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

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.