Piecewise linear model for transmission line with capacitive loading and ramp input

Transmission line effects become increasingly significant for on-chip high-speed interconnects. Efficient and accurate transmission line models are required for analysis and synthesis of such interconnects. In this paper, we first present an efficient model for the far-end response of a single transmission line considering ramp input and capacitive loading. Our model divides the time axis into a number of regions according to the time of flight and the input rising time, and then approximates the far-end response by piecewise linear (PWL) waveform in each region. We name the resulting model as the PWL model. Experiments show that the waveform from the PWL model differs from the SPICE simulation result with the average voltage difference less than 0.9% V_dd, and the PWL model is at least 1000× faster than SPICE simulation. We further apply the PWL model to calculate the delay, rising time, and oscillation amplitude of the coplanar waveguide structure, and achieve less than 10% average error compared to SPICE simulation. Combining the PWL model and decoupling technique, we analyze the far-end response of bus structures and obtain waveform almost perfectly matching the SPICE simulation result.