Test frequency for a target depth

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.

delta_required = x / n
f = rho / (pi · mu0 · mur · delta_required^2)
f [Hz] ~= 2533 · rho[uohm.cm] / (mur · delta[mm]^2)   (the familiar 2500 rule)
phase lag at x = 57.3 · n degrees        field at x = 100 · e^(-n) %