Rapid developments in VLSI technology and an ever-increasing quest for high-speed applications has highlighted previously negligible interconnect effects. These effects if not predicted at early design stages can severely degrade system performance. Generally, interconnect networks result in large systems of equations, simulation of which is prohibitively CPU expensive. Model-reduction is the key to fast simulation of interconnect networks. Conventional model-reduction techniques using Krylov-subspace methods, handle the distributed transmission lines by discretizing them into a set of ordinary differential equations. Discretization generally needs large number of sections and consequently leads to large circuit matrices.

In this thesis, a new technique is presented which enables the inclusion of distributed transmission line networks described by Telegrapher's equations directly using a congruent transformation based analysis. Next, an efficient sensitivity analysis algorithm of transmission line networks is presented that handles distributed transmission line circuit stamps including frequency dependent parameters. While this algorithm performs small-scale sensitivity analysis on large interconnect circuits, a new method to perform large-scale sensitivity is suggested that reduces a distributed transmission line system simultaneously with respect to frequency and any other parameter of the circuit. Next, a novel algorithm was developed for forming reduced-circuits for large interconnect networks without the need for partitioning the network into linear and nonlinear parts. This algorithm projects the full nonlinear circuit equations into a subspace of lower dimension. The reduced system can be solved using any of the conventional numerical integration techniques, resulting in significant reduction in the CPU time.