This article has been accepted and published on J-STAGE in advance of copyediting. Content is final as presented.

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1 This article has been accepted and published on J-STAGE in advance of copyediting. Content is final as presented. IEICE Electronics Express, Vol.* No.*,*-* Design of Broadband Inverse Class-F Power Amplifier Based on Resistive-Reactive Series of Inverse Continuous Modes Min Zhang a), Zongxi Tang, Weimin Shi and Xin Cao School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu, 673, China. a) Abstract: In this paper, a resistive-reactive series of continuous inverse modes is proposed for extending bandwidth of the series of Inverse continuous mode (SICM). A broadband class inverse F power amplifier (PA), which operates across.5-4.ghz (48.5% bandwidth), is designed by using bare GaN HEMT to prove this theory. Experiment results indicate that the PA mentioned above is able to output W saturation power and the drain efficiency can reach 47%-75% in the whole interested band. The average output power of this designed PA is 4. W and the average drain efficiency is 60.%. Keywords: Broadband, class inverse F, power amplifier, bare GaN HEMT, resistive-reactive, series of inverse continuous modes. Classification: Microwave and millimeter-wave devices, circuits, and modules References IEICE 07 DOI: 0.587/elex Received May, 07 Accepted June, 07 Publicized July 5, 07 [] S. C. Cripps, et al.: On the Continuity of High Efficiency Modes in Linear RF Power Amplifiers, IEEE Microw. Wireless Compon. Lett., 9 (009) 665 (DOI: 0.09/LMWC ). [] P. Wright, et al.: A methodology for realizing high efficiency class-j in a linear broadband PA, IEEE Trans. Microw. Theory Tech., 57(009) 396 (DOI: 0.09/TMTT ). [3] N. Tuffy, et al.: A simplified broadband design methodology for linearized high-efficiency continuous class-f power amplifiers, IEEE Trans. Microw. Theory Techn., 60 (0) 95 (DOI: 0.09/TMTT ) [4] V.Carrubba,, et al.: "Exploring the design space for broadband pas using the novel continuous inverse class-f mode." Microwave Conference IEEE, 0: [5] Ding, X, et al.: "-4 GHz wideband power amplifier with ultra-flat gain and high PAE." Electronics Letters 49.5 (03) 36 (DOI: 0.049/el.0.435) [6] Y. Sun, et al.: Simple Synthesized Harmonic Matching Strategy in Broadband PA Design Microwave Journal;pp.88-98, Oct 05 [7] L. Ma, et al.: High efficiency continuous inverse class f power amplifier with

2 harmonic impedance control. Microwave Journal, 06. [8] V. Carrubba, et al.: A novel highly efficient broadband continuous class-f RFPA delivering 74% average efficiency for an octave bandwidth Microwave Symposium Digest. IEEE, 0:-4.( DOI: 0.09/MWSYM ) [9] V. Carrubba, et al.: The Continuous Inverse Class-F Mode With Resistive Second-Harmonic Impedance. Microwave Theory & Techniques IEEE Transactions on 60.6(0) 98 (DOI: 0.09/TMTT.0.898). [0] Hu, Zhebin, et al. C Band General Class J Power Amplifier Using GaN HEMT. IEICE Electronics Express(06) (DOI: Introduction With the coming 5G (fifth-generation) waves, the communication systems desire the wider band operations for the higher rate transmission. Moreover, power amplifiers account for most of the energy consumption of communication systems. Therefore, the design of broadband and high-efficiency PAs is always a hotspot issue for PA researchers. In order to realize PAs with broadband and high-efficiency operation, many methods were proposed. S.C.Cripps presented the continuous working mode of PAs in 009[], firstly. Then the continuous class J, the continuous class F and the continuous class inverse F were appeared in succession []-[4]. A 4GHz wideband power amplifier with ultra-flat gain and high PAE was implemented by X.Ding in 03[5].For extending bandwidth of the continuous mode, the simple real frequency technique (SRFT) was applied to PA by Y.Sun in 05[6]. a new set of expressions for current and voltage in the continuous Class F - and mode was proposed to produce a variable third harmonic impedance in 06[7].these methods realize the expansion of the fundamental impedance space indeed, however, they still have the bandwidth limitations like traditional continuous class B/J and class F because of their working condition which require the second-harmonic impedance must be pure imaginary, thus it is difficult to match the fundamental impedance and the harmonic impedance in broadband simultaneously. Fortunately, the second harmonic impendence space could be relaxed by introducing the resistive second harmonic loads to the continuous modes. This method which was applied to the continuous class F mode was proposed by V. Carrubba in 0[8]. Subsequently, he used this method to design a class inverse F PA in 0[9]. The general Class-J mode, which offer a bigger design space for the fundamental and harmonic terminations, is introduced to implement wideband PA[0]. In this letter, the bandwidth is extended by adding the resistive part to the second harmonic impedance. Unlike [9], the voltage coefficients (α and β) are added to offer more freedom for impedance space. Extended Series of Inverse Continuous Modes The drain current of Resistive-Reactive SICMs PAs is defined in [9], as shown in

3 cos cos 3 sin cos I I i i i () ds MAX dc 3 Where i dc=0.37, i =0.43, i 3=0.06, - γ, δ (follows as same). The factor δ is added to introduce the resistive part to the second harmonic impedance so that the impedance space can be extended compared to SICMs PAs. The drain voltage of Resistive-Reactive SICMs is same as the SICMs PAs, as described in equation ds dd V V cos cos () In order to ensure the voltage over zero, the equation (3) must be satisfied. 4 for 3 4 for 8 3 Fig. shows the waveforms of voltage and current with respect to and γ (3) Fig.. Normalized voltage and current waveforms Apply equation () the expansion of equation (), ignore more than the second harmonic, we can obtain fundamental power P fund, the DC power P DC and the drain efficiency D as follows: Pfund Vdd IMAX i idc (4) i PDC Vdd IMAX idc P D P fund DC i i dc dc i i (5) (6) 3

4 (a) (b) Fig.. (a) Drain efficiencies of extended SICMs with respect to α and δ and (b) Output power decrease of extended SICMs with respect to α and δ. Fig..(a) depicts the three dimensional map of drain efficiency with α and δ, and Fig..(b) shows the output power decrease with α and δ changes. It is necessary to set δ greater than zero to avoid the real part of admittance is negative. According to Fig., we set α from 6/5 to, δ from 0 to 0.. Apparently, in this parameter range, we can get an impedance space, where the drain efficiency is greater than 65, the output power decrease is better than -.55dB. According to the equations (4a)-(4c) and (), the fundamental and harmonic admittance can be deduced as shown in equation (7a)-(7c), i i Y G i i j i 4 3 fund opt dc dc (7a) Ynd Gopt ( i i3) j i i3 idc (7b) Y3rd (7c) Fig. 3. Impedance spaces on smith chart 4

5 It is deduced from equation (7b) that the real part of second harmonic admittance is negative when δ is negative. However, negative resistance state is actually difficult to be achieved, hence δ is set to be greater than zero. The admittance space which is normalized by G opt is described in Fig.3. It can easily be seen that the second harmonic impedance is no longer pure imaginary, and correspondingly fundamental and harmonic impedance space is extended compare to [7] and [9]. The above is the principle of the whole impedance expansion process, the following section will describe the application of this principle. 3 PA Design and Experiment Results In this part, a PA working across.5-4.ghz is designed using bare die GaN HEMT CGH6005D to verify above-mentioned theory. The reason why we use bare die device is that there are less package parasitic parameter, its package model consists of a drain-source capacitor C ds and golden bondwires(as shown in Fig.4). The drain voltage is 8V and the gate voltage is -.9V. The substrate used in this design is RF35 ( r=3.5, H=0mil).The R opt is set to 3Ω, which is the typical R opt of a class-b PA. Fig. 4. The output matching network schematic and the simulated impedance trajectories of the synthesized output matching network at I-gen plane on smith chart Corresponding to the previous theoretical analysis, the theoretical impedance region shown in Fig.3 and the impedance of PA at current generate plane (I-gen plane), normalized by 50Ω, are plotted in the smith chart as shown in Fig.4. Fig.4 also shows the output matching network schematic. TL3 and TL4 are mainly used to control the second harmonic by providing reactance. TL5 and TL6 are mainly used to control the third harmonic impedance near the short point. All the transmission lines maintain great matching of fundamental impedance. By the simulation optimization in the whole band, it can be clearly observed from Fig.4 that all the fundamental and harmonic impedances at I-gen plane are in the resistive-reactive space analyzed before. 5

6 Fig. 5. Measured results and The Photographs of this design The measured results and the photographs of this design are displayed in Fig.5. The comparison between this work and some published PAs is illustrated in Table I. Due to the fundamental impedance is well matched, this PA can output 4.W average power in entire band. As the second harmonic impedance all fall within the theoretical area and the third harmonic impedance near the short-circuit point, the average drain efficiency is more than 60%. This work performs a great FOM performance due to the high working frequency band and the high output power of the designed PA. The calculation of FOM is below Table I. The whole measured results prove the feasibility of the theory of impedance space expansion. Table I. Comparison of Some Published PAs and This Work Ref Bandwidth Power PDE(AE) Gain FOM (GHz) (W) (%) (db) 0[3] (75.5) [5] (PAE) (46.7) [6] (6.5).-6(SG) [7] (77.7) This Work (60.) FOM=f0 *AE*AP*AG. AE: Average Drain Efficiency. AP: Average of maximum and minimum output power. AG: Average of maximum and minimum Gains. 4 CONCLUSION In this letter, a new theory which based on resistive-reactive series of inverse continuous modes for designing broadband PAs has been proposed and an example of an application of bare die device is provided as a reference. Since the impedance space is given more freedom, the bandwidth of the PA is expanded. A PA, which can output power of W (the average power is 4.W) with drain efficiency of 47%-75% (the average DE is 60.%) in the.5g-4.ghz band (48.5% bandwidth), has been designed to prove this theory. From the experimental results, the FOM of this work is higher than the reported ones. This theory has been well proven. 6