The parametric transformer
Eyup S. Tez
2134/7948
https://repository.lboro.ac.uk/articles/The_parametric_transformer/9520040
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.
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