Research of Dispersion Characteristics of a Rectangular Waveguide with a Corrugated Bottom Wall by the Coupled Wave Method

Abstract

The research on dispersive characteristics of a rectangular waveguide with the goffered bottom wall a method of the connected waves is presented.

Rectangular and round waveguides with the goffered walls usually are used in a superhigh-frequency range as band-pass and low-pass filters, irradiators of multiband mirror aerials of satellite communication; in radar-tracking gauges of a W-range for detection and creation of cards of space garbage, etc. Definition of a constant of distribution in a rectangular waveguide with the goffered bottom wall by the method of the connected waves is conducted by transformation of the homogeneous differential equation with non-uniform boundary conditions to the non-uniform differential equation with homogeneous boundary conditions. The electromagnetic field in the cells of the corrugation of a rectangular waveguide with a corrugated bottom wall is found through the vector potential, which depends on the radial coordinate. The function of changing the electromagnetic field along the radial coordinate is determined by solving the Bessel equation. The vector of the magnetic field strength and the amplitudes of the components of the magnetic field strengths in the cross section of a rectangular waveguide and the component of the electric field strength tangential to the cell surface are found through the vector potential.

The tangential component of the electric field strength along the narrow walls of a rectangular waveguide is calculated. An equivalent magnetic surface current is introduced along the wide and narrow walls of a rectangular waveguide. For a regular rectangular waveguide with magnetic currents on its walls, solutions of equations that satisfy the orthogonality conditions, for determining the amplitudes of electromagnetic fields in the positive and negative directions along the axis of the regular rectangular waveguide, correction to the wave propagation constant of the i-th k'_j type is given.

The graphs of the calculated and experimental dependences of the propagation constant k'_j on the ratio λ/a (λ - wavelength, m) for waves of quasi types H₁₀, H₂₀, and H₀₁ in a WR-112 rectangular waveguide with cross-sectional dimensions (a x b) mm = (28,5 x 12,64) mm with a corrugated bottom wall at fixed relative dimensions of the cell depth t, the distance between the corrugations s and the width of the lower base of the trapezoid of the cross-section of the corrugation D — δ=t/a, u=s/a, and p=D/a. The dependences of the propagation constant k'_j on the ratio λ/a for a quasi-type wave H₁₀ were studied in the frequency range from 5.2 GHz to 7.1 GHz, for a quasi-type wave H₂₀ - from 10.5 GHz to 11.8 GHz, for a quasi-type wave H₀₁ - from 11.7 GHz up to 18.1 GHz. The dispersion characteristics of waves of the types of quasi H₁₀, H₂₀, and H₀₁ a rectangular waveguide with a corrugated bottom wall with a decrease in the relative depth of the corrugation δ approach the dispersion characteristics of the types of waves of a regular rectangular waveguide and, in the case of the boundary (δ→0), coincide with them. The error of the calculated data relative to the experimental data is about 5%, which confirms the suitability of the proposed method for practical calculations even in the first approximation.

The proposed technique may be appropriate for choosing the approximation that provides the required calculation accuracy in practice with a minimum amount of computation.

The reliability and validity of the results obtained is ensured by the convergence of the results of the calculation according to the boundary conditions with the known results and the convergence of the formulas obtained by the units of measurement.