ESTIMATION OF RF PA NONLINEARITIES AFTER CROSS-CORRELATING

POWER SUPPLY CURRENT AND OUTPUT VOLTAGE

Ricardo Veiga, Pedro Mota, Jose Machado da Silva

INESC Porto, Faculdade de Engenharia, Universidade do PortoRua Dr. Roberto Frias, Campus FEUP, 4200-465 Porto, Portugal

[ee08064, dee05001, jms]@fe.up.pt

II. ESTIMATION OF NONLINEARITY

It has been shown that a weakly nonlinear, memoryless,time-invariant, PA's behaviour can be expressed by a third­order polynomial [11]. This fact has been explored todevelop in-circuit test circuits based in the observation ofthe input and output RF voltage signals [4, 12, 13].Likewise, one can estimate the PA's power transfercharacteristic after finding the polynomial

Pout = /31 Pin + /32 Pin 2 + /33 Pin 3 that best fits a set ofobserved input-output power pairs, and whose coefficientsallow us to compute Pin1dB and PinIIP3 points. Following

procedures similar to those presented in [11-13] one canobtain, respectively,

values. From this set of coordinates one can obtain thepolynomial that best fits the PA's input/outputcharacteristic and whose coefficients allow one to calculate1 dB compression ( Pin1dB ) and third order intercept

( PinIIP3 ) points values.

The methodology being presented here relies also on thepolynomial fitting approach, however, ordinates areprovided by the cross-correlation between output voltageand power supply current, instead. The remaining of thepaper presents in section II the procedure being proposed toestimate Pin1dB and PinIIP3 from the power transfer

characteristic curve, together with validating simulationresults. Section III shows how power measures can beobtained from the cross-correlation between voltage andcurrent signals, as well as, the mixer based circuit beingused as a correlator. Section IV highlights the mainconclusions.

Abstract - The present paper describes developmentscarried-out on estimating 1 dB compression and third­order intercept points after the cross-correlation betweenpower supply dynamic current and output voltage ofradio­frequency power amplifier. The underlining theory and acircuit that allows implementing this measurement on-chipare presented. Simulation results, including the analysis ofoptimum stimuli amplitudes and the Monte Carlo analysisto circuits' process variations are presented. These showthat good accuracy can be obtained with relatively simplemeasurement conditions.

I. INTRODUCTION

The search for on-chip RF testing methods has motivateddifferent research activities in the past decade [1-6].Nonlinearity estimation is among the most importantparameters which have driven this research [7, 8]. That isthe case with circuits operating with digital modulationssuch as Wide-bandwidth Code-Division for MultipleAccess (W-CDMA), which presents a high degree ofamplitude variation or, in other words, a high crest factor(CF). High linearity levels are required for transceiversoperating in these conditions to prevent signal compressionor clipping.

Traditional RF testing relying on high-end laboratoryinstruments provide accurate measures but are timeconsuming and expensive. On the other hand, accessingdeeply embedded circuits requires delicate electronicprobes. This is particularly true within modem systems-on­chip (SoC) devices that incorporate different circuits andfunctionalities on a monolithic substrate, such as, high­speed digital, memory, analog, and RF circuits. This highintegration of components makes SoC testing complex andcostly [9].

The lack of harmonized and universal RF structural testshave forced industries to resort to specifications' functionaltesting in order to ensure the required quality level of lowdefect ppm (ideally zero), eventually relying on both built­in and built-off test [9,10]. The methodologies presented in[12,13] allow testing a RF power amplifier (PA) fornonlinearity using a polynomial fitting approach, afterapplying single tone input stimuli sweeping the PA'sdynamic range and on capturing the respective output

978-1-4244-4617-9/09/$25.00 ©2009 IEEE

2 /31-/32- /32 -4/33(/31--1-)

10 10Pin1dB = ------------

2/33

and PinIIP3 = ~ :~ to estimate Pin1dB and PinIIP3 .

(1)

To obtain the coefficients of the best fitting polynomialthe following procedure was followed. If one obtains threeoutput power levels from the PA under test (Poutl,2,3 infigure 1), the values of the three coefficients ~l, ~2 and ~3,

can be obtained from the set of equations (2.a and 2.b)

Pout(\JV)

Pout3t----------~~

Pout2t--------....r

::p. Pin(\JV):::Iw

Pout1 = j31Pin1+ j32Pin1 2 + j33Pin13

Pout2 = j31Pin2 + j32Pin22 + j33Pin23 (2.a)

Pout3 = j31Pin3 + j32Pin3 2 + j33Pin33

which after applying Cramer's rule allows us to obtain

Pout11-------:tI

"'U"'U3·3·~ I'-Ja.OJ

Figure 1 - Weakly nonlinear, memoryless PA's transfercharacteristic.

Poutl Pin12 Pin13 Pin1 Poutl Pin13 Pin1 Pin12 Poutl

Pout2 Pin22 Pin23 Pin2 Pout2 Pin23 Pin2 Pin22 Pout2

Pout3 Pin32 Pin33 Pin3 Pout3 Pin33 Pin3 Pin32 Pout3 (2.b)/31= ;/32= ;/33=

Pin1 Pin12 Pin13 Pin1 Pin12 Pin13 Pin1 Pin12 Pin13

Pin2 Pin22 Pin23 Pin2 Pin22 Pin23 Pin2 Pin22 Pin23

Pin3 Pin32 Pin33 Pin3 Pin32 Pin33 Pin3 Pin32 Pin33

Pout \$ Pin (Real & Extrapolation)

Figure 2 - Power transfer curves obtained with a class ABamplifier.

Locating the intermediate stimulus in this zone allows also tominimize the deviation due to random noise in voltage andcurrent signals, as can be seen in figure 3.b), which was obtainedafter superimposing random noise, with a 30 dB signal to noiseratio, in the correlator's input signals. Similar conclusions wereobtained with different power transfer curves.

3.5 4 4.5 5

x 10.3

--Real

Measure 1

Measure 2Measure 3

~ Pin1dB (real)

-- Extrapolated

2.5Pin (yV)

1.5

0.14

0.12

0.1

_ 0.08~'S0c.. 0.06

0.04

0.02

00 0.5

Nevertheless, the three testing stimuli Pin1 ,2,3 have to beoptimized in order to obtain the best estimation accuracy forPin1dB and PinIIP3 . To find the best set of three stimuli to

be used a minimum search function min I (X), where X isx

the vector of the three stimuli amplitudes, and I(x) is the

error in the computation of Pin1dB, was employed.

Simulation results obtained within the Agilent ADS toolusing a class AB PA, revealed that choosing Pinl and

Pin3 in order that Pin} < Pin1dB < Pin3 , and Pin2 close

to the expected Pin1dB (figure 1), a very accurate Pin1dBestimation can be obtained. Figure 2 allows one to comparethe real power transfer curve against the extrapolated foundwith this procedure, and reveals that a very good match isobtained.

Figure 3.a) shows the variation of the Pin1dB estimation

error with the placement of the three stimuli in relation tothe expected Pin1dB ' keeping the distance among themconstant. It can be seen that when the middle value of thethree stimuli is close to the expected Pin1dB, the error is

very small. In fact, practically equal estimated and expectedvalues were obtained, i. e.,

PinldBest::::: PinldBexp =4,67dBm .

-2 0 2 4 6Mid:11e poirt dthe measulemen(dBm}

a)

; 10IJ..

o

-10

'"

I

".'I

\,"\\

"

\"',

.-....------

I--Pin1cB error I

8, , ,:2 04 ~

~IIIDlft~thIn-.""""(dIrn)

b)

Figure 3 - Pin1dB estimation error.

3.6 3.8 4 4.2 4.4 4.6 4.8 5Middle poi nt of the mess LJ'ernent{dB In)

Figure 4 - PinIIP3 estimation error.

Concerning the estimation of IIP3 small errors can also beobtained but the sensitivity to the placement of the threestimuli amplitude in the transfer characteristic is higher(figure 4) - anyway the obtained estimated value is

Pin//P3est = 12.5dBm while the expected one

is Pin//P3exp =13dBm , i. e., the error of 3.8 % occurs.

(4)

(3)1

R(r) =-XY cos(OJT+8)2

in the case x(t) and yet) are periodic signals of period T,

given by x(t)=Xsin(OX) and y(t)=Ysin(ox+8) . If

x(t) and yet) are the voltage and current of a circuit, (3)

gives us the circuit's active power when time delay t is null.That is,

9tvi(O) =!VIcos(O) ==2

1 T 1P =- fV(t)xI(t)dt =-(VxI)xcos(8)

TO 2

The correlation circuit implemented with a mixer and alow-pass filter shown in figure 5 was used to evaluate theapplicability of the cross-correlation between power supplycurrent and output voltage to estimate Pin1dB and PinIIP3 .

The voltage and current signals are filtered in order toobserving only the respective fundamental components,

Voutt and iddt .

1--IIP3enal

--------------------------------~--

\\,''\

5 ""'\.,.\.".,.,.

~ 0

gw('")

~ -5

-10

10

It is shown in [12,13] that IIP3 estimation from PA'sgain compression curves provides results with acceptableaccuracy, but which may eventually require consideringhigher order fitting polynomials. Further work will becarried-out on this matter.

III - CROSS-CORRELATION BASED POWER MEASUREMENT

Looking at voltage amplitudes, as it has been done in otherworks, does not provide a fully accurate power measure incase an impedance deviation has occurred. This requiresobserving the actual power in the nodes being observed.The cross-correlation between two signals, x(t) and y(t) is

+00defined as R(r) = fx(t)* y(t +r )dt, where t is a time Figure 5 - Correlator circuit.

delay, which becomes Figure 6 shows the correlator's output voltage as afunction of the power to be measured. It can be seen that a

linear correspondence exists between the correlator outputvoltage and the power to be measured.

accuracy estimations can be obtained with just three stimulilevels.

Power Input (mW)

Figure 7 - Comparison between the actual power transfercurve and that obtained with the correlator sensor.

0.1 +----.-------.-----~-----r---.....J

20 40 60 80 100Real Power (rnVV)

Figure 6 - Correlator output voltage vs. PA's output power.

This is also seen in figure 7, which shows both the PA'sactual transfer characteristic (Pout real) and that obtainedwith the correlation based sensor. The good matchingbetween the two curves allows us to estimate Pin1dB and

Pin//P3 with the same accuracy, Le.,

PinldBest = 4,67dBm and PinIIP3est = 12.5dBm .

REFERENCES

[1] M. Hafed, N. Abaskharoun, and G. Roberts, "A Stand­Alone Integrated Test Core for Time and FrequencyDomain Measurements", Proceedings of the InternationalTest Conference, 2000.

[2] John Ferrario, Randy Wolf, Steve Moss, and MustaphaSlamani, "A Low-Cost Test Solution for Wireless PhoneRFICs", IEEE Communications Magazine, September2003.

[3] Jee-Youl Ryu, Bruce C. Kim, Senior Member, IEEE, andIboun Sylla, "A New Low-Cost RF Built-In Self-TestMeasurement for System-on-Chip Transceivers", IEEETransactions on Instrumentation and Measurement, Vol.55, No.2, Page(s):381 - 388April2006.

[4] Valdes-Garcia, A.; Silva-Martinez, J.; Sanchez-Sinencio,E.; "On-Chip Testing Techniques for RF WirelessTransceivers", IEEE Design & Test of Computers,Vol. 23, No.4, pp. 268 - 277, April 2006.

[5] Fan, X.; Onabajo, M.; Fernandez-Rodriguez, F. 0.; Silva­Martinez, J.; Sanchez-Sinencio, E.; "A Current InjectionBuilt-In Test Technique for RF Low-Noise Amplifiers",IEEE Transactions on Circuits and Systems I, Vol. 55, No.7, pp. 1794 - 1804, Aug. 2008.

[6] Voorakaranam, R.; Akbay, S. S.; Bhattacharya, S.;Cherubal, S.; Chatterjee, A., "Signature Testing of Analogand RF Circuits: Algorithms and Methodology", IEEETransactions on Circuits and Systems I, Vol. 54, No.5, pp. 1018 - 1031, May 2007

[7] R. Hassun, N. Kuhm, R. Posner, R. Sweeney, B.Vassilakis, "Ultra-linear Power AmplifierCharacterization Using Dynamic Range ExtensionTechniques", IEEE Symposium MTT, 2001.

[8] Guillot, Farah; Garcia, Patrice; Mouis, Mireille; Belot,Didier; "Analysis of the intermodulation distortion andnonlinearity of common-base SiGeC HBTs. 13th IEEEInternational Conference Electronics, Circuits andSystems, ICECS '06. pp. 664 - 667,10-13 Dec. 2006.

[9] Strid, Eric W.; "High-Throughput RFIC Wafer Testing"ARFTG Conference Digest-Spring, 57th Vol. 39, pp. 1 - 5,May 2001.

[10] Ellouz, S.; Gamand, P.; Kelma, C.; Vandewiele, B.;Allard, B.; "Combining Internal Probing with ArtificialNeural Networks for Optimal RFIC Testing",IEEE International Test Conference, pp. 1 - 9, Oct. 2006.

[11] B. Razavi, RF Microelectronics, Englewood Cliffs, NJ,Prentice Hall, 1998.

[12] Choongeol Cho, William R. Eisenstadt, Bob Stengel,and Enrique Ferrer, "IIP3 Estimation From the GainCompression Curve", IEEE Trans. On Microwave Theoryand Techniques, Vol. 53, No.4, April 2005.

[13] Pedro Mota, Jose Machado da Silva, and John Long,"Estimation and Adaptive Correction of PA'sNonlinearities", 13th International Mixed Signals TestingWorkshop and 3rd GHz/Gbps Test Workshop, June 2007.

7.06.05.04.03.02.0

--Pout from Correlation circuit

Amplifier PoNer Curve

1.0

180.0

160.0

~ 140.0_ 120.0

!J! 100.0

o 80.0

I 60.0oD. 40.0

20.0

0.0 -F------r--~-____r--~-----r---~--.

0.0

~ 0.6

'S.& 0.5='o

:t::::=a 0.4

iia 0.3is1J~ 0.2u

IV - CONCLUSIONS

The development of built-in self-test solutions for radio­frequency circuits has not yet reached the required maturityto help replacing comprehensive but time-consumingcharacterization testing, for tests capable to screenmalfunctioning circuits due to processing defects andprocess variations. The work presented herein addresses theestimation of RF amplifiers' 1 dB compression and third­order intercept nonlinearity figures after cross-correlatingdynamic output voltage and power supply current. Thisallows estimating nonlinearity parameters using actualamplifiers' output power measures, instead voltagemeasures has it has been proposed before. A simple mixerand low-pass filter circuit is used for this purpose.Simulation results are presented which show that good