Search results for: Modified Chua's circuit.

Authors: S. J. Arif

Abstract:

In the presented technique, a simple method is given for accurate measurement and control of power frequency deviation. The sinusoidal signal for which the frequency deviation measurement is required is transformed to a low voltage level and passed through a zero crossing detector to convert it into a pulse train. Another stable square wave signal of 10 KHz is obtained using a crystal oscillator and decade dividing assemblies (DDA). These signals are combined digitally and then passed through decade counters to give a unique combination of pulses or levels, which are further encoded to make them equally suitable for both control applications and display units. The developed circuit using discrete components has a resolution of 0.5 Hz and completes measurement within 20 ms. The realized circuit is simulated and synthesized using Verilog HDL and subsequently implemented on FPGA. The results of measurement on FPGA are observed on a very high resolution logic analyzer. These results accurately match the simulation results as well as the results of same circuit implemented with discrete components. The proposed system is suitable for accurate measurement and control of power frequency deviation.

Keywords: Digital encoder for frequency measurement, frequency deviation measurement, measurement and control systems, power systems.

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Authors: Fei Long Wei, Hua Yang, Hai Tao Zhang, Zhou Ping Yin

Abstract:

In this study, an local invariant generalized Houghtransform (LI-GHT) method is proposed for integrated circuit (IC) visual positioning. The original generalized Hough transform (GHT) is robust to external noise; however, it is not suitable for visual positioning of IC chips due to the four-dimensionality (4D) of parameter space which leads to the substantial storage requirement and high computational complexity. The proposed LI-GHT method can reduce the dimensionality of parameter space to 2D thanks to the rotational invariance of local invariant geometric feature and it can estimate the accuracy position and rotation angle of IC chips in real-time under noise and blur influence. The experiment results show that the proposed LI-GHT can estimate position and rotation angle of IC chips with high accuracy and fast speed. The proposed LI-GHT algorithm was implemented in IC visual positioning system of radio frequency identification (RFID) packaging equipment.

Keywords: Integrated Circuit Visual Positioning, Generalized Hough Transform, Local invariant Generalized Hough Transform, ICpacking equipment.

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Authors: Julio Cesar Lopes de Oliveira, Carlos Henrique Gonc¸alves Treviso

Abstract:

The shortage of the automotive market in relation to options for sources of high power car audio systems, led to development of this work. Thus, we developed a source with stabilized voltage with 4320 W effective power. Designed to the voltage of 14.4 V and a choice of two currents: 30 A load option in battery banks and 300 A at full load. This source can also be considered as a source of general use dedicated commercial with a simple control circuit in analog form based on discrete components. The assembly of power circuit uses a methodology for higher power than the initially stipulated.

Keywords: DC-DC power converters, converters, power convertion, pulse width modulation converters.

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Authors: Mehdi Hosseinzadeh, Somayyeh Jafarali Jassbi, Keivan Navi

Abstract:

Residue Number System (RNS) is a modular representation and is proved to be an instrumental tool in many digital signal processing (DSP) applications which require high-speed computations. RNS is an integer and non weighted number system; it can support parallel, carry-free, high-speed and low power arithmetic. A very interesting correspondence exists between the concepts of Multiple Valued Logic (MVL) and Residue Number Arithmetic. If the number of levels used to represent MVL signals is chosen to be consistent with the moduli which create the finite rings in the RNS, MVL becomes a very natural representation for the RNS. There are two concerns related to the application of this Number System: reaching the most possible speed and the largest dynamic range. There is a conflict when one wants to resolve both these problem. That is augmenting the dynamic range results in reducing the speed in the same time. For achieving the most performance a method is considere named “One-Hot Residue Number System" in this implementation the propagation is only equal to one transistor delay. The problem with this method is the huge increase in the number of transistors they are increased in order m² . In real application this is practically impossible. In this paper combining the Multiple Valued Logic and One-Hot Residue Number System we represent a new method to resolve both of these two problems. In this paper we represent a novel design of an OHRNS-based adder circuit. This circuit is useable for Multiple Valued Logic moduli, in comparison to other RNS design; this circuit has considerably improved the number of transistors and power consumption.

Keywords: Computer Arithmetic, Residue Number System, Multiple Valued Logic, One-Hot, VLSI.

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Authors: Syed Javed Arif, Mohd Ayyub Khan, Saleem Anwar Khan

Abstract:

In this paper, a simple method is presented for measurement of power frequency deviations. A phase locked loop (PLL) is used to multiply the signal under test by a factor of 100. The number of pulses in this pulse train signal is counted over a stable known period, using decade driving assemblies (DDAs) and flip-flops. These signals are combined using logic gates and then passed through decade counters to give a unique combination of pulses or levels, which are further encoded. These pulses are equally suitable for both control applications and display units. The experimental circuit developed gives a resolution of 1 Hz within the measurement period of 20 ms. The proposed circuit is also simulated in Verilog Hardware Description Language (VHDL) and implemented using Field Programing Gate Arrays (FPGAs). A Mixed signal Oscilloscope (MSO) is used to observe the results of FPGA implementation. These results are compared with the results of the proposed circuit of discrete components. The proposed system is useful for frequency deviation measurement and control in power systems.

Keywords: Frequency measurement, digital control, phase locked loop, encoding, Verilog HDL.

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Authors: Eakkasak Susakunphaisan, Pichai Namprakai, Withaya Puangsombut

Abstract:

The objective of this paper was to designing a ventilation system to enhance the performance of roof solar collector (RSC) for reducing heat accumulation inside the house. The RSC has 1.8 m2 surface area made of CPAC monier roof tiles on the upper part and gypsum board on the lower part. The space between CPAC monier and gypsum board was fixed at 14 cm. Ventilation system of modified roof solar collector (modified RSC) consists of 9 tubes of 0.15m diameter and installed in the lower part of RSC. Experimental result showed that the temperature of the room, and attic temperature. The average temperature reduction of room of house used modified RSC is about 2oC. and the percentage of room temperature reduction varied between 0 to 10%. Therefore, modified RSC is an interesting option in the sense that it promotes solar energy and conserve energy.

Keywords: roof solar collector, heat accumulation

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Authors: Fatma Belghith, Hassen Loukil, Nouri Masmoudi

Abstract:

This paper presents the hardware design of a unified architecture to compute the 4x4, 8x8 and 16x16 efficient twodimensional (2-D) transform for the HEVC standard. This architecture is based on fast integer transform algorithms. It is designed only with adders and shifts in order to reduce the hardware cost significantly. The goal is to ensure the maximum circuit reuse during the computing while saving 40% for the number of operations. The architecture is developed using FIFOs to compute the second dimension. The proposed hardware was implemented in VHDL. The VHDL RTL code works at 240 MHZ in an Altera Stratix III FPGA. The number of cycles in this architecture varies from 33 in 4-point- 2D-DCT to 172 when the 16-point-2D-DCT is computed. Results show frequency improvements reaching 96% when compared to an architecture described as the direct transcription of the algorithm.

Keywords: HEVC, Modified Integer Transform, FPGA.

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Authors: Wang Zhulin, Min Fuhong, Peng Guangya, Wang Yaoda, Cao Yi

Abstract:

In this paper, a magnetron memristor model based on hyperbolic sine function is presented and the correctness proved by studying the trajectory of its voltage and current phase, and then a memristor chaotic system with the memristor model is presented. The phase trajectories and the bifurcation diagrams and Lyapunov exponent spectrum of the magnetron memristor system are plotted by numerical simulation, and the chaotic evolution with changing the parameters of the system is also given. The paper includes numerical simulations and mathematical model, which confirming that the system, has a wealth of dynamic behavior.

Keywords: Memristor, chaotic circuit, dynamical behavior, chaotic system.

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Authors: Neeraj K. Chasta

Abstract:

This paper presents an idea for analog current comparison which compares input signal and reference currents with high speed and accuracy. Proposed circuit utilizes amplification properties of common gate configuration, where voltage variations of input current are amplified and a compared output voltage is developed. Cascaded inverter stages are used to generate final CMOS compatible output voltage. Power consumption of circuit can be controlled by the applied gate bias voltage. The comparator is designed and studied at 180nm CMOS process technology for a supply voltage of 3V.

Keywords: Current Mode, Comparator, High Resolution, High Speed.

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Authors: A. Esmael, A. El Shrif

Abstract:

In this study the instability problem of a modified Taylor-Couette flow between two vertical coaxial cylinders of radius R1, R2 is considered. The modification is based on the wavy shape of the inner cylinder surface, where inner cylinders with different surface amplitude and wavelength are used. The study aims to discover the effect of the inner surface geometry on the instability phenomenon that undergoes Taylor-Couette flow. The study reveals that the transition processes depends strongly on the amplitude and wavelength of the inner cylinder surface and resulting in flow instabilities that are strongly different from that encountered in the case of the classical Taylor-Couette flow.

Keywords: Hydrodynamic Instability, Modified Taylor-Couette Flow, Turbulence, Taylor vortices.

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Authors: S. Jalaja, A. M. Vijaya Prakash

Abstract:

Recursive combination of an algorithm based on Karatsuba multiplication is exploited to design a generalized transpose and parallel Finite Impulse Response (FIR) Filter. Mid-range Karatsuba multiplication and Carry Save adder based on Karatsuba multiplication reduce time complexity for higher order multiplication implemented up to n-bit. As a result, we design modified N-tap Transpose and Parallel Symmetric FIR Filter Structure using Karatsuba algorithm. The mathematical formulation of the FFA Filter is derived. The proposed architecture involves significantly less area delay product (APD) then the existing block implementation. By adopting retiming technique, hardware cost is reduced further. The filter architecture is designed by using 90 nm technology library and is implemented by using cadence EDA Tool. The synthesized result shows better performance for different word length and block size. The design achieves switching activity reduction and low power consumption by applying with and without retiming for different combination of the circuit. The proposed structure achieves more than a half of the power reduction by adopting with and without retiming techniques compared to the earlier design structure. As a proof of the concept for block size 16 and filter length 64 for CKA method, it achieves a 51% as well as 70% less power by applying retiming technique, and for CSA method it achieves a 57% as well as 77% less power by applying retiming technique compared to the previously proposed design.

Keywords: Carry save adder Karatsuba multiplication, mid-range Karatsuba multiplication, modified FFA, transposed filter, retiming.

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Authors: Ujjal K Ghosh, Ling Teen

Abstract:

Pervaporation has the potential to be an alternative to the other traditional separation processes such as distillation, adsorption, reverse osmosis and extraction. This study investigates the separation of phenol from water using a polyurethane membrane by pervaporation by applying the modified Maxwell-Stephen model. The modified Maxwell-Stefan model takes into account the non-ideal multi-component solubility effect, nonideal diffusivity of all permeating components, concentration dependent density of the membrane and diffusion coupling to predict various fluxes. Four cases has been developed to investigate the process parameters effects on the flux and weight fraction of phenol in the permeate values namely feed concentration, membrane thickness, operating temperature and operating downstream pressure. The model could describe semi-quantitatively the performance of the pervaporation membrane for the given system as a very good agreement between the observed and theoretical fluxes was observed.

Keywords: Pervaporation, Phenol, Polyurethane, Modified Maxwell-Stefan equation, Solution Diffusion

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Authors: Lei Lei, Hongbo Zhang, Donald J. Bergstrom, Bing Zhang, K. Y. Song, W. J. Zhang

Abstract:

This paper presents a model for a modified T-junction device for microspheres generation. The numerical model is developed using a commercial software package: COMSOL Multiphysics. In order to test the accuracy of the numerical model, multiple variables, such as the flow rate of cross-flow, fluid properties, structure, and geometry of the microdevice are applied. The results from the model are compared with the experimental results in the diameter of the microsphere generated. The comparison shows a good agreement. Therefore the model is useful in further optimization of the device and feedback control of microsphere generation if any.

Keywords: CFD modeling, validation, microsphere generation, modified T-junction.

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Authors: Amit Kumar Gautam, Sudipta Majumdar

Abstract:

This paper presents parameter estimation of a single-phase rectifier using extended Kalman filter (EKF). The state space model has been obtained using Kirchhoff’s current law (KCL) and Kirchhoff’s voltage law (KVL). The capacitor voltage and diode current of the circuit have been estimated using EKF. Simulation results validate the better accuracy of the proposed method as compared to the least mean square method (LMS). Further, EKF has the advantage that it can be used for nonlinear systems.

Keywords: Extended Kalman filter, parameter estimation, single phase rectifier, state space modelling.

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Authors: M. Shariati, N. Tahouni, A. Khoshgard, M.H. Panjeshahi

Abstract:

Owing to extensive use of hydrogen in refining or petrochemical units, it is essential to manage hydrogen network in order to make the most efficient utilization of hydrogen. On the other hand, hydrogen is an important byproduct not properly used through petrochemical complexes and mostly sent to the fuel system. A few works have been reported in literature to improve hydrogen network for petrochemical complexes. In this study a comprehensive analysis is carried out on petrochemical units using a modified automated targeting technique which is applied to determine the minimum hydrogen consumption. Having applied the modified targeting method in two petrochemical cases, the results showed a significant reduction in required fresh hydrogen.

Keywords: Automated targeting, Hydrogen network, Petrochemical, Process integration.

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Authors: Ali M. Babalghaith, Hamad A. Alsoliman, Abdulrahman S. Al-Suhaibani

Abstract:

Flexible pavement made with neat asphalt binder is not enough to resist heavy traffic loads as well as harsh environmental condition found in Riyadh region. Therefore, there is a need to modify asphalt binder with polymers to satisfy such conditions. There are several types of polymers that are used to modify asphalt binder. The objective of this paper is to compare the rheological properties of six polymer modified asphalt binders (Lucolast7010, Anglomak2144, Paveflex140, SBS KTR401, EE-2 and Crumb rubber) obtained from asphalt manufacturer plants. The rheological properties of polymer modified asphalt binders were tested using conventional tests such as penetration, softening point and viscosity; and SHRP tests such as dynamic shear rheometer and bending beam rheometer. The results have indicated that the polymer modified asphalt binders have lower penetration and higher softening point than neat asphalt indicating an improvement in stiffness of asphalt binder, and as a result, more resistant to rutting. Moreover, the dynamic shear rheometer results have shown that all modifiers used in this study improved the binder properties and satisfied the Superpave specifications except SBS KTR401 which failed to satisfy the rutting parameter (G*/sinδ).

Keywords: Polymer modified asphalt, rheological properties, SBS, crumb rubber, EE-2.

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Authors: Chih Chin Yang, Chih Yu Lee, Jing Yi Wang, Mei Zhen Xue, Chia Yueh Wu

Abstract:

A well-defined frequency multiple dividing (FMD) circuit using a resonant model is presented in this research. The basic component of a frequency multiple divider as used in a resonant model is established by compositing a well-defined resonant effect of negative differential resistance (NDR) characteristics which possesses a wider operational region and high operational current at a bias voltage of about 1.15 V. The resonant model is then applied in the frequency dividing circuit with the above division ratio (R_D) of 200 at the signal input of middle frequency. The division ratio also exists at the input of a low frequency signal.

Keywords: Divider, frequency, resonant model.

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Authors: Cheng Zhang, James Marco, Walid Allafi, Truong Q. Dinh, W. D. Widanage

Abstract:

Equivalent circuit models (ECMs) are widely used in battery management systems in electric vehicles and other battery energy storage systems. The battery dynamics and the model parameters vary under different working conditions, such as different temperature and state of charge (SOC) levels, and therefore online parameter identification can improve the modelling accuracy. This paper presents a way of online ECM parameter identification using a continuous time (CT) estimation method. The CT estimation method has several advantages over discrete time (DT) estimation methods for ECM parameter identification due to the widely separated battery dynamic modes and fast sampling. The presented method can be used for online SOC estimation. Test data are collected using a lithium ion cell, and the experimental results show that the presented CT method achieves better modelling accuracy compared with the conventional DT recursive least square method. The effectiveness of the presented method for online SOC estimation is also verified on test data.

Keywords: Equivalent circuit model, continuous time domain estimation, linear integral filter method, parameter and SOC estimation, recursive least square.

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Authors: Mayank Shakya, Soundra Pandian. K. K

Abstract:

A linear feedback shift register (LFSR) is proposed which targets to reduce the power consumption from within. It reduces the power consumption during testing of a Circuit Under Test (CUT) at two stages. At first stage, Control Logic (CL) makes the clocks of the switching units of the register inactive for a time period when output from them is going to be same as previous one and thus reducing unnecessary switching of the flip-flops. And at second stage, the LFSR reorders the test vectors by interchanging the bit with its next and closest neighbor bit. It keeps fault coverage capacity of the vectors unchanged but reduces the Total Hamming Distance (THD) so that there is reduction in power while shifting operation.

Keywords: Linear Feedback Shift Register, Total Hamming Distance, Fault Coverage, Control Logic

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Authors: Mazhar B. Tayel, Amr H. Yassin

Abstract:

A proposed small-signal model parameters for a pseudomorphic high electron mobility transistor (PHEMT) is presented. Both extrinsic and intrinsic circuit elements of a smallsignal model are determined using genetic algorithm (GA) as a stochastic global search and optimization tool. The parameters extraction of the small-signal model is performed on 200-μm gate width AlGaAs/InGaAs PHEMT. The equivalent circuit elements for a proposed 18 elements model are determined directly from the measured S- parameters. The GA is used to extract the parameters of the proposed small-signal model from 0.5 up to 18 GHz.

Keywords: PHEMT, Genetic Algorithms, small signal modeling, optimization.

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Authors: Abhay Tawalare, Rajesh Lalwani

Abstract:

An attempt in this paper proposes a re-modification to the minimum moment approach of resource leveling which is a modified minimum moment approach to the traditional method by Harris. The method is based on critical path method. The new approach suggests the difference between the methods in the selection criteria of activity which needs to be shifted for leveling resource histogram. In traditional method, the improvement factor found first to select the activity for each possible day of shifting. In modified method maximum value of the product of Resources Rate and Free Float was found first and improvement factor is then calculated for that activity which needs to be shifted. In the proposed method the activity to be selected first for shifting is based on the largest value of resource rate. The process is repeated for all the remaining activities for possible shifting to get updated histogram. The proposed method significantly reduces the number of iterations and is easier for manual computations.

Keywords: Re-Modified, Resource Leveling, Resources Rate, Free Float, Resource Histogram

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Authors: Baha Vural Kök, Mehmet Yilmaz, Mustafa Akpolat, Cihat Sav

Abstract:

Various types of additives are used frequently in order to improve the rheological and mechanical properties of bituminous mixtures. Small devices instead of full scale machines are used for bitumen modification in the laboratory. These laboratory scale devices vary in terms of their properties such as mixing rate, mixing blade and the amount of binder. In this study, the effect of mixing rate and time during the bitumen modification processes on conventional and rheological properties of pure and crumb rubber modified binder were investigated. Penetration, softening point, rotational viscosity (RV) and dynamic shear rheometer (DSR) tests were applied to pure and CR modified bitumen. It was concluded that the penetration and softening point test did not show the efficiency of CR obtained by different mixing conditions. Besides, oxidation that occurred during the preparation processes plays a great part in the improvement effects of the modified binder.

Keywords: Bitumen, crumb rubber, modification, rheological properties.

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Authors: Binod Kumar Saha

Abstract:

The objective of the present paper is a numerical analysis of the flow forces acting on spool surfaces of a pressure regulated valve. The transient, compressible and turbulent flow structures inside the valve are simulated using ANSYS FLUENT coupled with a special UDF. Here, valve inlet pressure is varied in a stepwise manner. For every value of inlet pressure, transient analysis leads to a quasi-static flow through the valve. Spool forces are calculated based on different pressures at inlet. From this information of spool forces, pressure characteristic of the passive control circuit has been derived.

Keywords: Pressure Regulating Valve, Spool Opening, Spool Movement, Force Balance, CFD.

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Authors: Phang Chang, Phang Piau

Abstract:

Wavelet transform or wavelet analysis is a recently developed mathematical tool in applied mathematics. In numerical analysis, wavelets also serve as a Galerkin basis to solve partial differential equations. Haar transform or Haar wavelet transform has been used as a simplest and earliest example for orthonormal wavelet transform. Since its popularity in wavelet analysis, there are several definitions and various generalizations or algorithms for calculating Haar transform. Fast Haar transform, FHT, is one of the algorithms which can reduce the tedious calculation works in Haar transform. In this paper, we present a modified fast and exact algorithm for FHT, namely Modified Fast Haar Transform, MFHT. The algorithm or procedure proposed allows certain calculation in the process decomposition be ignored without affecting the results.

Keywords: Fast Haar Transform, Haar transform, Wavelet analysis.

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Authors: Maleika Heenaye- Mamode Khan , Naushad Mamode Khan, Raja K.Subramanian

Abstract:

Dorsal hand vein pattern is an emerging biometric which is attracting the attention of researchers, of late. Research is being carried out on existing techniques in the hope of improving them or finding more efficient ones. In this work, Principle Component Analysis (PCA) , which is a successful method, originally applied on face biometric is being modified using Cholesky decomposition and Lanczos algorithm to extract the dorsal hand vein features. This modified technique decreases the number of computation and hence decreases the processing time. The eigenveins were successfully computed and projected onto the vein space. The system was tested on a database of 200 images and using a threshold value of 0.9 to obtain the False Acceptance Rate (FAR) and False Rejection Rate (FRR). This modified algorithm is desirable when developing biometric security system since it significantly decreases the matching time.

Keywords: Dorsal hand vein pattern, PCA, Cholesky decomposition, Lanczos algorithm.

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Authors: Saad Mutashar, M. A. Hannan, S. A. Samad, A. Hussain

Abstract:

This paper deals with the modified wireless power transmission system for biomedical implanted devices. The system consists of efficient class-E power amplifier and inductive power links based on spiral circular transmitter and receiver coils. The model of the class-E power amplifier operated with 13.56 MHz is designed, discussed and analyzed in which it is achieved 87.2% of efficiency. The inductive coupling method is used to achieve link efficiency up to 73% depending on the electronic remote system resistance. The improved system powered with 3.3 DC supply and the voltage across the transmitter side is 40 V whereas, cross the receiver side is 12 V which is rectified to meet the implanted micro-system circuit requirements. The system designed and simulated by NI MULTISIM 11.02.

Keywords: Wireless Transmission, inductive coupling, implanted devices, class-E power amplifier, coils design.

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Authors: Rishikesh Pandey, Maneesha Gupta

Abstract:

A new low-voltage floating gate MOSFET (FGMOS) based squarer using square law characteristic of the FGMOS is proposed in this paper. The major advantages of the squarer are simplicity, rail-to-rail input dynamic range, low total harmonic distortion, and low power consumption. The proposed circuit is biased without body effect. The circuit is designed and simulated using SPICE in 0.25μm CMOS technology. The squarer is operated at the supply voltages of ±0.75V . The total harmonic distortion (THD) for the input signal 0.75Vpp at 25 KHz, and maximum power consumption were found to be less than 1% and 319μW respectively.

Keywords: Analog signal processing, floating gate MOSFETs, low-voltage, Spice, squarer.

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Authors: Muhammad Mujtaba Asad, Razali Bin Hassan, Fahad Sherwani

Abstract:

This paper explains about the voltage output for DC to DC boost converter between open loop, PID controller and fuzzy logic controller through Matlab Simulink. Simulink input voltage was set at 12V and the voltage reference was set at 24V. The analysis on the deviation of voltage resulted that the difference between reference voltage setting and the output voltage is always lower. Comparison between open loop, PID and FLC shows that, the open loop circuit having a bit higher on the deviation of voltage. The PID circuit boosts for FLC has a lesser deviation of voltage and proved that it is such a better performance on control the deviation of voltage during the boost mode.

Keywords: Boost Convertors, Power Electronics, PID, Fuzzy logic, Open loop.

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Authors: M. A. Koroma, Z. Chuangyi, A. F., Kamara, A. M. H. Conteh

Abstract:

In this work, we apply the Modified Laplace decomposition algorithm in finding a numerical solution of Blasius’ boundary layer equation for the flat plate in a uniform stream. The series solution is found by first applying the Laplace transform to the differential equation and then decomposing the nonlinear term by the use of Adomian polynomials. The resulting series, which is exactly the same as that obtained by Weyl 1942a, was expressed as a rational function by the use of diagonal padé approximant.

Keywords: Modified Laplace decomposition algorithm, Boundary layer equation, Padé approximant, Numerical solution.

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Authors: Ali Al-Ataby , Fawzi Al-Naima

Abstract:

Symbolic Circuit Analysis (SCA) is a technique used to generate the symbolic expression of a network. It has become a well-established technique in circuit analysis and design. The symbolic expression of networks offers excellent way to perform frequency response analysis, sensitivity computation, stability measurements, performance optimization, and fault diagnosis. Many approaches have been proposed in the area of SCA offering different features and capabilities. Numerical Interpolation methods are very common in this context, especially by using the Fast Fourier Transform (FFT). The aim of this paper is to present a method for SCA that depends on the use of Wavelet Transform (WT) as a mathematical tool to generate the symbolic expression for large circuits with minimizing the analysis time by reducing the number of computations.

Keywords: Numerical Interpolation, Sparse Matrices, SymbolicAnalysis, Wavelet Transform.

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