This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS 1 Nonlinear Embedding Model-Based Continuous Class E/F Power Amplifier Y. Mary Asha Latha , Student Member, IEEE, Karun Rawat , and Patrick Roblin , Senior Member, IEEE Abstract— This letter presents the design of a continuous class E/F power amplifier (PA) using model-based nonlinear embedding. The theoretically calculated continuous class E/F loads defined at the current source reference plane (CRP) may not guarantee feasible loads at the extrinsic package reference plane (ERP) due to nonlinear parasitic. Hence, a design space is analyzed to map the correct mode of the class E/F continuum over broadband to obtain feasible loads. A scheme is presented to assign fundamental current component (φ) to various frequencies over the band to obtain a tradeoff between best bandwidth and feasibility of a passive matching network. A nonlinear embedding model is used to project the loads from CRP to ERP. As a proof of concept, a continuous class E/F PA is designed using CGH27015F. The prototype developed has measured a drain efficiency of 60.2%–76.5% from 1.5 to 2.9 GHz which corresponds to 63.6% fractional bandwidth. Index Terms—Broadband, continuous class E/F, design space, GaN HEMT, nonlinear embedding model, power amplifier (PA). I. I NTRODUCTION S EVERAL schemes have been proposed in the past to enhance the bandwidth of class E power amplifier (PA) [1]–[4]. Among them, the class E/F continuum has been proposed considering the second-harmonic load ( Z 2,CRP ) in addition to the fundamental load ( Z 1,CRP ) to take care of the zero voltage switching and zero voltage derivative switching conditions [5]. The phase of the fundamental current component (φ) in this continuum varies from 43.3 ◦ to 78 ◦ . The conventional class E corresponds to φ = 57.5 ◦ [5]. Fig. 1(a) shows the voltage and current waveforms of the class E/F continuum. Theoretically, one can map these modes to different frequencies over broadband. However, due to the device parasitic, this mapping may not be as simple as proposed in [5]. Each mode of the class E/F continuum defines different loads at the current source reference plane (CRP). These CRP loads when projected to the extrinsic package reference plane (ERP) may lead to the non-Foster loads based on the device parasitic. Such loads are impractical to match using the passive components which translate to clockwise Manuscript received July 17, 2019; revised September 6, 2019; accepted September 12, 2019. This work was supported in part by the Department of Science and Technology (DST) IMPRINT under Grant IMP-1305-ECD, in part by SERB under Grant CRG/2018/003869, and in part by the Ministry of Electronics and Information Technology (MeitY), Government of India, through the Visvesvaraya Ph.D. Scheme. (Corresponding author: Y. Mary Asha Latha.) Y. Mary Asha Latha and K. Rawat are with the Department of Electron- ics and Communication Engineering, IIT Roorkee, Roorkee 247667, India (e-mail: ymashalatha@ieee.org; karun.rawat.in@ieee.org). P. Roblin is with the Department of Electrical and Computer Engineering, The Ohio State University, Columbus, OH 43210 USA (e-mail: roblin.1@ osu.edu). Color versions of one or more of the figures in this article are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/LMWC.2019.2941919 Fig. 1. (a) Fundamental and second-harmonic CRP loads for φ [43.3 ◦ , 78 ◦ ]. (b) Normalized switch waveforms for φ = 43.3 ◦ , 57.5 ◦ , and 78 ◦ [5]. rotation on the Smith chart with increasing frequency [6], [7]. The CRP refers to the intrinsic switch plane before the shunt capacitor in the conventional class E [3]. This letter presents a new scheme to choose various class E/F continuum modes with the frequency. This letter presents a unique trend to map φ with the frequency is observed which is quite different from other continuous classes [6], [7]. A tradeoff between bandwidth and feasibility of a passive network is also analyzed. The nonlinear embedding model is used to project loads from CRP to ERP using the embedding transfer network (ETN) which can provide a quick solution while analyzing a design space [8], [9]. II. DESIGN EQUATIONS OF CONTINUOUS CLASS E/F MODE The class E load network comprises a capacitance C con- nected in shunt with an ideal switch. Hence, the theoretically calculated loads of the class E/F continuum, when computed along with this C , can give load conditions at the CRP as [5] Z 1,CRP (φ) = R (1 + jx 1 )π π + j 2(1 + jx 1 ) cos 2 φ (1) Z 2,CRP (φ) = R jx 2 π π - 4x 2 cos 2 φ (2) where R = ( 8V 2 DD sin 2 φ ) / ( π 2 P out ) (3) x 1 = (16π cos 2 φ cot φ +2π sin 2φ +3π 2 -32)/(12π cos 2 φ) (4) x 2 = π sec 2 φ 24(π - 2 tan φ)  4 sin(2 tan -1 (2 cot φ)) + 3π + 2(cos(2 tan -1 (2 cot φ)) -2) tan φ  . (5) These CRP loads, plotted in Fig. 1(b) for φ [43.3 ◦ , 78 ◦ ], can provide an output power comparable to class E mode. One can see that Z 2,CRP is an open circuit for class E/F 2 mode (φ = 43.3 ◦ ) and a short circuit for class EF 2 mode (φ = 78 ◦ ), while 1531-1309 © 2019 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.