Resumo: This paper presents an analysis about the results of experiments using planar coils inner ring coils to determine a transformer. The excitation of this system was a square wave voltage, where experiments were realized in two ways: considering planar coil as primary and observing responses on secondary being ring coil (direct system) and the inverse (ring coil as primary and planar coil as secondary-inverted system). In this study, a phenomenon not common in literature on system response is analyzed, showing effects of changes on transfer function in both cases when varying turn numbers of each coil and several variations on responses due to changes on resistances, parasitic capacitances, self and mutual inductances of the coils. The uncommon phenomenon appears as modulated response on specific turn ratio. The obtained results can be used to researches in areas as power electronics and pulse transformers.

3. Costa, E. M. M., Resonance Between Planar Coils vs Ring Coils Excited by Square Waves, Progress In Electromagnetics Research B - PIER B, Vol. 18, pp. 59-81, 2009.

Resumo: This paper presents a basic analysis about experiment results using planar coils inner ring coils, defining a transformer, when this system is excited by square wave voltage. In this study phenomena of response to step voltage due to parasitic capacitances is analyzed, and a sum of responses when the input square wave frequency increases is given too. These phenomena are uncommon in literature, which can be applied to several areas of researches in electrical engineering, pulse transformers and power electronics.

Resumo: In this paper is presented an analysis of found results of experiments developed with transformers built with planar coils, when they are excited by square waves, in comparison with transformers built with planar coils inner ring coils. The transformer was built joining two planar coils one over the other. In this kind of transformer, similar responses as analysis of transformers built with planar coil inner ring coil is found, as well the results of resonance. Because the low self-inductances and parasitic capacitances obtained in these configurations, although the coils resistance are low, what generates low exponential drops on responses, the resonance is found in higher frequencies, but satisfying conditions of sum of responses in resonance.

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Resumo: In this paper effects of induced emf on coils excited by square waves are shown, as well as how these influence resonance phenomena. The work was based on experimental results, using planar coils and inner ring coils. A priori, the resonance is presented as effects of parasitic capacitances on coils, which through inclusion of external capacitances, is established that the phenomenon of high voltage on output is the sum of responses of the induced emf added with response to step voltage on rise and fall of the square wave. Consequently, the found results explicate the phenomenon of high energy (or high voltage) in the output of Tesla transformer.

Resumo: In this paper are presented some effects observed on induced electromotive force (emf) in transformers built with planar coils. Several experiments were realized crossing the planar coils with different turn number, exciting primary with square wave and observing responses on secondary. The results obtained are analyzed through transfer function of the transformer, showing important results about systems excited with square waves, which can be used in several researches as pulse transformers.

Resumo: (Introduction of Chapter Proposal)In all analysis of resonance at RLC circuits, the concept of equality in the inductive reactance and capacitive reactance generates the maximum energy transfer. In the same way, this concept is applied to transformers, due to parasitic capacitances present inter turns (Costa, 2009). 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; Costa, 2010) 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. Several analysis of coils, considering planar coils and ring coils, forming special transformers has been analysed, exciting one (primary) and verifying the other (secondary), in a experimental way, to find new expectations in this area. When exciting primary coil in these transformers, built with planar coil versus ring coil (having the planar coil or the ring coil as primary, and the other as the secondary) or planar coil versus planar coil, the effect of induced EMF at secondary coil presents some common characteristic previously yields studied in circuit theory (as resonance due the RLC characteristic of the transformer). However, with the experimental analysis of the induced EMF in these transformers, when exciting primary coil with square wave and sinusoidal wave, although are found resonance frequencies in medium frequencies (above 3 MHz) depending of the configuration (number of turns in each coil, and type of coil – planar or ring), gain variations are seen. Also, on resonance frequencies, other phenomena are seen, as high voltage gain in the transformer, even if the primary coil of the transformer presents less turns than the secondary, which contradicts ideal transformer theory. These cases are analysed here, showing these phenomena, and checking the problem in some mathematical analysis. The induced EMF from primary coil to secondary coil at transformers in the resonance has shown several properties that generates new perspectives in electromagnetic theory, as formalisms to develop new type of transformers, others explanations about resonance theory, analysis of energy transfer through resonance on coils, generation of high energy from low power sources, analysis about parasitic capacitances and others characteristics at coils and transformers, and others. This chapter treats of these analysis, checking some experimental results, and mathematical formalisms that explain some properties and phenomena that occurs at secondary coil when the resonance frequency is reached in the coupled circuit (transformer), due to induced EMF generated by the excitation of the primary coil with square wave or sinusoidal wave. .

Resumo: Este trabalho apresenta resultados de observações dos efeitos da força eletromotriz senoidal induzida em transformadores com núcleo de ar formados por bobinas planas e anelares. Nos experimentos do trabalho foram utilizadas bobinas planas e em anel, alternando primário e secundário, e variando a frequência a fim de se observar picos de ressonância, onde esses transformadores apresentaram altos ganhos de tensão no secundário, onde verificou-se um aumento expressivo no ganho desses transformadores com base na relação de ganho por número de espiras.