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The complete frequency spectrum of the circularly- shielded slot line and strip line are determined using an efficient domain decomposition and mode matching method. Asymptotic analyses show that, when the gap width of the slot line or the width of the strip line are too small, the TE frequencies may drop singularly and the TM frequencies may rise singularly. These new properties greatly affect the cutoff frequencies.doi:10.5281/zenodo.3667104 fatcat:nyigqnffkbednkllaa3qgaamuq