Continuous Class-B/J Power Amplifier Using Nonlinear Embedding Technique

Continuous Class-B/J Power Amplifier Using Nonlinear Embedding Technique Samarth Saxena, Student Member, IEEE, Karun Rawat, Senior Member, IEEE, and Patrick Roblin, Senior Member, IEEE Abstract This brief explores the design space for realizable solution of a broadband class-b/j continuous mode of power amplifier (PA). The PA is initially designed at the current-source reference plane with the correct voltage and current waveforms. The intrinsic impedances are then projected to the package reference plane using the model-based nonlinear-embedding technique. An insight is provided into engineering the extrinsic harmonic impedance to rotate clockwise on the Smith chart to be able to match it using a Foster circuit. It is concluded that decreasing the empirical parameter of a general class-b/j voltage equation with increasing frequency leads to a clockwise trajectory on the Smith chart of the second harmonic at the package plane. In order to validate the advantage of this analysis, the PA is implemented using a 15 W GaN HEMT transistor in the frequency range of 1.3 to 2.4 GHz and drain efficiency between 63% and 72% in measurement was achieved over the entire bandwidth. Index Terms Broadband, power amplifier, class-j, continuous mode, embedding, Foster, Gallium Nitride, HEMT. H I. INTRODUCTION IGH-EFFICIENCY and wide bandwidth clubbed together with high output power are extremely desirable characteristics of a modern day power amplifier (PA). Harmonic tuning techniques have been used in the past to boost efficiencies in class F (and class-f -1 ) designs as reported in [1] and [2]. However, precise multi-harmonic impedance control is difficult to implement practically over large bandwidths. There is, thus, a need to further explore PAs working in the RF regime with a greater operational bandwidth capability along with comparable high efficiencies. Continuous Class-B/J, continuous class-f (and class-f -1 ) have recently been proposed and implemented to overcome this limitation. The primary focus of this brief is designing a broadband class-b/j PA with the help of model-based nonlinear embedding technique as detailed in [3]. The required mode of operation is defined at the intrinsic current source planes, followed by the projection of the impedances at the extrinsic Manuscript received July 15, 2016. This work was supported in part by the DST, SERB Grant No. SB/S3/EECE/047/2014. S. Saxena and K. Rawat are with the Department of Electronics and Communication, Indian Institute of Technology (IIT) Roorkee, Uttarakhand 247 667, India (e-mail: samarthsaxena100@gmail.com, karunfec@iitr.ac.in) P. Roblin is with the Department of Electrical and Computer Engineering, The Ohio State University, Columbus, Ohio, 43210, USA (e-mail: roblin.1@osu.edu) Fig. 1. Continuum of theoretical voltage waveforms for Class-B/J. plane. Another problem in dealing with the design space of any continuous class of PAs is the anti-clockwise nature of the intrinsic impedance contour versus frequency at the current source reference planes which is impractical to be realized through Foster circuit. This will be resolved in this brief by selecting a frequency parameterization for the Class-J at the intrinsic current-source reference planes, which yields Foster impedances at the device package reference planes after projection with the embedding device model. The organization of the brief is as follows. Section II studies the key parameters of the continuous class-b/j PA for exploring the design space. Section III describes nonlinearembedding technique along with analyzing the design space with possibility of extrinsic second harmonics rotating clockwise on the Smith chart. Section IV elaborates the prototype designed to validate the proposed methodology. Section V mentions simulation and measurement results followed by conclusions in Section VI. II. CONTINUOUS CLASS-B/J MODE OF OPERATION The class-j mode of operation is an extension of the classical class-b amplifier. Class-B/J continuum utilizes the concept of a family of optimal impedance solutions instead of a singular one maintaining the expected output power and linearity as their reference traditional mode. Fig.1 illustrates some of these normalized waveforms possible. These can be mathematically represented as [4]: DS ( θ ) = ( 1 cosθ )( 1 α sinθ ) V, 1 α +1 (1) The continuous values of the constant parameter determine

the set of solutions known as the class-b/j continuum. Varying controls the phase shift between the voltage and current. The three special cases of are known as class J, class B and class J -1 respectively. For every there is a specific load which needs to be presented to the transistor, given as: Z Z = R + jαr 1 f L L (2a) 3π = 0 jα (2b) 8 2 f R L It should be noted that these impedances need to be presented at the current source reference planes of the gallium nitride (GaN) high electron mobility transistor (HEMT). For the remaining part of the brief Z 1f will be referred to as Z 1int and Z 2f as Z 2int. R L is calculated from the load line as 20.75 Ω for the 15 W Cree CGH27015F GaN HEMT which will be used for the design. For a positive the fundamental load has a positive reactance and the second harmonic a negative reactance. As decreases and crosses 0, the fundamental reactance becomes capacitive and the second harmonic inductive. At, the continuum assumes a class-b type of operation with the fundamental impedance purely resistive and the second harmonic termination as short. The continuous locus of Z 1int /Z 2int pairs on the Smith chart is known as the design space. The load for the matching network can now be chosen from a family of impedances instead of just one. All the solutions deliver the same output power and efficiency as conventional class-b but now over a broadband frequency range. Fig. 2. Nonlinear-embedding transfer model layout for calculating extrinsic impedances from intrinsic impedances. τ Fig. 3. Calculated fundamental and second harmonic impedances at the intrinsic plane (in grey). Projection of Z int (in red) for 0.5<α<1 to Z ext (in blue) rotating anti-clockwise model for 1.3 to 2.4 GHz using the embedded. III. DESIGN SPACE ANALYSIS WITH NONLINEAR-EMBEDDING TECHNIQUE To design the actual PA circuit it is essential to know the correct impedances at the package plane. Waveforms and impedances at these planes are distorted by both linear and nonlinear parasitic elements of the device. The conventional approach relies on load-pull measurements for optimal external load locations [5] and later de-embedding the data based on a suitable device model available to reach the internal reference plane. As reported in [3], a nonlinearembedding device model for the Angelov model has been implemented for designing PAs and applied to the 15 W Cree CGH27015F GaN HEMT. The representation of such a model is drawn in Fig. 2. The design starts at the current-source intrinsic plane with the gate and drain voltages selected by the designer so as to maintain the required class of operation at the intrinsic plane. The Z 1int and Z 2int are selected in order to match the intrinsic waveforms as close as possible to the ideal waveforms of Fig. 1. Once the intrinsic settings are complete the external multiharmonic currents and voltages are computed in one direct step considering all the device parasitics and capacitances. The corresponding extrinsic loads at the package reference plane at fundamental and second harmonic frequency known as Z 1ext and Z 2ext respectively are obtained [6]. The impedances calculated from (2) are plotted on the Smith chart (marked in grey) in Fig. 3 for the GaN HEMT device. Despite these useful predictions there still lies a bottleneck in terms of matching the extrinsic loads using a realizable matching network. All passive components can lead to only Foster reactance which translates to clockwise rotation on the Smith chart with increasing frequency. Consequently, all practical matching networks require the fundamental and second harmonic impedance pairs to be rotated in a continuous clockwise fashion on the Smith chart across the frequency band [7]. But the output loads predicted for the class-b/j design space rotate anti-clockwise. This is also illustrated in Fig. 3 where the Z int corresponding to a few values from among the continuum of class-b/j (marked in red) project the extrinsic impedances from 1.3 to 2.4 GHz (marked in blue). Moreover, the matching is more demanding for the second harmonic impedance which is significantly expanded on the Smith chart compared to the fundamental impedance for a specified frequency range. As α varies from 0.5 to 1, Z 2ext calculated from the model varies from -j37 Ω at 1.3 GHz to j102 Ω at 2.4 GHz respectively. To overcome this challenge this brief explores the design space in terms of selecting the appropriate variation of the design parameter α with frequency such that the second harmonic at extrinsic plane moves clockwise on the Smith chart. There are two considerations: first, the gradient of α with frequency and second, the range of values of α that can be chosen over the band. To realize the effect of gradient λ of α, the following relation

(a) (a) (b) Fig. 4. (a) Different λ for the same starting value of α=0.5 and their corresponding (b) Z 2ext projected by embedded model. (b) Fig. 5. (a) Different ranges of α and their corresponding (b) Z 2ext projected by embedded model. is defined: α λ = (3) f where, is the change in for every successive increase in frequency. Four different cases have been plotted in Fig. 4(a) each with a different λ and their corresponding Z 2ext on the Smith chart in Fig. 4(b). At 1.3 GHz is maintained at 0.5 (Z 2ext = -j37 Ω) for all the cases but a different λ leads to a distinct final value of at 2.4 GHz. A positive λ as shown in fig 5(a) steers the impedance to follow a highly non-foster rotation with Z 2ext extending from -j37 Ω at 1.3 GHz to j102 Ω at 2.4 GHz. As shown in Fig. 4(b), reducing λ diminishes the extent of anticlockwise rotation. Reduction in λ is carried out until it gets to zero throughout the frequency band and Z 2ext becomes -j105.2 Ω at 2.4 GHz. During the successive stages λ starts becoming negative or in other words begins to decrease from 0.5. The extent of anti-clockwise rotation reduces too with further decrease in λ. There will come a stage where the movement of Z 2ext will cease to become anticlockwise. Any further decrease in λ will make the movement clockwise. This threshold value of λ causes Z 2ext to be extremely concentrated on the Smith chart as seen in Fig. 4(b). In this work the value of λ is selected sufficiently below the threshold value. The Z 2ext reaches -j15.4 Ω at 2.4 GHz for α = -0.65. This leads to an adequate spread of the Z 2ext on the Smith chart to ease the matching requirement at the second harmonic. The parameter λ can even be further reduced to expand the trajectory of Z 2ext as required with not dipping below -1 at the upper frequency. There are multiple solutions of λ and subsequently to design a Foster matching network for the output in the frequency range of 1.3 to 2.4 GHz. The family of solutions is illustrated as the shaded region below the threshold slope in Fig. 4(a). However, only those solutions are allowed in which λ is more negative than that of the threshold case in the corresponding frequency step. It should be noted here that λ need not be kept constant throughout the frequency range. The family of solutions for is not unique and will vary with the frequency of operation, the starting value of and even the device chosen. In order to analyze range of the values of α, different sets of range of the values are selected for the same operation band between 1.3 GHz to 2.4 GHz. Fig 5(a) shows three such ranges for. First, α varies from 1 (class-j) to -0.2, second, it varies from 0.5 to -0.65 and third, from 0.2 to -1 (class-j -1 ). The nonlinear embedding model of 15 W GaN HEMT is then used to predict the extrinsic loads Z 2ext at harmonic frequencies as shown in Fig. 5(b). One can see from this figure that all the three sets lead to Foster matching networks. Among these solutions, the designer can choose the one which can result an easy implementation of the matching network. In this brief, the case where α varies from 0.5 to -0.65 is chosen for the

matching network design. Extending the definition in (3), let be the change in for each frequency step. If the designer selects n as the total number of times occurs in the frequency band, the following relation holds true: n αk 2, (4) k= 1 since is bounded between -1 and 1. To demonstrate the dependence of the bandwidth of operation on consider a lower frequency f 1 MHz and an upper frequency f 2 MHz for a band of operation. Therefore, one can write: f2 = f 1 + n f (5) Fig. 6. Extrinsic impedances projected by the embedded model (in blue) and extrinsic impedances of the final matching network (in red). where, the second term defines the overall bandwidth as a sum of n the number of frequency steps f. In order to maximize the bandwidth it therefore becomes essential to increase n as much as possible if f is fixed. In this brief, the f is taken as a constant value of 100 MHz. Also, according to (4) a high value of n would require lower values of. In other words, a higher bandwidth in continuous class-b/j mode is achieved when is only slightly reduced as frequency increases. As an example, consider reducing in large steps. Starting from at 1.3 GHz and keeping as -1 for MHz the upper frequency will result as 1.5 GHz. The fractional bandwidth drastically reduces to 11%, negating the usefulness of using a class-b/j continuum. There seems to be a clear trade-off between making the impedance rotate clock-wise and achieving a high bandwidth. While Z 2ext necessitates decreasing sufficiently as frequency increases, a large fractional bandwidth calls for to only slightly decrease from its initial value. The final decision rests with the PA designer. The parameter has already been shown to control the output voltage in (1) and output impedance in (2) at the current reference plane. Henceforth, it is explained that it can also be used to maneuver the extrinsic impedance and control the bandwidth more easily. Such an investigation can be extended to other continuous modes of PAs such as the continuous class-f and class-f -1 as well. IV. BROADBAND PA DESIGN The 15 W Cree CGH27015F GaN HEMT packaged device is biased and stabilized at 30 V and the quiescent current of 103 ma. The fundamental and second harmonic terminations at the intrinsic plane were set according to the methodology opted in Section III. Using embedding transfer technique [3], the required values of impedances Z 1ext and Z 2ext (in red) are obtained as shown in Fig. 6. Z 1ext was slightly adopted to follow a clockwise trajectory using load-pull simulation. The figure also shows the load synthesized using the broadband matching network (in blue). The corresponding intrinsic voltage and current waveforms at three different frequencies are illustrated in Fig. 7. The schematic of the PA is shown in Fig. 8, where, the broadband output matching network Fig. 7. Voltage (red) and current (blue) waveforms set at the current reference plane. consists of six microstrip line sections. The broadband input matching uses unequally terminated band-pass filter prototype approach [8]. A parallel combination of resistor and capacitor at the input stabilized the device. Fig. 9 shows the photograph of the fabricated PA, where, the circuit is developed on Rogers substrate RO4350B with ε r = 3.66, thickness of 20 mil and loss tangent = 0.0037. V. SIMULATION AND MEASUREMENT RESULTS The measurement setup is excited with continuous wave signals from 1.3 GHz to 2.4 GHz at every 50 MHz step. The measured drain efficiency (DE), power added efficiency (PAE), output power and gain are plotted in Fig. 10. One can see from Fig. 10 that a minimum drain efficiency of 63.2% is observed at 1.95 GHz and maximum value of 72% at 1.4 GHz. The average drain efficiency for the entire bandwidth (59% fractional bandwidth) comes out to be 66%. Output power varies between 40.1 dbm to 41.1 dbm through the frequency range with average output power as 40.5 dbm. The gain of the PA was measured between 11.4 and 14.3 db across the band. Fig. 11 depicts the measured carrier to third order intermodulation suppression ration (C/IMD3) with output power back-off from saturation at three frequencies. The value is better than -15 dbc for both the upper and lower side IMD3 product. Table I outlines the comparison between the current work and some recent state-of-the-art broadband PA results.

Fig. 8. Schematic diagram of the proposed continuous class-b/j PA. TABLE I COMPARISON WITH STATE-OF-THE-ART BROADBAND PAS Ref PA Type Bandwidth (GHz), (%) DE (%) Power (dbm) [9] Class-J 1.5-2.5 (50) 60-70 39.5-40.5 [10] Class-J 2.3-2.7 (15) >60 40-40.7 [11] Class-J 1.6-2.2 (32) 55-68 40-41 [12] Class-E 1.4-2.7(63) 63-73 39.7-41.5 This Work Class-B/J 1.3-2.4 (59) 63-72 40.1-41.2 Fig. 9. Photograph of the final designed continuous class-b/j PA. technique the waveforms and impedances are synthesized at the extrinsic package reference plane in a straightforward way respecting the intrinsic drain-source conditions. In order to generate a clockwise rotation of the extrinsic impedances on the Smith chart the variation with frequency of the parameter of the class-b/j voltage equation was probed. Studying the behavior of the extrinsic impedances in terms of the frequency dependence of allows the designer to make an informed decision about the matching circuit requirements. Based on this technique a highly efficient broadband PA has been fabricated displaying state-of-the-art performance. Fig. 10. Measured and simulated results of the PA from 1.3 to 2.4 GHz. Fig. 11. Measured IMD3 results for lower and upper side band intermodulation at 1.3 GHz, 1.9 GHz and 2.4 GHz. The present broadband amplifier sufficiently reaches close to the theoretical maximum efficiency of 78.5% of class-j mode. VI. CONCLUSION The continuous class-b/j mode of operation has been analyzed in this brief using the nonlinear embedding approach. In this REFERENCES [1] Q. Guo, X. Zhang, J. Xu, Y. Li, Q. Xue, Bandpass class-f power amplifier based on multi-function hybrid cavity-microstrip filter, IEEE Trans. Circuits Syst. II, Exp. Briefs, Digital print, DOI: 10.1109/TCSII.2016.2600575, Aug. 2016. [2] F. Xin, B. Dylan, B. Slim, Novel Dual Band matching Network for effective design of concurrent dual-band power amplifier, IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 61, no.1, pp. 293-301, Jan. 2014. [3] H. Jang, P. Roblin, and Z. Xie, Model-based nonlinear embedding for power amplifier design, IEEE Trans. Microw. Theory Techn., vol. 62, no. 9, pp. 1986 2002, Sep. 2014. [4] S. C. Cripps, P. J. Tasker, A. L. Clarke, J. Lees, and J. Benedikt, On the continuity of high efficiency modes in linear RF power amplifiers, IEEE Microw. Wireless Compon. Lett., vol. 19, no. 10, pp. 665 667, Oct. 2009. [5] M. Seo, H. Lee, J. Gu, H. Kim, J. Ham, W. Choi, Y. Yun, K. O. Kenneth, and Y. Yang, High-efficiency power amplifier using an active second-harmonic injection technique under optimized third-harmonic termination, IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 61, no. 8, pp. 549 553, Aug. 2014. [6] A. Raffo, F. Scappaviva, and G. Vannini, A new approach to microwave power amplifier design based on the experimental characterization of the intrinsic electron-device load line, IEEE Trans. Microw. Theory Tech., vol. 57, no. 7, pp. 1743 1752, Jul. 2009. [7] T. Sharma, R. Darraji, F. Ghannouchi, A methodology for implementation of high efficiency broadband power amplifiers with second harmonic manipulation, IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 63, no. 1, pp. 54-58. Jan. 2016. [8] B. Gowrish, K. Rawat, A. Basu, and S.K. Koul, Broadband matching network using band-pass filter with device parasitic absorption, in 82 nd ARFTG Microw. Meas. Conf., Columbus, OH, Nov. 2013. [9] P. Wright, J. Lees, J. Benedikt, P. J. Tasker, and S. C. Cripps, A methodology for realizing high efficiency class-j in a linear and broadband PA, IEEE Trans. Microw. Theory Tech., vol. 57, no. 12, pp. 3196 3204, Dec. 2009. [10] N. Tuffy, A. Zhu, and T. J. Brazil, Class-J RF power amplifier with wideband harmonic suppression, in IEEE MTT-S Int. Microwave Symposium Dig., Jun. 2011, pp. 1-4. [11] K. Mimis, K. A. Morris, S. Bensmida, and J. P. McGeehan, Multichannel and wideband power amplifier design methodology for 4G communication systems based on hybrid class-j operation, IEEE Trans. Microw. Theory Tech., vol. 60, no. 8, pp. 2562 2570, Jul. 2012. [12] A. Grebennikov. High-efficiency class-e power amplifier with shunt capacitance and shunt filter. IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 63, no. 1, pp. 12-22, Jan. 2016.