Intermodal Coupling at the Junction Between Straight and Curved Waveguides

Abstract

This paper analyses the coupling of electromagnetic modes at the junction between straight and continuously curved rectangular waveguides. The method of solution is based on an integral equation formulation, applicable for sharp as well as gradual bends. Such quantities as the average power transmitted or reflected into each of the various modes propagating in the straight and curved waveguide sections are readily obtained. The article presents the results of representative calculations for the two types of waveguide bends. These include graphs of the energy distribution in the transmitted and reflected modes as a function of dimensionless ratios for a sharp bend; the range of values considered allows immediate application of the results to standard C‐band waveguides. The gradual bend example uses parameters encountered in the waveguide connections to an antenna in a typical microwave relay network.

Analytic-Numerical Analysis of Waveguide Bends

“…The obtained numeric results are compared with the data presented by Bates (1969) and Wu (1987). They agree well with our data within drawing precision.…”

“…Note also that a peak of the reflected power for the mode LE 01 in the straight guide was lost near the point l/λ = 3.3, where l is the waveguide height. Downloaded by [University of Connecticut] at 13:35 12 October 2014 Table 1 Intermodal coupling for a square guide with r 1 /r 2 = 0.516441 Reflected mode power Transmitted mode power Incident mode Bates (1969) This work Bates (1969) This work ka = 1.19π LM s 10 LM s 10 ≈ 10 −7 9.677 · 10 −8 LM c 10 = 9.52174 · 10 −1 9.531 · 10 −1 LM s 20 = 1.2 · 10 −5 1.247 · 10 −5 LM c 20 = 4.7815 · 10 −2 4.693 · 10 −2 LE s 01 LE s 01 = 10 −6 1.312 · 10 −6 LE c 01 = 6.18860 · 10 −1 6.203 · 10 −1 LE s 11 = 4.6 · 10 −5 4.701 · 10 −5 LE c 11 = 3.76074 · 10 −1 3.749 · 10 −1 LE s 21 = 2.2 · 10 −5 2.421 · 10 −5 LE c 21 = 4.997 · 10 −3 4.777 · 10 −3 ka = 1.79π LM s 10 LM s 10 = 10 −9 7.731 · 10 −10 LM c 10 = 7.36720 · 10 −1 7.370 · 10 −1 LM s 20 = 10 −6 1.003 · 10 −7 LM c 20 = 2.58699 · 10 −1 2.584 · 10 −1 LM s 30 ≈ 10 −7 2.215 · 10 −8 LM c 30 = 4.581 · 10 −3 4.553 · 10 −3 LE s 01 LE s 01 ≈ 10 −7 2.562 · 10 −7 LE c 01 = 4.56751 · 10 −1 4.568 · 10 −1 LE s 11 = 5 · 10 −6 5.123 · 10 −6 LE c 11 = 3.84346 · 10 −1 3.845 · 10 −1 LE s 21 = 10 −6 9.711 · 10 −7 LE c 21 = 1.53564 · 10 −1 1.534 · 10 −1 LE s 31 = 2.7 · 10 −5 2.737 · 10 −5 LE c 31 = 5.306 · 10 −3 5.281 · 10 −3 Figure 3. Intermodal coupling at E-plane bend with r 1 /r 2 = 0.53445 and the normalized waveguide height l/a = 4.3 for the incident mode LE s 01 of a unit amplitude.…”

“…In Table 1, the calculated values of the reflected and transmitted mode power are compared with the data obtained by Bates (1969). In that method-of-moments solution, Downloaded by [University of Connecticut] at 13:35 12 October 2014 the Liouville-Green approximations were employed for evaluation of the functions (4), (5), and (8) with large-in-modulus, purely imaginary indices (see also Wu, 1987).…”

Dyadic Green's functions for curved waveguides and cavities and their reformulation

“…[7] The eigenmodes in curved waveguides can be classified as either LSE modes or LSM modes [Bates, 1969;Mittra, 1972]. For the LSE modes, their vector wave functions are defined in terms of scalar wave functions y mmn…”

“…Continuously curved waveguides are used not only as waveguide bends but also as feeding or radiating guides for cylindrically conformal waveguide slot antenna arrays [ Fan , 1995]. In analyzing these problems, one often uses the dyadic Green's functions (DGFs) for curved waveguides and cavities [ Fan , 1995; Bates , 1969; Mittra , 1972]. Although many expressions of DGFs have been derived for various straight waveguides and cavities [ Collin , 1960; Tai , 1994; Rahmat‐Samii , 1975; Tai and Rozenfeld , 1976; Wang , 1978, 1982; Kisliuk , 1980; Daniele , 1982; Pathak , 1983; Yang , 1992; Li et al , 1995], to our knowledge, no expressions of DGFs for curved waveguides and cavities are available in literature.…”