IEEE TRANSACTIONS ON MICROWAVE THEORY AND …ecee.colorado.edu/microwave/docs/publications/2012/Dani2012.pdf · demonstration of a high-efﬁciency linear power ampliﬁer (PA) with

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 60, NO. 12, DECEMBER 2012 4097

PA Efficiency and Linearity Enhancement UsingExternal Harmonic Injection

Asmita Dani, Student Member, IEEE, Michael Roberg, Student Member, IEEE, and Zoya Popović, Fellow, IEEE

Abstract—This paper presents analysis and experimentaldemonstration of a high-efficiency linear power amplifier (PA)with second-harmonic injection at the output. In this circuit,the transistor is not driven hard into compression and does notproduce significant harmonic content. External injection at theoutput enables voltage and current wave-shaping to achieve highefficiency. Theoretical analysis of the waveforms shows that themaximal drain efficiency is 89.9% with, at most, 0.13 dB of reduc-tion in output power compared with the class-A case. The overallPA efficiency is derived in terms of the injector circuit efficiency.A harmonically injected prototype GaN HEMT 2.45-GHz PAdemonstrates over 80% efficiency with linearity improved overthe class-AB PA without harmonic injection. Two-tone measure-ments show a reduction of the third-order intermodulation by 30dBc in the linear region and greater than 10 dBc in saturation.

Index Terms—Amplifier drain efficiency, Fourier coeffi-cients, harmonics, linearity, microwave power amplifiers (PAs),third-order intercept, waveform shaping.

I. INTRODUCTION

A large portion of current research in high-power amplifi-cation of signals with carriers in the microwave range

focuses on improving efficiency and linearity. There are manypower amplifier (PA) topologies that achieve high efficiency bydriving the active device into a nonlinear region and shapingvoltage and current waveforms across the device via proper se-lection of the output loading network at harmonic frequencies.These techniques, such as class-F and PA topologies, relyon the nonlinear active device for harmonic current or voltagegeneration [1]–[4]. The concept of harmonic injection, however,refers to architectures in which power at one or more harmonicsof the operating frequency is supplied externally to either theinput, output, or both input and output of the active device.Analysis of efficiency improvement of tube PAs using har-

monic injection into both the grid (input) and plate (output)has been presented in [5]–[7]. A harmonic-injection schemereferred to as a harmonic reaction amplifier was presented in[8]. The harmonic reaction amplifier uses two parallel devices

Manuscript received July 09, 2012; revised September 19, 2012; acceptedSeptember 20, 2012. Date of publication November 15, 2012; date of currentversion December 13, 2012. This work was supported in part by the BerrieHill research Corporation and the U.S. Air Force under Contract FA8650-10-D-1746-0006. This paper is an expanded paper from the IEEE MTT-S Interna-tional Microwave Symposium, Montreal, QC, Canada, June 17–22, 2012.A. Dani and Z. Popović are with the Department of Electrical, Computer and

Energy Engineering, University of Colorado, Boulder, CO 80309-0425 USA(e-mail: [email protected]; [email protected]).M. Roberg is with TriQuint Semiconductor, Richardson TX 75080 USA

(e-mail: [email protected]).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.2012.2222918

Fig. 1. Block diagram of a harmonic-injection PA (HI-PA) with second-har-monic injection at the output. A three-port network at the output allows isola-tion between waves at and between ports 2 and 3, while allowing lowloss at between ports 1 and 2. The phase of the injected harmonic is criticalto obtaining high efficiency.

and effectively acts as a push–pull amplifier with respect tothe second harmonic. In 1992, a patent was issued for a har-monic injection amplifier in which the harmonic signal createdusing a frequency multiplier is injected into the transistor output[9]. A class-E VHF PA at 3.5 MHz with a secondary class-E7-MHz PA injector is presented in [10]. An experiment demon-strating 15.2% efficiency improvement of a 2-GHz GaN PAusing second-harmonic injection at the input is reported in [11].More recently, a concept for efficiency improvement via injec-tion of harmonics into the output of a class-B/J amplifier wasdemonstrated [12]. A novel scheme of efficiency improvementof a class-E amplifier using input harmonic injection via a feed-back loop was shown in [13].In this paper, we discuss injection of power at the second har-

monic, as shown in the block diagram of Fig. 1 and the implica-tions on efficiency and linearity. The approach is valid for anyamplifier mode, not just for class-B/J as in [12] and [14]. Thecontributions of this work are organized as follows.• Section II presents, for the first time, a theoretical Fourier-expansion analysis of output harmonic injection. A rela-tionship between the total efficiency and injected power ispresented for the case of second-harmonic injection. Theanalysis gives an insight into the impedance that needs tobe synthesized at the output of the transistor at the funda-mental and harmonic frequencies. The effect of efficiencyof the injector circuit on the total efficiency is calculated.

• Section III discusses two prototypes used for experimentalvalidation, one based on a packaged Cree GaN 10-W 50-class-AB PA and the other based on a TriQuint GaN diewith an injection network designed for a non-50- envi-ronment.

• Section IV presents measurement results for the relevantamplifier parameters as a function of the phase and ampli-tude of the injected harmonic signal for both prototypes.

0018-9480/$31.00 © 2012 IEEE

4098 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 60, NO. 12, DECEMBER 2012

The experimental results demonstrate an improvement from58% to 80% in efficiency with an output power of 37 dBm andover 20-dB gain from a single TriQuint 6-W device. In addition,the amplifier linearity is shown to be improved with harmonicinjection w.r.t. the class-AB case, which implies significant lin-earity improvement compared with the same device used in har-monically terminated compressed nonlinear PAs.

II. THEORETICAL ANALYSIS

The theoretical analysis of a harmonically injected PA(HI-PA) shown in Fig. 1 is developed based on Fourier ex-pansions of the voltage and current waveforms at the currentsource of the transistor, expanding on the approach in [12]and [15]. First, expressions are derived for injected voltagewhich optimizes efficiency, followed by the analysis of totaldissipated power and a discussion of linearity. To obtain anHI-PA, a linear three-port network is cascaded at the output ofa linear PA, and the required -parameters of that network aregiven in [15].

A. Waveform Analysis

Consider the normalized drain voltage and current wave-forms at the virtual drain of a linear field-effect transistor (FET)PA, which are given by

(1)

(2)

where , and the bar indicates a normalized quan-tity. For instance, when , the normalizedclass-A output power is 1 W, and the waveforms result in 50%efficiency. If the drain waveforms can be shaped by harmoniccontent in a manner such that the overlap of the voltage andcurrent is minimized for a given fundamental frequency outputpower, then drain efficiency will be maximized.Consider the addition of only the second-harmonic term in

(1) and (2). In order to maintain waveform symmetry, only cos-inusoidal components are added. Such a condition will result inthe voltage waveform of the same shape but 180 out of phasewith the current waveform. The waveforms following additionof a second-harmonic term become

(3)

(4)

as shown in Fig. 2, showing minimal overlap of the voltage andcurrent waveforms.From (3) and (4), it can be concluded that the impedance atis the negative of that at . Effectively, this requires that

power is delivered to the transistor at the second harmonic. Anoptimal value of that maximizes the efficiency can be found.First, the critical points of the drain current and voltage wave-forms are expressed as

(5)

(6)

Fig. 2. Optimal drain current and voltage waveforms for second-harmonic in-jection amplifier, normalized to 1-W output power.

where corresponds to a point at which the first deriva-tive of the voltage waveform w.r.t. is equal to zero. Note that(5) is only valid when

(7)

Therefore, the range of over which (5) is valid is limited to

(8)

It remains to be proven which critical points correspond to theglobal minima and globalmaxima. Substituting the critical pointin (5) into the second partial derivative of (3) results in

(9)

If is negative in sign, the critical point corresponds to a min-imum, while, if it is positive in sign, then it corresponds to amaximum. Applying the second derivative test to the criticalpoint described by (6) results in

(10)

Therefore, the critical point described by (6) will be an ex-tremum as follows:

is a minimum (11)

is a maximum (12)

B. Efficiency Analysis

The normalized total DC power consumed by the amplifier isexpressed as

(13)

where is the efficiency of the injector circuit. Note that, dueto the symmetry of the current and voltage waveforms,

, the optimal dc supply voltage is that which results in adrain voltage waveform with minimum of zero. Therefore, from(3), we have

(14)

DANI et al.: PA EFFICIENCY AND LINEARITY ENHANCEMENT USING EXTERNAL HARMONIC INJECTION 4099

Fig. 3. Contour plot for as a function of and injector circuit efficiency.

The total dc power may now be expanded to the form

(15)

(16)

Since we use a normalization that sets the fundamental outputpower to 1 W, the total efficiency is calculated as the inverse ofthe normalized dc power

(17)

Fig. 3 shows the total efficiency plotted as a function of bothinjector efficiency and normalized magnitude of second-harmonic .The value of is optimized by setting the partial derivative

of w.r.t. the Fourier coefficient to zero and solving foras follows:

(18)

(19)

These values minimize . Given , the optimalFourier coefficient reduces to . A plot of ,which corresponds to the amplitude of the required injectedsecond-harmonic versus , is shown in Fig. 4. As one wouldexpect, the magnitude of the Fourier coefficient decreases asthe injector efficiency decreases. Another interesting parameterto investigate is the ratio of the delivered fundamental outputpower to the required delivered second-harmonic injected

Fig. 4. Optimal solution for Fourier coefficient and second-harmonic de-livered power relative to fundamental frequency output power versus secondharmonic injector circuit efficiency .

Fig. 5. Total efficiency versus injector circuit efficiency .

power , also shown in Fig. 4. The PA effi-ciency is determined by inserting into (15) and (16) to yield

(20)

(21)

(22)

(23)

A plot of the total efficiency versus injector circuit efficiencyis shown in Fig. 5 for optimized solution at and a plot for

the total efficiency as a function of , and is shown inFig. 3. The maximum value is 89.9%, and it rolls off reasonablyslowly with decreasing injector efficiency. This is intuitive be-cause the power required from the injector is significantly lower


Fig. 6. Power reduction and normalized supply voltage relative to class-Aversus injector efficiency .

than the fundamental output power of the amplifier, as shown inFig. 4. As expected, when the amplifier efficiency reaches 50%,the injector circuit is turned off. In this case, the amplifier de-generates to the canonical class-A mode.As previously mentioned, the load presented to the transistor

at the second harmonic is the negative of that presented at thefundamental, so the load resistance normalized to the class-Afundamental load is 1. To find the output power of the PAnormalized to class-A output power, normalization conditionscorresponding to peak voltage and current constraints are en-forced. and are now found, enabling determination ofthe maximum instantaneous normalized voltage and cur-rent , and the output power normalized to the class-A am-plifier output power is determined. The normalized dc voltageis expressed as

(24)

(25)

Note that, due to the symmetry of the current and voltage wave-forms , the maximum normalized voltage is calcu-lated as

(26)

(27)

The output power normalized to class-A is then given by

(28)

(29)

Fig. 6 depicts the fundamental frequency output power reduc-tion relative to a class-A amplifier versus the injector efficiency.This was calculated by computing as a function of , thencomputing the output power from and determining the ratio

relative to 1 W. When , the output power is only re-duced by only 0.13 dB relative to the class-A amplifier.Also, it is of practical interest to find the supply voltage and

current normalized to class-A:

(30)

Fig. 6 shows the normalized supply voltage which is approxi-mately 0.7107 for .A similar analysis can be performed for third-harmonic in-

jection at the output, since symmetric square waveforms can beachieved using odd harmonics only. In the case of third-har-monic injection, the impedance at the third harmonic is positiverather than negative, so the ideal waveforms can be realized witha passive set of output terminations. The analysis shows, how-ever, that the total efficiency given by (22) and (23) is around65% for injector efficiencies above 40% and does not reach thehigh efficiencies of the second-harmonic injection case. Detailsof the analysis can be found in [16].

C. Linearity

Transistors exhibit nonlinearities due to various factors suchas input and output device capacitance, transconductance, anddrain–source resistance resulting in a characteristic between

and , which can be represented using the power series

(31)

where . As seen in (31), the second-order non-linearity causes an additional dc component and a signal at twicethe fundamental frequency to appear in the output voltage. For atwo-tone signal, the second-order nonlinearity can be easily fil-tered out and does not cause any in-band distortion of the signal.However, the third-order nonlinearity results in in-band distor-tion products. The gain of the fundamental component undernonlinear operation can be expressed in terms of the funda-mental gain and the third-order gain and amplitude, and thederivation is given in [17]. The analysis in [17] also showsthat the amplitude of the second-harmonic output signal is in-versely proportional to the magnitude of the transfer character-istic of the amplifier at the third harmonic, which is referred to inSection IV. A good discussion on extracting linearity informa-tion from a continuous-wave (CW)-fed amplifier by measuringthe third-harmonic output content is presented in [18]. Based onthis theory, in this paper, a CW signal is used for harmonic in-jection analysis as the device enters saturation. In particular, wemeasure second and third harmonic as a function of the injectedpower and phase in order to assess the linearity.

III. PROTOTYPE PA DESIGN

Two prototype PAs were used to demonstrate the HI-PA con-cept. A packaged device in a demo board with class-AB broad-band PA configuration is injected through a 50- three-portinjection circuit described in more detail in [12], [14], and [15].In order to have more design freedom and lower matching net-work loss, a TriQuint GaN die was used in the second narrow-band prototype with a non-50- three-port injector circuit.


Fig. 7. Hybrid HI-PA with a 6-W TriQuint TGF2023-01 die. The outputnetwork integrates the harmonic injection three-port network with atmatched to 65 and at matched to 71 . The input network does animpedance transformation from 50 to 10 in order to achieve high gain and

at the fundamental.

A. Packaged Device Prototype PA

A Cree GaN HEMT with 10-W is used in a broad-band (DC-6 GHz) demo board provided by the manufacturer(CGH40006P-TB) with a packaged device and matched to50 as the first prototype. This PA gives 40 dBmat 2.45 GHz with and 12 dBm [15]. Theinput power to the fundamental PA is swept from 22 to 34 dBm(linear to saturation) with the drain bias at 22 and 28 V. Thegate bias was set to 1.6, 1.8, and 2 V for a class AB mode.The fundamental PA starts compressing at an input power levelof 27 dBm when no harmonic injection is present.

B. Discrete Die Prototype PA

A hybrid class-AB PA is designed using load-pull measure-ments on the TriQuint TGF2023-01 device at 2.45 GHz, asshown in Fig. 7. The reference plane for all measurements onthis PA is the virtual drain of the transistor, i.e., the currentsource behind the output capacitance of the device. The HI-PAis designed with the three-port injection network integrated intothe output matching circuit of the amplifier in order to minimizeloss. Design and performance of the injection network is similarto the one presented in [12] and [15] with the fundamental andsecond-harmonic impedances matched close to 65as explained in (3) and (4). Due to fabrication tolerances, thefundamental impedance at the virtual drain of the device wasfound to be matched to 65 and the impedance to 71(10% higher).This class-AB PA has 58% drain efficiency with an output

power of 37 dBm without any harmonic injection at a drain biasvoltage of 28 V. Fig. 8 shows the measured drain effi-ciency , output power at fundamental , third har-monic , and the gain as a function of fundamentalinput drive power .

IV. HI-PA MEASUREMENTS AND ANALYSIS

The block diagram shown in Fig. 9 shows the measurementsetup for HI-PA prototypes. A portion of the fundamental inputis frequency doubled to create the second harmonic forinjection. A voltage-controlled phase shifter and variable gain

Fig. 8. Measured drain efficiency at and and gain for the class-ABPA shown in Fig. 7 without injection.

Fig. 9. Block diagram of the HI-PAmeasurement setup. The input signal is splitand frequency doubled to create the injected harmonic, . A voltagecontrolled phase shifter and variable gain amplifier are used to control the am-plitude and phase of .

amplifier (VGA) are used to control the amplitudeand phase at . All of the measurements are de-embedded tothe virtual drain of the transistor by calibrating the loss in theoutput network and taking into account the intrinsic transistorparasitics, i.e., output capacitance of the device. A bondwiremodel in Ansoft High Frequency Structure Simulator (HFSS)was simulated to consider the inductance loss in the bondwiretransition for the hybrid PA design.The drain efficiency for an HI-PA takes into account the

amount of second-harmonic power injected into the virtualdrain of the device assuming as follows:

(32)

where .

A. Packaged Device Prototype HI-PA

Fig. 10 compares the measured efficiency, output power, andgain for the PA with and without harmonic injection. It is seenthat the HI-PA saturates at a higher input power (32 dBm) ascompared with the class-AB PA (27 dBm), resulting in higher


Fig. 10. Comparison of measured (a) drain efficiency, (b) , and (c)gain for the HI-PA to the PA with no harmonic injection at 22 V, 28 Vand 1.6 V (class-AB). The dashed green line indicates input power atwhich the PA becomes nonlinear.

linearity. The gain of the HI-PA is lower by about 1 dB ascompared with the fundamental PA in the linear region, but re-mains higher in saturation. Harmonic balance simulations usinga nonlinear model provided by the manufacturer show the sametrends for gain as the measured data.Measured results show that higher efficiency can be achieved

for a constant output power with HI-PA by changing the op-erating bias point. For instance, the drain efficiency of the PAimproves from 58% with no injection to 75% with injection foran output power of 40 dBm by changing the drain bias from 28to 22 V.A two-tone linearity test is performed at 22 V

and 1.8 V. The two tones are kept 5 MHz apartwith 2.45 GHz and third-order intermodulation(IMD3) products generated at 2.455 GHzand 2.46 GHz. Simultaneously, , , or

is injected at the output, each requiring a different

Fig. 11. Comparison of power levels for single-tone and third-order IMD prod-ucts for HI-PA and class-AB PA without harmonic injection.

phase adjustment. The measured results in Fig. 10 show thatthe HI-PA (marked line) saturates at a higher input power thanthe PA with no harmonic injection (solid line). At lower inputpowers, the IMD3 level is over 30 dB lower for the HI-PA andremains 10 dB lower after the PA saturates. In Fig. 11, only the

frequency is injected, resulting in a decrease in theIMD while the remains unchanged. Symmetrically,when is injected, the will decrease. Both of theIMD products will be reduced equally for a signal injectedat . This is consistent with measurements obtainedwith tube amplifiers in [19] and harmonic injection at input ofsolid-state amplifiers in [20], [21].

B. Discrete Die Prototype HI-PA

The HI-PA using a TriQuint 6-W GaN discrete high-electronmobility transistor (HEMT) in a class-AB PA achieves a hightotal drain efficiency of 89% with external second-harmonic in-jection at the output at a bias voltage of 22 V. Thisefficiency is very close to the theoretical efficiency of 89.9%from Fig. 3, though one would expect it to be lower. The reasonbeing that the theory is derived for an ideal device with ideal– curves which do not take into account knee voltage of thetransistor and does not generate any odd-order harmonics. Inpractice, the PA always generates some harmonic content evenat lower input power levels. The gain of the amplifier reducesby 1 dB as compared with the amplifier without any harmonicinjection. Fig. 12 shows a comparison of the measured perfor-mance for the HI-PA and PA without harmonic injection. Thesemeasurements are optimized for high efficiency and hence theamplifier is nonlinear at . It is seen that a better perfor-mance is achieved with the discrete device as compared with theresults presented in Fig. 10 for the packaged device, as expected.As seen in the theoretical analysis (30), harmonic injection

implies a shift in the bias voltage in order to get the optimumperformance from the amplifier. Fig. 13 shows the performanceof the HI-PA at different drain bias voltages for a fundamentalinput drive of 16.2 dBm. The HI-PA is then optimizedin order to get high efficiency along with linearity.As explained in Section II-C, for a CW amplifier, the values

of can give an estimate of the linearity. It is seenfrom Fig. 13 that, at 24 V, the drain efficiency of theHI-PA is improved by over 20% as compared with the class-AB


Fig. 12. Comparison of measured (a) , (b) , and (c) gain for dis-crete die prototype of HI-PA optimized for maximum efficiency.

Fig. 13. Drain efficiency , for different bias voltageswith the ratio 0.1 and 16.2 dBm.

PA with no injection, and the output power at the third har-monic is lowered by 30 dB for an input drive levelof 16.2 dBm. At this bias point, conditions for high linearity

Fig. 14. Contour plots of (a) measured fundamental output power indBm and (b) drain efficiency .

and high drain efficiency are obtained with a nominal funda-mental output power reduction of 0.26 dB over thePA without any injection. Note that, when harmonic injection isperformed, it results in higher fundamental output power due toreduction in other harmonic content. In order to keep the outputpower constant and reduce the dc power dissipation, the drainsupply voltage can be reduced to a certain extent, as shown inFig. 13. The supply voltage reduction is only advantageous upto a device-dependent lower value when the output power startsdecreasing. In the case of packaged prototype, 22 V was foundto be optimal, and, in the case of discrete prototype, this valuewas 24 V. Note that the PA with no injection is not designed forhigh efficiency, since it is biased in class-AB, and the gate biasis kept the same for the PA with and without injection. All ofthe measurements presented in the remainder of the paper willbe at 24 V.As discussed in Section II-A, the injected second-harmonic

signal needs to be at a particular phase and amplitude in order toshape the voltage and current waveforms at the virtual drain ofthe amplifier. If the input drive is kept constant, various param-eters affecting the performance of the HI-PA such as ,drain efficiency , drain current , and power at theharmonics vary with the amplitude andphase of injected second harmonic power as shownin Figs. 14 and 15.Figs. 14 and 15 show that, for 9 dBc and a

phase shift of 80 , high drain efficiency of 79% is achievedusing (32) along with extremely low values of . Notethat this efficiency takes into account the power of the injected


Fig. 15. (a) Drain current (amperes) and (b) third-harmonic output powerin dBm for 16.2 dBm depicting the variation in the

values of these parameters as a function of phase and power level (dBc w.r.t.) of the injected second harmonic . Analogous plots can be

obtained for the second-harmonic output power .

signal. However, the efficiency of the injector circuit is not in-cluded in this proof-of-concept experiment in which the HI-PAis not fully integrated. The value of obtained at thispoint is approximately 37 dBm, which is only 0.2 dB lowerthan the fundamental output power obtained with no injection(Fig. 8).The measurements show that, if is not at the op-

timum phase and amplitude, the performance of the amplifiercan severely degrade. When the second-harmonic voltage isout of phase relative to the optimal value, the amplitude of

increases, making the amplifier extremely nonlinear.The efficiency reduces from 80% to 40%while the output powerdrops more than 3 dB. If is higher than the optimumvalue (in this case, 9 dBc), then, even at the optimum phaseof the injected harmonic, the HI-PA is highly nonlinear. Thisis due to undesired additional second-harmonic content in theoutput voltage and current waveforms generated by the deviceunder hard drive.A sweep is performed at in order to achieve the op-

timal performance of the HI-PA at various input drive levels.Since an amplifier undergoes AM–AM and AM–PM distortion,the optimal phase and amplitude of the injected second-har-monic changes for different input drive levels. Fig. 16 shows acomparison of the gain and drain efficiency obtained for HI-PAand PA without harmonic injection as a function of .The efficiency obtained at each input drive level is for an op-timal value of amplitude and phase which are also dependent on

Fig. 16. Comparison of drain efficiency and gain for HI and PA with no injec-tion as a function of .

Fig. 17. Comparison of and as a function of forHI and PA with no injection. The graph also shows the amplitude ofas a function of in order to achieve high efficiency and linearity perfor-mance for the HI-PA.

. The overall gain of the HI-PA is reduced by 1 dB, andthe 1-dB compression point of the HI-PA is shifted to a higher

of 15.7 dBm, implying improved linearity. The drain ef-ficiency improvement ranges from 8% to 20% as the input drivelevel increases.The comparison of and for the HI-PA and

PA with no injection is shown in Fig. 17 along with asa function of . As derived in [17], the transconductanceat the third harmonic is inversely proportional to the amplitudeof the second harmonic. The value for gain of an amplifier undernonlinear operation can be given from (31) as

(33)

where and are values for transconductance at funda-mental and third harmonic. Therefore, it is seen that the valueof required to lower the value of for theHI-PA is exactly equal to .The nominal class-A operation of the PA without harmonic

injection with a 50% drain efficiency is achieved at13 dBm. Fig. 17 shows that, at this input drive level, the am-plitude of required in order to achieve an optimumperformance in terms of efficiency and linearity for the HI-PAis 10 dBc. This result matches with the theoretical analysispresented in Fig. 4 where, for a 100% injector efficiency, theratio of to is 0.1 for a class-A bias point.


Fig. 18. Comparison of power at ,for HI-PA and PA without harmonic injection as a function of input drive level.The graph also shows the power injected at the second harmonic tone toachieve lowest .

Two-tone measurements with optimization for the amplitudeand phase of the injected second harmonic in order to achievelowest IMD3 products in both lower and upper sidebands

are performed. This measurement is similar tothe one presented in Section IV-A for the packaged deviceprototype HI-PA where either or are injected at theoutput of the HI-PA. Here, the injection of affects the per-formance of at and at due toactive impedance synthesis at the injection port. It is importantto note that the reduction in results from mixing of

and distortion products caused due to second-ordernonlinearities. It is seen that the reduction in usingexternal second-harmonic injection is greater than 15 dB fordifferent input drive levels, whereas at and

at remain unaffected. Fig. 18 shows thereduction in power levels for and achieved fordifferent fundamental input drive levels along with the amountof injected power.For practical communication signals, the harmonic injection

path needs to be modified in order to inject an exactly dou-bled spectrum of the signal. As seen in the two-tone measure-ments, injection at one harmonic tone only affects the distortionproducts which are a function of that harmonic tone frequency.Since, a modulated signal in general is a multitone signal, it willrequire a injected signal with twice the modulation bandwidthand RF carrier. This can be accomplished by baseband signalup-conversion.

V. DISCUSSION

The results above show that a PA with harmonic injectionin the output can be both efficient and linear. In the demon-strated results above, we start with a class-AB PA, which isnot perfectly linear. In fact, the theory shown in Section II as-sumes that some second-harmonic content is generated by theactive device. If the transistor fails to generate second-harmonicpower and presents an impedance other than that of the fun-damental frequency output termination, the necessary negativeimpedance cannot be synthesized using harmonic injection. Inthis case, harmonic injection at both the input and output of thetransistor would be required.

Fig. 19. Minimum and measured at virtual drain of theHI-PA for 16.2 dBm. The minimum for is obtained with

17.8 dBc w.r.t. , whereas minimum for isobtained for 8.9 dBc.

It is of interest to discuss some limitations on linearity andefficiency that are practically achievable. We have shown thatthe third harmonic, which directly affects IMD performance, isminimized for a specific phase and amplitude of the injectedsecond harmonic. However, the injected signal also affects thenonlinear content in the waveform produced by the transistor,which can be evaluated bymeasuring the level of the second har-monic at the output. The amount of injected second-harmonicpower that results in a minimum of harmonic content in theoutput is shown in Fig. 19. Note that the second and third har-monic have minima for different injected power levels of thesecond harmonic. The amplitude of needed to lower

is approximately 10 dB less than that needed to lower. Also, the phase shift for injection differs

by 50 . As seen from Fig. 14, the drain efficiency drops by ap-proximately 10% between these two points in amplitude andphase.For a modulated input signal, the third-order nonlinearities

have to be minimized since they create in-band distortion whichis extremely difficult to filter. The third-order distortion prod-ucts are a function of the amplitude of second harmonic pro-duced by the amplifier itself. Hence, a point in the amplitudeand phase of the injected signal needs to be chosen to optimizelinearity by a tradeoff between the second- and third-harmoniccontent.The main practical limitation on efficiency is the imple-

mentation of an efficient injector circuit. Fig. 5 shows that aninjector efficiency of 40% or higher, with a power level 10dB below the output power, is required to obtain an overallefficiency above 80%. This might present a challenge for veryhigh-power PAs, but is otherwise not a difficult constraint. Inthe prototype characterization presented in this paper, a passivedoubler was used to produce the harmonic. This is not onlyinefficient but also impractical for amplifying a real signal,in which case significant distortion would be introduced. Thelinearity tests (Fig. 11) show that a clean doubled frequencyspectrum needs to be injected. Therefore, for signal amplifica-tion, a different approach is needed than was done for the CWtests in this paper. A topic of current research is integrationof an up-converter in the injection circuit with a synchronizedsecond baseband input. For very broadband signals, the phasecontrol that achieves linearity might prove to be challenging.An interesting extension of the concept to a broadband HI-PA


will require a three-port injection network design with goodharmonic isolation and low fundamental frequency loss over abroad frequency range.In summary, this paper presents a theoretical Fourier analysis

of PAs with harmonic injection at the output, showing limitson total circuit efficiency. The theory is experimentally verifiedon class-AB 2.45-GHz PAs using both packaged and discreteGaN HEMTs, resulting in 75% and 80% efficiencies, respec-tively, at the 1-dB compression points. The linearity of the PA isshown to be significantly improved for specific phase and ampli-tude of injected second harmonic, with simultaneous improve-ment in efficiency. To the best of our knowledge, these are thefirst reported efficient linear PAs of this type using solid-statedevices.

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Asmita Dani (S’011) received the B.Tech degreein electronics engineering from the University ofMumbai, Mumbai, India, in 2008, and the M.S.E.E.degree from the University of Colorado at Boulderin 2010, where she is currently working towardthe Ph.D. degree in microwave circuits and systemdesign.Her research interests include linearization and ef-

ficiency enhancement of power amplifiers using ex-ternal harmonics, monolithic microwave integratedcircuit design and analysis of communication system

transmitters and receivers.

Michael Roberg (S’09) received the B.S.E.E degreefrom Bucknell University, Lewisburg, PA, in 2003,the M.S.E.E. degree from the University of Pennsyl-vania, Philadelphia, in 2006, and the Ph.D. degreefrom the University of Colorado at Boulder in 2012.From 2003 to 2009, he was an Engineer with

Lockheed MartinMS2, Moorestown, NJ, where hewas involved with advanced phased-array radarsystems. His current research interests includehigh-efficiency microwave PA theory and design,microwave power rectifiers, monolithic microwave

integrated circuit (MMIC) design, and high-efficiency radar and communicationsystem transmitters. He is currently with TriQuint Semiconductor—DefenseProducts and Foundry Services, Richardson, TX, where he is involved withwideband high-efficiency GaN MMIC power amplifier design.

Zoya Popović (S’86–M’90–SM’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.

Documents

IEEE TRANSACTIONS ON MICROWAVE THEORY AND …ecee.colorado.edu/microwave/docs/publications/2012/Dani2012.pdf · demonstration of a high-efﬁciency linear power ampliﬁer (PA) with