Balanced-Output CCCFOA and Its Utilization in Grounded Inductance Simulator with Various Orders

In this paper, a new realization of current-controlled current feedback operational amplifier with balanced voltage outputs (BO-CCCFOA) is presented. A resistorless grounded lossless positive inductance simulator (PIS) using two BO-CCCFOAs and a grounded capacitor is reported. The resulting equivalent inductance value of PIS can be adjusted either via change of input intrinsic resistance of BO-CCCFOAs by means of biasing currents or by order of fractional-order capacitor (FoC). FoCs of order = (0.25; 0.5; 0.75; 1) were emulated via 5th-order Foster II RC network and values optimized using modified least squares quadratic (MLSQ) method. In frequency range 30 kHz - 30 MHz the obtained phase angle deviation of FoCs and mean values of corresponding relative phase error are below ±1 degree and ±4.3%, respectively. Considering the bandwidth for phase angle deviation less than 3 degree, the proposed fractional-order PIS operates over two decades. The behavior of the PIS circuit with various orders was tested via implementation in RLC ladder prototype of voltage-mode high-pass filter. Theoretical results are verified by SPICE simulations using TSMC 0.18 m level-7 LO EPI SCN018 CMOS process parameters with ±1 V supply voltages.In this paper, a new realization of current-controlled current feedback operational amplifier with balanced voltage outputs (BO-CCCFOA) is presented. A resistorless grounded lossless positive inductance simulator (PIS) using two BO-CCCFOAs and a grounded capacitor is reported. The resulting equivalent inductance value of PIS can be adjusted either via change of input intrinsic resistance of BO-CCCFOAs by means of biasing currents or by order of fractional-order capacitor (FoC). FoCs of order = (0.25; 0.5; 0.75; 1) were emulated via 5th-order Foster II RC network and values optimized using modified least squares quadratic (MLSQ) method. In frequency range 30 kHz - 30 MHz the obtained phase angle deviation of FoCs and mean values of corresponding relative phase error are below ±1 degree and ±4.3%, respectively. Considering the bandwidth for phase angle deviation less than 3 degree, the proposed fractional-order PIS operates over two decades. The behavior of the PIS circuit with various orders was tested via implementation in RLC ladder prototype of voltage-mode high-pass filter. Theoretical results are verified by SPICE simulations using TSMC 0.18 m level-7 LO EPI SCN018 CMOS process parameters with ±1 V supply voltages

Analog Implementation of Fractional-Order Elements and Their Applications

With advancements in the theory of fractional calculus and also with widespread engineering application of fractional-order systems, analog implementation of fractional-order integrators and differentiators have received considerable attention. This is due to the fact that this powerful mathematical tool allows us to describe and model a real-world phenomenon more accurately than via classical “integer” methods. Moreover, their additional degree of freedom allows researchers to design accurate and more robust systems that would be impractical or impossible to implement with conventional capacitors. Throughout this thesis, a wide range of problems associated with analog circuit design of fractional-order systems are covered: passive component optimization of resistive-capacitive and resistive-inductive type fractional-order elements, realization of active fractional-order capacitors (FOCs), analog implementation of fractional-order integrators, robust fractional-order proportional-integral control design, investigation of different materials for FOC fabrication having ultra-wide frequency band, low phase error, possible low- and high-frequency realization of fractional-order oscillators in analog domain, mathematical and experimental study of solid-state FOCs in series-, parallel- and interconnected circuit networks. Consequently, the proposed approaches in this thesis are important considerations in beyond the future studies of fractional dynamic systems