Attenuation of the dominant mode in a lossy rectangular waveguide

We present a fundamental and accurate approach to compute the attenuation of electromagnetic waves propagating in a rectangular waveguide with imperfect conducting walls. The wavenumbers in the x and y directions, i.e. k_x and k_y, respectively, are first computed as roots of the transcendental equations developed by matching the tangential fields with the constitutive properties of the wall material at the boundary of the waveguide. The propagation constant k_z is solved by substituting k_x and k_y into the dispersion relation. We have compared the attenuation constant of the dominant TE₁₀ mode computed using our technique with that using the approximate perturbation method. The results from the two methods agree very well at a reasonable range of frequencies above the cutoff. The two curves, however, deviate below cutoff and at millimeter wave frequencies. We attribute the discrepancies to the dispersive effect and the presence of the longitudinal electric field in a lossy waveguide. The presence of the longitudinal field is not accounted for in the perturbation method.