Time domain envelope characterization of power amplifiers for linear andhigh efficiency design solutions

P. Medrel�, T. Reveyrand�, A. Martin�, Ph. Bouysse�, J.-M. Nebus�, J. Sombrin��XLIM -

°LIM, 123 Avenue Albert Thomas, 87060 Limoges Cedex, France

pierre.medrel@xlim.fr

Abstract—This paper focuses on the time domain envelopemeasurements based analysis of power amplifiers in order toimprove both linearity and efficiency of microwave transmitters.First of all, a versatile time domain envelope test bench ispresented. Then, two applications related to those RF PA mea-surements are reported. The first application concerns linearitycharacterization that can be specified in term of Noise PowerRatio (NPR) and Error Vector Magnitude (EVM). Those figuresof merit are essential to compute the final bit error rate ina system level simulation tool. A relationship between NPRand EVM is presented and validated by measurements. As aresult it can be advantageously used to simplify simulation andmeasurement procedures for the linearity characterisation ofdevices and subsystems. The second application is regardingenhancement of the trade-off between linearity and energyefficiency. In order to have a good efficiency, a 10 W class-BGaN Power amplifier is considered. The work presented here,proposes a solution for linearity specifications at large outputpower back-off thanks to a dynamic gate bias control related tolow instantaneous envelope power level. Meanwhile, a dynamicdrain bias control handles good efficiency at a constant gain forhigh instantaneous envelope power level. The measurement-basedgate and drain bias trajectory extraction will be fully detailedand take into account GaN dispersive effects such as thermaland trapping effects.

Index Terms—Instrumentation, NPR, EVM, nonlinear circuits,power amplifiers, dynamic bias, envelope tracking, linearity,Class-B.

I. INTRODUCTION

During the last years, most designs of RF transmit-ter/receivers were no longer based on CW characteristicsonly. The large spectrum widening increases considerably theneed for dynamic modulations analysis and characterizationof RF power amplifiers. In term of instrumentation, VectorialSignal Analyzer (VSA) has become a major tool for RFcharacterizations of power amplifiers in order to extract systemlevel criteria for linearity and efficiency. This paper presentsa calibrated VSA-based setup to measure RF time-domainenvelopes at the input and output of RF power amplifiersunder test. Two kinds of applications are presented. The firstone, is related to the linearity criterion for a multi-carrierdriven power amplifier : the noise power ratio. This ratiocan be measured thanks to an Error-Vector-Magnitude (EVM)measurement and does not require the acquisition of the wholespectrum. The second application concerns the validation ofenvelope tracking power amplifier demonstrator. A class-Bpower amplifier, opitimized in term of linearity thanks to adynamic bias voltage technique applied to both the gate andthe drain bias ports is described.

II. TIME-DOMAIN RF BASEBAND MEASUREMENT SETUP

The RF time-domain envelope measurement setup is de-picted on figures 1 and 2. This bench is combining a genera-tion/emission block and a reception/analyzing block.

The generation/emission block is dedicated to the shapingof the modulated signals expected to drive the power amplifierunder test. It is basically composed of a computer and a RFgenerator (SMU-200A by Rohde & Schwarz) and a linear50dB gain amplifier used to feed the RF signal into the PAunder test with an appropriate power level.

The receiver block focuses on the calibrated measurementsof the signals at reference planes where the power amplifierunder test is connected. The RF receiver is a vector signalanalyzer (FSQ-8 Rohde & Schwarz), which demodulates theRF signal, and returns the IQ flows. Clock and 10MHzsynchronization signals are provided by the SMU-200A. Ahardware envelope trigger is used to synchronize signal gen-eration and data acquisition. The input and output envelopesat the PA reference planes are collected sequentially throughcouplers with a switch, which requires input and output signalsto be software post-synchronized and time aligned.

The RF path between the VSA and the reference planesare taken into acount thanks to S-parameters measurementsof the test-set (couplers and cables connected to the VSA).The signal measured by the VSA is then de-embedded to thereference plane.

A 4-channels time-domain envelope measurement setupwould enable the phase consistancy in the measurementswaveform according to the simultaneous acquisition by allreceivers [1]. Unfortunatly, as depicted on figures 1 and 2,the receiver has only one RF input. Thus, input xptq andoutput yptq complex envelope measurements are performedsequentially. We need to perform a time-domain alignment asexplained in [2]. This time-domain alignment between inputand output signals is based on a correlation method detailedin [3]. When the DUT is removed and replaced by a directconnection, we can establish the relation between xptq andyptq as :

yptq � xpt� τq.e�j.φ (1)

The calculation of the crosscorrelation function Γyxptq, in thefrequency domain, leads us to :

FFT tΓyxptqu ����Xpfq

���2 .ej.p2π.f.τ�φq (2)

Then the group delay τ of the DUT (i.e. the complex envelopdelay) and the phase of the RF carrier frequency φ can be

extracted from a linear regression according to :

Arg tFFT tΓyxptquu � 2π.f.τ � φ (3)

In this paper, all signals measured at the input xptq andthe output yptq are time-domain aligned and phase correctedthanks to the crosscorrelation method applied with the idealsignal (the IQ data generated with the computer) such asXpfq � Xmeaspfq.e

j.p2π.fτ�φq.

A. Bench for Noise Power Ratio measurements

This setup (figure 1) is related to section III which demon-strates the capability of a commercially available EVM equip-ment to measure NPR as expected by theoretical analysis andsimulations in [4]. For this analysis, the SMU-200A is used

DUTSMU

NPRgenerator

RF PA

VSA

50Ω

RF Meas.

Fig. 1. Test set-up built for the experimental measurement of NPR with anEVM analyzer.

to supply a digitally modulated signal (a filtered 16-QAM).An auxiliary generator (a Rhode & Schwarz SMBV-100A) isused to generate a notched NPR signal. For that purpose, thesetwo signals are combined through a resistive 3-dB coupler andthe resulting signal is linearly amplified to drive the input ofthe power amplifier under test. The filtered 16-QAM signalspectrum is inserted within the notched bandwidth of theNPR Signal stimulus and is used as a noise probe for NPRcalculation. In this paper, the VSA is used both for spectrummeasurement and for EVM measurement in order to compareNPR calculated from different methods, but it is possible todetermine the NPR value only from EVM measurements. TheNPR signal has to be generated but not necessary measured.

B. Bench setup for Envelope Tracking measurements

This setup (figure 2), related to section IV, is a versatilebench dedicated to envelope tracking power amplifier (ET PA)characterizations [5].

The test bench used here is similar to the previous one butincludes two arbitrary waveform generators (AWG) to drivethe bias ports of the power amplifier under test. Dynamic biasvoltages and currents are aquired with a scope. The computercontrolled set-up enables the tuning of time alignment betweenRF signal envelope and dynamic biasing signals. The align-ment can be checked with a diode envelope detector connectedto the scope. The computer is used to generate and upload IQ

SMU

AWG

SCOPE

COMPUTER

AWG

IQEnvelope

LF PA

RF PA 50Ω

Gate bias function

computation

Drain bias function

computation

VSA

DUT

Vin Vg VdIdLF Meas.

RF Meas.

I

Q

Fig. 2. Test bench used for gate and drain envelope tracking purposes.

flow into the RF generator, and to process base band signalsloaded into arbitrary waveform generators (AWG) for drainand/or gate bias tracking purpose. A high current broadbandamplifier (DC-5MHz) is used to amplify the drain bias signal.

III. NOISE POWER RATIO : THE LINEARITY CRITERIONFOR MULTI-CARRIER BEHAVIOR OF POWER AMPLIFIERS

Noise power ratio (NPR) criterion is well suited for theanalysis of linearity of power amplifiers driven by a multi-carrier signals [6]. NPR gives a better indication of the amountof intermodulation distortion as far as two-tone IM3 is nota communication signal and ACPR figure of merit is oftenconsidering only one modulated carrier. The knowledge ofNPR value is of prime importance for the design of transpon-der used in satellite systems. This section will present threedifferent ways to measure NPR at the output of a RF poweramplifier. The first method is a RF spectrum measurementfor which intermodulation product power is displayed thanksto a notch. The second method does not require a notch butneeds the acquistion of both input and output fundamentalcomplex envelopes in order to calculate an equivalent gain ofthe PA. The last method can be performed with a MER orEVM analyzer.

A. NPR spectral measurement : the notch method

Fig. 3. NPR measurement using the notch method.

As far as a sum of several modulated signals can bemodeled as Gaussian noise, the classical approach for NPRmeasurement is based on the generation of a band-limited

gaussian white noise including a notch impressed at thecenter frequency. The power amplifier nonlinearities generateintermodulation products partially filling the notch in terms ofpower spectrum as illustrated on figure 3. NPRmeasured isthen defined as the ratio of the average output power withinthe notch (N ) to the average output power outside the notch(C �N ).

NPRmeasured �C �N

N(4)

The true NPR is then equal to :

NPR �C

N� NPRmeasured � 1 (5)

where NPR and NPRmeasured are linear power quantities.

B. NPR envelope measurement : the equivalent gain method

If NPR signal is digitally generated, one have to take into ac-count a trade-off : on one hand the ratio of the notch bandwidthhas to be as small as possible but should include at least 100intermodulation tones in order to minimize the variance of thein-notch average power [7]. This spectrum-based measurementtechnique only involves the output spectrum but requires thegeneration of very large number of tones as presented in [8]and [9]. An alternative method, which requires both inputand output RF complex envelopes, consists in measuring theNPR from a notch-less signal. This method introduced by [10]and already used with multitone SSPA designs [7] may bemeasured with a VSA based measurement setup such as theone described in the first section. This method, the equivalentgain approach, assumes that the power amplifier exhibits amemoryless non-linearty fNL such as :

yptq � fNL pxptqq (6)

where x and y are the measured complex envelopes around thefundamental frequency at the input and output of the poweramplifier, respectively.

According to x is a zero-mean stationary Gaussian randomsignal, one can apply the Bussgang theorem [11] extendedto the complex case, to include phase as well as amplitudenonlinearities [12], to define the equivalent gain λ such as :

yptq � λ.xptq � nptq (7)

where the output signal yptq is represented as a sum of anundistorted component λ.xptq and the intermodulation noisenptq generated by the nonlinearity. The equivalent gain λ canbe calculated from input/output measured complex envelopesas :

λ �RxyRxx

�E ryptqx�ptqs

E rxptqx�ptqs(8)

The NPR is a carrier-to-noise ratio measurement that canbe expressed thanks to the equivalent gain :

NPR �C

N�E�pyptq � nptqq pyptq � nptqq

��E rnptqn�ptqs

(9)

with

nptq � yptq � λ.xptq (10)

This ratio is consistant with the notch method for NPRmeasurements when the calculation is done only in a lim-ited frequency bandwidth of interrest ∆ around the centerfrequency:

NPR|dB � 10 log10

���

°fiP∆

}λ.X pfiq}2

°fiP∆

}Y pfiq � λ.X pfiq}2

�� (11)

C. Measuring NPR with an EVM analyzer

In phase (I)

In quadrature (Q)

Ij

Qj

δQj

δIj

Fig. 4. Top right quarter IQ quadrant for a 16-QAM modulation. For a givensymbol j, ideal (cross) and actual (circle) locations define Ij , Qj , δIj andδQj in volts.

Single tone digital modulations are mainly tested accordingto two criteria : the error vector magnitude (EVM ) andthe modulation error ratio (MER) defined according to thecontellation of the IQ voltage data as following voltage ratio[13] :

MER �

gffffffe

N°j�1

�I2j �Q2

j

�N°j�1

�δI2j � δQ2

j

� (12)

EVM �

gfffe 1N

N°j�1

�δI2j � δQ2

j

�

V 2max

(13)

where Vmax is the magnitude of the vector to the outermoststate of the constellation. The in-band carrier-to-noise powerratio can be expressed as :

C

N�MER2 �

�1

EVM � V

2

(14)

where V � Vmax

Vrmsis the voltage peak-to-mean ratio of the ideal

constellation. Some values of this ratio are given on Table IThe main test signal for NPR measurement is a band-

limited white gaussian noise with a notch of less than 5%of the total bandwidth located at the center of the bandwidth.

TABLE IPEAK-TO-MEAN RATIOS FOR CONTELLATION SIZES

Modulation format VBPSK 1QPSK 1

16-QAM 1.34132-QAM 1.30364-QAM 1.527

The main test signal for EVM measurement is a carrier withdigital modulation of either phase (PSK) or two-dimensionamplitude (QAM) or amplitude and phase (APSK). EVM canbe measured on a single carrier driving the non-linear amplifieror on one test carrier in a multiplex of many carriers. The othermodulated carriers in the multiplex can be replaced by whiteGaussian noise. The measurement of EVM is then performedon the modulated carrier inside the notch in the center of thewhite Gaussian noise bandwidth

Fig. 5. Signal composed of notched white Gaussian noise and test carrierwith digital modulation inside the notch.

Figure 5 illustrates the spectrum of the signal used forNPR characterization from EVM measurements. In the workreported here, the white gaussian noise is 5 MHz bandwidthwith a 5% notch at the center frequency. A filtered (roll-off=0.35) 200 ksymbol/s 16-QAM has been added at the centerfrequency as illustrated in figure 1. This modulation is used asa NPR probe. The EVM measured from this modulation willbe related to the global NPR as far as the power density ofthe digital modulation is the same than the white noise. NPRin dB is then :

NPR|dB � 20 log10 pEVM � V q � 10 log10 pRq (15)

where R is the ratio of white noise power density (outsidethe notch) to modulated tone power density located within thenotch. It is better to set R close to 1 in order to minimize thedisturbance produced by the modulation into the NPR signal.Figure 6 presents NPR measurements performed both with thenotch method and with the EVM method. Measurements ofNPR and EVM show good agreement when performed in thesame conditions. The great advantage of this method is thatthe white noise does not need to be measured.

measured NPR

NPR derived from measured EVM

measured EVM

NPR

(dB

)

10

15

20

25

30

35

40

45

50

EVM

(%

)

0

2

4

6

8

10

12

Output power (dBm)−10 0 10 20 30 40

Fig. 6. Measured NPR, measured EVM and NPR derived from measuredEVM for a Cree CGH40010 GaN HEMT amplifier at Freq=3.2 GHz,Vds0=28V, Idsq=200 mA, Vgs0=3.1 volts.

IV. LINEARITY AND EFFICIENCY IMPROVEMENT OF RFPOWER AMPLIFIERS

The second application reported here concerns an experi-mental study of combined dynamic gate and drain biasing forhigh efficiency and linear power amplifier. This technique isapplied here to a class-B 10W GaN power amplifier at S-band.

The PA under test is a commercially available test boardCGH27015-TB from CREE. The purpose of this study is todemonstrate the benefit to apply a dynamic gate bias controlat low instantantaneous envelope power levels of the RF inputmodulated signal [14], while a dynamic drain bias control isapplied at medium and high instantantaneous envelope powerlevels.

The test bench has been already presented in section IIand figure 2. An important aspect of this work concerns thecharacterization of the dynamic behaviour of GaN devices forthe gate and drain bias trajectory extraction. A time domainenvelope measurement system is necessary to take into accountdispersive effects such as trapping and self heating effects [15].The proposed technique has been applied to the amplificationof a 16-QAM modulated signal at 2.5 GHz. The figure 7illustrates the purpose of handling : a dynamic gate bias controlis applied at low input power (below Pth2) to obtain a constantpower gain. This approach requires to pull the gate voltage alittle above the pinch-off point for any input power level belowPth2. During the dynamic gate bias control, the drain biasvoltage is kept constant to its minimal value of 15V. For inputpower levels above the threshold Pth2, the gate bias voltageis kept constant at the pinch-off value (-3V ) and a variabledrain bias voltage is applied.

Althought a quasi-static characterization of the PA is nec-essary to identify the bias strategy, a dynamic characteri-zation of the PA is compulsory for an accurate extractionof appropriate gate and drain bias trajectories taking intoaccount the dispersive effects. In a first step, dynamic AM/AMcharacteristics between PA output signal and base band signalare measured for a 1MSymb/s 16-QAM modulated signal.During this first step, the gate bias of the PA is fixed atthe pinch-off value (VGS0 � �3V ) and measurements areperformed at different DC drain bias values varying from 15V

gate bias function drain bias

function

Pth2=23dBm

Pth2=23dBm

Input power range 1constant VDSO=15V

variable gate bias VGSO

illustration of gate bias control

Input power range 2variable drain bias VDS0

constant VGSO=-3V

VDS0=28V

VDS0=15Vconstant gain trajectory targetted

Input power (dBm)

Gai

n (

dB

)G

ate

bia

s vo

ltag

e (V

olt

s)

Dra

in b

ias

volt

age

(Vo

lts)

16

14

12

3632282420

6

8

10

-2.6

4 8 16120

-2.9

-3.0

-2.7

-2.8

26

22

28

20

14

16

18

24

0 4 8 12 16 20 24 28 32 36

Fig. 7. Principle of the proposed method to target a constant gain trajectoryfor a class-B PA (up), and representation of drain and gate bias functions(down).

up to 28V . Measurement results are plotted in figure 8.

Normalized instantaneous magnitude of the base band signal (Volts)

Inst

anta

neou

s en

velo

pe g

ain

(dB

)

High level range :VGSO has to be fixed

at the pinch-off point (-3V)VDSO has to be dynamically controlled from 22V to 28V

Low level range :VDSO has to be fixed to 22VVGSO has to be dynamically

pulled-up above the pinch off Vinth

VDSO=28V

VDSO=15V

VDSO=22Vconstant gain

trajectory targetted

Fig. 8. Extraction of the drain and gate bias functions from dynamic AM/AMmeasurements.

A corresponding threshold of the input envelope V inth isidentified as indicated in figure 8. For instantaneous envelopelevels smaller than V inth a dynamic gate bias control must beapplied. It consists in weakly pulling the gate bias voltage alittle above the pinch-off value until the instantaneous envelopegain characteristic becomes constant versus input power at lowlevel. Above the threshold value V inth, the gate bias voltageis maintained at a fixed value of -3V (class-B operation) andthe drain bias voltage is varied over the 22V - 28V rangeas a function of input instantaneous envelope variations. In alast step, time alignment between input envelope and gate anddrain biasing signals is performed to ensure optimal operationof the transistor.

One of the main interest of this characterization tool, isthat it provides visual criteria for the extraction and the

tuning of drain and gate bias functions. An important criterionused during successive experiments is the dynamic AM/AMcharacteristic flatness.

0 0.4 0.8 10.2 0.9 0 40 80 120 160 200 240 2800

1

2

4

5

6

3

6

0

1

2

4

5

6

3

0

20

10

14

24

6

18

0

20

10

14

24

6

18

0 40 80 120 160 200 240 2800 0.4 0.8 10.2 0.9

Inst

anta

neou

s en

velo

pe

gain

(dB

)

0

1

2

3

4

5

6

7

0

2

4

6

8

10

12

Inst

anta

neou

s en

velo

pe

gain

(dB

)

Normalized instantaneous magnitude of the base band signal (Volts)

Samples

Vin

Vin

Vou

tV

out

Vin

Vin

Vout

VoutNon constant

gain at low level

Constant instantaneous gain

Fig. 9. Dynamic AM/AM between PA output signal and base band signal(left). Corresponding magnitudes of RF signal envelopes at the PA under testinput and output reference planes (right). PA is in class-B operation withonly the dynamic drain bias control applied (up) and with both drain and gatedynamic biases (down).

Figure 9 (up) shows dynamic AM/AM obtained when thePA is biased at the pinch-off point and when only a dynamicdrain bias is applied (22V<VDSO<28V ). The correspondingmagnitude of input and output RF signal envelope waveformsclearly indicates a non-linear behavior of the PA under testat low level. Optimized dynamic AM/AM profile is shown infigure 9 (down) when both dynamic gate and drain signals areapplied and tuned. AM/PM conversion remains low (below 5degrees) for this amplifier under test. The corresponding drainand gate bias trajectories extracted from dynamic AM/AMmeasurements are presented in figure 10.

−3,1

−3

−2,9

−2,8

−2,7

−2,6

−2,5

21

22

23

24

25

26

27

28

29

0 0,2 0,4 0,6 0,8 1

gate bias function

drain bias function

Gat

e bi

as v

olta

ge (

Vol

ts)

Dra

in b

ias

volta

ge (

Vol

ts)

Normalized instantaneous magnitude of the base band signal (Volts)

Fig. 10. Drain and gate bias functions extracted from dynamic AM/AMmeasurements.

Time domain waveforms of the input RF signal envelopeband dynamic gate and drain bias voltages are shown in figure11.

In figure 12, power added efficiency and EVM measurementresults are shown for two different cases. A first measurementis performed when the PA is biased in class-B mode (IDS0 =

drain bias voltage

gate bias voltage

input envelope at high RFinput level

28V

22V

-2.6V

-3V

input envelope at low RFinput level

gate bias voltage

drain bias voltage

22V

25.5V

-3V

-2.6V

Fig. 11. Time domain waveforms at 37dBm output power level (left) and at33dBm output power (right).

0mA) with a fixed drain voltage of 28V. A second measure-ment is done when dynamic gate and drain bias are applied.Significant improvement of EVM is obtained at backed-offpower while ensuring efficiency enhancement.

30

35

40

45

50

55

60

65

33 34 35 36 37 38 39 40 41

Dynamic gate and drain biasing

Conventional class-B

1

2

3

4

5

6

7

8

9

10

33 34 35 36 37 38 39 40 41

Conventional class-B

Dynamic gate and drain biasing

Output power (dBm) Output power (dBm)

PA

E (

%)

EV

M (

%)

Fig. 12. PAE (left) and EVM (right) measurements versus output power.

V. CONCLUSION

This work has presented an experimental test bench thatis expected to be a usefull tool for the characterization ofpower amplifier driven by multi-carrier stimuli. Two differentapplications have been carried out.

In the first one, a relationship between two system metricshas been experimentally demonstrated. We prove that EVMcan be used as a baseband figure of merit to access themulticarrier NPR. A digitally modulated carrier is used as anoise probe to derive the NPR from EVM. The mutlicarrierbehavior is emulated by a digital generation of multisine withrandom phases. It is important to note that, in this approach,the notched wide-band gaussian noise signal does no longerhave to be measured to compute the NPR. The main benefitis that one can predict the multicarrier behavior of a PA, evenif it is driven by broadband stimuli, by measuring the in-band distorsions, with a simple commercial high resolutionand narrow-band IQ demodulator.

In the second one, we have focused on a dispersive-consciousness approach to precisely build an envelope trackingPA architecture. Several points have been discussed in ourstudy, and have been taken into account, such as dynamicAM-AM and AM-PM transfer characteristics, when the PAis driven by the useful signal. The test bench allows us toprecisely tune the drain and gate bias signals in real time byusing instantaneous EVM measurements.

The ultimate goal that can be achieved is the comparisonof several configurations in term of multiple optimizationconstraints such as DC-consumption, energy-per-bit transmit-ted, optimum receiver CNR, in order to reach the optimumoperating point of power amplifiers according to system levelspecifications.

ACKNOWLEDGMENT

The authors would like to thank the french space agencyCNES and Thales Alenia Space for their financial supports.

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