# Computational Design of a Broadband In-Line Coaxial-to-Rectangular Waveguide Transition
[PERSON] used a stepped wire loop to experimentally design an in-line transition operating at 8.2-12.0 GHz (1.46:1 bandwidth) with a VSWR \(<\) 1.25 or a reflection coefficient \(<-19.1\) dB [8]. [PERSON] and co-workers employed a dual stepped-ridge transformer along with a rectangular coaxial matching section for the theoretical design of an in-line transition operating at 0.85-1.16 GHz (1.36:1 bandwidth) with a reflection coefficient \(<-32.3\) dB [9]. They analyzed the transition using the mode-matching method. [PERSON] and [PERSON] used an equivalent-circuit method and an in-house computer program to theoretically design an in-line transition with a three-step ridge transformer [10]. Their transition showed a reflection coefficient \(<-30.0\) dB at 3.05-4.60 GHz (1.51:1 bandwidth). [PERSON] and co-workers [11] and [PERSON] and co-workers [12] used a stepped-ridge transformer in their design of an in-line transition. Their transition showed performance similar to that in the preceding works. [PERSON] and [PERSON] achieved a 2:1 bandwidth in an in-line rectangular waveguide-to-coaxial transition [13] using oversized mode conversion and a stepped-ridge transformer. Subsequent works [14; 15; 16; 17; 18; 19] on the in-line transition were not targeted for extending the bandwidth beyond 2:1. In [14], a two-step ridge transformer was employed in a transition working at 9.5-10.8 GHz with a reflection coefficient of less than \(-20\) dB. [PERSON] and co-workers used a single waveguide and a three-step ridge transformer to design an in-line transition operating at 11.5-19.0 GHz (1.65:1 bandwidth) with a reflection coefficient \(<-20.0\) dB [15]. [PERSON] employed a two-step ridge transformer in a high-power in-line transition design working at 2.4-2.5 GHz with a reflection coefficient of less than \(-25\) dB [16]. In [17], a triple-stepped probe extended out of a coaxial cable was used to design an in-line transition working at 7.6-12.2 GHz (1.61:1 bandwidth) with a VSWR of less than 1.5 (reflection coefficient \(<-14.0\) dB). [PERSON] and co-workers realized a five-step ridge transition operating at 33-50 GHz (1.52:1 bandwidth) with a reflection coefficient \(<-25.0\) dB [18]. [PERSON] and co-workers used a four-step ridge transformer to realize WR28, WR22, and WR19 transitions operating at 26.5-40.0 GHz (1.51:1 bandwidth), at 33-50 GHz (1.52:1 bandwidth), and at 40-60 GHz (1.50:1 bandwidth) with a reflection coefficient of less than \(-23.0\) dB, \(-28.0\) dB, and \(-25.0\) dB, respectively [19]. A patent for an in-line coaxial-to-rectangular waveguide transition was granted as early as in 1973 [20]. In [20], a four-step ridge transformer was employed to design a transition working at 7.0-11.0 GHz (1.57:1 bandwidth) with a VSWR of less than 1.28 or a reflection coefficient \(<-18.2\) dB. A comprehensive literature survey shows that the concept of the stepped-ridge transformer and the stepped waveguide height transformer has been applied to the design of the broadband right-angle coaxial-to-rectangular waveguide transitions [21; 22; 23; 24; 25; 26; 27]. In [26], a double stepped-ridge transformer was used. Study of the literature shows that the stepped-ridge transformer has been a preferred choice in the design of broadband coaxial-to-rectangular waveguide transitions. In this Communication, we present a design approach for the broadband in-line coaxial-to-rectangular waveguide transition and two design examples having a bandwidth exceeding 2.8:1. The proposed transition employs a stepped-ridge transformer for the conversion of the coaxial TEM mode into the rectangular waveguide TE\({}_{10}\) mode. The transformer was placed in a converter waveguide whose broad-wall width is slightly larger than that of the output waveguide. The narrow-wall height of the converter waveguide was reduced from a standard height (one-half of the broad-wall width) so that the TE\({}_{11}\)-mode cutoff coincided with the TE\({}_{30}\)-mode cutoff in the converter waveguide.