This paper studies a computationally efficient algebraic graph theory engine for simulating time-domain one-dimensional waves in a multi-segment transmission line, such as for reflectometry applications. Efficient simulation of time-domain signals in multi-segment transmission lines is challenging because the number of propagation paths (and therefore the number of operations) increases exponentially with each new interface. We address this challenge through the use of a frequency-domain, algebraic graphical model of wave propagation, which is then converted to the time domain via the Fourier transform. We use this model to achieve an exact, stable, and computationally efficient (O(NQ), where N is the number of segments and Q is the bandwidth) approach for studying one-dimensional wave propagation. Our approach requires the reflection and transmission coefficients for each interface and each segment's complex propagation constant. We compare our simulation results with known analytical solutions.
Joel B. Harley,
Mashad Uddin Saleh,
Michael A. Scarpulla,
"Fast Transient Simulations for Multi-Segment Transmission Lines with a Graphical Model," Progress In Electromagnetics Research,
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