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

Area of Science:

• Magnetic Resonance Imaging (MRI)
• Electrical Engineering
• Spectroscopy

Background:

• The circuit filling factor (CFF) quantifies magnetic energy in NMR coils.
• Multi-tuned, multi-inductor circuits present complex energy distribution challenges.
• Understanding CFF is crucial for optimizing probe performance in Nuclear Magnetic Resonance (NMR).

Purpose of the Study:

• To re-examine the circuit filling factor (CFF) concept for multi-tuned, multi-inductor probe circuits.
• To demonstrate and confirm the CFF theorem using analytical calculations.
• To provide guidance for selecting optimal circuits and inductances in multi-nuclear probes.

Main Methods:

• Analytical calculations were performed for two-mode and triple-resonance circuits.
• The CFF theorem was mathematically demonstrated and confirmed.
• Experimental CFF measurements were obtained using ball frequency-shift techniques.

Main Results:

• The CFF theorem was confirmed, showing CFF sums to unity across resonant modes.
• Significant performance trade-offs were demonstrated in multi-mode circuits.
• Experimental CFF measurements showed good agreement with calculated values.

Conclusions:

• The CFF theorem accurately describes energy distribution in multi-tuned NMR circuits.
• The theorem provides valuable insights for designing high-performance multi-nuclear probes.
• Ball frequency-shift measurements offer a practical method for determining CFF.