Closed-Form Spectral Computation of Intermodulation Distortion for Shunt-Based Current Measurements

This work presents a closed-form analytic approach to calculate the distortion introduced in resistive current measurements due to thermal properties of shunt resistors. As a shunt’s resistance varies with temperature, the sensed voltage becomes distorted. This non-linear effect depends on the thermal interface, dissipated power and material properties of the shunt resistor. It is presented, how to simplify the non-linear equation of the shunt temperature and calculate the resulting voltage spectrum, without the use of computationally extensive time-to-frequency-domain transforms. The results of the presented method match simulations including the non-linear behaviour, enabling a quick search through a solution space. The method is experimentally verified by use of a linear amplifier with an output distortion of −90 dB at low frequencies. In the experiment, a total harmonic distortion of up to −70 dB is observed in several shunt resistors covering a range of different thermal properties. Based on the presented method, shunt resistors can be chosen according to the minimum distortion required in a given application. Depending on the frequencies of interest, shunt resistors with a high temperature coefficient might still offer sufficient distortion performance.