Propagation constant of HE11 mode near the cutoff frequency in a circular waveguide

In this letter, the propagation characteristics of normal mode near the cutoff region of a circular waveguide surrounded by a medium of finite conductivity and given permeability is discussed. Several real-time applications require an accurate solution of the characteristic equation at low computational cost. A fast computed approximate solution for external medium with infinite conductivity is available but inaccurate in the cut off region. Besides, field solvers and other numerical techniques give a precise solution in the whole frequency range, but unacceptable computational time. The proposed solution is derived by a perturbation approach once the characteristic equation has been expanded. A comparison between computed and exact values shows that the approximate solution is quite good for a wide range of conductivity and permeability values of the external medium.