If you’ve ever built your own RF circuit for NMR you know that calculating the inductance for a solenoid can be challenging. This article gives some insight where the discrepancies are coming from and how to make the prediction more accurately. However, in the end you still need to get the soldering iron out and adjust capacitors to make it work.
Giovannetti, Giulio, and Francesca Frijia. “Inductance Calculation in Magnetic Resonance Solenoid Coils with Strip and Wire Conductors.” Applied Magnetic Resonance 51, no. 8 (August 2020): 703–10.
Solenoids are employed in Magnetic Resonance (MR) as radiofrequency (RF) coils due to their high sensitivity. In particular, their cylindrical symmetry is optimal for circular cross-sectional samples. Solenoid inductance estimation is a constraint for a correct design and tuning of the resonant circuit constituting the RF coil, suitable to be used for transmitting and receiving the RF signal of the given X-nucleus with the available MR scanner. However, the different literature formulation for solenoid inductance estimation is not optimized for a wide variety of coil geometries and doesn’t take into account conductor geometry. This paper proposes an analytical method for the solenoid inductance calculation in dependence on the conductor cross-sectional geometry (flat strip and circular wire). Simulations accuracy was evaluated with workbench experimental measurement performed on a home-built strip solenoid and by comparisons with literature data referred to wire solenoids.