Vol. 18

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2009-10-09

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

By Eduard Montgomery Meira Costa
Progress In Electromagnetics Research B, Vol. 18, 205-224, 2009
doi:10.2528/PIERB09090305

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.

Citation


Eduard Montgomery Meira Costa, "Resonance on Transformers Excited by Square Waves and Explanation of the High Voltage on Tesla Transformer," Progress In Electromagnetics Research B, Vol. 18, 205-224, 2009.
doi:10.2528/PIERB09090305
http://test.jpier.org/PIERB/pier.php?paper=09090305

References


    1. Xiong, J. and L. He, "Extended global routing with RLC crosstalk constraints," IEEE Transactions on Very Large Scale Integration (VLSI) Sytems, Vol. 13, No. 3, 319-329, 2005.
    doi:10.1109/TVLSI.2004.842896

    2. Ding, W. and G. Wang, "Efficient timing modelling of coupled inductance dominant RLC interconnects," Electronic Letters, Vol. 45, No. 1, 2009.
    doi:10.1049/el:20092201

    3. Kim, S. Y. and S. S. Wong, "Closed-form RC and RLC delay models considering input rise time," IEEE Transactions on Circuits and Systems: Regular Papers, Vol. 54, No. 9, 2001-2010, 2007.
    doi:10.1109/TCSI.2007.902539

    4. Agarwal, K., D. Sylvester, and D. Blaauw, "Modeling and analysis of crosstalk noise in coupled RLC interconnects," IEEE Transactions on Computer-aided Design of Integrated Circuits and Systems, Vol. 25, No. 5, 892-901, 2006.
    doi:10.1109/TCAD.2005.855961

    5. Chakravarty, T., S. M. Roy, S. K. Sanyal, and A. De, "Loaded microstrip disk resonator exhibits ultra-low frequency resonance," Progress In Electromagnetics Research, Vol. 50, 1-12, 2005.
    doi:10.2528/PIER04042601

    6. Psarros, I. and I. D. Chremmos, "Resonance splitting in two coupled circular closed-loop arrays and investigation of analogy to traveling-wave optical resonators," Progress In Electromegnetics Research, Vol. 87, 197-214, 2008.
    doi:10.2528/PIER08102202

    7. Yagashi, A., "Highly improved performance of a noise isolation transformer by a thin-film short circuit ring," IEEE Transactions on Electromagnetic Compatibility, Vol. 41, No. 3, 246-250, 1999.
    doi:10.1109/15.784162

    8. Oshiro, O., H. Tsujimoto, and K. Shirae, "Structures and characteristics of planar transformers," IEEE Translation Journal on Magnetics in Japan, Vol. 4, No. 5, 332-338, 1989.
    doi:10.1109/TJMJ.1989.4564431

    9. Rissing, L. H., S. A. Zielke, and H. H. Gatzen, "Inductive microtransformer exploiting the magnetoelastic effect," IEEE Transactions on Magnetics, Vol. 34, No. 4, 1378-1380, 1998.
    doi:10.1109/20.706554

    10. Castaldi, G., V. Fiumara, and I. Gallina, "An exact synthesis method for dual-band Chebyshev impedance transformers," Progress In Electromegnetics Research, Vol. 86, 305-319, 2008.
    doi:10.2528/PIER08100605

    11. Lu, J. and F. Dawson, "Analysis of eddy current distribution in high frequency coaxial transformer with faraday shield," IEEE Transactions on Magnetics, Vol. 42, No. 10, 3186-3188, 2006.
    doi:10.1109/TMAG.2006.880093

    12. Stadler, A. and M. Albach, "The influence of the winding layout on the core losses and the leakage inductance in high frequency transformers," IEEE Transactions on Magnetics, Vol. 42, No. 4, 735-738, 2006.
    doi:10.1109/TMAG.2006.871383

    13. Cheng, K. W. E., et al., "Examination of square-wave modulated voltage dip restorer and its harmonics analysis," IEEE Transactions on Energy Conversion, Vol. 21, No. 3, 759-766, 2006.
    doi:10.1109/TEC.2006.877366

    14. Bortis, D., S. Waffler, J. Biela, and J. W. Kolar, "25-kW three-phase unity power factor buckboost rectifier with wide input and output range for pulse load applications," IEEE Transactions on Plasma Sciences, Vol. 36, No. 5, 2747-2752, 2008.
    doi:10.1109/TPS.2008.2003532

    15. Evans, P. D. and M. R. D. Al-Mothafar, "Harmonic analysis of a high frequency square wave cycloconvertor system," IEE Proceedings B, Vol. 136, No. 1, 19-31, 1989.

    16. Huang, Z., Y. Cui, and W. Xu, "Application of modal sensitivity for power system harmonic resonance analysis," IEEE Transactions on Power Systems, Vol. 22, No. 1, 222-231, 2007.
    doi:10.1109/TPWRS.2006.883678

    17. Popov, A. V. and V. V. Kopeikin, "Electromagnetic pulse propagation over nonuniform earth surface: Numerical simulation," Progress In Electromagnetics Research B, Vol. 6, 37-64, 2008.
    doi:10.2528/PIERB08031102

    18. Qi, J. and A. H. Sihvola, "Truncation effect on precursor field structure of pulse propagation in dispersive media," Progress In Electromagnetics Research B, Vol. 14, 65-86, 2009.
    doi:10.2528/PIERB09030205

    19. Butrym, A. Y. and M. N. Legenkiy, "Charge transport by a pulse E-wave in a waveguide with conductive medium," Progress In Electromagnetics Research B, Vol. 15, 325-346, 2009.
    doi:10.2528/PIERB09050703

    20. Hussain, M. G. M. and S. F. Mahmoud, "Energy patterns for a conducting circular disc buried in a homogeneous lossy medium and excited by ultra-wideband generalized gaussian pulses," Progress In Electromagnetics Research, Vol. 43, 59-74, 2003.
    doi:10.2528/PIER02120201

    21. Besieris, I., M. Abdel-Rahman, A. Shaarawi, and A. Chatzipetros, "Two fundamental representations of localized pulse solution to the scalar wave equation," Progress In Electromagnetics Research, Vol. 19, 1-48, 1998.
    doi:10.2528/PIER97072900

    22. Ala, G., M. L. D. Silvestre, F. Viola, and E. Francomano, "Soil ionization due to high pulse transient currents leaked by earth," Progress In Electromagnetics Research B, Vol. 14, 1-21, 2009.
    doi:10.2528/PIERB09022103

    23. Lord, H. W., "Pulse transformers," IEEE Transactions on Magnetics, Vol. 7, No. 1, 17-28, 1971.
    doi:10.1109/TMAG.1971.1066994

    24. Redondo, L. M., J. F. Silva, and E. Margato, "Pulse shape improvement in core-type high-voltage pulse transformers with auxiliary windings," IEEE Transactions on Magnetics, Vol. 43, No. 5, 1973-1982, 2007.
    doi:10.1109/TMAG.2006.888744

    25. Brown, D. and D. Martin, "Subnanosecond high-voltage pulse generator," Rev. Sci. Instrum., Vol. 58, No. 8, 1523-1529, 1987.
    doi:10.1063/1.1139392

    26. Luthjens, L. H., M. L. Hom, and M. J. W. Vermeulen, "Subnanosecond pulsing of a 3-MV Van de Graaff electron accelerator by means of a passive coaxial pulse shaper," Rev. Sci. Instrum., Vol. 49, No. 2, 230-235, 1978.
    doi:10.1063/1.1135373

    27. Riabi, M. L., R. Thabet, and M. Belmeguenai, "Rigorous design and efficient optimizattion of quarter-wave transformers in metallic circular waveguides using the mode-matching method and the genetic algorithm," Progress In Electromagnetics Research, Vol. 68, 15-33, 2007.
    doi:10.2528/PIER06072103

    28. Wu, Y., Y. Liu, and S. Li, "A compact pi-structure dual band transformer," Progress In Electromagnetics Research, Vol. 88, 121-134, 2008.
    doi:10.2528/PIER08102601

    29. Design of Tesla transformers used in direct-voltage accelerators, Atomic Energy, Vol. 46, No. 3, 1979.

    30. Jain, K. K., D. Chennareddy, P. I. John, and Y. C. Saxena, "Design and performance of a Tesla transformer type relativistic electron beam generator," Sadhana, Vol. 9, No. 1, 1986.
    doi:10.1007/BF02812173

    31. Korovin, S. D. and V. V. Rostov, "High-current nanosecond pulse-periodic electron accelerators utilizing a Tesla transformer," Russian Physics Journal, Vol. 39, No. 12, 1996.

    32. Ying, P. and R. Jiangjun, "Investigation of very fast transient overvoltage distribution in taper winding of tesla transformer," IEEE Transactions on Magnetics, Vol. 42, No. 3, 434-441, 2006.
    doi:10.1109/TMAG.2005.862759

    33. Costa, E. M. M., "A basic analysis about induced EMF of planar coils to ring coils," Progress In Electromagnetic Research B, Vol. 17, 85-100, 2009.
    doi:10.2528/PIERB09071202

    34. Grandi, G., et al., "Stray capacitances of single-layer solenoid air-core inductors," IEEE Transactions on Industry Applications, Vol. 35, No. 5, 1162-1168, 1999.
    doi:10.1109/28.793378

    35. Hole, M. J. and L. C. Appel, "Stray capacitance of a two-layer air-cored Inductor," EE Proc. --- Circuits Devices Syst., Vol. 152, No. 6, 565-572, 2005.
    doi:10.1049/ip-cds:20045217

    36. Marin, D., et al., "Modelling parasitic capacitances of the isolation transformer," In. Simpozionul National de Eletrotehnica eoretica, SNET 2004, 2004.

    37. Kamarudin, M. R. and P. S. Hall, "Switched beam antenna array with parasitic elements," Progress In Electromagnetics Research B, Vol. 13, 187-201, 2009.
    doi:10.2528/PIERB09011603

    38. Costa, E. M. M., "Responses in transformers built with planar coils inner ring coils excited by square waves," Progress In Electromagnetic Research B, Vol. 18, 43-58, 2009.

    39. Costa, E. M. M., "Resonance between planar coils vs ring coils excited by square waves," Progress In Electromagnetic Research B, Vol. 18, 59-81, 2009.

    40. Kaware, K., H. Kotama, and K. Shirae, "Planar inductor," IEEE Transactions on Magnetics, Vol. 20, No. 5, 1984-1806, 1984.

    41. Babic, S. I. and C. Akyel, "Improvement in calculation of the self-and mutual inductance of thin-wall solenoids and disk coils," IEEE Transactions on Magnetics, Vol. 36, No. 4, 1970-1975, 2000.
    doi:10.1109/TMAG.2000.875240

    42. Matsuki, H., N. Fujii, K. Shirakawa, J. Toriu, and K. Murakami, "Planar coil inductor with closed magnetic circuit," IEEE Translation Journal on Magnetics in Japan, Vol. 7, No. 6, 474-478, 1992.
    doi:10.1109/TJMJ.1992.4565426

    43. Babic, S. I., S. Kincic, and C. Akyel, "New and fast procedures for calculating the mutual inductance of coaxial circular coils (circular coildisk coil)," IEEE Transactions on Magnetics, Vol. 38, No. 5, 2367-2369, 2002.
    doi:10.1109/TMAG.2002.803576

    44. Su, Y. P., X. Liu, and S. Y. R. Hui, "Mutual inductance calculation of movable planar coils on parallel surfaces," IEEE Transactions on Power Electronics, Vol. 24, No. 4, 1115-1124, 2009.
    doi:10.1109/TPEL.2008.2009757

    45. Oshiro, O., H. Tsujimoto, and K. Shirae, "A novel miniature planar inductor," IEEE Transactions on Magnetics, Vol. 23, No. 5, 3759-3761, 1987.
    doi:10.1109/TMAG.1987.1065746

    46. Anioin, B. A., et al., "Circuit properties of coils," EE Proc. --- Sci. Mes. Technol., Vol. 144, No. 5, 234-239, 1997.
    doi:10.1049/ip-smt:19971316

    47. Asdler, M. S., "A field-theoretical approach to magnetic induction of thin circular plates," IEEE Transactions on Magnetics, Vol. 10, No. 4, 1118-1125, 1974.
    doi:10.1109/TMAG.1974.1058526

    48. Dudek, C., et al., "A new type of highly compact planar inductor," IEEE Transactions on Magnetics, Vol. 43, No. 6, 2621-2623, 2007.
    doi:10.1109/TMAG.2007.893711

    49. Kim, Y., F. Yang, and A. Z. Elsherbeni, "Compact artificial magnetic conductor desings using planar square spiral geometries," Progress In Electromagnetics Research, Vol. 77, 43-54, 2007.
    doi:10.2528/PIER07072302

    50. Conway, J. T., "Noncoaxial inductance calculations without the vector potential for axissymmetric coils and planar coils," IEEE Transactions on Magnetics, Vol. 44, No. 4, 453-462, 2008.
    doi:10.1109/TMAG.2008.917128

    51. Hurley, W. G. and M. C. Duffy, "Calculation of self- and mutual impedances in planar sandwich inductors," IEEE Transactions on Magnetics, Vol. 33, No. 3, 2282-2290, 1997.
    doi:10.1109/20.573844