High-Precision Fractional-Order Integrator for Generating Pink Noise from White Noise

Pulse density modulation (PDM) can find applications in consumer electronics, power and switch control systems. PDM signals can be generated by asynchronous sigma delta modulator (ASDM) structures and improvement of ASDM performance provides significant contribution for practical applications. This study numerically investigates effects of fractional order integration (FOI) on the PDM signal, produced by ASDM. We implemented fractional order integratorin ASDM structure and present numerical analysis to discuss effects of fractional order integrator on PDM signals, obtained for bipolar digital signal transmission application. Theoretical analysis indicates that FOI provides finer pulse trains and thus improves representation of original signal. In simulations, we tested FOI for various fractional-order values. Signal to noise ratio and signal to noise and distortion ratio (SINAD) levels of demodulated signals are reported for sinusoidal and audio test signals. Simulation results demonstrate that FOI can improve SNR and SINAD performance of ASDMs.

This article investigates the optimal results of new improved fractional order integrators (FOIs) of different orders. Mathematical models of FOIs have been first developed by a single-step procedure of direct linear interpolation of fractional integrators based on Al-Alaoui operator in fractional domain itself, instead of using three steps of the well-known conventional method, namely, digital interpolation, series expansion and truncation. Later, these transfer functions (TFs) are optimised for their coefficient values for finding a minimum error function by particle swarm optimisation (PSO) algorithm. Simulation results of magnitude responses, phase responses and relative magnitude errors (dB) for all the proposed half integrators have validated the effectiveness of this new technique of interpolation of fractional order operators, mixed with PSO algorithm. A parallel comparison has been also drawn between the proposed optimised half integrators and those obtained by discretisation of PSO optimised integer order digital integrators (DIs) to properly support the proposed novel combination of interpolation and PSO, both applied together in fractional domain.

In CMOS integrated circuit (IC) design, operational amplifiers are one of the most useful active devices to enhance applications in analog signal processing, signal conditioning and so on. However, due to the CMOS technology downscaling, along the very large number of design variables and their trade-offs, it results difficult to reach target specifications without the application of optimization methods. For this reason, this work shows the advantages of performing many-objective optimization and this algorithm is compared to the well-known mono- and multi-objective metaheuristics, which have demonstrated their usefulness in sizing CMOS ICs. Three CMOS operational transconductance amplifiers are the case study in this work; they were sized by applying mono-, multi- and many-objective algorithms. The well-known non-dominated sorting genetic algorithm version 3 (NSGA-III) and the many-objective metaheuristic-based on the R2 indicator (MOMBI-II) were applied to size CMOS amplifiers and their sized solutions were compared to mono- and multi-objective algorithms. The CMOS amplifiers were optimized considering five targets, associated to a figure of merit (FoM), differential gain, power consumption, common-mode rejection ratio and total silicon area. The designs were performed using UMC 180 nm CMOS technology. To show the advantage of applying many-objective optimization algorithms to size CMOS amplifiers, the amplifier with the best performance was used to design a fractional-order integrator based on OTA-C filters. A variation analysis considering the process, the voltage and temperature (PVT) and a Monte Carlo analysis were performed to verify design robustness. Finally, the OTA-based fractional-order integrator was used to design a fractional-order chaotic oscillator, showing good agreement between numerical and SPICE simulations.

Introduction to Circuit Analysis and Design

This paper presents the analog realizations and the numerical evaluation of the second definition given by Lorenzo and Hartley of the variable fractional order integrator Iα(t){.} using an analog dynamical model. The analog realization of Iα(t){.} is obtained using an analog realization based on Charef s approximation of an adjustable fractional order integrator and the numerical evaluation of Iα(t){.} is obtained as the time response of its proposed analog dynamical model. The efficiency and the accuracy of the proposed Iα(t){.} numerical evaluation results obtained are compared to the ones of Lorenzo and Hartley using illustrative examples.

Current conveyors are widely used to implement current mode, voltage mode and mixed mode circuits of integer order. In this paper, a fractional order system is implemented using second generation current conveyor and a fractance device i.e. an RC network. The fractional order integrator of order half is designed for various s-domain models available in literature. The proposed integrators are realized in PSpice using 0.25um CMOS technology parameters.

This paper presents a novel digital instrument designed for measuring radiation doses in Ethanol-Chlorobenzene (ECB) dosimeters, based on oscillometry method. ECB dosimeters are versatile tools for radiation measurement, particularly in medical and industrial applications. Various components of the device including measuring cell, analog and digital circuits were designed, simulated, optimized and verified. The measuring cell was manufactured to maximize the sensitivity in detecting changes in the conductivity of the ECB solution inside the ampoules. The analog oscillating circuit was fabricated using new and common elements in the market such as operational amplifiers (Op Amps), diodes and transistors. The oscillator frequency was set to the lowest possible value to reduce the adverse effects of high frequencies. However, further decrease in frequency causes the conductivity changes of the ECB solution to be measured by the analog circuit inefficiently. The digital circuit was designed and constructed to interface with the analog circuit, processing its output voltage. This digital circuit included an ATmega8A microcontroller, a DS18B20 temperature sensor, a graphic LCD, and other widely used integrated circuits (ICs). The overall performance of the apparatus was validated by reading the absorbed dose of a set of dosimeters irradiated at doses of 1, 5, 10, 30, 70, and 100 kGy in the Gamma cell GC-220 of our laboratory. The maximum absolute relative difference between the average dosimeter readouts and expected values was about 7% and the average value of the absolute relative differences at different doses was about 3.3%. The negligible discrepancy between the values read by the manufactured device and the actual values demonstrates the accuracy of the device operation. Therefore, this device can be considered as an appropriate apparatus for reading the ECB dosimeters and can serve as a key component of an ECB dosimetry system for high-dose dosimetry applications.

This paper is concerned with the discretization of the fractional-order differentiator and integrator, which is the foundation of the digital realization of fractional order controller. Firstly, the parameterized Al-Alaoui transform is presented as a general generating function with one variable parameter, which can be adjusted to obtain the commonly used generating functions (e.g. Euler operator, Tustin operator and Al-Alaoui operator). However, the following simulation results show that the optimal variable parameters are different for different fractional orders. Then the weighted square integral index about the magtitude and phase is defined as the objective functions to achieve the optimal variable parameter for different fractional orders. Finally, the simulation results demonstrate that there are great differences on the optimal variable parameter for differential and integral operators with different fractional orders, which should be attracting more attentions in the design of digital fractional order controller.

The strong motion accelerograms recorded during the 1990 Eastern Sicily earthquake have been analyzed to investigate source and attenuation parameters. Peak ground motions (peak acceleration, velocity and displacement) overestimate the values predicted by the empirical scaling law proposed for other Italian earthquakes, suggesting that local site response and propagation path effects play an important role in interpreting the observed time histories. The local magnitude, computed from the strong motion accelerograms by synthesizing the Wood-Anderson response, is ML = 5.9, that is sensibly larger than the local magnitude estimated at regional distances from broad-band seismograms (ML = 5.4). The standard omega-square source spectral model seems to be inadequate to describe the observed spectra over the entire frequency band from 0.2 to 20 Hz. The seismic moment estimated from the strong motion accelerogram recorded at the closest rock site (Sortino) is Mo = 0.8 x 1024 dyne.cm, that is roughly 4.5 times lower than the value estimated at regional distances (Mo = 3.7 x 1024 dyne.cm) from broad-band seismograms. The corner frequency estimated from the accelera- tion spectra i.5 J; = 1.3 Hz, that is close to the inverse of the dUl.ation of displacement pulses at the two closest recording sites. This value of corner tì.equency and the two values of seismic moment yield a Brune stress drop larger than 500 bars. However, a corner frequency value off; = 0.6 Hz and the seismic moment resulting from regional data allows the acceleration spectra to be reproduced on the entire available frequency band yielding to a Brune stress drop of 210 bars. The ambiguity on the corner frequency value associated to this earthquake is due to the limited frequency bandwidth available on the strong motion recordil1gs. Assuming the seismic moment estimated at regional distances from broad-band data, the moment magnitude for this earthquake is 5.7. The higher local magnitude (5.9) compared with the moment magnitude (5.7) is due to the weak regional attenuation. Beside this, site amplifications due to surface geology have produced the highest peak ground motions among those observed at the strong motion sites.

Model reference adaptive control systems (MRACS) is the one of the useful systems to control the plant containing unknown variable parameters. However, to design MRACS, it has been needed to satisfy model matching condition. In this paper, to improve the response in the case unsatisfying model matching condition, we design an adaptive law containing fractional order integrator in adaptive law, and prove the system's Lyapnov stability.

International audience

In this research paper, a design for circuit of an operational amplifier (OP-AMP) is formulated utilizing model characteristics of FinFET using high-k gain in the context of 22 nm technological advancements. To create an OP-AMP based on FinFET technology, the standard design equations for MOSFET-based OP-AMP design are tuned to FinFET based OPAMP. The OP-AMP architecture is well-suited for implementation as a subordinate circuit in the ADC design since it supports lower voltage, elevated velocity, and diminished power dissipation. The geometries of the transistors are organised to accomplish an OP-AMP that exhibits superior fulfilment and energy efficiency. Using cadence tool schematic is captured. Results show that the developed OPAMP exhibits a UGB of 100 GHz based on simulation experiments and a slew rate below 10V/µS. The inverter circuit amounts to power dissipation of 800nW, thereby rendering it suitable for a wide range of low-power analog and digital circuits.

At a macroscopic level derivatives and integrals are the usual mathematical tools to model real time processes and to perform the basic control and signal processing actions. However, the analysis, design, synthesis and implementation of fractional order differentiator and integrator is a difficult task because of its irrational behaviour. Therefore, for mathematical evaluation of any fractional order system, conversion to its approximate integer order equivalent is essential. In this paper approximated integer order models of fractional differentiator and integrator are developed using the continued fraction expansion technique. A continued fraction is an expression obtained through an iterative process. For any iteration to terminate, a finite numerical value is assigned, which in this paper is equal to the number of frequency points within the desired frequency band. It includes both the lower and upper limit values. A set of coefficients are obtained by finding the gains of the fractional term at respective frequencies and thereby applying the recursive formula. The coefficients thus obtained are substituted in the expression of continued fraction which results in a polynomial function of finite order. The developed models can be directly applied for analysis and realization of fractional order systems. The models are developed for fractional terms 0.1 to 0.9 in steps of 0.1, and also for 0.25 and 0.75. A detailed discussion on the sensitivity analysis is presented, which includes the influence of variable parameters on the accuracy and length of the order. Simulations have been performed in MATLAB. A comparison with both, the ideal values and also with existing methods is performed and tabulated to validate the correctness of the developed models both in terms of accuracy and integer order of the model. It shows that the Matsuda method yield very good results both in terms of magnitude and phase. And, is most suitable for linear phase circuits. Also, the proposed models can be directly used for the realization of customized fractional order Proportional Integral (PI), Proportional-Derivative (PD) and PID controllers. To establish the correctness of CFE based technique for hardware realization, the integer order approximated model of one-tenth and seven-tenth differentiator is decomposed to obtain the circuit parameters resistor (R) and capacitor (C). Then its implementation in OrCAD Capture CIS is performed. It can be seen that the results of realization closely match the actual response.

A wideband circularly polarized (CP) stacked rectangular dielectric resonator antenna (RDRA) is proposed in this article. The 3 dB axial ratio (AR) and 10 dB impedance bandwidth overlap of more than 66% is obtained. For increased bandwidth, the antenna comprises two dielectric resonators separated by an air gap. The upper dielectric layer is rotated at relative to the lower layer to obtain orthogonal modes for CP Both layers have dielectric constant . The rotation aids excitation of orthogonal modes , and in RDRA. The higher‐order modes generate left‐hand circular polarization at frequencies 6.75, 7.8, and 10.7 GHz, respectively. The upper layer consists of three holes giving a 10 dB impedance bandwidth of 66.7% from 6.52 to 11.02 GHz. The CP gain of 8.7, 6.8, and 6.4 dBi for 6.75, 7.8, and 10.7 GHz, respectively, is measured. The conformal orthogonal feeds enable a 72 3 dB AR bandwidth across the entire frequency band. The radiation efficiency is observed above 89 in the entire band (6.5–11 GHz). This work demonstrates a 66.7 overlap of 10 dB impedance and 3 dB AR bandwidth along with high gain in a single design which is suitable for 5G applications in C‐band as well as other X‐band applications.

Automatic Initialization and Model Selection for Li-ion Battery Impedance Identification in the Frequency Domain