Proceedings of Asia-Pacific Microwave Conference 2007

Dual Baseband Injection Method

for Amplifier Linearization

Pui Ching Chun, Chi Hou Chan, Quan XueDepartment of Electronic Engineering

City University of Hong KongHong Kong SAR, China

Abstract-We propose a simple and effective linearizationtechnique based on low frequency signal injections. Theimprovement of the third-order intermodulation product (IMD3) \performance is obtained by feeding the baseband signals,generated by the baseband generation circuit, to the amplifierthrough the input and output biasing circuitries. With the v, (6) /addition of the low-frequency signals at both input and output ofthe amplifier, 43dB improvement on the third-order /intermodulation distortion has been achieved at 1-dBcompression point in the two-tone test.

Keywords-component-Amplifiers, baseband injection, v(linearization

I. INTRODUCTION

With the continuing growth of modem wirelesscommunications and the increasing number of users, frequencybands are becoming more and more congested. In order toachieve a higher data rate and reliable data transmission,spectral efficient digital modulation schemes are in highdemand in wireless applications. These digital modulationformats are usually possessed of a time-varying waveformenvelope with high peak-to-average ratio. Therefore, afteramplification, these signals are not only enlarged, but alsodistorted by AM-to-AM and AM-to-PM distortions. Usually,this distortion level is specified as the carrier tointermodulation ratio (C/I) (often measures the third-orderintermodulation distortion, IMD3) in the two-tone test, or inadjacent channels, the adjacent channel power ratio (ACPR).As a result, power amplifiers have an excellent linearityperformance with an acceptable power-added efficiency are ofgreat importance in the communication systems to maintainmodulation accuracy and minimize the ACPR. Therefore,researchers are motivated to investigate special techniques toimprove the intermodulation behavior of an amplifier.Different linearization techniques, such as the feedforwardmethod [1], the feedback method [2], the predistortion method[3], etc., have been proposed.

Recently, the influences of carriers' second ordercomponents to the third-order intermodulation products inmicrowave power amplifiers have been investigated [4-8].Based on the interaction of the second order components withthe carrier frequencies through the second-order nonlinearity ofthe amplifier, the intermodulation distortion can be greatlysuppressed. This signal injection technique can be divided intothe baseband (difference frequency) and second-harmonic

Figure 1. Conceptual diagram of the proposed technique.

schemes. Both schemes are based on using the nonlinearity ofthe amplifier itself to generate another set of IMD3 which hasthe same magnitude but is out-of-phase to the original one, so

as to realize the IMD3 cancellation. Compared to otherapproaches, this technique tends to be simple and low cost, butcan still achieve a good linearity improvement. However, sincethe second-harmonic approach utilizes a relatively higherfrequency to realize the IMD3 suppression, the adjustmentrequired for both amplitude and phase of the injected signalwould be more precise. In [8], baseband and harmonicinjections are simultaneously used and a very good suppressionon the IMD3 has been achieved. However, the whole circuitinvolves the design ofthree different frequencies, including thefundamental frequency, and would raise the overall circuitcomplexity.

From a practical point of view, it is simpler to use basebandrather than harmonic signal in the injection linearizationtechnique. However, the theoretical investigation shows thatthe single baseband injection cannot provide the completeelimination of IMD3 [8]. Therefore, a novel linearizationscheme based on the injection of baseband signal is proposedin this paper to realize the complete elimination of IMD3. Inthis approach, baseband signals are simultaneously injected tothe input and output ports of the amplifier. Experimental resultshows that it is possible to use baseband injections only tocompletely suppress the IMD3. As a result, this newlyproposed method, unlike the conventional second-harmonicinjection method, does not need the precise phase adjustment

This work was supported by the Hong Kong Research Grants CouncilGrant No. CityU 110605.

1-4244-0749-4/07/$20.00 w2007 IEEE.

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of the injected signal. And it can provide a good linearity forthe microwave amplifier while maintaining a simple design ofthe additional circuitry for the injected signal generation.

II. THEORETICAL ANALYSISThe proposed technique is based on the conventional

injection approach to utilize the amplifier nonlinearcharacteristic to generate the additional third-order distortedsignal that are produced by the fundamental and injectedbaseband signals. In additional to the baseband signal which isinjected together with the fundamental signal at the amplifierinput, one more baseband signal is fed to the amplifier outputso that more terms can be generated to cancel the originalIMD3 signals generated by the cubic term of the amplifiernonlinearity. In order to have a theoretical analysis on theproposed approach, the output current, id, is related to the gate-source voltage, vgs and drain-source voltage, Vds, of thetransistor. The nonlinearity of the amplifier such as nonlineargate-to-source capacitance and nonlinear drain current source,etc., are expressed in terms of Taylor series expansion aroundthe quiescent point ID, VGS, and VDS, leading to the expressionfor the nonlinear drain AC current as

'd (Vgs ¢ Vd5) =gmvg((t) + gn ( g (t) + g0vds (t)

+ g02V (I) + g03v ds() + g svg (t)vds(t) (1)

where id is the output current, gm is the transconductance of theamplifier and go is the output conductance. On the other hand,gmo is the nonlinear mixing term of transconductance andoutput conductance and it depends on vgs and Vds. All theseterms are bias-dependent coefficients. The series is based on asimplified expression for a small-signal output current and istruncated beyond the third-order term as it is assumed that thehigher order mixing products are negligibly small and do notinclude any memory effect to simplify the explanation of theproposed technique.

Two sinusoidal signals at frequencies co, and C02 are injectedto the amplifier input together with the baseband signal atfrequency Cw2-C1. Therefore, the input voltage can berepresented by

Vgs (t) = A[cos(cwlt) + cos(cw2t)]+ Bcos[(o2 - q)t +q'] (2)

where Cw2 > c1 and A and B are the magnitude of thefundamental and baseband signals, respectively. y is the phaseof the injected baseband signal. At the same time, anotherbaseband signal, having the same frequency C2-C1 but differentmagnitude and phase, is also fed to the amplifier output as well.As a result, the drain voltage will be modified as v d and can bewritten as:

v> (t) - Vds (t) -C KCs[(w)2 - ) )t + w] (3)

where Vds is the drain-source voltage before feeding thebaseband signal at the output. xV is the phase of the post-

injected baseband signal. According to [9], go, go2 and g, havenegligible effect on the IMD3 when the fundamental signalsare low and therefore, they are ignored in the higher powercase to simplify our analysis. As a result, not only thefundamental frequencies will generate the IMD3 terms throughthe nonlinearity, gm3, but the injected baseband signals alsointeract with fundamental signals via the nonlinearity of theamplifier. Thus, new IMD3 components come into existence.The output current for the frequency 2w02-CwI can be expressedas:

id (0)(2o2-q) = 9A3g,3cos(2..2t3-)wi

+ ABgm2 cos(2o2t- colt + (o)

+3AB2gm3 cos(2wv21-wlt + 2o)

-ACgg0 cos(2c2t - colt + w) (4)It is clear that the first term in (4) is caused by the

interaction between fundamental signals and cannot bechanged by injected baseband signals. The second and thirdterms are the mixing product of the fundamental and theinjected baseband signals coming from the input biasing.Similarly, the fourth term is the mixing product between thefundamental and the injected baseband signal coming from theoutput biasing. The phases of injected signals are specified forthe analysis only. It can be practically neglected as the phasevariation is small for the low frequency. Therefore, if theinjected signals can be properly adjusted such that (4) becomeszero, the IMD3 can be eliminated completely.

III. EXPERIMENTS AND DISCUSSIONS

The simplified block diagram of the entire experimentalsetup, including the main amplifier, pre-amplifier, envelopedetector and variable gain operational amplifiers, is given inFig 2. The main amplifier used is NEC NE6951R479A.Besides the input and output matching and biasing circuits,other parts are utilized for the baseband generation. When theinput signal is applied to the power amplifier, portion of thesignal is coupled out. In order to generate a larger magnitude ofthe baseband signal, the coupled signal passes through the pre-amplifier before feeding to a p-n detector diode. For simplicity,the pre-amplifier and the p-n diode can be replaced by atransistor which operates at the pinch-off region to generate thebaseband signal. After passing through the p-n diode, thedifference frequency is generated and split into twoindependent paths. Then, the baseband signals are injected intothe circuit through the gate- and drain-biasing networks. Theirmagnitude can be appropriately adjusted by changing the gainof operational amplifiers independently so that the optimumIMD3 suppression can be achieved. The polarity selection maybe required to provide the non-inverting or inverting basebandsignals. For the two-tone test, signals centered at 1.95GHz witha frequency spacing of 100KHz are used. Fig. 3 shows theoutput frequency spectrum of the amplifier measured at theoutput power of 18dBm per tone, which is the 1 -dB

Two - tone

at 1.95GHz (with OOKHz

tone spacing

Figure 2. Experimental setup of the proposed tenchique.

compression point of the amplifier, for both before and afterapplying linearization. By using the proposed dual-injectiontechnique, IMD3 is substantially suppressed by 43dB uponvarying the magnitude ofbaseband signals.

IV. CONCLUSIONSA novel linearization technique of dual-baseband injection

for the amplifiers is presented. The proposed techniqueprovides a significantly reduction on third-orderintermodulation products by using a simple and inexpensivecircuitry. 43dB suppression on IMD3 has been experimentallydemonstrated by using this method.

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0-

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1.9496 1.9498 1.9500

Frequency (GHz)

1.9502 1.9504

Figure 3. Output power spectrum oftwo-tone test with and without

linearization.

ACKNOWLEDGMENT

The authors would like to thank Mr. L. Chiu and Mr. K. W.Lau for their useful technical advice and discussion on thisresearch.

REFERENCES

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[4] Y. Hu, J.C. Mollier, and J. Obregon,"A new method of third-orderintermodulation reduction in nonlinear microwave systems," IEEETrans Microwave Theory Tech., vol. 34, pp. 245-250, Feb. 1986.

[5] N. Males-Ilic, B. Milovanovic and D. Budimir, "Low intermodulationamplifiers for RF and microwave wireless systems," Asia-PacificMicrowave Conf, vol. 3, pp. 984-987, Dec 2001.

[6] T. Nesimoglu, R.J. Wilkinson, C.N. Canagarajah and J.P. McGeehan,"Second harmonic zone injection for amplifier linearization," Proc.IEEE Veh. Technol. Conf., vol. 3, pp. 2353-2357, May 1999.

[7] C.S. Aitchison, M. Mbabele, M.R. Moazzam, D. Budimir and F. Ali,"Improvement of third-order intermodulation product of RF andmicrowave amplifiers by injection," IEEE Trans Microwave TheoryTech., vol. 49, pp. 1148-1154, June 2001.

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[9] J.C. Pedro and J. Perez, "Accurate simulation of GaAs MESFET'sintermodulation distortion using a new drain-source current model,"IEEE Trans Microwave Theory Tech, vol. 42, pp. 25-33, Jan 1994.

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