A simple method to calculate the signal‐to‐noise ratio of a circular‐shaped coil for MRI

Abstract

Abstract The introduction of the ultrafast imaging sequences has renewed the interest in development of RF coils. The theoretical frame of the SNR of MRI coils is a challenge because it requires a deep mathematical background to master the associated concepts. Here, a simpler method is proposed based on Legendre polynomials. This approximation method, together with a quasi‐static approach, was used to derive a signal‐to‐noise ratio expression for a circular‐shaped coil. Legendre polynomials were used instead of a weighting function to simplify the vector potential of the power loss, and an SNR formula was then derived. The simplified version of the SNR formula of a circular coil was compared with the weighting function‐derived SNR expression using the quasi‐static approach. SNR‐vs.‐depth plots were computed to theoretically compare both SNR formulas. Results showed a strong agreement between SNR values for the circular‐shaped coil. This approach can be used as a tool to derive SNR expressions for more complex geometries. © 2006 Wiley Periodicals, Inc. Concepts Magn Reson Part A 28A: 422–429, 2006