We develop a new causal power-normalized wave-guide equivalent-circuit theory that, unlike its predecessors, results in network parameters usable in both the frequency and time domains in a broad class of waveguides. Enforcing simultaneity of the voltages, currents, and fields and a power normalization fixes all of the parametrs of the new theory within a single normalization factor, including both the magnitude and phase of the characteristic impedance of the waveguide. Enforcing simultaneity also ensures that the theory's voltages and currents do not start before their excitation, and that the network parameters of passive devices are causal, a necessary condition for stable time-domain simulations.
IEEE Transactions on Microwave Theory and Techniques
causality, characteristic impedance, circuit theory, frequency domain, time domain
and Alpert, B.
Causality and Waveguide Circuit Theory, IEEE Transactions on Microwave Theory and Techniques, [online], https://doi.org/10.1109/22.915434
(Accessed September 22, 2021)