Design criteria for a lumped-element directional coupler

The lumped-element directional coupler described uses one inductor and one capacitor as the lossless junction of a four-port network. The directional coupler effect and the infinite directivity are frequency independent, at least, from dc to the frequencies at which the inductor and/or the capacitor deviates from the ideal, but the coupling properties are frequency dependent. However, the forward coupling from the input arm and the reversed coupling from the output arm form a ratio which is also frequency independent. A technique is described to obtain wide-band operation which is particularly useful for large coupling. By this technique multidecade-bandwidth operation is possible. The properties are expressed in terms of the scattering matrix, and the frequency dependence of the coupling and the insertion loss are formulated. General design criteria for single-frequency (narrow-band) and wide-band operations are provided by means of which a directional coupler with required characteristics can readily be designed