This paper proposes an adaptive equivalent RL-circuit model for eddy-current devices with a single electrical port (one terminal voltage and current) and translational movement. The device is first characterised by means of frequency-domain finite-element computations in the relevant frequency and position intervals, for subsequently fitting constant-coefficient RL-ladder circuits of adjustable size (i.e. variable number of branches and loops). The accuracy of the ladder-circuit model is assessed in both frequency and time domain. The time-varying position involves the force computation from the circuit and the coupling with the mechanical equation. By way of validation, we study the axisymmetric magnetic-levitation device of TEAM Workshop problem 28. Results exhibit good convergence to reference finite-element ones with the increasing number of branches.