Signal-to-noise ratio (SNR) is the fundamental figure of merit of any MRI coil. Understanding the sources of noise and the factors that affect SNR guides coil design decisions.

Signal Source

The MRI signal is the EMF induced in the receive coil by the precessing transverse magnetisation in the sample. It scales with: field strength B0 (approximately B0^7/4 for a given experiment time), coil filling factor, and sample magnetisation density.

Noise Sources

At MRI frequencies, two main noise sources compete:

• Coil resistance noise — Johnson noise from the ohmic resistance of the coil conductor. Dominates for small coils (surface coils <~5 cm at 3 T) or at low field.
• Sample noise — noise from induced currents (eddy currents) in the conductive biological tissue. Dominates for large coils, at high field, and near large conductive samples. Unavoidable — it sets the SNR ceiling.

Filling Factor

The filling factor \(\eta\) is the fraction of the coil's inductance that is "filled" by the sample volume of interest. \(\eta = \int_{sample}|B_1|^2 dV / \int_{all}|B_1|^2 dV\). Maximising filling factor (placing the coil as close as possible to the anatomy) directly improves SNR.

Optimal Coil Size

A smaller coil placed close to the anatomy intercepts less noise (smaller sensitive volume) but provides high B1 per unit current near the coil. The optimal coil size roughly matches the depth of the structure of interest — a good rule of thumb is: for a structure at depth d below the surface, the optimal surface coil radius is approximately d.

Preamplifier Noise

The preamplifier (preamp) also contributes noise. For a sample-noise-dominated coil, preamp noise figure adds directly to system NF. Modern MRI preamps achieve NF of 0.3–0.7 dB. The preamp should be physically close to the coil (short coax) to minimise cable losses that degrade SNR.