Dynamical Model of an Electromagnet using Cauer Ladder Network Representation of Eddy-current Fields

Abstract

This paper presents a novel dynamical modeling method for magnetic actuators. The magnetic field is decomposed into orthogonal distribution functions by using the Cauer ladder network representation of eddy-current fields. The linearized transfer function of the magnetic force is derived by using the Maxwell's stress tensor and distribution functions. The numerical example of an electromagnet is presented to show the effectiveness of this method. It is revealed that the eddy current not only reduces the main flux but also induces a repulsive force at the air gap. The details of the Cauer ladder network representations are also clarified.

Multi-Port Model Order Reduction Using a Matrix Cauer Ladder Network

“…where G is the node-edge incidence matrix that corresponds to the grad operator, which satisfies CG = 0. If a unit direct current is given as the power input to port m and it imposes current density j0m, then the initial condition is given by with the Dirichlet or Neumann boundary condition without power inputs in the following steps [13].…”