Small-signal analysis of frequency-controlled electronic ballasts

This paper presents analytical tools aimed at improving and simplifying the development of frequency-controlled dimming electronic ballasts. A modified phasor transformation is proposed that converts a frequency-modulated signal into an equivalent time-varying phasor. The proposed transformation is applied to develop a complete small-signal phasor model of the LCC resonant ballast, which explicitly models the effect of the frequency modulation on the envelopes of the outputs. A Spice-compatible implementation of the model is presented that facilitates ac analysis of the ballast in addition to envelope transient simulation, and is verified through comparison of experimental and simulation results. A closed-form solution of the control-to-output current transfer function for the ballast-resistor system is presented, along with key observations of the pole locations and low-frequency gain that facilitate simple and intuitive compensator design. The effects of lamp dynamics on the controller design are discussed, followed by a design example for the feedback controller.