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The characterization and modeling of piezoelectric transformers are studied and developed for use in electronic ballasts. By replacing conventional L-C resonant tanks with piezoelectric transformers, inductor-less piezoelectric transformer electronic ballasts have been developed for use in fluorescent lamps. The piezoelectric transformer is a combination of piezoelectric actuators as the primary side and piezoelectric transducers as the secondary side, both of which work in longitudinal or transverse vibration mode. These actuators and transducers are both made of piezoelectric elements, which are composed of electrode plates and piezoelectric ceramic materials. Instead of the magnetic field coupling between the primary and secondary windings in a conventional magnetic core transformer, piezoelectric transformers transfer electrical energy via electro-mechanical coupling that occurs between the primary and secondary piezoelectric elements for isolation and step-up or step-down voltage conversion. Currently, there are three major types of piezoelectric transformers: Rosen, thickness vibration mode, and radial vibration mode, all three of which are used in DC/DC converters or in electronic ballasts for fluorescent lamps. Unlike the other two transformers, the characterization and modeling of the radial vibration mode piezoelectric transformer have not been studied and developed prior to this research work. Based on the piezoelectric and wave equations, the physics-based equivalent circuit model of radial vibration mode piezoelectric transformers is derived and verified through characterization work. Besides the major vibration mode, piezoelectric transformers have many spurious vibration modes in other frequency ranges. An improved multi-branch equivalent circuit is proposed, which more precisely characterizes radial vibration mode piezoelectric transformers to include other spurious vibration modes in wide frequency ranges, as compared with the characterizations achieved by prior circuits. Since the equivalent circuit of piezoelectric transformers is identical to the conventional L-C resonant tank used in electronic ballasts for fluorescent lamps, piezoelectric transformers replace the conventional L-C resonant tank in order to reduce the amount and cost of electronic components for the electronic ballasts. With the inclusion of the radial vibration mode piezoelectric transformer, the design and implementation of inductor-less piezoelectric transformer electronic ballast applications have been completed. Ph. D.