Comparison between circular and square loops for low-frequency magnetic resonance applications: theoretical performance estimation

Radiofrequency receiver coils in magnetic resonance (MR) systems are used to pick up the signals emitted by the nuclei with high signal-to-noise ratio (SNR) in a small region of sensitivity. The quality of obtained images strongly depends upon the correct choice of the coils geometry and size. The simplest design of such coils is circular and square loops, both producing in the central region-of-interest a magnetic field perpendicular to the coil plane, with an amplitude that decreases along the coil axis. This work reviews a method for coil SNR model development employing an equivalent electric circuit and applies it for circular and square loop design. Coil inductance and resistance were analitically calculated by taking into account for the conductors cross-geometry and the magnetic field pattern was estimated using Biot-Savart law, while the sample-induced resistance was calculated with a method employing a quasi-static approach. Coil performance prediction permitted to compare circular and square loops and demonstrated that when a simple relationship between loops size is satisfied, the performance of both coils resulted to be very similar in terms of SNR. Since the theoretical approach formulation is largely detailed, this article could be interesting for graduate students and researchers working in the field of MR coil design and development.