| In this dissertation, we investigate the notion of signal delay and propose a new, abstract model of delay to enable accurate functional timing analysis of digital circuits. We begin by examining the definition of delay for non-ideal gates and signals. Using a combination of analytical and experimental techniques, we find that delay measurement using the unity differential gain thresholds of the DC voltage transfer curve of the gate never results in non-physical values of delay, such as negative delay. We then generalize this result to multi-input gates and interconnects.;We next investigate the behavior of delay for multi-input gates and coupled, uniform, RC (URC) interconnects, when the inputs experience temporally close transitions (i.e. switch in proximity). We first address the problem of identifying the correct reference input for measuring delay in the presence of proximity. We next present delay macromodels for simple, multi-input gates to estimate delay, which are then validated on both CGaAs and CMOS technologies. Finally, we present a modeling technique to estimate signal delay in coupled, URC interconnect wires. Comparison with circuit simulation shows that our approach gives good results.;We next present an abstract delay model, AFTA (Automaton for Functional Timing Analysis), that accounts for the important analog factors affecting delay, such as signal transition times and the proximity effects, while maintaining the logic level of abstraction. AFTA builds upon the foundation provided by the waveform calculus--a recently proposed symbolic model of digital circuits that links circuit function and timing. We describe AFTA's operation in both transient logic simulation and timing analysis environments, through several illustrative examples. In particular, we show the estimation of signal early and late arrival times, the two principal tasks in timing analysis, while accounting for signal transition times and proximity effects. We then extend AFTA to handle symbolic waveforms which gives it the flexibility to represent several possible waveform combinations compactly. Although the focus of the dissertation is on issues concerning accuracy, we also provide a brief discussion on the computational complexity of the proposed model. This work thus provides the foundation for performing functional timing analysis of digital circuits. |
