Wave Equation

The field pattern of a traveling wave inside a waveguide can be determined by solving Maxwell's equations. For each mode m, the port solver solves the following equation obtained from Maxwell's equation.

(1)

where

• k₀ = w/c is the wave number of free-space
• m_r(x,y) is the complex relative permeability.
• e_r(x,y) is the complex relative permittivity.

By solving the equation, the electric field mode pattern E_m(x,y) and the propagation constant g_m are both obtained for all the modes specified for a given port. For the current based impedance calculations, the port solver also solves independently for H_m(x,y) using a corresponding equation for the magnetic field.

Also note that the excitation field pattern computed by the port solver is valid only at a given frequency. A different excitation field pattern is computed for each frequency point of interest.