Scalable compact models for embedded passives

This paper presents a new comprehensive methodology for the development of scalable models for embedded passives. These models are derived from fundamental lossy transmission line theory. Using Taylor's series and continued fractions approximation, very accurate second and third order intrinsic capacitor and inductor models have been demonstrated. With the second order model, we are able to match the measured response up to the first resonance frequency. With the third order models, we are able to match the measured response beyond the first resonance frequency. The wideband accuracy provided by the third or higher order intrinsic models are necessary in transient and harmonic frequency analysis. The parameter extraction does not require any optimization and is accurate and unambiguous. The third order continued fractions model, introduced in this paper, matches the frequency dependent non-linear effects observed in the passives without a need for frequency dependent elements.