The parametric transformer

Although parametric devices have been known for many years, very little attention had been paid to the possibilities of exploiting the principles involved for low frequency power conversion purposes, until tfie recent advent of the parametric transformer. The theory of this device is developed in the thesis, and the unusual performance characteristics are explained. Possible application areas are discussed, for an assessment of the future potential of the device as a power-control element. The operation of the parametric transformer is considered initially on the basis of the Mathieu-Hill equations. The stability chart for these equations is extensively used to permit graphical interpretation of the behaviour and characteristics. As no complete theory exists for non-linear systems with time-varying parameters, other analytical methods are also considered, although since all of these regard the device as a parametric oscillator they throw little light an the inherent transformer action. By considering the parametric-transformer as a conventional saturable reactor with a capacitor connected across the load winding and the control winding driven from an alternating source, it can be placed within the perspective of non-linear magnetic devices already known. Many possible magnetic constructions with parallel and/or orthogonal flux. interactions are investigated, with special attention paid to the bridged magnetic core analogue of the two-C-core construction. The illustration of parametric coupling as a result of flux interaction in saturable reactor devices leads to a derivation of the overall equations directly from the physical system. The functions representing the magnetic structure of the parametric transformer are first evaluated graphically, ard using various analytical representations of the B/H curve their explicit expressions are then formulated for different magnetic configurations. The introduction into the study of the concept of a relative magnetisation curve is invaluable in explaining the current waveforms and many other aspects of the device. A mathematical model is established for the parametric transformer and the system equations are solved numerically by a digital computer. The voltage and current waveforms and performance characteristics are demonstrated, and the correctness of the theory is ascertained by comparison with experimental results. Based on considerations of losses and efficiency, the advantages and disadvantages of parametric transformers are discussed. Possible applications in such areas as power supplies, inverters and converters are viewed and examples are given.