Analog-to-digital conversion and harmonics error due to its nonlinearity

Rotating coil-based magnetic field measurement systems include an analog-to-digital converter (ADC) system triggered by an encoder system, which inherently introduces unwanted harmonics due to its nonlinearity error. The authors modeled the nonlinearity via a simple function with a single parameter and calculated, analytically and numerically, the magnitude of the harmonics generated by the sigmoidal shape of the ADC transfer function. For a typical ADC, a model x^{(1 + ν)} is reasonably adopted, which produces the most significant harmonic noise at the third order multipole with the size of πν/4 over the fundamental dipole of the size π