The multi-order response of the tuned secondary circuit of a Tesla transformer, following impulse excitation from its tuned primary circuit, is presented and analysed at the fundamental resonant frequency and at higher-order mode frequencies. A novel way of modifying the frequency response of the secondary coil is then investigated by utilising a technique normally applied to the design of a certain type of filter known as a helical filter. In general, these are used in radio and microwave frequency circuits in order to pass certain frequencies with little attenuation whilst significantly attenuating other frequencies. Design techniques, developed over several decades, modify and optimise the performance of such filters. The frequency response of the helical filter is modified by altering the geometry of the helical resonator component therein, which is typically in the form of an air-cored single-layer solenoid. A Tesla transformer whose secondary is constructed to be some form of single-layer solenoidal winding resonates at its designed frequency - its fundamental mode - but also at non-integer harmonics (higher-order anharmonic frequencies, also known as overtones). Those multi-order oscillatory voltages and currents energised in the secondary circuit have been identified and measured and research has determined the fundamental and higher-order mode frequencies and amplitudes for various experimental secondary winding configurations derived from helical filter design techniques. Applied to the Tesla transformer secondary winding, such techniques lead to a new design with a performance that is improved by the suppression of higher- order anharmonic frequencies whilst imparting little change to the fundamental response. It is anticipated that this feature will lead to Tesla transformers which exhibit enhanced spectral purity and which will be better suited to use in certain pulsed power applications than conventionally wound designs.

Transients encountered by transformers in power stations during normal operation can have complex oscillatory overvoltages containing a large spectrum of frequency components. These transients can coincide with the natural frequencies of the transformers windings, leading to voltages that can be greater or more severe than the current factory proof tests. This may lead to insulation breakdown and catastrophic failures. Existing lumped parameter RLCG transformer models have been proven to be less accurate for very fast transient overvoltages (VFTO) with frequencies over 1 MHz. A white box model for transient analysis of transformer windings has been developed using Multiconductor Transmission Line (MTL) Theory. This model enables the simulation of natural frequencies of the transformer windings up to frequencies of several MHz, and can be used to compute voltages between turns by representing each turn as a separate transmission line. Both continuous and interleaved disk windings have been modelled and a comparison and validation of the results is presented. / May 2017