Resonance on Transformers Excited by Square Waves and Explanation of the High Voltage on Tesla Transformer

Abstract

Abstract-This paper presents an analysis about resonance on coupled systems when excited by square waves, generated through experiments using planar and ring coils. Because of the phenomenon described by its transfer function, a sum of responses appear when the square wave frequency increases, which causes a resonance response with high voltage, in several cases, greater than common turn ratio of the transformer. With parallel capacitances inserted on output, the resonance frequency reduction and change of gain is observed. Due to this effect, explanation of how output of Tesla transformer presents high voltage which is shown and strategies to reach the maximal value on output are proposed.

Planar Transformers Excited by Square Waves

“…This is because the changes on parameters (resistances, parasitic capacitances, self and mutual inductances) in the equivalent circuit causes changes in these frequencies, and consequently, values in the transfer function changes the system response. In this way, although these changes are verified in comparison with the system described in [19,20], the problem is seen similarly, such that the increase in the frequency excitation (input square wave) results in a sum of responses and resonance effect with output high voltage, as seen in [21,28]. This analysis is presented in the next section.…”

“…In some cases, several analyses about transformers built with planar coils [7][8][9][10][11] are found in literature, which generally is made in integrated circuits [12][13][14][15][16][17][18] and few in large dimensions (in the order of centimeters) with crossing of planar coils and ring coils excited by square waves [19][20][21]. In other studies, analysis of the responses when the transformer is excited by square waves is generally applied to pulse transformers [22][23][24][25][26][27][28], or power electronics [29][30][31].…”

Effects of Induced Electromotive Force (EMF) in Transformers Built with Planar Coils

“…Nessa área, pouco se encontra de estudos a respeito de respostas de indução eletromagnética em transformadores construídos com bobinas planas excitados por ondas quadradas, em que se vêem trabalhos como [18]- [21] para o caso de bobinas planas internas a bobinas em anel. As respostas transitórias vistas nestes trabalhos se mostram como importantes formulações para análises de capacitâncias parasitas [22]- [25], bem como estudos de ressonância [20], [21], [25], [26] e aplicações em transformadores de pulso [27]- [33].…”

Resonance Analysis of Induced EMF on Coils

“…Such concept determines explanation of several phenomena of the induced EMF on coils, showing through differential equations and others formalisms of how happens this phenomenon (Costa, 2009a). However, phenomena as secondary energy at Tesla Transformer (that is a pulse transformer (Lord, 1971), where the input energy is a square wave) present some problems that are not fully comprehensible, as the high energy in secondary coil apparently greater then input energy, which was explained in (Costa, 2009b; as the sum of responses of the induced EMF at secondary coil. By other side, when analysing these same transformers with input energy as sinusoidal excitation, the induced EMF at resonance appears in the same way, but with smaller gain.…”