An eddy current probe coil is an inductor with a resistance. Its inductive reactance XL = 2 . pi . f . L rises linearly with frequency, its total impedance is Z = sqrt(R^2 + XL^2), and that impedance sits at an angle atan(XL/R) from the resistive axis. Everything an eddy current instrument displays is a small perturbation of this operating point: bringing the coil to a conductor loads it, the induced currents reflect back an impedance change, and the flying dot on the screen is that change amplified and rotated.

Where the coil sits on the impedance plane decides how much of that perturbation you can actually see. If the winding resistance dominates, a reactance change is a small fraction of a large number and the useful signal is buried in thermal and cable noise. If the reactance dominates, the same physical change moves a much larger fraction of the vector. A Q of roughly 5 to 10 at the test frequency is a sensible working target for a conventional probe; far below that the probe is resistive and insensitive, far above it the probe is sharply tuned and unstable.

Coil inductance and cable capacitance form a resonant circuit at fr = 1 / (2 . pi . sqrt(L . C)). Just below resonance signals grow rapidly, which looks like sensitivity but is really instability – small changes in cable position, temperature or connector contact move the resonance and therefore the calibration. Above resonance the probe presents a capacitive load and behaves in the opposite sense to expectation. Keeping the test frequency comfortably below half the resonant frequency avoids both problems, which is why probe cable length is a controlled item in a procedure rather than a convenience.

Use this when matching a probe to an instrument drive, when diagnosing why a probe that worked on a short cable misbehaves on an extension, and when a probe balances poorly or drifts at the top of its frequency range.

Worked example

Test frequency	100 kHz
Coil inductance	100 uH
Coil resistance	10 ohm
Capacitance entered as	direct
Coil and cable capacitance	4.7 nF
Probe cable length	2 m
Cable capacitance per metre	100 pF/m
Inductive reactance	62.83 ohm
Coil impedance	63.62 ohm
Impedance phase angle	80.96 deg
Quality factor	6.28 x
Resonant frequency	232.15 kHz
Test frequency / resonance	0.431 x

A 100 uH probe coil with 10 ohm effective resistance driven at 100 kHz. XL = 2.pi x 1e5 Hz x 1e-4 H = 62.83 ohm. Z = sqrt(10^2 + 62.832^2) = sqrt(100 + 3947.84) = sqrt(4047.84) = 63.62 ohm. Phase angle = atan(62.832/10) = atan(6.2832) = 80.96 degrees, so the coil is strongly inductive. Q = 62.832/10 = 6.28, in the usual working range. With 4.7 nF of cable capacitance, L.C = 1e-4 x 4.7e-9 = 4.7e-13, sqrt = 6.8557e-7, and fr = 1/(2.pi x 6.8557e-7) = 232151 Hz = 232.15 kHz. The test frequency is 0.431 of resonance - acceptable, but a longer cable would push this into the unstable region. In cable-length mode, 2 m of 100 pF/m cable would instead give 2 x 100 / 1000 = 0.2 nF and a resonance of about 1125 kHz.

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