Lossy microwave circuits — Systematic synthesis of equivalent lumped element model based on extended Foster canonical expansion

An application of systematic network model synthesis approach for representation of distributed passive lossy microwave circuits is investigated in the paper. This approach is based on a Foster canonical expansion for lossless circuits and its modification to account for losses. Equivalent compact lumped element model is extracted from the data provided by numerical TLM method in the time-domain and then embedded into a conventional circuit simulator. The synthesis procedure is applied to a lossy band-pass microstrip filter and a lossy coupled line coupler. Impact of dielectric losses of a substrate is also highlighted with the respect of the presented approach applicability.