Nowadays, the interconnect circuits’ conduct plays a crucial role in determining the performance of the CMOS systems, especially those related to nano-scale technology. Modeling the effect of such an influential component has been widely studied from many perspectives. In this article, we propose a new general formula for $RLC$ interconnect circuit model in CMOS technology using the fractional-order elements approach. The study is based on approximating an infinite transfer function of the CMOS circuit with a noninteger distributed $RLC$ load to a finite number of poles. It is accurate due to the effect of adding fractional-order variables and since these variables are utilized for tuning the model to match the design regardless of its complexity. As such, delay calculations employing our analytical model are within 0.4 absolute error of COMSOL-computed delay across a range of interconnect lengths. Furthermore, the effect of the interconnect conductivity $G$ has been taken into account tacitly although the model included the resistance $R$ , inductance $L$ , and capacitance $C$ of the interconnect. A number of analyses were set up at different levels of the design to evaluate the effectiveness. First, demonstrating the significant effects of generalizing parameters was gained by studying the fractional-order impedance and propagation constant of the transmission line for a range of frequencies. Second, using MATLAB we assessed the potential of the proposed approximated model besides the exact one, which shows similarity in the fundamental features of the system, such as stability and resonance. Third, the proposed approach showed that with a very small tuning reach 0.01 of the generalizing parameters can achieve up to 15% improvement in the model accuracy.

中文翻译：

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使用分数阶元素的高级互连电路建模设计

如今，互连电路的行为在决定 CMOS 系统的性能方面起着至关重要的作用，尤其是那些与纳米级技术相关的系统。对这种有影响力的成分的影响建模已经从许多角度进行了广泛的研究。在本文中，我们提出了一个新的通用公式 $RLC$ 使用分数阶元素方法的 CMOS 技术中的互连电路模型。该研究基于使用非整数分布逼近 CMOS 电路的无限传递函数 $RLC$ 加载到有限数量的极点。由于添加分数阶变量的影响，并且这些变量用于调整模型以匹配设计而不管其复杂性，因此它是准确的。因此，使用我们的分析模型进行的延迟计算与 COMSOL 计算的延迟的绝对误差在 0.4 绝对误差范围内，跨越一系列互连长度。此外，互连电导率的影响 $G$ 尽管模型包括阻力，但已被默认考虑 $R$ , 电感 $L$ , 和电容 $C$ 的互连。在设计的不同级别设置了许多分析以评估有效性。首先，通过研究传输线在一定频率范围内的分数阶阻抗和传播常数，证明了泛化参数的显着影响。其次，我们使用 MATLAB 评估了所提出的近似模型的潜力，除了精确的模型，这表明系统基本特征的相似性，例如稳定性和共振。第三，所提出的方法表明，通过非常小的调整达到 0.01 的泛化参数可以使模型精度提高 15%。