Advance Interconnect Circuit Modeling Design Using Fractional-Order Elements

Abstract

Nowadays, the interconnect circuits' conduct plays a crucial role in determining the performance of the CMOS systems, especially those related to nano-scale technology. Modelling the effect of such an influential component has been widely studied from many perspectives. In this work, we proposed a new general formula for RLC interconnect circuit model in CMOS technology using fractional-order elements approach. The study is based on approximating an infinite transfer function of the CMOS circuit with a non-integer 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 utilised 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 generalising parameters was gained by studying the fractionalorder 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 generalising parameters can achieve up to 15% improvement in the model accuracy.Index Terms-fractional calculus, modelling, on-chip interconnect, RLC interconnect, transmission line.

Nonlinear Fractional-Order Circuits and Systems: Motivation, A Brief Overview, and Some Future Directions

“…possessing fractional orders very near to 1 (see [45, Table 1] and [46, Table 3]), the straightforward current-voltage relation i(t) = Cdv(t)/dt has been simply used for describing their dynamical behavior. Some more advanced samples of benefiting from fractional-order dynamics in modeling of electrical components are modeling of onchip inductors constructed by the Siliconbenzocyclobutene technology [47], voltammetric sensors [48], on-chip interconnects in nanoscale CMOS circuits [49], CMOS metamaterial transmission lines [50] [51], and large three-dimensional RC networks [52].…”

Modeling and Analysis of Caputo–Fabrizio Definition-Based Fractional-Order Boost Converter with Inductive Loads

“…However, the pronounced nonlinearity inherent in DC-DC converters poses significant challenges in the construction of their precise mathematical models [7,8]. Studies have shown that fractional-order models are superior in characterizing the electrical properties of components in the context of DC-DC converters [9][10][11][12][13]. Applying fractional-order operators to mathematical modeling of DC-DC converters can provide a more comprehensive and accurate description of the electrical characteristics of DC-DC converters [14,15].…”

Generalized Fractional-order Electrical Element: Modeling, Response Characteristic Analysis and Circuit Simulation

“…Recently, much research [17,18] has emerged on the practical realization of FOE and fractional-order systems, such as resistor and capacitor networks [19,20], singlecomponent realization [21], field-programmable gate arrays (FPGAs) [22] and generalized impedance converter [23]. The FOE model has demonstrated its applicability in fitting physical devices or systems, such as supercapacitors [24][25][26][27], ferromagnetic core coils [28,29], and on-chip inductors [30], and so on [31,32] producing more satisfactory fitting results than the conventional integer-order model.…”