Guide to simulating complex NMR probe circuits

S-parameter-based circuit simulators are well suited to obtaining accurate solutions of even the most complex rf probe circuits. The basic theory necessary for determining the relative S/N of the probe circuit, based on B₁/P^0.5, from the voltage, current, impedance, and S-parameter data that come from circuit simulators, is presented. Examples of simulator applications to circuits of increasing complexity are presented. A key requirement for effective utilization of circuit simulators in probe circuit optimizations is constructing an approximate analytical solution of the circuit, or an inverse simulation program, to accompany the direct circuit simulation, that calculates all the needed circuit component values based on minimal input data, such as B₀, desired nuclides, sample coil description, and hardware options and details such as characteristics of various leads. A method of developing the needed inverse simulation program is presented for a simplified single-coil HXY probe circuit. The inverse program is validated by the direct simulation itself. The methods are then applied to a detailed circuit that includes all significant leads, stray capacitances, couplings, and losses for a NB 28.2-T 1-mm HXYZ MAS probe. Similar HXY circuit models were validated by NMR experiments with rotor sizes from 0.75 mm to 3.2 mm at fields from 11.7 T to 21 T. Detailed HXYZ circuit model results at 11.7 T, including pulse widths, component values, voltages, and port isolations, agreed with experimental results within a few per cent. The 1200-MHz HXYZ simulation predicted a ¹H π/2 pulse of 1.3 μs at 25 W.