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Numerical studies of transient and steady state one-dimensional transport through resonant tunneling structures (RTSs) have been widely reported. For the most part, the structures studied have been symmetric with a single well. Following the method of Buot-Jensen, we apply a lattice Weyl-Wigner 1D single band transport code to both double barrier (DBRTS) and multiple barrier (TBRTS) GaAs/AlGaAs structures which are spatial and energetically asymmetric. Both the transient and steady state behaviors are studied. We show that the current-voltage characteristics can (a) vary drastically from those obtained from the associated symmetric structure, and (b) do not follow in a smooth manner with varying asymmetries. We also show how a n-barrier system behaves when approaching a superlattice (n∼6), and discuss the feasibility of using a Bloch function approach to simulate a superlattice.