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The authors realize a 50% length reduction of short-slot couplers in a post-wall dielectric substrate by two techniques. One is to introduce hollow rectangular holes near the side walls of the coupled region. The difference of phase constant between the TE 10 and TE 20 propagating modes increases and the required length to realize a desired dividing ratio is reduced. Another is to remove two reflection-suppressing posts in the coupled region. The length of the coupled region is determined to cancel the reflections at both ends of the coupled region. The total length of a 4-way Butler matrix can be reduced to 48% in comparison with the conventional one and the couplers still maintain good dividing characteristics; the dividing ratio of the hybrid is less than 0.1 dB and the isolations of the couplers are more than 20 dB.
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S. Yamamoto (2005) studied this question.
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