmitter

Nestor D. Lopez, Xufeng Jiang, Dragan Maksimovic and Zoya Popovic

Department of Electrical and Computer EngineeringUniversity of Colorado, Boulder, Colorado 80309, USA

Abstract- This paper presents the design and characterizationof a 880-MHz class-E power amplifier (PA) designed to operate ina polar transmitter for EDGE signals. The amplifier is intendedto be supplied from a 3.6 V battery using a linear amplifier asan envelope tracker, which limits the maximum drain voltage to3.3 V. With a +7.6 dBm input signal the maximum output power(VDD = 3.3V) is +22.4 dBm with 14.9 dB of gain, a drain efficiencyof 71.6% and PAE of 69%. An output power dynamic range of15.4dB is achieved when the voltage is varied from 0.5-3.3V.Taking into account the statistics of an EDGE signal, the meandrain efficiency and PAE are 75.7% and 64.4%, with a meanoutput power of +18.26 dBm.

Index Terms- Envelope elimination and restoration, envelopetracking, envelope amplifier, power amplifiers, Class-E amplifier,EDGE

I. INTRODUCTION

Polar modulation has become increasingly popular in RFtransmitters due to its potential to simultaneously improvelinearity and efficiency [1]-[7]. Increasing the transmitterefficiency extends battery life and reduces heat dissipation.

In current wireless communication systems, in order toimprove the spectral efficiency, the RF carrier is usuallymodulated with quadrature I and Q signals that result in anon-constant signal envelope with a relatively large peak-o-average ratio. This requires a high degree of power amplifier(PA) linearity. Therefore, the PA is usually operated in classA or a backed-off AB mode with maximum efficiencies below30%. In this paper, the use of a high-efficiency class-E PA in apolar transmitter that operates with a constant envelope phasemodulated RF signal and the signal envelope restored throughthe RF power supply using a linear amplifier.

Figure 1 shows a possible polar transmitter architecture.The RF signal is divided into two paths; a constant-envelopephase-varying RF signal which is directly fed to the PA, andthe envelope signal processed by an envelope tracker whichmodulates the supply voltage to the PA. As in the EnvelopeElimination and Restoration technique (EER) [8], the signalsare combined at the PA output, making the output signal anamplified version of the original signal.The class-E mode of operation lends itself well to the polar

transmitter architecture. In class E, the transistor is operatedas a switch and the output circuit provides specific waveformshaping of the current and voltage across the active devicethat minimizes losses and is relatively tolerant to device andparasitic variations [9]-[12]. As shown in [12], for a 50% dutycycle of the switch drive, the voltage across the transistor isgiven by:

- _D/A Converters

Fig. 1. Block diagram of a polar transmitter. A random string of symbolsis stored in the FPGA board as a look up table and transmitted at 2.17MHzwith an over-sampling ratio of 8. The FPGA outputs the amplitude and phasecomponents of the EDGE signal. The phase signal is fed to the input of theamplifier while the envelope is fed through the supply. The envelope trackercan be either a linear amplifier or a switching converter.

vs(t) w Ct-1.86(cos(5t -32.50) -cos(32.50))],coutwjs

(1)where ID is the average drain current, Cout is the device non-linear output capacitance, and fs is the switching frequency. Ifthe DC supply voltage is provided through an ideal RF choke,the average value of the switch voltage has to be equal to theDC drain supply voltage VDD:

VDD = If vs(t)dt = IDTS o TbS Cot0 (2)By properly terminating the ideal class-E PA, the power

delivered is

Pout= IREI2tt 1 )-RE(1.861D)2 (3)where RE is the real part of the optimal class-E loadimpedance, ZE = RE +JXE and 'out is the magnitude of theoutput current i,ut. Equation 3 becomes,

Pot =2IRE(1.86wSCOut )2V2DPu=2 V (4)For a lossless output matching network, the output power is

linearly proportional to VDD. As a result, the output voltageof a class-E PA across a 50 Q can be linearly varied byvarying the drain voltage. Ideally, the optimal efficiency is notaffected when the bias is varied, since the transistor current and

0-7803-9542-5/06/$20.00 C2006 IEEE

Authorized licensed use limited to: UNIVERSITY OF COLORADO. Downloaded on January 14, 2009 at 19:34 from IEEE Xplore. Restrictions apply.

786

10

10 II I

-1 -050 0.1,

I 1-20

-30 -.

-40 -I/ %-50 -I

670-80

-90 ~-1 -05 0 0.5

Frequency [MHz]

(a)

10F0

-10

.F.2 -20-2030

g -40

6-50

X -60i

Frequency [MHz]

(b)

).7 tb

).6 >

).5 9

).4 -

).3 :~

).2

I I

Normalized Output Voltage

(c)

Fig. 2. EDGE signal spectral and statistical characteristics: (a) standardized spectral mask (dashed line) and simulated baseband signal spectrum (solid line);(b) simulated frequency spectrum of a constant-envelope phase-varying IQ baseband signal, when modulated this signal is fed directly to the amplifier; and (c)probability density function (solid line) and cumulative distribution function (dashed line) of the normalized signal voltage.

voltage amplitudes change with bias, but not their waveforms.In addition, the power can theoretically vary between zeroand the maximal available power from the device. However,the minimum power is constrained by feed-hrough and themaximum power depends on the power handling capabilitiesof the device. In class-E mode of operation, efficiencies above90% percent can be achieved in the low MHz range andaround 65% has been demonstrated at 10GHz [12]. In [10],the linearity of 10-GHz class-E PAs are examined and it isdemonstrated that these highly saturated PAs can be linearizedto some degree using polar modulation.

II. POLAR EDGE TRANSMITTER

EDGE is a communication standard that uses 8-PSK as itsmodulation scheme. This produces an RF signal modulatedboth in amplitude and phase. Figure 2a shows a basebandfrequency spectrum of the EDGE signal. The dashed linecorresponds to the envelope mask and the solid line to theEDGE signal produce from the FPGA in Figure 1. Figure2b shows the frequency spectrum of the normalized I and Qsignals at the output of an ideal IQ modulator. The combinedmodulated signal has a constant envelope and is directly fedto the amplifier.EDGE signals have a dynamic range of 16.4 dB with a peak-

to-average ratio of 3.7 dB over a 200-kHz bandwidth. Thereare several characteristics that make EDGE suitable for polarmodulation. For example, zero crossings are hard to implementin polar transmitters due to feed through in the PA. This isavoided in the EDGE 8-PSK modulation scheme. In addition,the power distribution function is weighted to a higher powerregion, optimizing the use of a saturated PA. Figure 2c showsthe probability density function and the cumulative distributionfunction of the EDGE envelope signal. From this data, themean value for a EDGE signal limited to 3.3V from its supplyvoltage can be estimated to be 2.16V.

In the implementation shown in Figure 1, a EDGE signalsegment consisting of 256 random symbols is stored as look uptable in a Xilinx Virtex II FPGA and streamed out repeatedly.Given the standard EDGE transmission rate of 270.833 kHz,

and an over-sampling factor of 8, the signals are streamedout of the FPGA at the rate of 2.17 MHz. Digital to AnalogConverters (DAC) and analog buffer circuits are used at each ofthe three outputs from the FPGA board: a normalized stringof the I and Q signals for producing the constant-envelopephase modulated signal, and the envelope signal which isused as a reference input for a linear amplifier that servesas the envelope tracker for the PA. As an alternative, we arealso considering a high-efficiency buck converter operated ata switching frequency of 4.3 MHz which is designed to have aBessel low-pass filter characteristic with a tracking bandwidthof 1.3 MHz [13]. With the nominal voltage of a single-cell Li-Ion battery equal to 3.6 V, the buck converter limits the PAsupply voltage VDD to a maximum of 3.3 V. The normalizedI and Q signals are combined in a commercial MiniCircuitsIQ modulator and mixed with a 880MHz oscillator. Theclass-E PA is driven by an off-he-shelf class-A 25-dB gainpre-amplifier capable of delivering +13.5 dBm with powerconsumption of 90mW.

III. DESIGN OF 880-MHz CLASS-E POWER AMPLIFIER

This section details the design and characterization of thehigh-efficiency class-E PA for the polar EDGE transmitter,Figure 3. The design method combines transmission lines andlumped components for the implementation of the match-ing networks. Transmission lines are used at the output topresent a high impedance to the transistor second harmonic.The fundamental-frequency input and output matching circuitsare implemented with lumped inductors and capacitors. Theamplifier is implemented on a Rogers TMM6 0.635-mm thicksubstrate (Er = 6). A 10-Q series resistor is included in thegate of the transistor for stabilizing the PA at the operatingfrequency.As presented in, e.g., [11], the class-E impedance is given

by

ZE 0.28 (5)ws Cout

).9

).8

Authorized licensed use limited to: UNIVERSITY OF COLORADO. Downloaded on January 14, 2009 at 19:34 from IEEE Xplore. Restrictions apply.

787

Fig. 3. Photograph of the hybrid 880-MHz class-E power amplifier withintegrated bias lines and DC blocking capacitors which also serve forimpedance matching. A 10f2 chip resistor in series with the gate terminalensures stability of the PA.

where the output capacitance for this particular device isestimated to be 1 pF based on measured S-parameters. Becausethe exact value of the output capacitance is not known, asource and load-pull measurement is performed to determinethe high-efficiency impedances. The only unknown in (5) isthe transistor output capacitance. If the value of this unknownis assumed to be in the order of 1 pF a load-pull can beperformed for the class-E impedances obtained with outputcapacitances in the range from 0.5 pF to 1.1 pF, as shownin Table I. Measurements are taken for VGG = -2 V, VDD= 3.5V and +lOdBm of input power. A trade-off analysisneeds to be made in terms of gain, output power and efficiencyfor choosing the desired impedances. Since the main goal ofthe project is to improve linearity and efficiency, the outputimpedance of 42 +j48 Q is chosen, corresponding to an outputcapacitance of 0.8 pF. The resulting PAE is 58% with a drainefficiency of 67%, a gain of 9.7 dB and an output power of+19.7 dBm.

TABLE ILOAD-PULL RESULTS PERFORMED ON THE TRANSISTOR USED TO

ESTIMATE THE OPTIMAL HIGH-EFFICIENCY IMPEDANCE.

Cout Ze 7id PAE G Pout(pF) (Q) (%) (%) (dB) (dBm)0.5 66 + j77 49 41 8 +180.6 55 + j64 58 48 8.2 +18.20.7 47 + jSS 55 47 8.7 +18.70.8 42 + j48 67 58 9.7 +19.70.9 37 + j43 62 55 9.6 +19.61.0 33 + j38 62 56 9.8 +19.81.1 30 + j35 62 56 10 +20

The amplifier final design is biased at VDD = 2.16 V (EDGEmean) and VGG = -1.7 V. The gate to source voltage isincreased from -2 V to -1.7 V in order to increase the gainand the output power. With VGG = -1.7 V, the drain current is72 mA. The input is matched to 15 + j35Q for an input returnloss of -10 dB. Figure 4a shows the measured power sweep,which resulted in a choice for the input power of +7.6 dBm.If the transistor is compressed further, the drain efficiencywill continue to increase but at the expense of gain and PAE.For this particular bias point, with +7.6 dBm of input power,

the output power is +19dBm with a gain of 11.46dB, drainefficiency of 75% and PAE of 70%.

IV. CHARACTERIZATION OF PA FOR EDGE OPERATIONFigure 4b shows the results for the measured output power,

gain and efficiencies for the class-E PA when VDD is sweptfrom 0.5V to 3.3V with VGG = -1.7V and an input powerof +7.6dBm. As can be observed from the figure the rid iShigh trough out the whole range, while the PAE is above 50%during substantial part of the sweep, ensuring high-efficiencyperformance for this particular applications. Considering theEDGE statistics the mean values Td, PAE and Pout are 75.7%,64.4% and + 18.26 dBm, respectively.

Figure 4c shows the AM4o-AM (solid line) and the AM4o-PM (dashed line) conversion. The AM4o-AM measurementsshow the output voltage variations produced to a 50Q loadby sweeping the supply voltage for fixed input power. For asupply voltage of OV the output voltage is non-zero due tofeed-hrough. A linear relationship is observed in the range ofinterest (0.5V to 3.3V) and can be described by,

Vout = 1.2VDD + 0.091V. (6)The AM4o-PM conversion curve shows the phase offset pro-duced by the amplifier as the supply is swept. As desired thisvalue is almost constant throughout the range of interest. Themeasurement shows significant variations in phase for supplyvoltages below 0.5 V.A summary of the measured PA properties is as follows:* When the drain bias is swept from 0.5V to 3.3 V, the

output power varies from +7.01 dBm to +22.45 dBmgiving a dynamic range of 15.44 dB.

* The drain efficiency, PAE and gain for maximal outputpower at VDD = 3.3V are 71.6%, 69% and 14.9dB,respectively.

* The maximal PAE is 70.2% obtained for a drain voltage of2.6 V. At this bias point, the output power is +20.55 dBm,with a gain of 13 dB and a drain efficiency of 74%.

* At a drain voltage of 0 V the output power is -4 dBm dueto feed-hrough.

* Due to feed-hrough, drain efficiencies higher than 100%can be achieved since the input power is not consideredin drain efficiency calculations.

* At high drain voltages the drain efficiency and PAEexceed 70%. Signals with statistics that are weightedtowards higher output powers are the ones that benefitfrom this technique.

Figure 5 shows the measured spectrum as compared to thestandardize EDGE mask. The deviation from the EDGE maskat the -50dB level can be attributed to the IQ modulatorinsufficient dynamic range, as well as various delays in thecircuit. These are topics of current investigations.

V. CONCLUSIONS

In summary, this paper presents a demonstration of a high-efficiency class-E PA suitable for a polar EDGE transmitter

Authorized licensed use limited to: UNIVERSITY OF COLORADO. Downloaded on January 14, 2009 at 19:34 from IEEE Xplore. Restrictions apply.

788

Input power [dBm]

(a)

Supply Voltage [V]

(b)

-20 b

Supply Voltage [V]

(c)

Fig. 4. Measurements for EDGE 880-MHz class-E PA with VGG =-1.7V. (a) Power sweep for VDD = 2.16V, the maximal PAE is 70% with a drainefficiency of 75%, gain of 11.46 dB and output power of +19 dBm for input power of +7.6dBm. (b) Measured output power, gain, drain efficiency and PAE forsupply sweep with input power of +7.6 dBm. (c) Measured AM-o-AM (solid line) and AM-o-PM conversion (dashed line).

10

E

C/)0ac-a-)

Fig. 5. Measured output spectrum of a PA in polar configuration.

at 880 MHz. The polar transmitter consists of an FPGA-controlled envelope tracker, a phase modulator, and the class-EPA. When the drain of the class-E PA is varied from 0.5 V to3.3 V, the amplifier shows a dynamic range of 15.44 dB, witha linear V,,t/VDD relationship and maximum output powerof +22.45 dBm. Considering the EDGE statistics the meanvalues r1d, PAE and Pout are 75.7%, 64.4% and +18.26dBm,respectively.

VI. ACKNOWLEDGEMENTS

This work is funded by National Semiconductors throughCoPEC, and by a Department of Education GAANN fellow-ship in Hybrid Signal Electronics.

[4] T. Sowlati, D. Rozenblit, R. Pullela, M. Damgaard, E. McCarthy, D. Koh,D. Ripley, F. Balteanu, and I. Gheorghe "Quad-band GSM/GPRS/EDGEpolar loop transmitter," IEE Journal of Solid-State Circuits, vol. 39, No.12, pp. 2179-2189, December 2004.

[5] F. Wang, D. Kimball, J. Popp, A. Yang, D. Lie, P. Asbeck and L. Larson,"Wideband Envelope Elimination and Restoration Power Amplifier withHigh Efficiency Wideband Envelope Amplifier for WLAN 802.1 1g Ap-plications," IEEE MTT-S Int. Microwave Symp. Dig., 2005, pp. 413-416.

[6] Wendell B. Sander, Stephan V. Schell, Mark Heimbach and Brian L.Sander, "Polar Modulator for Multi-mode Cell Phones," Tropian Inc.technology white paper

[7] J. Popp, D. Lie, F. Wang, D. Kimball, L. Larson, "A Fully-IntegratedHighly-Efficiency RF Class-E SiGe Power Amplifier with an Envelope-Tracking Technique for EDGE Applications," IEEE Radio and WirelessSymp. Dig., 2006, pp. 231-234

[8] L.R. Kahn, "Single sideband transmission by envelope elimination andrestoration," Proc. IRE, vol. 40, pp. 803-806, July 1952.

[9] F.H. Raab, "Idealized operation of class-E tuned power amplifier," IEEETrans. Circuits Syst. vol. CAS-24, No. 12, pp. 725-735, Dec. 1977.

[10] N. Wang, X. Peng, V. Yousefzadeh, D. Maksimovic, S. Pajic andZ. Popovic, "Linearity of X-Band Class-E Power Amplifiers in EEROperation," IEEE Transactions on Microwave Theory and Techniques,vol. 53, No. 3, March 2005.

[11] T. Mader and Z. Popovic, "The Transmission-Line High-EfficiencyClass-E Amplifier," IEEE Microwave Guided Wave Letters, vol. 5, No. 9,pp. 290-292, September 1995.

[12] S. Pajic, N. Wang, P. Watson, T. Quach, and Z. Popovic, "X-BandTwo-Stage High-Efficiency Switched-Mode Power Amplifiers," IEEETransactions on Microwave Theory and Techniques, vol. 53., No. 9.,September 2005.

[13] X. Jiang, N. L6pez, D. Maksimovfc and Z. Popovfc, "A Switched ModeEnvelope Tracker for Polar EDGE Transmitter," Paper Accepted to thePower Electronics Specialists Conference, 2006. PESC 2006.

[14] F.H. Raab, P. Asbeck, S. Cripps, P.B. Kenington, Z.B. Popovic, N.Pothecary, J.F. Sevic and N.O. Sokal, "Power Amplifiers and Transmittersfor RF and Microwave," IEEE Transactions on Microwave Theory andTechniques, vol. 50, No. 50, pp. 814-826, March 2002.

REFERENCES

[1] S. Mann, M. Beach, P. Warr and J. McGeehan, "Increasing the talk-ime ofmobile radios with efficient linear transmitter architectures," Electronics& Communication Engineering Journal, pp. 65-76, April 2001.

[2] M.R. Elliott, T. Montalvo, B. Jeffries, F. Murden, J. Strange, A. Hill,S. Nandipaku, and J. Harrebek, "A Polar Modulator Transmitter forGSM/EDGE," IEEE Journal of Solid-State Circuits, vol. 39, No. 12, pp.2190-2199, December 2004.

[3] F. Wang, A.H. Yang, D.F. Kimball, L.E. Larson, P.M. Asbeck, "Designof Wide-Bandwidth Envelope-Tracking Power Amplifiers for OFDMApplications," IEEE Transactions on Microwave Theory and Techniques,vol. 53, No. 4, pp. 1244-1255, April 2005.

Authorized licensed use limited to: UNIVERSITY OF COLORADO. Downloaded on January 14, 2009 at 19:34 from IEEE Xplore. Restrictions apply.