Self inductance formulas for quadrupole loops used with vehicle detectors

This paper describes the derivation and application of a formula to calculate the self inductance of a multi-turn, quadrupole loop of round wire. The wire of a quadrupole loop is installed in a figure-eight pattern instead of the normal rectangular pattern of a typical inductive loop used for detecting vehicles. The quadrupole design improves the detection of bicycles and reduces the detection of adjacent lane vehicles. The multi-turn quadrupole loop is modeled as a number of series connected, single-turn loops which exhibit mutual coupling between each other. The derived formula is used to calculate tables of inductance for various size quadrupole loops. A straight line approximation is used to derive a simplified formula for calculating quadrupole loop inductance.