| This thesis presents new numerical algorithms for extracting Spice-compatible equivalent-lumped circuits both for single and multiconductor transmission lines. The quasi-transverse electromagnetic condition is assumed in this thesis. The methods introduced in this thesis are a new moment-matching approach (NMA) that extends the traditional moment-matching technique and the eigenmode approach (EMA) that also extends the technique applied to model slot-embedded conductor by Silvester. Both the NMA and EMA have taken advantage of the most recent techniques available such as the finite element method, mesh generation; moment matching, model order reduction and numerical eigenvalue/eigenvector solution techniques.; NMA extracts a Foster equivalent circuit, which is known to model the transmission lines (including eddy current effects) at high frequency, by a moment-matching solution of the eddy-current equation. NMA is an approximation in that it uses a model order reduction (MOR) technique to select poles that contribute most to time-domain transient behavior.; EMA also extracts a Foster equivalent circuit by expressing the vector potential (hence impedance) in terms of eigenvalues and eigenvectors of the discretized eddy-current equation. Even though EMA takes additional time due to the calculation of eigenvectors, the new impedance formula derived in EMA guarantees that all circuit elements are positive. A novel scheme based on so-called importance criteria for selecting some of poles is developed.; The same NMA and EMA are successfully applied to multiconductor transmission line cases. Although EMA fails to generate a guaranteed passive equivalent circuit, it is shown that EMA can generate a passivity-guaranteed model when the layout has symmetry. |
