A Simplified Synthesis of Transmission Lines with a Tree Structure

The limiting factor for high-performance systems is being set by interconnection delay rather than transistor switching speed. The advances in circuits speed and density are placing increasing demands on the performance of interconnections, for example chip-to-chip interconnection on multichip modules. To address this extremely important and timely research area, we analyze in this paper the circuit property of a generic distributed RLC tree which models interconnections in high-speed IC chips. The presented result can be used to calculate the waveform and delay in an RLC tree. The result on the RLC tree is then extended to the case of a tree consisting of transmission lines. Based on an analytical approach a two-pole circuit approximation is presented to provide a closed form solution. The approximation reveals the relationship between circuit performance and the design parameters which is essential to IC layout designs. A simplified formula is derived to evaluate the performance of VLSI layout.