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Theoretical analysis of top- and side-emitting terahertz-wave generation by difference frequency generation in LiNbO3 channel waveguides with domain-inverted grating is presented. The analysis is based on Green's function and plane-wave expansion approaches. Mathematical expressions and numerical data for the conversion efficiency and the directionality were obtained. The results are consistent with those using two-dimensional model, but are more accurate and apply for various realistic device configurations. It was shown that higher efficiencies can be accomplished with narrow channel guides, although the radiation is highly divergent.