Design and characterization of CMOS differential pair circuits for membership function generation with noise analysis in fuzzy logic systems

With the growing demand for energy-efficient and sustainable electronic systems, CMOS technology plays a crucial role in advancing green electronics and had emerged as a key enabler for low-power analog hardware implementations in intelligent systems. This paper presents a comprehensive study of CMOS differential pair implementations for generating bell-shaped and sigmoid membership functions, which serve as fundamental components in fuzzy logic systems and directly influence decision-making accuracy. By employing CMOS differential-pair circuits, a hardware-efficient approach is proposed to realize smooth, continuous analog membership functions suitable for fuzzy inference applications. The study encompasses detailed mathematical modeling, circuit design methodologies, and performance evaluation through LTspice simulations of 45 nm technology. Particular emphasis is placed on noise characterization, where both flicker (1/ f ) noise and thermal noise contributions are analyzed to assess their impact on circuit performance. Simulation results demonstrate how circuit topology and membership function shape affect noise behavior and power consumption (below 12 μ W) and achieve a noise floor below 1 μ V/ Hz beyond 10 kHz, confirming the circuits’ low-power and low-noise performance. A comparative analysis of the sigmoid function and bell-shaped implementations further supports these results. Additionally, the characteristic curves of both membership functions are extracted and discussed, validating their operational suitability for analog fuzzy logic systems. The findings provide valuable insights for designing low-noise analog fuzzy inference systems, thus enhancing the reliability, precision, and energy efficiency of intelligent electronic systems.