论文标题

多输入门的精确混合延迟模型

An Accurate Hybrid Delay Model for Multi-Input Gates

论文作者

Ferdowsi, Arman, Schmid, Ulrich, Salzmann, Josef

论文摘要

为了促进信号跟踪中各个过渡之间的时序关系的分析,动态数字时序分析提供了一个较少精确但更快的替代数字电路模拟替代方案。这主要需要门延迟模型,这也解释了以下事实:特定输入过渡的输入到输出延迟也取决于与先前输出过渡的时间距离。在多输入门的情况下,延迟还经历了由多输入切换(MIS)效果引起的变化,即在近距离接近时发生的不同输入的过渡。在本文中,我们主张通过用时间变化的电阻代替晶体管获得的CMOS大门的混合延迟模型的开发。我们通过将其应用于Nor Gate(因此,将其应用于双NAND门)和Muller C门来体现我们的方法。我们通过分析用非恒定效果求解所得的一阶微分方程,并为所得的MIS门延迟得出分析表达式。最终的公式不仅为声音模型参数化过程铺平了道路,而且对实施快速有效的数字时序模拟也起着重要作用。通过与模拟模拟数据进行比较,我们表明我们的模型忠实地代表了所有相关的MIS效果。使用涉及工具中的实现,我们证明了我们的模型超过了我们在准确性方面已知的NOR大门的替代数字延迟模型,并且运行时间相当短。

In order to facilitate the analysis of timing relations between individual transitions in a signal trace, dynamic digital timing analysis offers a less accurate but much faster alternative to analog simulations of digital circuits. This primarily requires gate delay models that also account for the fact that the input-to-output delay of a particular input transition also depends on the temporal distance to the previous output transitions. In the case of multi-input gates, the delay also experiences variations caused by multi-input switching (MIS) effects, i.e., transitions at different inputs that occur in close temporal proximity. In this paper, we advocate the development of hybrid delay models for CMOS gates obtained by replacing transistors with time-variant resistors. We exemplify our approach by applying it to a NOR gate (and, hence, to the dual NAND gate) and a Muller C gate. We analytically solve the resulting first-order differential equations with non-constant-coefficients, and derive analytic expressions for the resulting MIS gate delays. The resulting formulas not only pave the way to a sound model parametrization procedure, but are also instrumental for implementing fast and efficient digital timing simulation. By comparison with analog simulation data, we show that our models faithfully represent all relevant MIS effects. Using an implementation in the Involution Tool, we demonstrate that our model surpasses the alternative digital delay models for NOR gates known to us in terms of accuracy, with comparably short running times.

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