Analysis, design and optimization of compact ultra-high sensitivity coreless induction coil sensors

We require a compact magnetic field measurement system that is able to measure alternating magnetic flux densities in the nanotesla range on the background of signals with constant amplitudes of some hundred millitesla. The signal of interest has a frequency of a few Hertz and must be measured with an amplitude error smaller than 0.1% and a phase error no larger than 10⁻¹ deg. For this we present theoretical and experimental analyses of absolute and first order gradiometric induction coil sensors with sensitivities larger than 500 V/T/Hz and diameters of 28 mm. From their equivalent circuits, we derive the associated complex-valued transfer functions and fit these to calibration measurements, thereby determining the value of the equivalent circuit components. This allows us to compensate their non-linear frequency-dependent amplitude and phase behaviour. Furthermore, we demonstrate the optimization of coils based on Brooks' design of equal squares in the adaptation by Murgatroyd, which maximizes the inductance (and thereby most likely the sensitivity) of the coils. Finally, we design a new coil with a diameter of 74 mm and a sensitivity of 577 V/T/Hz with an analytically predicted equivalent magnetic field noise of around 40 pT/√Hz in the 1 Hz frequency range, which is then confirmed by measurements on the manufactured prototype.