Digital filtering of oscillations intrinsic to transmission line modeling based on lumped parameters

A correction procedure based on digital signal processing theory is proposed to smooth the numeric oscillations in electromagnetic transient simulation results from transmission line modeling based on an equivalent representation by lumped parameters. The proposed improvement to this well-known line representation is carried out with an Finite Impulse Response (FIR) digital filter used to exclude the high-frequency components associated with the spurious numeric oscillations. To prove the efficacy of this correction method, a well-established frequency-dependent line representation using state equations is modeled with an FIR filter included in the model. The results obtained from the state-space model with and without the FIR filtering are compared with the results simulated by a line model based on distributed parameters and inverse transforms. Finally, the line model integrated with the FIR filtering is also tested and validated based on simulations that include nonlinear and time-variable elements. © 2012 Elsevier Ltd. All rights reserved.

Reducing the spurious oscillations in the lumped parameters model using low-pass filter

Voltages and currents in the transmission line are described by differential equations that are difficult to solve due soil and skin effect that has to be considered for accurate results, but it increases their complexity. Therefore there are some models to study the voltages and currents along in transmission line. The distributed parameters model that transforms the equations in time domain to the frequency domain and once the solutions are obtained, they are converted to time domain using the Inverse Laplace Transform using numerical methods. Another model is named lumped parameters model and it considers the transmission line represented by a pi-circuit cascade and the currents and voltages are described by state equations. In the simulations using the lumped parameters model, it can be observed the presence of spurious oscillations that are independent of the quantity of pi-circuits used and do not represent the real value of the transient. In this work will be projected a passive low-pass filter directly inserted in the lumped parameters model to reduce the spurious oscillations in the simulations, making this model more accurate and reliable for studying the electromagnetic transients in power systems.

Modelling the mechanical response of the reed-mouthpiece-lip system of a clarinet. Part II: A lumped model approximation

A non-linear lumped model of the reed-mouthpiece-lip system of a clarinet is formulated, in which the lumped parameters are derived from numerical experiments with a finite-difference simulation based on a distributed reed model. The effective stiffness per unit area is formulated as a function of the pressure signal driving the reed, in order to simulate the effects of the reed bending against the lay, and mass and damping terms are added as a first approximation to the dynamic behaviour of the reed. A discrete-time formulation is presented, and its response is compared to that of the distributed model. In addition, the lumped model is applied in the simulation of clarinet tones, enabling the analysis of the effects of using a pressure-dependent stiffness per unit area on sustained oscillations. The analysed effects and features are in qualitative agreement with players' experiences and experimental results obtained in prior studies.

Proposal of a Transmission Line Model Based on Lumped Elements: An Analytic Solution

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Sectional analysis of the pollutant wash-off process based on runoff hydrograph

The validity of using rainfall characteristics as lumped parameters for investigating the pollutant wash-off process such as first flush occurrence is questionable. This research study introduces an innovative concept of using sector parameters to investigate the relationship between the pollutant wash-off process and different sectors of the runoff hydrograph and rainfall hyetograph. The research outcomes indicated that rainfall depth and rainfall intensity are two key rainfall characteristics which influence the wash-off process compared to the antecedent dry period. Additionally, the rainfall pattern also plays a critical role in the wash-off process and is independent of the catchment characteristics. The knowledge created through this research study provides the ability to select appropriate rainfall events for stormwater quality treatment design based on the required treatment outcomes such as the need to target different sectors of the runoff hydrograph or pollutant species. The study outcomes can also contribute to enhancing stormwater quality modelling and prediction in view of the fact that conventional approaches to stormwater quality estimation is primarily based on rainfall intensity rather than considering other rainfall parameters or solely based on stochastic approaches irrespective of the characteristics of the rainfall event.

Equivalent Circuit Analysis of Serpentine Folded-waveguide Slow-wave Structures for Millimeter-wave Traveling-wave Tubes

A simple equivalent circuit model for the analysis of dispersion and interaction impedance characteristics of serpentine folded-waveguide slow-wave structure was developed by considering the straight and curved portions of structure supporting the dominant TE10-mode of the rectangular waveguide. Expressions for the lumped capacitance and inductance per period of the slow-wave structure were derived in terms of the physical dimensions of the structure, incorporating the effects of the beam-hole in the lumped parameters. The lumped parameters were subsequently interpreted for obtaining the dispersion and interaction impedance characteristics of the structure. The analysis was simple yet accurate in predicting the dispersion and interaction impedance behaviour at millimeter-wave frequencies. The analysis was benchmarked against measurement as well as with 3D electromagnetic modeling using MAFIA for two typical slow-wave structures (one at the Ka-band and the other at the W-band) and close agreement observed.

Analysis of Rectangular Folded-Waveguide Millimeter-Wave Slow-wave Structures using Conformal Transformations

An analysis of rectangular folded-waveguide slow-wave structure was developed using conformal mapping technique through Schwarz's polygon transformation and closed form expressions for the lumped capacitance and inductance per period of the slow-wave structure were derived in terms of the physical dimensions of the structure, incorporating the effects of the beam hole in the lumped parameters. The lumped parameters were subsequently interpreted for obtaining the dispersion and interaction impedance characteristics of the structure. The analysis was benchmarked for two typical millimeter-wave structures, one operating in Ka-band and the other operating in Q-band, against measurement and 3D electromagnetic modeling using MAFIA.

Analysis of serpentine folded-waveguide slow-wave structure using elliptical conformal transformation

Elliptical conformal transformation was used to derive closed form expressions for the equivalent circuit series inductance and shunt capacitance per period of a serpentine folded-waveguide slow-wave structure including the effects of the beam-hole. The lumped parameters were subsequently interpreted for the dispersion and interaction impedance characteristics of the structure. The analysis was benchmarked for two typical millimeter-wave structures operating in Ka- and W-bands, against measurement, 3D electromagnetic modeling using CST Microwave Studio, parametric analysis and equivalent circuit analysis. (C) 2010 Elsevier GmbH. All rights reserved.

The Effect of Evacuated Backside Cavity on the Dynamic Characteristics of a Capacitive Micromachined Ultrasonic Transducer

In this paper, we investigate the effect of vacuum sealing the backside cavity of a Capacitive Micromachined Ultrasonic Transducer (CMUT). The presence or absence of air inside the cavity has a marked effect upon the system parameters, such as the natural frequency, damping, and the pull-in voltage. The presence of vacuum inside the cavity of the device causes a reduction in the effective gap height which leads to a reduction in the pull-in voltage. We carry out ANSYS simulations to quantify this reduction. The presence of vacuum inside the cavity of the device causes stress stiffening of the membrane, which changes the natural frequency of the device. A prestressed modal analysis is carried out to determine the change in natural frequency due to stress stiffening. The equivalent circuit method is used to evaluate the performance of the device in the receiver mode. The lumped parameters of the device are obtained and an equivalent circuit model of the device is constructed to determine the open circuit receiving sensitivity of the device. The effect of air in the cavity is included by incorporating an equivalent compliance and an equivalent resistance in the equivalent circuit.

A MICROMACHINED WIDE-BAND IN-PLANE SINGLE-AXIS CAPACITIVE ACCELEROMETER WITH A DISPLACEMENT-AMPLIFYING COMPLIANT MECHANISM

With the premise that electronic noise dominates mechanical noise in micromachined accelerometers, we present here a method to enhance the sensitivity and resolution at kHz bandwidth using mechanical amplification. This is achieved by means of a Displacement-amplifying Compliant Mechanism (DaCM) that is appended to the usual sensing element comprising a proof-mass and a suspension. Differential comb-drive arrangement is used for capacitive-sensing. The DaCM is designed to match the stiffness of the suspension so that there is substantial net amplification without compromising the bandwidth. A spring-mass-lever model is used to estimate the lumped parameters of the system. A DaCM-aided accelerometer and another without a DaCM-both occupying the same footprint-are compared to show that the former gives enhanced sensitivity: 8.7 nm/g vs. 1.4 nm/g displacement at the sensing-combs under static conditions. A prototype of the DaCM-aided micromachined acclerometer was fabricated using bulk-micromachining. It was tested at the die-level and then packaged on a printed circuit board with an off-the-shelf integrated chip for measuring change in capacitance. Under dynamic conditions, the measured amplification factor at the output of the DaCM was observed to be about 11 times larger than the displacement of the proof-mass and thus validating the concept of enhancing the sensitivity of accelerometers using mechanical amplifiers. The measured first in-plane natural frequency of the fabricated accelerometer was 6.25 kHz. The packaged accelerometer with the DaCM was measured to have 26.7 mV/g sensitivity at 40 Hz.

On the Equivalence of Acoustic Impedance and Squeeze Film Impedance in Micromechanical Resonators

In this work, we address the issue of modeling squeeze film damping in nontrivial geometries that are not amenable to analytical solutions. The design and analysis of microelectromechanical systems (MEMS) resonators, especially those that use platelike two-dimensional structures, require structural dynamic response over the entire range of frequencies of interest. This response calculation typically involves the analysis of squeeze film effects and acoustic radiation losses. The acoustic analysis of vibrating plates is a very well understood problem that is routinely carried out using the equivalent electrical circuits that employ lumped parameters (LP) for acoustic impedance. Here, we present a method to use the same circuit with the same elements to account for the squeeze film effects as well by establishing an equivalence between the parameters of the two domains through a rescaled equivalent relationship between the acoustic impedance and the squeeze film impedance. Our analysis is based on a simple observation that the squeeze film impedance rescaled by a factor of jx, where x is the frequency of oscillation, qualitatively mimics the acoustic impedance over a large frequency range. We present a method to curvefit the numerically simulated stiffness and damping coefficients which are obtained using finite element analysis (FEA) analysis. A significant advantage of the proposed method is that it is applicable to any trivial/nontrivial geometry. It requires very limited finite element method (FEM) runs within the frequency range of interest, hence reducing the computational cost, yet modeling the behavior in the entire range accurately. We demonstrate the method using one trivial and one nontrivial geometry.

Three-phase, three-limb, steady-state transformer model

This paper presents the development and implementation of a digital simulation model of a threephase, three-leg, three-winding power transformer. The proposed model, implemented in MATLAB environment, is based on the simultaneous analysis of both magnetic and electric lumped-parameters equivalents circuits, and it is intended to study its adequacy to incorporate, at a later stage, the influences of the occurrence of windings interturn short-circuit faults. Both simulation and laboratory tests results, obtained so far, for a three-phase, 6 kVA transformer, demonstrate the adequacy of the model under normal operating conditions.

Concepts and dimensionality in modeling unsaturated water flow and solute transport

Many environmental studies require accurate simulation of water and solute fluxes in the unsaturated zone. This paper evaluates one- and multi-dimensional approaches for soil water flow as well as different spreading mechanisms to model solute behavior at different scales. For quantification of soil water fluxes,Richards equation has become the standard. Although current numerical codes show perfect water balances, the calculated soil water fluxes in case of head boundary conditions may depend largely on the method used for spatial averaging of the hydraulic conductivity. Atmospheric boundary conditions, especially in the case of phreatic groundwater levels fluctuating above and below a soil surface, require sophisticated solutions to ensure convergence. Concepts for flow in soils with macro pores and unstable wetting fronts are still in development. One-dimensional flow models are formulated to work with lumped parameters in order to account for the soil heterogeneity and preferential flow. They can be used at temporal and spatial scales that are of interest to water managers and policymakers. Multi-dimensional flow models are hampered by data and computation requirements.Their main strength is detailed analysis of typical multi-dimensional flow problems, including soil heterogeneity and preferential flow. Three physically based solute-transport concepts have been proposed to describe solute spreading during unsaturated flow: The stochastic-convective model (SCM), the convection-dispersion equation (CDE), and the fraction aladvection-dispersion equation (FADE). A less physical concept is the continuous-time random-walk process (CTRW). Of these, the SCM and the CDE are well established, and their strengths and weaknesses are identified. The FADE and the CTRW are more recent,and only a tentative strength weakness opportunity threat (SWOT)analysis can be presented at this time. We discuss the effect of the number of dimensions in a numerical model and the spacing between model nodes on solute spreading and the values of the solute-spreading parameters. In order to meet the increasing complexity of environmental problems, two approaches of model combination are used: Model integration and model coupling. Amain drawback of model integration is the complexity of there sulting code. Model coupling requires a systematic physical domain and model communication analysis. The setup and maintenance of a hydrologic framework for model coupling requires substantial resources, but on the other hand, contributions can be made by many research groups.

Efficient procedure to evaluate electromagnetic transients on three-phase transmission lines

This paper presents a hybrid way mixing time and frequency domain for transmission lines modelling. The proposed methodology handles steady fundamental signal mixed with fast and slow transients, including impulsive and oscillatory behaviour. A transmission line model is developed based on lumped elements representation and state-space techniques. The proposed methodology represents an easy and practical procedure to model a three-phase transmission line directly in time domain, without the explicit use of inverse transforms. The proposed methodology takes into account the frequency-dependent parameters of the line, considering the soil and skin effects. In order to include this effect in the state matrices, a fitting method is applied. Furthermore the accuracy of proposed the developed model is verified, in frequency domain, by a simple methodology based on line distributed parameters and transfer function related to the input/output signals of the lumped parameters representation. In addition, this article proposes the use of a fast and robust analytic integration procedure to solve the state equations, enabling transient and steady-state simulations. The results are compared with those obtained by the commercial software Microtran (EMTP), taking into account a three-phase transmission line, typical in the Brazilian transmission system.

Proposal of an alternative transmission line model for symmetrical and asymmetrical configurations

This article shows a transmission line model for simulation of fast and slow transients, applied to symmetrical or asymmetrical configurations. A transmission line model is developed based on lumped elements representation and state-space techniques. The proposed methodology represents a practical procedure to model three-phase transmission lines directly in time domain, without the explicit or implicit use of inverse transforms. In three-phase representation, analysis modal techniques are applied to decouple the phases in their respective propagation modes, using a correction procedure to set a real and constant matrix for untransposed lines with or without vertical symmetry plane. The proposed methodology takes into account the frequency-dependent parameters of the line and in order to include this effect in the state matrices, a fitting procedure is applied. To verify the accuracy of the proposed state-space model in frequency domain, a simple methodology is described based on line distributed parameters and transfer function associated with input/output signals of the lumped parameters representation. In addition, this article proposes the use of a fast and robust integration procedure to solve the state equations, enabling transient and steady-state simulations. The results obtained by the proposed methodology are compared with several established transmission line models in EMTP, taking into account an asymmetrical three-phase transmission line. The principal contribution of the proposed methodology is to handle a steady fundamental signal mixed with fast and slow transients, including impulsive and oscillatory behavior, by a practical procedure applied directly in time domain for symmetrical or asymmetrical representations. (C) 2011 Elsevier Ltd. All rights reserved.