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

For contactless inductive flow tomography we require a compact magnetic field measurement system with a dynamic range of 5 orders of magnitude in order to detect the amplitude and the phase of an alternating magnetic field of 1 mT strength with a precision better than 5 nT and a phase error no larger than 10^-2 deg. In some applications also a static magnetic field of about 300 mT is present, resulting in a total dynamic range of 7~orders of magnitude. 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 / sqrt(Hz) in the 1Hz frequency range, which is then confirmed by measurements on the manufactured prototype.