Search results for: multiplicative phase noise

Authors: Zakir Husain

Abstract:

This paper presents modeling and analysis of 12-phase distribution static compensator (DSTATCOM), which is capable of balancing the source currents in spite of unbalanced loading and phase outages. In addition to balance the supply current, the power factor can be set to a desired value. The theory of instantaneous symmetrical components is used to generate the twelve-phase reference currents. These reference currents are then tracked using current controlled voltage source inverter, operated in a hysteresis band control scheme. An ideal compensator in place of physical realization of the compensator is used. The performance of the proposed DTATCOM is validated through MATLAB simulation and detailed simulation results are given.

Keywords: DSTATCOM, Modeling, Load balancing, Multiphase, Power factor correction.

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Authors: Ankit Mitra

Abstract:

Speed, power consumption and area, are some of the most important factors of concern in modern day memory design. As we move towards Deep Sub-Micron Technologies, the problems of leakage current, noise and cell stability due to physical parameter variation becomes more pronounced. In this paper we have designed an 8T Read Decoupled Dual Port SRAM Cell with Dual Threshold Voltage and characterized it in terms of read and write delay, read and write noise margins, Data Retention Voltage and Leakage Current. Read Decoupling improves the Read Noise Margin and static power dissipation is reduced by using Dual-V_t transistors. The results obtained are compared with existing 6T, 8T, 9T SRAM Cells, which shows the superiority of the proposed design. The Cell is designed and simulated in TSPICE using 90nm CMOS process.

Keywords: CMOS, Dual-Port, Data Retention Voltage, 8T SRAM, Leakage Current, Noise Margin, Loop-cutting, Single-ended.

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Authors: A. Jawahar

Abstract:

In this paper, the dependence of soliton pulses with respect to phase in a 10Gbps, single channel, dispersion uncompensated telecommunication system was studied. The characteristic feature of periodic soliton interaction was noted at the Interaction point (I=6202.5Km) in one collision length of L=12405.1 Km. The interaction point is located for 10Gbps system with an initial relative spacing (qo) of soliton as 5.28 using Perturbation theory. It is shown that, when two in-phase solitons are launched, they interact at the point I=6202.5 Km, but the interaction could be restricted with introduction of different phase initially. When the phase of the input solitons increases, the deviation of soliton pulses at the ‘I’ also increases. We have successfully demonstrated this effect in a telecommunication set-up in terms of Quality factor (Q), where the Q=0 for in-phase soliton. The Q was noted to be 125.9, 38.63, 47.53, 59.60, 161.37, and 78.04 for different phases such as 10o, 20o, 30o, 45o, 60o and 90o degrees respectively at Interaction point (I).

Keywords: Soliton interaction, Initial relative spacing, phase, Perturbation theory and telecommunication system.

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Authors: Rasmus Engholm, Eva B. Vedel Jensen, Henrik Karstoft

Abstract:

In this paper we present a noise reduction filter for video processing. It is based on the recently proposed two dimensional steering kernel, extended to three dimensions and further augmented to suit the spatial-temporal domain of video processing. Two alternative filters are proposed - the time symmetric kernel and the time asymmetric kernel. The first reduces the noise on single sequences, but to handle the problems at scene shift the asymmetric kernel is introduced. The performance of both are tested on simulated data and on a real video sequence together with the existing steering kernel. The proposed kernels improves the Rooted Mean Squared Error (RMSE) compared to the original steering kernel method on video material.

Keywords: Adaptive image filtering, noise reduction, kernel methods, video processing.

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Authors: Seung-Yeon Kim

Abstract:

The square-lattice Ising model is the simplest system showing phase transitions (the transition between the paramagnetic phase and the ferromagnetic phase and the transition between the paramagnetic phase and the antiferromagnetic phase) and critical phenomena at finite temperatures. The exact solution of the squarelattice Ising model with free boundary conditions is not known for systems of arbitrary size. For the first time, the exact solution of the Ising model on the square lattice with free boundary conditions is obtained after classifying all ) spin configurations with the microcanonical transfer matrix. Also, the phase transitions and critical phenomena of the square-lattice Ising model are discussed using the exact solution on the square lattice with free boundary conditions.

Keywords: Phase transition, Ising magnet, Square lattice, Freeboundary conditions, Exact solution.

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Authors: P. Panichnumsin, B. K. Ahring, A. Nopharatana, P. Chaipresert

Abstract:

In this study, we illustrated the performance and microbial community of single- and two-phase systems anaerobically co-digesting cassava pulp and pig manure. The results showed that the volatile solid reduction and biogas productivity of two-phase CSTR were 66 ± 4% and 2000 ± 210 ml l-1 d-1, while those of singlephase CSTR were 59 ± 1% and 1670 ± 60 ml l-1 d-1, respectively. Codigestion in two-phase CSTR gave higher 12% solid degradation and 25% methane production than single-phase CSTR. Phylogenetic analysis of 16S rDNA clone library revealed that the Bacteroidetes were the most abundant group, followed by the Clostridia in singlephase CSTR. In hydrolysis/acidification reactor of two-phase system, the bacteria within the phylum Firmicutes, especially Clostridium, Eubacteriaceae and Lactobacillus were the dominant phylogenetic groups. Among the Archaea, Methanosaeta sp. was the exclusive predominant in both digesters while the relative abundance of Methanosaeta sp. and Methanospirillum hungatei differed between the two systems.

Keywords: Anaerobic co-digestion, Cassava pulp, Microbialdiversity, Pig manure.

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Authors: Naima Ikken, Abdelhadi Bouknadel, Nour-eddine Tariba Ahmed Haddou, Hafsa El Omari

Abstract:

The operation of grid-connected inverters necessity a single-phase phase locked loop (PLL) is proposed in this article to accurately and quickly estimate and detect the grid phase angle. This article presents the improvement of a method of phase-locked loop. The novelty is to generate a method (PLL) of synchronizing the grid with a Notch filter based on adaptive fuzzy logic for inverter systems connected to the grid. The performance of the proposed method was tested under normal and abnormal operating conditions (amplitude, frequency and phase shift variations). In addition, simulation results with ISPM software are developed to verify the effectiveness of the proposed method strategy. Finally, the experimental test will be used to extract the result and discuss the validity of the proposed algorithm.

Keywords: Phase locked loop, PLL, notch filter, fuzzy logic control.

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Authors: Yiping Wang, Zhengqi Gu, Weiping Li, Xiaohui Lin

Abstract:

The aerodynamic noise radiation from a side view mirror (SVM) in the high-speed airflow is calculated by the combination of unsteady incompressible fluid flow analysis and acoustic analysis. The transient flow past the generic SVM is simulated with variable turbulence model, namely DES Detached Eddy Simulation and LES (Large Eddy Simulation). Detailed velocity vectors and contour plots of the time-varying velocity and pressure fields are presented along cut planes in the flow-field. Mean and transient pressure are also monitored at several points in the flow field and compared to corresponding experimentally data published in literature. The acoustic predictions made using the Ffowcs-Williams-Hawkins acoustic analogy (FW-H) and the boundary element (BEM).

Keywords: Aerodynamic noise, BEM, DES, FW-H acousticanalogy, LES

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Authors: Dag A.H. Samuelsen, Olaf H. Graven

Abstract:

Introducing Electromagnetic Interference and Electromagnetic Compatibility, or “The Art of Black Magic", for engineering students might be a terrifying experience both for students and tutors. Removing the obstacle of large, expensive facilities like a fully fitted EMC laboratory and hours of complex theory, this paper demonstrates a design of a laboratory setup for student exercises, giving students experience in the basics of EMC/EMI problems that may challenge the functionality and stability of embedded system designs. This is done using a simple laboratory installation and basic measurement equipment such as a medium cost digital storage oscilloscope, at the cost of not knowing the exact magnitude of the noise components, but rather if the noise is significant or not, as well as the source of the noise. A group of students have performed a trial exercise with good results and feedback.

Keywords: EMC, EMI, engineering project, student laboratory.

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Authors: M. H. Al-Mansoori, W. S. Al-Ghaithi, F. N. Hasoon

Abstract:

In this paper, we experimentally investigate the performance of an efficient high gain triple-pass L-band Erbium-Doped Fiber (EDF) amplifier structure with a single pump source. The amplifier gain and noise figure variation with EDF pump power, input signal power and wavelengths have been investigated. The generated backward Amplified Spontaneous Emission (ASE) noise of the first amplifier stage is suppressed by using a tunable band-pass filter. The amplifier achieves a signal gain of 55 dB with low noise figure of 3.8 dB at -50 dBm input signal power. The amplifier gain shows significant improvement of 12.8 dB compared to amplifier structure without ASE suppression.

Keywords: Optical amplifiers, EDFA, L-band, optical networks.

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Authors: H. A. Majid, N. Razali, M. S. Sulaiman, A. K. A'ain

Abstract:

A new interface circuit for capacitive sensor is presented. This paper presents the design and simulation of soil moisture capacitive sensor interface circuit based on phase differential technique. The circuit has been designed and fabricated using MIMOS- 0.35"m CMOS technology. Simulation and test results show linear characteristic from 36 – 52 degree phase difference, representing 0 – 100% in soil moisture level. Test result shows the circuit has sensitivity of 0.79mV/0.10 phase difference, translating into resolution of 10% soil moisture level.

Keywords: Capacitive sensor, interface, phase differential.

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Authors: Mustafa Resa Becan, Ahmet Kuzucu

Abstract:

A fuzzy predictive pursuit guidance is proposed as an alternative to the conventional methods. The purpose of this scheme is to obtain a stable and fast guidance. The noise effects must be reduced in homing missile guidance to get an accurate control. An aerodynamic missile model is simulated first and a fuzzy predictive pursuit control algorithm is applied to reduce the noise effects. The performance of this algorithm is compared with the performance of the classical proportional derivative control. Stability analysis of the proposed guidance method is performed and compared with the stability properties of other guidance methods. Simulation results show that the proposed method provides the satisfying performance.

Keywords: Fuzzy, noise effect, predictive, pursuit.

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Authors: Ruchika, Munish Vashisht, S. Qamar

Abstract:

Detection of small ship is crucial task in many automatic surveillance systems which are employed for security of maritime boundaries of a country. To address this problem, image de-noising is technique to identify the target ship in between many other ships in the sea. Image de-noising technique needs to extract the ship’s image from sea background for the analysis as the ship’s image may submerge in the background and flooding waves. In this paper, a noise filter is presented that is based on fuzzy linguistic ‘most’ quantifier. Ordered weighted averaging (OWA) function is used to remove salt-pepper noise of ship’s image. Results obtained are in line with the results available by other well-known median filters and OWA based approach shows better performance.

Keywords: Linguistic quantifier, impulse noise, OWA filter, median filter.

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Authors: Mohamed Hafid, Marcel Lacroix

Abstract:

This study presents an inverse analysis for predicting the thermal conductivities and the heat flux of a high-temperature metallurgical reactor simultaneously. Once these thermal parameters are predicted, the time-varying thickness of the protective phase-change bank that covers the inside surface of the brick walls of a metallurgical reactor can be calculated. The enthalpy method is used to solve the melting/solidification process of the protective bank. The inverse model rests on the Levenberg-Marquardt Method (LMM) combined with the Broyden method (BM). A statistical analysis for the thermal parameter estimation is carried out. The effect of the position of the temperature sensors, total number of measurements and measurement noise on the accuracy of inverse predictions is investigated. Recommendations are made concerning the location of temperature sensors.

Keywords: Inverse heat transfer, phase change, metallurgical reactor, Levenberg–Marquardt method, Broyden method, bank thickness.

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Authors: Hyunwon Moon

Abstract:

It is necessary to realize new biomedical wireless communication systems which send the signals collected from various bio sensors located at human body in order to monitor our health. Also, it should seamlessly connect to the existing wireless communication systems. A 5.8 GHz ISM band low power RF front-end receiver for a biomedical wireless communication system is implemented using a 0.5 µm SiGe BiCMOS process. To achieve low power RF front-end, the current optimization technique for selecting device size is utilized. The implemented low noise amplifier (LNA) shows a power gain of 9.8 dB, a noise figure (NF) of below 1.75 dB, and an IIP3 of higher than 7.5 dBm while current consumption is only 6 mA at supply voltage of 2.5 V. Also, the performance of a down-conversion mixer is measured as a conversion gain of 11 dB and SSB NF of 10 dB.

Keywords: Biomedical, low noise amplifier, mixer, receiver, RF front-end, SiGe.

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Authors: A. Soltani, M. Karimi Demneh

Abstract:

In this paper, modeling of an acoustic enclosed vehicle cabin has been carried out by using boundary element method. Also, the second purpose of this study is analyzing of linear wave equation in an acoustic field. The resultants of this modeling consist of natural frequencies that have been compared with resultants derived from finite element method. By using numerical method (boundary element method) and after solution of wave equation inside an acoustic enclosed cabin, this method has been progressed to simulate noise inside a simple vehicle cabin.

Keywords: Boundary element method, natural frequency, noise, vehicle cabin.

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Authors: Mehrdad Nouri Khajavi, Sajjad Ahoui Ghazvin, Ghader Rezazadeh, Mohammad Fathalilou

Abstract:

In this paper static and dynamic response of a varactor of a micro-phase shifter to DC, step DC and AC voltages have been studied. By presenting a mathematical modeling Galerkin-based step by step linearization method (SSLM) and Galerkin-based reduced order model have been used to solve the governing static and dynamic equations, respectively. The calculated static and dynamic pull-in voltages have been validated by previous experimental and theoretical results and a good agreement has been achieved. Then the frequency response and phase diagram of the system has been studied. It has been shown that applying the DC voltage shifts down the phase diagram and frequency response. Also increasing the damping ratio shifts up the phase diagram.

Keywords: MEMS, Phase Shifter, Pull-in Voltage, PhaseDiagram

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Authors: B. Rezaei, N. Amiri, N. Azizi

Abstract:

Using calculated phase- shift values, for pp, nn, and np elastic scattering in the energy range 1MeV to 350MeV, the charge independence breaking of nucleon-nucleon interaction is investigated. We have used Darboux transformation to calculate phase-shift for the first three values of

Keywords: Phase-shift, charge independence breaking, Darboux transformation.

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Authors: Sun-Ki Hong, Ki-Seok Kim, Yong-Ho Cho

Abstract:

Lots of motors have been being used in industry. Therefore many researchers have studied about the failure diagnosis of motors. In this paper, the effect of measuring environment for diagnosis of gear fault connected to a motor shaft is studied. The fault diagnosis is executed through the comparison of normal gear and abnormal gear. The measured FFT data are compared with the normal data and analyzed for q-axis current, noise and vibration. For bad and good environment, the diagnosis results are compared. From these, it is shown that the bad measuring environment may not be able to detect exactly the motor gear fault. Therefore it is emphasized that the measuring environment should be carefully prepared.

Keywords: Motor fault, Diagnosis, FFT, Vibration, Noise, q-axis current, measuring environment.

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Authors: Irtaza M. Syed, Kaamran Raahemifar

Abstract:

This paper presents a model predictive control (MPC) of a utility interactive (UI) single phase inverter (SPI) for a photovoltaic (PV) system at residential/distribution level. The proposed model uses single-phase phase locked loop (PLL) to synchronize SPI with the grid and performs MPC control in a dq reference frame. SPI model consists of boost converter (BC), maximum power point tracking (MPPT) control, and a full bridge (FB) voltage source inverter (VSI). No PI regulators to tune and carrier and modulating waves are required to produce switching sequence. Instead, the operational model of VSI is used to synthesize sinusoidal current and track the reference. Model is validated using a three kW PV system at the input of UI-SPI in Matlab/Simulink. Implementation and results demonstrate simplicity and accuracy, as well as reliability of the model.

Keywords: Matlab/Simulink, Model Predictive Control, Phase Locked Loop, Single Phase Inverter, Voltage Source Inverter.

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Authors: S. Rozhkova, O. Rozhkova, A. Harlova, V. Lasukov

Abstract:

For optimal unbiased filter as mean-square and in the case of functioning anomalous noises in the observation memory channel, we have proved insensitivity of filter to inaccurate knowledge of the anomalous noise intensity matrix and its equivalence to truncated filter plotted only by non anomalous components of an observation vector.

Keywords: Mathematical expectation, filtration, anomalous noise, memory.

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Authors: M. R. Dolatian, A. Jalilian

Abstract:

The behavior of three phase five leg transformer under voltage sag is studied in this paper. This paper proposes a simple, practical model of a three phase-five leg, saturated transformer with accurate performance. Transformer saturation is produced when the voltage sag is recovered and it causes inrush current in transformer. Effects of voltage sag depth, duration and initial point on wave have been analyzed in this paper. Initial point on wave can produce maximum inrush current in five leg transformers while comparing with three leg transformers. The magnetic circuit symmetry of five leg transformer produces the more symmetrical shape of inrush current curves versus initial point on wave and sag duration than three leg transformer. The simulations show that current peak has a periodical dependence on sag duration and linear dependence on sag depth. Inrush current that is produced in three phase five leg transformer is higher than three phase three leg transformer.

Keywords: Inrush current, three phase five leg transformer, saturation, voltage sag.

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Authors: T. K. Mondal, N C Shivaprakash

Abstract:

A piston cylinder based high pressure differential thermal analyzer system is developed to investigate phase transformations, melting, glass transitions, crystallization behavior of inorganic materials, glassy systems etc., at ambient to 4 GPa and at room temperature to 1073 K. The pressure is calibrated by the phase transition of bismuth and ytterbium and temperature is calibrated by using thermocouple data chart. The system developed is calibrated using benzoic acid, ammonium nitrate and it has a pressure and temperature control of ± 8.9 x 10 -4 GPa , ± 2 K respectively. The phase transition of Asx Te100-x chalcogenides, ferrous oxide and strontium boride are studied using the indigenously developed system.

Keywords: double stage crystallization, Phase transition, Quasi hydrostatic, Rigidity percolation

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Authors: Z. Nemec, R. Matousek

Abstract:

The paper describes the evaluation of quality of control for cases of controlled non-minimal phase plants. Control circuits containing non-minimal phase plants have different properties, they manifest reversed reaction at the beginning of unit step response. For these types of plants are developed special criterion of quality of control, which considers the difference and can be helpful for synthesis of optimal controller tuning. All results are clearly presented using Matlab/Simulink models.

Keywords: control design, non-minimal phase system, optimalcriteria, power plant, heating plant, water turbine, Matlab, Simulink.

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Authors: Ahmed Kamil Hasan Al-Ali, Bouchra Senadji, Ganesh Naik

Abstract:

We propose a system to real environmental noise and channel mismatch for forensic speaker verification systems. This method is based on suppressing various types of real environmental noise by using independent component analysis (ICA) algorithm. The enhanced speech signal is applied to mel frequency cepstral coefficients (MFCC) or MFCC feature warping to extract the essential characteristics of the speech signal. Channel effects are reduced using an intermediate vector (i-vector) and probabilistic linear discriminant analysis (PLDA) approach for classification. The proposed algorithm is evaluated by using an Australian forensic voice comparison database, combined with car, street and home noises from QUT-NOISE at a signal to noise ratio (SNR) ranging from -10 dB to 10 dB. Experimental results indicate that the MFCC feature warping-ICA achieves a reduction in equal error rate about (48.22%, 44.66%, and 50.07%) over using MFCC feature warping when the test speech signals are corrupted with random sessions of street, car, and home noises at -10 dB SNR.

Keywords: Noisy forensic speaker verification, ICA algorithm, MFCC, MFCC feature warping.

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Authors: G. Bal, D. Uygun

Abstract:

This paper describes the design and modeling procedure of a novel 5-phase segment type switched reluctance motor (ST-SRM) under simultaneous two-phase (bipolar) excitation of windings. The rotor cores of ST-SRM are embedded in an aluminum block as well as to improve the performance characteristics. The magnetic circuit of the produced ST-SRM is constructed so that the magnetic flux paths are short and exclusive to each phase, thereby minimizing the commutation switching and eddy current losses in the laminations. The design and simulation principles presented apply primarily to conventional SRM and ST-SRM. It is proved that the novel 5-phase switched reluctance motor under two-phase excitation is superior among the criteria used in comparison. The purposed model is particularly well suited for high torque and weight constrained applications such as automobiles, aerospace and military applications.

Keywords: Segmental Rotor Pairs, Two-phase Excitation, Commutation Switching, Aluminum Block.

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Authors: A.O. Boudraa, J.C. Cexus, Z. Saidi

Abstract:

This paper introduces a new signal denoising based on the Empirical mode decomposition (EMD) framework. The method is a fully data driven approach. Noisy signal is decomposed adaptively into oscillatory components called Intrinsic mode functions (IMFs) by means of a process called sifting. The EMD denoising involves filtering or thresholding each IMF and reconstructs the estimated signal using the processed IMFs. The EMD can be combined with a filtering approach or with nonlinear transformation. In this work the Savitzky-Golay filter and shoftthresholding are investigated. For thresholding, IMF samples are shrinked or scaled below a threshold value. The standard deviation of the noise is estimated for every IMF. The threshold is derived for the Gaussian white noise. The method is tested on simulated and real data and compared with averaging, median and wavelet approaches.

Keywords: Empirical mode decomposition, Signal denoisingnonstationary process.

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Authors: Kamaldeep Joshi, Rajkumar Yadav, Sachin Allwadhi

Abstract:

Image steganography is the best aspect of information hiding. In this, the information is hidden within an image and the image travels openly on the Internet. The Least Significant Bit (LSB) is one of the most popular methods of image steganography. In this method, the information bit is hidden at the LSB of the image pixel. In one bit LSB steganography method, the total numbers of the pixels and the total number of message bits are equal to each other. In this paper, the LSB method of image steganography is used for watermarking. The watermarking is an application of the steganography. The watermark contains 80*88 pixels and each pixel requirs 8 bits for its binary equivalent form so, the total number of bits required to hide the watermark are 80*88*8(56320). The experiment was performed on standard 256*256 and 512*512 size images. After the watermark insertion, histogram analysis was performed. A noise factor (salt and pepper) of 0.02 was added to the stego image in order to evaluate the robustness of the method. The watermark was successfully retrieved after insertion of noise. An experiment was performed in order to know the imperceptibility of stego and the retrieved watermark. It is clear that the LSB watermarking scheme is robust to the salt and pepper noise.

Keywords: LSB, watermarking, salt and pepper, PSNR.

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Authors: A. Leelasantitham, B. Srisuchinwong

Abstract:

A high-frequency low-power sinusoidal quadrature oscillator is presented through the use of two 2nd-order low-pass current-mirror (CM)-based filters, a 1st-order CM low-pass filter and a CM bilinear transfer function. The technique is relatively simple based on (i) inherent time constants of current mirrors, i.e. the internal capacitances and the transconductance of a diode-connected NMOS, (ii) a simple negative resistance RN formed by a resistor load RL of a current mirror. Neither external capacitances nor inductances are required. As a particular example, a 1.9-GHz, 0.45-mW, 2-V CMOS low-pass-filter-based all-current-mirror sinusoidal quadrature oscillator is demonstrated. The oscillation frequency (f0) is 1.9 GHz and is current-tunable over a range of 370 MHz or 21.6 %. The power consumption is at approximately 0.45 mW. The amplitude matching and the quadrature phase matching are better than 0.05 dB and 0.15°, respectively. Total harmonic distortions (THD) are less than 0.3 %. At 2 MHz offset from the 1.9 GHz, the carrier to noise ratio (CNR) is 90.01 dBc/Hz whilst the figure of merit called a normalized carrier-to-noise ratio (CNRnorm) is 153.03 dBc/Hz. The ratio of the oscillation frequency (f0) to the unity-gain frequency (fT) of a transistor is 0.25. Comparisons to other approaches are also included.

Keywords: Sinusoidal quadrature oscillator, low-pass-filterbased, current-mirror bilinear transfer function, all-current-mirror, negative resistance, low power, high frequency, low distortion.

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Authors: M. Tarawneh

Abstract:

Two-phase frictional pressure drop data were obtained for condensation of carbon dioxide in single horizontal micro tube of inner diameter ranged from 0.6 mm up to 1.6 mm over mass flow rates from 2.5*10-5 to 17*10-5 kg/s and vapor qualities from 0.0 to 1.0. The inlet condensing pressure is changed from 33.5 to 45 bars. The saturation temperature ranged from -1.5 oC up to 10 oC. These data have then been compared against three (two-phase) frictional pressure drop prediction methods. The first method is by Muller-Steinhagen and Heck (Muller-Steinhagen H, Heck K. A simple friction pressure drop correlation for two-phase flow in pipes. Chem. Eng. Process 1986;20:297–308) and that by Gronnerud R. Investigation of liquid hold-up, flow-resistance and heat transfer in circulation type evaporators, part IV: two-phase flow resistance in boiling refrigerants, Annexe 1972. Then the method used by FriedelL. Improved friction pressures drop in horizontal and vertical two-phase pipe flow. European Two-Phase Flow Group Meeting, Paper E2; 1979 June, Ispra, Italy. The methods are used by M.B Ould Didi et al (2001) “Prediction of two-phase pressure gradients of refrigerant in horizontal tubes". Int.J.of Refrigeration 25(2002) 935- 947. The best available method for annular flow was that of Muller- Steinhagen and Heck. It was observed that the peak in the two-phase frictional pressure gradient is at high vapor qualities.

Keywords: Two-phase flow, frictional pressure drop, horizontalmicro tube, carbon dioxide, condensers.

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