A Discrete-Time Technique for the Steady-State Analysis of Nonlinear Class-E Amplifiers

Abstract

Abstract-Switched circuits are widely used, particularly for power electronic applications in which efficiency is important. Of these applications, the class-E amplifier has been given particular attention, since it is theoretically a 100% efficient switched circuit that has been successfully demonstrated in applications such as ballasts, converters, frequency multipliers and communication amplifiers at frequencies as high as 10GHz. However, with increasing power or frequency, nonlinearities become extremely important, for instance, in order to achieve actual class E operation and even to avoid destruction of the switching device.In this paper, a new method for determining the steady-state response of nonlinear circuits containing ideal switches is proposed. While the method is more general, the description is based on the Class E amplifier because of its inherent interest. The method is based on a time-domain Gear discretization of the circuit equations. A technique for determining the initial samples of the discretized equation of each topology is developed, based on the fact that state variables are constant during switching. Finally, assuming a periodic steady-state, a single algebraic system of nonlinear equations is obtained in which the unknowns are the samples of the control variable of the nonlinearity in the whole signal period. To validate the method described, a comparison with PSpice simulations is provided.

The nonlinear class-E amplifier: A case study of harmonic balance applied to switched circuits

“…If we consider s 1,Ο , the use of k=1 is enough to wipe out the effects of aliasing. Viewing (8) in the frequency domain as the convolution of the N FC of v(t) and the 2N free-of-aliasing FC of s 1 (t), the N FC obtained from the truncation of this convolution have no aliasing at all, either from the switching function or from the product in (8). Obviously, when s 1,Ο is used, no improvement is obtained with k>1, while when s 2,Ο or s 3,Ο are used, higher values of k yield lower RMSE (see Fig.…”

“…where the impedances Z n are given by and, in accordance with the notation in (3), s is the vector of samples of the switching function s(t), EH n is the product of the FC of the constant input e(t) and a network function (which is zero except for EH 0 =v DD ), I Cs n are the FC of the current flowing through C s defined by [8] …”

“…Such techniques are required mainly for dealing with hard nonlinearities. The same technique is useful for improving the evaluation of (8) in the time domain. It consists in artificially increasing the total number of FC, by adding kN (with k usually integer) zero coefficients,…”

An Overview of Resonant Circuits for Wireless Power Transfer

“…The energy is injected into the LC tank when the switch S1 is turned off. At the beginning, the switch S1 is turned on to charge the inductor LD with the current increasing at the rate of VDC/LD for several cycles of the LC resonance [40]. After the S1 is turned off, the energy is injected into the CD so that the LC tank performs oscillations via the CP, LP and D1.…”

Computer-Aided Multi-Layer Design of Switch-Mode Power Circuits

“…Therefore, algorithms must be extremely efficient since they are repeated a lot of times to reach convergence. A wide spectrum of steady-state analysis algorithms have been elaborated, so far, for these circuits [1], [2], [7], [9], [13], [17], [18], [22], [24], [28], [29], [30], [33], [39], [45], [57], [60], [62], [66]. One of very efficient approaches is the secant method [7], [39], implemented in SWITCH [40], [41] and OPTIMA [39].…”