Transient response of a driver coil in transient eddy current testing

• Novel approach for obtaining exact solutions for transients in inductively coupled circuits.
• Method pertains to inductive coupling with ferromagnetic and conducting structures.
• EM field solutions incorporated into circuit equations for exact driver response.
• First time that a transient driver signal is completely analytically modelled and yields excellent agreement.
• Arbitrary excitation waveforms, including sinusoidal and step, may be considered.
• Expressions for material-dependant complex self-inductance coefficients naturally arise from the theory.

A solution is presented for the case of a driver coil encircling a ferromagnetic conducting rod. The differential circuit equation is formulated in terms of the rod׳s impulse response using convolution theory, and solved by Fourier transform. The final solution accounts for feedback between the ferromagnetic rod and the driver coil, providing correct voltage response of the coil. Also arising from the solution is an analytical expression for the complex inductance in the circuit, which accounts for real (inductive) and imaginary (loss) elements associated with the rod. Experimental results, obtained for the case of square wave excitation, show excellent agreement.