Generalized traveling-wave-based waveform approximation technique for the efficient signal integrity verification of multicoupled transmission line system

As very large scale integration (VLSI) circuit speed rapidly increases, the inductive effects of interconnect lines strongly impact the signal integrity of a circuit. Since these inductive effects make the signal integrity problems much more serious as well as intricate, they become one of the critical issues in today´s high-speed/high-density VLSI circuit design. In this paper, a generalized traveling-wave-based waveform approximation (TWA) technique is presented which can be accurately as well as efficiently employed for the signal integrity verification of the inductively dominated (moderate Q) multicoupled RLC transmission line system. The technique is composed of three steps. First, the signals in the multicoupled (n-coupled) transmission line system are decoupled into n-isolated eigen-modes (i.e., basis vectors). Next, the slow-transient low-frequency characteristics of the system response are determined, approximately, in the frequency-domain by using the dominant poles of the basis vectors. Finally, the fast-transient high-frequency characteristics of the system response are calculated in the time domain by using the traveling wave characteristics of the basis vectors. It is shown that the time-domain responses of the multicoupled RLC transmission line system can be accurately as well as efficiently modeled with the generalized TWA technique. Then, in inductance-dominant multicoupled interconnect networks, switching-dependent signal integrity, i.e., signal delay, crosstalk, ringing, and glitches are investigated extensively with the proposed technique.