In this study, the electromagnetic characteristics of a flat-type two-dimensional proportional solenoid were analyzed by the magnetic reluctance method. The equivalent magnetic circuit equation for the solenoid was derived by modeling the reluctance of air gaps and magnetic structural components such as pole core, armature and yoke. It was solved iteratively because of the nonlinear magnetization properties of the iron parts. The solutions showed good agreement with experimental data. Based on the equivalent magnetic circuit equation, the influence of design parameters on the force-to-armature displacement curves was mathematically derived and experimentally verified. In this way, dominant design parameters could be analytically determined.
