A passive circuit representation of boundary conditions for modelling periodic microwave structures using the TLM method

We present a new circuit representation of the boundary conditions for simulating periodic microwave structures using the transmission line method (TLM). Our formulation leads to an algorithm that enforces the Bloch conditions at the cell sidewalls while preserving energy. This formulation eliminates the introduction of high frequency components which cause instability in previously published methods (Walter, M. et al., IEEE Trans. Microwave Theory Tech, vol.48. no.9, p.1574-6. 2000). Our approach is validated by simulating two structures: a periodically loaded microwave waveguide and a 2D array of dielectric materials. The dispersion relations obtained with this method compare very well with those obtained by alternative means.