Frequency is the variable the operator controls directly, and it sets the standard depth of penetration through delta = 1 / sqrt(pi f mu sigma). Rearranged for frequency this becomes f = rho / (pi mu0 mur delta^2). The relationship is inverse-square: quadrupling the frequency halves the depth, so frequency selection is coarse and a factor of two either way is a real change in what the test can see.

Rather than asking for a depth directly, working practice asks how many standard depths deep the target lies. At n standard depths the eddy current field has fallen to e^-n of its surface value and lags the surface current by 57.3 x n degrees. Setting n = 1 puts the target at 37 % field and 57 degrees of lag, which is the usual compromise between penetration and signal. Setting n near 2 or 3 buys depth at the cost of amplitude (13 % and 5 %) and pushes the phase lag towards 115 and 172 degrees.

Beyond roughly three standard depths the response is unusable rather than merely weak: the phase has rotated so far that a deep flaw plots close to the lift-off direction and can be mistaken for probe wobble. If the wall is thicker than about three standard depths at the frequency you need for sensitivity, the answer is a different method or a dual-frequency approach, not more gain.

What comes out of this calculation is a starting frequency. Confirm it on the calibration standard: the frequency that gives the required signal-to-noise and the required phase separation between the shallowest and deepest calibration reflectors is the frequency the procedure gets.

Worked example

Material property entered as	rho
Electrical resistivity	72 uohm.cm
Conductivity	2.39 %IACS
Relative permeability	1
Target depth	1.5 mm
Standard depths at the target	1
Required standard depth	1.5 mm
Test frequency	81.06 kHz
Phase lag at target depth	57.3 deg
Field strength at target depth	36.8 %

304 stainless (rho = 72 uohm.cm, mur = 1), 1.5 mm wall, one standard depth at the far surface. Required delta = 1.5/1 = 1.5 mm. In SI: rho = 7.2e-7 ohm.m, delta = 1.5e-3 m, delta^2 = 2.25e-6 m^2, pi.mu0 = 3.947842e-6. f = 7.2e-7 / (3.947842e-6 x 2.25e-6) = 7.2e-7 / 8.882644e-12 = 81057 Hz = 81.06 kHz. Cross-check with the engineering form 2533 x 72 / 2.25 = 81057 Hz. Phase lag at one standard depth = 1 radian = 57.3 degrees; field = 100 x e^-1 = 36.8 %.

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