Modelling and analysis of radial mode piezoelectric transformers and inductor-less resonant power converters.

Within the electronics industry there is a continual demand for DC-DC power
converters that achieve high power density at low cost. Since a piezoelectric transformer
(PT) has an electrical equivalent circuit that is similar to several resonant converter
topologies, a PT can be used to replace many of the reactive components in these
topologies with a single ceramic component, thereby offering potential savings in cost,
size, and mass.
The first part of this thesis presents a new equivalent circuit model for one of the most
promising types of PT, the radial mode Transoner. This model relates the electrical
characteristics of the PT to the physical dimensions and material properties.
Considerable insight is then gained about how to design these devices to meet a
particular set of converter specifications whilst simultaneously maximising PT power
density.
The second part of this thesis concerns the effect of the rectifier topology on PT power
density. Using concepts from material science, together with equivalent circuit models
of both the PT and the rectifier topologies, it is shown that a given PT will always
achieve a higher thermally limited maximum output power when used in an AC-output
topology compared to a DC-output topology.
The half-bridge inductor-less PT-based converter topology is particularly attractive
because it requires no additional components between the half-bridge and the rectifier.
However, it is difficult to achieve zero-voltage-switching (ZVS) without significantly
compromising PT power density when using this topology. The third part of this thesis
details the development and experimental verification of a new model for the ZVS
condition. Using a normalisation scheme and numerical optimisation techniques, the
requirements for achieving inductor-less ZVS are accurately quantified for the first
time. The impact of these requirements on PT power density is assessed, and design
guidelines for maximising PT power density are given.