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Describes a new method to calculate the signal-to-noise ratio (SNR) of MR signals obtained from single receiver coils and arrays of receiver coils. The coils are assumed to be placed on the surface of a conducting half-space and the SNR is sample-noise dominated. While in conventional methods line integrals over the electric currents in the coils are chosen to calculate the electric and magnetic fields, this new method uses surface integrals over magnetic dipoles covering the area enclosed by the antenna to derive these fields. Using this method, the SNR for simple circular and square coils was analytically calculated. The calculations show that the theoretical difference in SNR between circular and square antennas is very low. Furthermore, based on the new method, a derivation of the ultimate gain in SNR for arrays of surface coils is presented. The SNR of such an array approaches a limit even if the total number of coils is increased to infinity. This ultimate SNR of a coil array is 35.8% above that of a single circular-shaped, size-optimized and linear polarized coil.