This paper presents the theory, properties, types, and applications of high impedance wires (HIWs). The effective permeability of a transmission line that consists of an HIW and a second conductor has a resonating behavior. Consequently, slow-wave and stop-band regions appear in the dispersion relation. In the slow wave regions, a new implementation for dual-mode filter is presented. The proposed filter size is reduced by 33%. In the stop band region, a new application is presented; dual-band balun where the common mode is rejected by the HIW. The novel design has a total area of 4 x 2.4 cm2 and exhibits reliable performances at 2.75 GHz with a 40% bandwidth (2.2--3.3 GHz) and at 4.75 GHz with a 15% bandwidth (4.4--5.1 GHz) with an amplitude imbalance less than 1 dB, a return loss better than 13 dB, and phase imbalance less than 5°. Theoretical expectations were confirmed by EM simulations and measurements.
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