Delay extraction and passive macromodeling of lossy coupled transmission lines

Recently, several algorithms were proposed for time-domain macromodeling of distributed transmission line networks. It has been demonstrated that preserving passivity of the macromodel is essential to guarantee a stable global transient simulation. Techniques such as method-of-characteristics yield fast transient results for long delay lines. However, they do not guarantee the passivity of the macromodel. On the other hand, methods such as matrix rational approximation provide efficient macromodels for lossy coupled lines, while preserving passivity. However, for long lossy delay lines this may require higher order approximations, making the macromodel inefficient. In order to address the above difficulty, this paper presents a new algorithm for efficient macromodeling of lossy coupled lines with long delay. The proposed method employs delay extraction prior to approximating the exponential stamp of the line and guarantees the macromodel passivity. The paper also provides guidelines on the practical applicability of the delay extraction and the matrix rational approximation, based on the knowledge of line parameters.