# Computational Design of a Broadband In-Line Coaxial-to-Rectangular Waveguide Transition
## 4 Conclusions  
The design approach proposed in this paper enables a realization of an in-line rectangular waveguide-to-coaxial transition with a bandwidth close to the theoretical limit of 3:1. The maximum bandwidth in previous works was 2:1. The proposed design approach employs three waveguides--output, matching, and converter waveguides. A standard waveguide was used at the output, and a mode-converter waveguide was used at the input. A matching waveguide was placed between the input and the output. Making the broad-wall width of the converter waveguide slightly larger than that of the output waveguide ensured an operation close the TE\({}_{10}\)-mode cutoff. The narrow-wall height of the converter waveguide was reduced such that the TE\({}_{11}\)-mode cutoff frequency was the same as the TE\({}_{30}\)-mode cutoff frequency. For low reflection over a broad frequency range, a four-step ridge transformer was used for the coaxial TEM to waveguide TE\({}_{10}\) mode conversion. With the proposed scheme, a transition can operate with a maximum bandwidth of 3:1. It was found that the discontinuity-induced generation of the unwanted higher-order modes should be suppressed by a careful optimization of the stepped-ridge transformer. A WR75 transition designed according to the proposed approach showed a 2.83:1 bandwidth, close to the theoretical limit of 3:1 with a reflection coefficient \(<-22.6\) dB. We expect that the proposed design approach will pave the way for a significant extension in the bandwidth of microwave devices and antennas that employ coaxial-to-rectangular waveguide transitions. Possible future research topic may include (1) reduction of the transition's reflection coefficient to \(-30\) dB level, (2) further extension of the transition's bandwidth by suppressing higher-order modes, and (3) design integration of the proposed transition in such devices as near-field antenna measurement probes and materials measurement fixtures.  
Conceptualization, S.L. and S.-G.C. methodology, C.-S.L., Q.Z., S.L. and S.-G.C.; validation, Q.Z., J.H., E.A., D.O., S.X., G.-X.A., C.-S.L., S.L. and S.-G.C.; formal analysis, Q.Z., S.X., J.H., C.-S.L., D.O., S.-G.C. and B.-C.A.; formal data curation, G.-Y.A., D.O., J.H., E.A. and B.-C.A.; writing--original draft, E.A., Q.Z., S.L. and G.-Y.A.; writing--review and editing, S.X., S.-G.C. and B.-C.A. All authors have read and agreed to the published version of the manuscript.  
This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (No. 2020R1A6 A1A12047945) and by the MSIT (Ministry of Science and ICT), Korea, under the Grand Information Technology Research Center support program (IITP-2023-2020-0-01462) supervised by the IITP (Institute for Information & communications Technology Planning & Evaluation).  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Work** & **Year** & **Feature** & **Frequency (GHz)/** & **Reflection** \\  & & & **Ratio Bandwidth** & **Coefficient (dB)** \\ \hline
[4] & 1957 & Three-step ridge and & 2.5–4.1/1.64:1 & \(-20.1\) \\  & coaxial quarter-wave transformer & & 2.5–4.1/1.64:1 & \(-20.1\) \\ \hline
[8] & 1979 & Stepped wire loop & 8.2–12.0/1.46:1 & \(-19.1\) \\ \hline
[9] & 1990 & Dual stepped ridge & 0.85–1.16/1.36:1 & \(-32.3\) \\ \hline
[10] & 1998 & Three-step ridge & 3.05–4.60/1.51:1 & \(-30.0\) \\ \hline
[13] & 2017 &
\begin{tabular}{c} Oversized mode conversion and \\ four-step ridge \\ \end{tabular} & 10.0–20.0/2.00:1 & \(-30.0\) \\ \hline
[15] & 2018 & Three-step ridge & 11.5–19.0/1.65:1 & \(-20.0\) \\ \hline
[18] & 2021 & Five-step ridge & 33–50/1.52:1 & \(-25.0\) \\ \hline
[19] & 2021 & Four-step ridge & 40–60/1.50:1 & \(-25.0\) \\ \hline
[28] & In production & Commercial product & 21–34/1.62:1 & \(-22.7\) \\ \hline This work & 2023 &
\begin{tabular}{c} Four-step ridge and \\ linear taper \\ \end{tabular} & 8.14–23.00/2.83:1 & \(-22.6\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Comparison with previous works.