Still, in practice it is often convenient to use the concept of magnetic currents (and fictitious magnetic charges). However, no magnetic charge has been found to exist in nature. The magnetic current density may be associated with an external impressed voltage. The driving sources may be also given by a (volumetric) magnetic current density J ms with the units of V/m2 and by volumetric magnetic charge density ms. Instead of volumetric currents one may consider surface currents (a blade metal dipole) or line current (an infinitesimally thin cylindrical dipole/wire).
Fdtd matlab code free#
The free charges are free electrons in a metal or free electrons and/or holes in a semiconductor. Driving sources and lossy space The driving sources for the electromagnetic fields are given by (generally volumetric) electric current density J s of free charges with the units of A/m2, and by volumetric free charge density s with the units of C/m3. Gauss’ law for magnetic field (no magnetic charges)Ģ.2. Gauss’ law for electric field (no electric charges)
In free lossless space (space without sources), Maxwell’s equations for the electric field (or the electric field intensity) E and for the magnetic field (or the magnetic field intensity) H in time domain have the form Lossless space with no sources Consider an arbitrary (inhomogeneous) medium with electric permittivity having the units of F/m and with magnetic permeability having the units of H/m. Maxwell’s equations in three dimensions 2.1. Is located exactly halfway between magnetic field nodes Similarly, when the indexing system for the electric field is used, For example, when the indexing system for the magnetic field is used, the nodal magnetic field H y i, j ,k is located exactly halfway between electric field nodes E z i 1 / 2, j ,k and E z The system based on cube nodes (for magnetic permeability/magnetic loss values) The interleaving feature of those systems is mathematically described by half-integer indexes. The system based on cube edge centers (for the electric field) the system based on cube face centers (for the magnetic field) the system based on cube centers (for electric permittivity/conductivity values) 2 Therefore, four interleaving indexing systems (i,j,k) in space may be introduced and used simultaneously: i. The electric field is defined at the edge centers of a cube The magnetic field is defined at the face centers of a cube The electric permittivity/conductivity is defined at the cube center(s) The magnetic permeability/magnetic loss is defined at the cube nodes (corners). Yee grid A cubic Yee unit cell (uniform cell size in all directions) is shown in Fig. Yee grid and finite differences Yee grid Maxwell’s equations in three dimensions Maxwell’s equations on Yee grid Exponential time-stepping MATLAB implementation of the Yee method Referencesġ. Model of an impressed electric field or voltage source (loop of magnetic current) Model of a small coil antenna (magnetic dipole)
Model of a small dipole antenna (electric dipole)