Vol. 50

Front:[PDF file] Back:[PDF file]
Latest Volume
All Volumes
All Issues

Analysis of the Magnetic Field Homogeneity for an Equilateral Triangular Helmholtz Coil

By Andres Fernando Restrepo Alvarez, Edinson Franco Mejia, Hector Cadavid Ramirez, and Carlos Rafael Pinedo Jaramillo
Progress In Electromagnetics Research M, Vol. 50, 75-83, 2016


This paper presents a mathematical analysis of the magnetic field homogeneity for an Equilateral Triangular Helmholtz (ETH) coil. The magnetic field analysis is based on the Biot-Savart law in which a Taylor series approximation is performed to obtain the analytical distance that complies with the Helmholtz condition between the pair of coils. This is done to compare the magnetic field distributions of the ETH and the Circular Helmholtz (CH) coils for the parameters side length (2a, 3a) and radius (a) respectively. Furthermore, an approximate expression of the magnetic field homogeneity with regard to the side length parameter is obtained and finally a computational model of the ETH coil using COMSOL® is performed in order to validate the calculated and experimental results. The results show that the ETH coils have a lower magnetic field homogeneity than the CH coils for the described parameters, and the implementation of either one basically depends on the application specifications.


Andres Fernando Restrepo Alvarez, Edinson Franco Mejia, Hector Cadavid Ramirez, and Carlos Rafael Pinedo Jaramillo, "Analysis of the Magnetic Field Homogeneity for an Equilateral Triangular Helmholtz Coil," Progress In Electromagnetics Research M, Vol. 50, 75-83, 2016.


    1. De Seze, R., A. Lahitte, J. M. Moreau, and B. Veyret, "Generation of extremely-low frequency magnetic fields with standard available commercial equipment: Implications for experimental bioelectromagnetics work," Bioelectrochem. Bioenerg., Vol. 35, No. 1-2, 127-131, 1994.

    2. Farina, M., M. A. Mariggio, T. Pietrangelo, J. J. Stupak, A. Morini, and G. Fano, "ELF-EMFs induced effects on cell lines: Controlling ELF generation in laboratory," Progress In Electromagnetics Research B, Vol. 24, 131-153, 2010.

    3. Satav, S. M. and V. Agarwal, "Design and development of a low-cost digital magnetic field meter with wide dynamic range for EMC precompliance measurements and other applications," IEEE Trans. Instrum. Meas., Vol. 58, No. 8, 2837-2846, 2009.

    4. Forte, G. O., G. Farrher, L. R. Canali, and E. Anoardo, "Automatic shielding-shimming magnetic field compensator for excluded volume applications," IEEE Trans. Control Syst. Technol., Vol. 18, No. 4, 976-983, 2010.

    5. Schuderer, J., W. Oesch, N. Felber, D. Spät, and N. Kuster, "In vitro exposure apparatus for ELF magnetic fields," Bioelectromagnetics, Vol. 25, No. 8, 582-591, 2004.

    6. Alamgir, A. K., J. Fang, C. Gu, and Z. Han, "Square Helmholtz coil with homogeneous field for magnetic measurement of longer HTS tapes," Physica C: Superconductivity, Vol. 424, No. 1-2, 17-24, 2005.

    7. Martino, C. F., L. Portelli, K. McCabe, M. Hernandez, and F. Barnes, "Reduction of the Earths magnetic field inhibits growth rates of model cancer cell lines," Bioelectromagnetics, Vol. 31, No. 8, 649-655, 2010.

    8. Kirschvink, J. L., "Uniform magnetic fields and double-wrapped coil systems: Improved techniques for the design of bioelectromagnetic experiments," Bioelectromagnetics, Vol. 13, No. 5, 401-411, 1992.

    9. Nouri, N. and B. Plaster, "Comparison of magnetic field uniformities for discretized and finite-sized standard cos, solenoidal, and spherical coils," Nucl. Instr. Meth. Phys. Res. A, Vol. 723, 30-35, 2013.

    10. Pittman, M. E. and D. L. Waidelich, "Three and four coil systems for homogeneous magnetic fields," IEEE Trans. Aerosp., Vol. 2, No. 1, 36-45, 1964.

    11. Herceg, D., A. Juhas, and M. Milutinov, "A design of a four square coil system for a biomagnetic experiment," Facta Universitatis Series: Electronics and Energetics, Vol. 22, No. 3, 285-292, 2009.

    12. Azpúrua, M. A., "A semi-analytical method for the design of coil-systems for homogeneous magnetostatic field generation," Progress In Electromagnetics Research B, Vol. 37, 171-189, 2012.

    13. Restrepo, A. F., E. Franco, and C. R. Pinedo, "A design and implementation methodology of a system to generate uniform magnetic field volume with tri-axial square Helmholtz coils," Inf. Tecnol., Vol. 25, No. 2, 3-14, 2014.

    14. Haghnegahdar, A., H. Khosrovpanah, A. Andisheh-Tadbir, G. Mortazavi, M. Saeedi, S. M. Mortazavi, A. Zamani, M. Haghani, M. Shojaei, and H. Parsaei, "Design and fabrication of Helmholtz coils to study the effects of pulsed electromagnetic fields on the healing process in periodontitis: Preliminary animal results," J. Biomed. Phys. Eng., Vol. 4, No. 3, 83-90, 2014.

    15. Enoki, S., T. Asahi, S. Watanabe, T. Mizuno, and K. Takeshita, "Electromagnetic measurement of the rail displacement by two triangular coils," IEEE Trans. Magn., Vol. 38, No. 5, 3303-3305, 2002.

    16. Choi, H., S. Jeong, C. Lee, B. Park, S. Ko, J.-O. Park, and S. Park, "Three-dimensional swimming tadpole mini-robot using three-axis Helmholtz coils," Int. J. Control Autom., Vol. 12, No. 3, 662-669, 2014.

    17. Hossain, A. B., M. H. Cho, and S. Y. Lee, "Magnetic nanoparticle density mapping from the magnetically induced displacement data: A simulation study," Biomed. Eng. Online, Vol. 11, No. 1, 13, 2012.

    18. Cao, Q., X. Han, B. Zhang, and L. Li, "Analysis and optimal design of magnetic navigation system using Helmholtz and Maxwell coils," IEEE Trans. Appl. Supercond., Vol. 22, No. 3, 4401504, 2012.

    19. Go, G., H. Choi, S. Jeong, C. Lee, S. Y. Ko, J.-O. Park, and S. Park, "Electromagnetic navigation system using simple coil structure (4 coils) for 3-D locomotive microrobot," IEEE Trans. Magn., Vol. 51, No. 4, 1-7, 2015.

    20. Ha, Y. H., B. H. Han, and S. Y. Lee, "Magnetic propulsion of a magnetic device using three square-Helmholtz coils and a square-Maxwell coil," Med. Biol. Eng. Comput., Vol. 48, No. 2, 139-145, 2010.

    21. Bell, G. B. and A. A. Marino, "Exposure system for production of uniform magnetic fields," Journal of Bioelectricity, Vol. 8, No. 2, 147-158, 1989.

    22. Al-Sowayan, S., "Generation of homogenous magnetic field using equilateral triangular coils," Int. J. Appl. Eng. Res., Vol. 9, No. 1, 137-143, 2014.

    23. Kdzia, P., T. Czechowski, M. Baranowski, J. Jurga, and E. Szczesniak, "Analysis of uniformity of magnetic field generated by the two-pair coil system," Appl. Magn. Reson., Vol. 44, No. 5, 605-618, 2013.

    24. Beiranvand, R., "Analyzing the uniformity of the generated magnetic field by a practical one-dimensional Helmholtz coils system," Rev. Sci. Instrum., Vol. 84, No. 7, 075109, 2013.

    25. Restrepo, A. F., L. J. Martinez, C. R. Pinedo, E. Franco, and H. Cadavid, "Design study for a cellular culture bioreactor coupled with a magnetic stimulation system," IEEE Lat. Am. T., Vol. 11, No. 1, 130-136, 2013.

    26. Wang, J., S. She, and S. Zhang, "An improved Helmholtz coil and analysis of its magnetic field homogeneity," Rev. Sci. Instrum., Vol. 73, No. 5, 2175-2179, 2002.