Complex-Polynomial Compensation of Wideband Harmonic Measurement Errors: A Closed-Loop Fluxgate Sensor Model Study

Finite feedback dynamics cause frequency-dependent errors in harmonic current measurement. This work presents a theoretical and numerical study of complex-polynomial compensation for a closed-loop fluxgate sensor model. A complex frequency response is derived from residual ampere-turn balance under stated small-signal and demodulation assumptions, linking feedback dynamics to ratio error and phase displacement. Measurements of a physical sensor’s uncompensated response over 50 Hz–2 kHz show overall trends similar to model predictions, providing experimental support for the modeled frequency dependence within the tested range. First- and second-order polynomials are fitted to the reciprocal model response over 50 Hz–2 kHz and numerically evaluated at unfitted in-band points and extrapolation points up to 15 kHz. For the nominal model, the quadratic fit gives smaller maximum in-band residuals, whereas the first-order fit gives smaller maximum extrapolation errors. At 15 kHz, the first-order absolute ratio and phase errors are 0.00175% and 0.689 arcmin, compared with 0.0313% and 15.44 arcmin for the quadratic fit. Fixed-coefficient parameter changes can increase residual errors and alter the order ranking, highlighting model-dependent trade-offs between in-band fitting, extrapolation, and parameter mismatch.