A mathematical model of the Class D converter for compactfluorescent ballasts

The time-harmonic analysis is often used to design the class D converter. Since the Q of the resonant network is often low, this analysis, in the form of the sinusoidal approximation, begins to lose accuracy. This paper explores an improved method of designing compact fluorescent ballasts via the square wave approximation (SWA), where the time domain equations are solved for the general case of arbitrary Q, duty ratio, and frequency. A precise mathematical model of the Class D converter is developed that predicts the currents and voltages of the converter and these solutions are compared with computer simulation. Nonlinear programming (NLP) is introduced as a means to design the ballast for the lowest conduction losses. The equations developed in the mathematical model are formulated into a NLP format that includes the self-oscillating case