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Five different types of transmission line systems are analyzed and are shown to possess directional properties at the lower radio frequencies. The conditions of mismatch on either transmission line or on both transmission lines have been taken into account, as well as lengths of coupling greater than a fractional wavelength. A new and more general scatter matrix for directional couplers which includes the condition of mismatch is developed. In addition, lumped circuit directional couplers have been developed as a consequence of the general transmission line theory.