Explanation in frequency domain:
All CW metal detectors are discriminatory until a frequency fr.
The 'r' is subscript meaning resonance. At this frequency, the phase difference of received signal relative to current in TX coil is zero. This is illustrated below with loci in complex (impedance) plane. The frequency fr depends on eddy size of target made of ferrous metal. Operating above frequency fr, the metal detector can not tell you if the metal of target is ferrous because it sees all metal targets as nonferrous.
Here is an explanation in time domain:
All PI metal detectors are disciminatory above a sample delay tr. The tr depends on eddy diameter of the ferrous metal target. Subscript 'r' means resonance because at this delay the odd part of decay curve is equal to its even part. When the sample delay is less than tr, the metal detector can not tell you if the metal of target is ferrous because it sees all metal targets as nonferrous.
Explanation of loci in impedance plane:
The phase of TX current is represented with Re axis.
1. Locus of lossless ferrite. It is not shown because coincidents with Im axis. The signal has 90 deg phase angle for all frequencies.
2. Locus of lossy ferrite is also a straight line. The signal has less than 90 deg phase angle and it is constant for all frequencies.
3. Locus of nonferrous metal. The signal has negative phase angle for all frequencies. Point C represents cutoff frequency at which the phase angle is minus 45 deg.
4. Locus of ferrous metal. It is created by combination of loci 2 and 3. Point Q represents the resonance frequency. Point D appears in mirror position of cutoff frequency (phase angle +45 deg).
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