Super broadband lumped models for embedded passives

This paper presents novel equivalent lumped circuits to model three-dimensional inductors and capacitors embedded in a multilayer organic or LTCC substrate with extremely large bandwidth. The developed models combine a core circuit, a five-element modified-T section, to include up to half-wavelength long transmission-line effects, and parallel and series feedback resonators to account for non-conductive and common-ground coupling phenomena. It is emphasized that all the circuit elements in such equivalent models can be extracted mathematically from the measured S parameters. In our establishment of an embedded passives library, the modeled S parameters can agree quite well with measured results over the entire measurement frequency range of 20 GHz. The effective modeling bandwidth is estimated at least several times larger than in the conventional PI-section models.