The coupling properties of supermodes guided by grating-assisted directional couplers (GADCs) can be phrased in rigorous modal theory. Such a modal solution for TE modes expressed by simple electrical transmission-line networks is utilized to analyze the power distribution of GADCs with three guiding channels. In particular, the modal transmission-line theory can serve as a template for computational algorithms that systematically evaluate the coupling efficiency that are not readily obtained by other methods.