Fast Simulation of Complicated 3-D Structures Above Lossy Magnetic Media

Abstract

A fast numerical method is presented for the simulation of complicated 3D structures, such as inductors constructed from litz or stranded wires, above or sandwiched between planar lossy magnetic media. Basing upon its smoothness, the quasistatic multilayer Green's function is numerically computed using finite differences, and its source height dependence is computed using an optimal Toeplitz-plus-Hankel decomposition. We show that a modified precorrected FFT method can be applied to reduce the dense linear algebra problem to near-linear time, and that frequency-dependent setups can be avoided to result in a considerable speed-up. Experimental verifications are made for a 16-strand litz wire coil, realistically modeled down to each individual strand. Results are obtained in 2-3 hours, showing an excellent agreement to measurements, and can be used to study the impact of transposition patterns in litz wire construction.

Realistic litz wire characterization using fast numerical simulations

“…The simulations in this paper were performed using the tool presented in [7], based upon an integral formulation of Maxwell's equations often known as the Partial Element Equivalent Circuit (PEEC) method [12], [13]. In essence, the PEEC method maps the electromagnetic problem into an equivalent circuit problem, by subdividing the conductive volume of an electromagnetic problem along its length and crosssection into current-carrying filaments, as shown in Fig.…”

“…The method has found extensive use in the analysis of microelectronics and interconnects [13], [15]. Our PEEC implementation is similar to FastHenry [13], but with a number of optimizations in speed and accuracy specific to wire-based problems and magnetic field excitations [7].…”

“…2, where the grid is generated using a quadratic rule, and the "discretization parameter" is defined to be the number of elements along the radius of the circular cross-section, including the center element. Rectangular, brick-shaped elements were used in order to maximize computation speed [7]. Three computer platforms were tested, a dual-core 2.1 GHz laptop, a quad-core 2.5 GHz desktop workstation, and a dual-processor, 32-core 3 GHz computation server.…”

“…in [7]. Existing theory, which lies at the heart of prior litz wire optimizations, computes copper losses as the sum of two loss components, one driven by the net current flow, and the other driven by the external magnetic field [8].…”

Design of Efficient Air Core Inductors Using a Partial Element Equivalent Circuit Method

“…The general PEEC method is accurate from dc to high frequencies. In magneto-quasi-static applications, the capacitive displacement currents are typically neglected [35], resulting in a sparser equation matrix. In addition, hybrid methods (e.g., [36]) use PEEC to represent conductors, and FEM to represent general surrounding elements.…”