# Design, Simulation, Modeling, and Implementation of a Square Helmholtz Coil in Contrast with a Circular Coil for MRI Applications

• S. M. A. Ghaly Electrical Engineering Department, College of Engineering, Al-Imam Mohammad Ibn Saud Islamic University, Saudi Arabia
• M. O. Khan Electrical Engineering Department, College of Engineering, Al-Imam Mohammad Ibn Saud Islamic University, Saudi Arabia
Volume: 9 | Issue: 6 | Pages: 4990-4995 | December 2019 | https://doi.org/10.48084/etasr.3171

### Abstract

This paper focuses on Helmholtz-type coils that can produce a second-order homogeneity field to be used for Magnetic Resonance Imaging (MRI) applications. A Helmholtz coil is a device used for producing a region of a nearly uniform magnetic field. It consists of two identical magnetic coils that are placed symmetrically along a common axis, one on either side of the experimental area, separated by a distance equal to the radius of the circular coil and half-length of the side of the square coils. Each coil carries an equal electrical current flowing in the same direction. The main objective of this article is to calculate the magnetic field provided by the coils at any point in space and to show and compare the uniform magnetic field induced by the square and circular Helmholtz coils. With the aid of MATLAB simulation tool, mathematical equations are simulated to demonstrate the axial magnetic field produced by one and two loops. Also, the design and simulation of electrical modeling for square and circular Helmholtz coils are performed using PSPICE. Finally, these coils are realized and tested experimentally, and the results for square and circular Helmholtz coils are compared.

Keywords: square and circular Helmholtz coil, radiofrequency coils, modeling, simulation, MATLAB, PSPICE, electromagnetic field measurement, impedance measurements, MRI

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