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We show here that a transverse electric field, as in field-effect devices, leads to interesting interfering phenomena in the electronic transport. Using the Sylvester Theorem for matrix-valued functions, we study the transmission properties of a multi-propagating modes (multichannel) quasi-two-dimensional electron gas in the presence of a channel mixing transverse electric field. We observe interesting resonant coupling effects, which explain the fundamentals of the giant superlattice-conductance as well as giant superlattice-resistance effects.