Circuit filling factor (CFF) for multiply tuned probes, revisited.

The concept of circuit filling factor (CFF) is re-examined for multi-tuned, multi-inductor probe circuits. The CFF is the fraction of magnetic stored energy residing in the NMR coil. The CFF theorem states that the CFF sums to unity across all the resonant normal modes. It dictates that improved performance from a large CFF in one mode comes at the expense of CFF (and performance) at the other mode(s). Simple analytical calculations of two-mode circuits are used to demonstrate and confirm the CFF theorem. A triple-resonance circuit is calculated to show the large trade-offs involved there. The theorem can provide guidance for choosing the best circuit and relative inductances in multi-nuclear probes. The CFF is directly accessible from ball frequency-shift measurements. We give experimental measures of the CFF from ball shifts and compare to calculated values of the CFF, with good agreement.