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A hybrid simulation technique that integrates transmission line matrix method with electromagnetic topology solutions has been employed to link a field scattering problem at an aperture in order to analyze the frequency and temporal characteristics of electromagnetic pulses. Using this same unified multiconductor transmission line network formulation any subsequent coupling with cables at the other side of the aperture can be integrated into the solution. The hybrid circuit can also be integrated to any existing topological simulation circuit for analyzing very large electrical systems. Incorporation of the compaction technique in the topological simulation reduces the number of simulation grids significantly, resulting in efficient computation without sacrificing accuracy. The simulation results for scattering fields at the aperture compare well with the finite-difference time domain method.