Estimation and measurement of flat or solenoidal coil inductance for radiofrequency NMR coil design

The inductance of a radiofrequency coil determines its compatibility with a given NMR probe circuit. However, calculation (or estimation) of inductance for radiofrequency coils of dimensions suitable for use in an NMR probe is not trivial, particularly for flat-coils. A comparison of a number of formulae for calculation of inductance is presented through the use of a straightforward inductance measurement circuit. This technique relies upon instrumentation available in many NMR laboratories rather than upon more expensive and specialized instrumentation often utilized in the literature. Inductance estimation methods are suggested and validated for both flat-coils and solenoids. These have proven very useful for fabrication of a number of new coils in our laboratory for use in static solid-state NMR probes operating at 1H frequencies of 300 and 600 MHz. Solenoidal coils with very similar measured and estimated inductances having inner diameters from 1 to 5 mm are directly compared as an example of the practical application of inductance estimation for interchange of coils within an existing solid-state NMR probe.