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<p>This work reports the design of analog systems for linear fractional-order (FO) systems with Caputo-Fabrizio (CF) fractional derivatives. The CF derivatives are occupying a center stage in the modelling of physical systems due to their non-singular kernel and ease of computation. This study presents a systematic design procedure for the development of analog circuits for the single-input-single-output and multiple-input-multiple-output linear systems with CF derivative. The design is based on Foster network analysis. The time and frequency domain validations confirm that the analog systems faithfully capture the dynamics of the FO linear systems. The designed systems are implemented in Cadence for 45nm, 90nm, and 180nm with CMOS technologies. A rigorous analysis of the performance of the designed analog systems, in terms of propagation delay and power dissipation, is also carried out. The trade-offs between these two indices are reported.</p>

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Analog implementation of linear systems with Caputo-Fabrizio fractional derivative: design and analysis

  • 期刊论文

  • 发表日期：

    2026年6月15日

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  • Sushma Kodagali,
  • Vishwesh Vyawahare

摘要

This work reports the design of analog systems for linear fractional-order (FO) systems with Caputo-Fabrizio (CF) fractional derivatives. The CF derivatives are occupying a center stage in the modelling of physical systems due to their non-singular kernel and ease of computation. This study presents a systematic design procedure for the development of analog circuits for the single-input-single-output and multiple-input-multiple-output linear systems with CF derivative. The design is based on Foster network analysis. The time and frequency domain validations confirm that the analog systems faithfully capture the dynamics of the FO linear systems. The designed systems are implemented in Cadence for 45nm, 90nm, and 180nm with CMOS technologies. A rigorous analysis of the performance of the designed analog systems, in terms of propagation delay and power dissipation, is also carried out. The trade-offs between these two indices are reported.