In this paper

the closed-form impedance model is provided for an arbitrary orthogonal polyline coil using vertex position-shape description. Firstly

the second order vector potential (SOVP) formula is used for the description of the electromagnetic fields produced by a filamentary rectangular coil. And the scalar potential of the rectangular coil is derived with an integral item described by the position factors and shape factors of the four vertexes of the rectangle. Secondly

two important properties of the shape factors are deduced

with which the analytical expressions of scalar potential can be generalized to the case of arbitrary orthogonal polyline coils. The analytical impedance expressions of arbitrary orthogonal polyline coils are finally derived and applied to a rectangular spiral coil. The theoretical results are compared with the experimental measurements. The comparison results show that the calculated and measured values are in good agreement. The proposed method greatly simplifies the modeling process compared with existing rectangle description method.