Simulator for Interconnects and General Multiline Analysis (SIGMA): Simulation Algorithm of Lossy Multiple Transmission Lines

Fast and accurate evaluation of signal transients on interconnects become an essential part of today’s highspeed and high-density digital system design. Particularly, as the electrical length of interconnects continues to increase, the transmission line effects such as crosstalk, propagation delay, reflection, and dispersion on the interconnects of the high-performance systems significantly degrade signal integrity [1,2]. The segmented ladder network model for SPICE simulation cannot be adapted to an accurate simulation of the frequency-dependent effects of the lossy transmission lines. Since the transmission lines can be inherently well characterized in the frequency domain, they have been mathematically formulated in the frequency domain with telegrapher equations. In contrast, the non-linear semiconductor devices can be more suitably modeled in the time domain. Thus it is very difficult to directly integrate the transmission line model into an existing transient circuit simulator. In order to overcome such problems, several methods have been proposed which can analyze the transmission lines in the time domain [3,4]. Once the transfer functions of the transmission line are determined in the frequency domain, its time domain counter part can be yielded by inverse Fourier or Laplace transform. The system response, including the transmission line effects, can be formulated by convolution integral in the time domain with boundary conditions [5–7]. Then finally, modeling them as an equivalent circuit, the time domain response of the transmission line can be implemented into a time domain circuit simula-