On Optimal Truncated Biharmonic Current Waveforms for Class-F and Inverse Class-F Power Amplifiers

• Published in: Mathematical problems in engineering Vol. 2017; no. 2017; pp. 1 - 19
• Main Authors: Juhas, Anamarija, Novak, Ladislav A., Dautovic, Stanisa
• Format: Journal Article
• Language: English
• Published: Cairo, Egypt Hindawi Publishing Corporation 01.01.2017; Hindawi; Hindawi Limited
• Subjects: Discontinuity; Efficiency; Fourier series; Harmonics; Inverse; Mathematical analysis; Mathematical problems; Optimization; Parameters; Power amplifiers; Series expansion; Waveforms
• ISSN: 1024-123X; 1563-5147
• DOI: 10.1155/2017/1390295

In this paper, two-parameter families of periodic current waveforms for class-F and inverse class-F power amplifiers (PAs) are considered. These waveforms are obtained by truncating cosine waveforms composed of dc component and fundamental and either second (k=2) or third (k=3) harmonic. In each period, waveforms are truncated to become zero outside of a prescribed interval (so-called conduction angle). The considered families of waveforms include both discontinuous and continuous waveforms. Fourier series expansion of truncated waveform contains an infinite number of harmonics, although a number of harmonics may be missing. Taking into account common assumptions that for class-F PA the third (n=3) harmonic is missing in current waveform and for inverse class-F PA the second (n=2) harmonic is missing in current waveform, we consider the following four cases: (i) n=k=3, (ii) n=3, k=2, (iii) n=k=2, and (iv) n=2, k=3. We show that, in each of these cases, current waveform enabling maximal efficiency (optimal waveform) of class-F and inverse class-F PA is continuous for all conduction angles of practical interest. Furthermore, we provide closed-form expressions for parameters of optimal current waveforms and maximal efficiency of class-F (inverse class-F) PA in terms of conduction angle only. Two case studies of practical interest for PA design, involving suboptimal current waveforms, along with the results of nonlinear simulation of inverse class-F PA, are also presented.