Near- and far-regions of mode splitting in coupled magnetic resonators and use in passive ranging

The monostatic backscattered magnetoquasistatic field coupling measured at the terminals of a resonant coil due to strongly coupled magnetic resonance (SCMR) coupling with a nearby passive resonant coil exhibits dual orthogonal mode splitting. The difference between the center frequencies of the orthogonal modes, known as the coupled mode frequency split, is sensitive to range of the nearby passive resonant coil. Near- and far-region relationships are derived for the SCMR coupling which are important in practical passive magnetoquasistatic systems. Measurements of this frequency split is presented and inverted for range using the exact theory. The results are compared to inversions using the near- and far-region solutions.