Lumped Approximation Research Articles

Analysis on the low-frequency electromagnetic pulse coupling to horizontal electrically short lines

In this study, we investigated the coupling features of the nuclear electromagnetic pulse (NEMP) on overhead cables in the middle-and-far regions, different from the transmission line model commonly used for field-line coupling in high-frequency cases, using a simpler lumped approximation to solve the electrically small size model in low-frequency cases. To verify its effectiveness, a simulation model with the same conditions was set up using the software of Computer Simulation Technology (CST), and cable coupling experiments were performed in a laboratory environment using a bounded-wave electromagnetic pulse simulator. The calculated results of the lumped approximation circuit were compared with the CST simulation and measured results, and the agreement was good. The results also shows that the load exhibits a differential response in the case of the low impedance and it is consistent with the excitation signal in the case of the high impedance. Finally, some more experiments were constructed to analyzed the effect of different cable parameters on the cable load response through experiments, and the experimental results are also in general agreement with the theoretical analysis, in which the induced signal of the low-impedance load is mainly determined by the magnetic field in the direction normal to the cable and the ground loop and the induced signal of the high-impedance load is mainly determined by the electric field in the direction of the height of the cable erection.

A Posteriori Error Estimates for Lumped Mass Finite Element Method for Linear Parabolic Problems Using Elliptic Reconstruction

ABSTRACTWe study residual-based a posteriori error estimates for both the spatially discrete and the fully discrete lumped mass finite element approximation for parabolic problems in a bounded convex polygonal domain in ℝ2. In particular, the space discretization uses finite element spaces that are assumed to be nested one and the time discretization is based on the backward Euler approximation. The main key features used in the analysis are the reconstruction technique and energy argument combined with the stability of L2 projection in H1(Ω). The a posteriori error estimates we derive are optimal order in both the and -norms.

Theoretical and experimental study of the dynamic response of absorber-based, micro-scale, oscillatory probes for contact sensing applications.

This paper presents two models for predicting the frequency response of micro-scale oscillatory probes. These probes are manufactured by attaching a thin fiber to the free end of one tine of a quartz tuning fork oscillator. In these studies, the attached fibers were either 75 μm diameter tungsten or 7 μm diameter carbon with lengths ranging from around 1 to 15 mm. The oscillators used in these studies were commercial 32.7 kHz quartz tuning forks. The first theoretical model considers lateral vibration of two beams serially connected and provides a characteristic equation from which the roots (eigenvalues) are extracted to determine the natural frequencies of the probe. A second, lumped model approximation is used to derive an approximate frequency response function for prediction of tine displacements as a function of a modal force excitation corresponding to the first mode of the tine in the absence of a fiber. These models are used to evaluate the effect of changes in both length and diameter of the attached fibers. Theoretical values of the natural frequencies of different modes show an asymptotic relationship with the length and a linear relationship with the diameter of the attached fiber. Similar results are observed from experiment, one with a tungsten probe having an initial fiber length of 14.11 mm incrementally etched down to 0.83 mm, and another tungsten probe of length 8.16 mm incrementally etched in diameter, in both cases using chronocoulometry to determine incremental volumetric material removal. The lumped model is used to provide a frequency response again reveals poles and zeros that are consistent with experimental measurements. Finite element analysis shows mode shapes similar to experimental microscope observations of the resonating carbon probes. This model provides a means of interpreting measured responses in terms of the relative motion of the tine and attached fibers. Of particular relevance is that, when a "zero" is observed in the response of the tine, one mode of the fiber is matched to the tine frequency and is acting as an absorber. This represents an optimal condition for contact sensing and for transferring energy to the fiber for fluid mixing, touch sensing, and surface modification applications.

Numerical quadrature and operator splitting in finite element methods for cardiac electrophysiology

We study the numerical accuracy and computational efficiency of alternative formulations of the finite element solution procedure for the monodomain equations of cardiac electrophysiology, focusing on the interaction of spatial quadrature implementations with operator splitting and examining both nodal and Gauss quadrature methods and implementations that mix nodal storage of state variables with Gauss quadrature. We evaluate the performance of all possible combinations of 'lumped' approximations of consistent capacitance and mass matrices. Most generally, we find that quadrature schemes and lumped approximations that produce decoupled nodal ionic equations allow for the greatest computational efficiency, this being afforded through the use of asynchronous adaptive time-stepping of the ionic state variable ODEs. We identify two lumped approximation schemes that exhibit superior accuracy, rivaling that of the most expensive variationally consistent implementations. Finally, we illustrate some of the physiological consequences of discretization error in electrophysiological simulation relevant to cardiac arrhythmia and fibrillation. These results suggest caution with the use of semi-automated free-form tetrahedral and hexahedral meshing algorithms available in most commercially available meshing software, which produce nonuniform meshes having a large distribution of element sizes.

A New Millimeter-Wave Fixture Deembedding Method Based on Generalized Cascade Network Model

In this letter, a universal cascade-based deembedding technique was presented for on-wafer characterization of the RF CMOS device. As compared with existing deembedding approaches, it is developed based on unique combinations of two THRU structures that enable efficient deembedding of fixture parasitics without any inaccurate lumped approximation or requirement of known standards. The proposed deembedding technique is validated on 0.13- μm CMOS devices and has been proven to be more accurate than existing lumped and cascade-based deembedding techniques. As a result, it gives deeper physical prediction on transistor gate capacitances and transconductance. Therefore, it is highly suitable to be applied for device characterization at millimeter-wave frequencies.

Establishing a Methodology for Resolving Convective Heat Transfer From Complex Geometries

Current turbine airfoils must operate at extreme temperatures, which are continuously driven higher by the demand for high output engines. Internal cooling plays a key role in the longevity of gas turbine airfoils. Ribbed channels are commonly used to increase heat transfer by generating turbulence and to provide a greater convective surface area. Because of the increasing complexity in airfoil design and manufacturing, a methodology is needed to accurately measure the convection coefficient of a rib with a complex shape. Previous studies that have measured the contribution to convective heat transfer from the rib itself have used simple rib geometries. This paper presents a new methodology to measure convective heat transfer coefficients on complex ribbed surfaces. The new method was applied to a relatively simple shape so that comparisons could be made with a commonly accepted method for heat transfer measurements. A numerical analysis was performed to reduce experimental uncertainty and to verify the lumped model approximation used in the new methodology. Experimental measurements were taken in a closed-loop channel using fully rounded discontinuous skewed ribs oriented 45 deg to the flow. The channel aspect ratio was 1.7:1 and the ratio of rib height to hydraulic diameter was 0.075. Heat transfer augmentation levels relative to a smooth channel were measured to be between 4.7 and 3 for Reynolds numbers ranging from 10,000 to 100,000.

Numerical Design of the Cavity for the Uniform Atmospheric Microwave Plasma Source

A single ridge cavity was designed for the 60 kw, 915 MHz uniform atmospheric microwave plasma source which does not need an igniter for the initial discharge. The single ridge cavity in the shape of a resonator was built in the grid structures for the wide cavity torch of the atmospheric pressure microwave plasma. This cavity was studied by using an analytical calculation with a lumped circuit approximation and by using a simulation with the commercial 3D HFSS code. The designed plasma cross-sectional area was uniformly 810 mm 5 mm. We developed a design formula that used the lumped circuit approximation and we compared its results with the results of the HFSS simulation. The analytically calculated cavity frequency, 915 MHz, matched the HFSS's simulation result, 904 MHz, well for the fundamental TE10-like mode. A self-dischargeable study was conducted for the breakdown feasibility in the cavity gap region These cavities showed a uniform electromagnetic wave distribution between the grids through which a large-sized microwave plasma could be generated when the cavities were connected in parallel pairs so that the crests of the electric eld intensity compensate for its troughs.

Analysis and design of parallel mechanisms with flexure joints

Flexure joints are frequently used in precision-motion stages and microrobotic mechanisms due to their monolithic construction. The joint compliance, however, can affect the static and dynamic performance of the overall mechanism. In this paper, we consider the analysis and design of general platform-type parallel mechanisms containing flexure joints. Based on static performance measures such as task-space stiffness and manipulability, and constraints such as joint stress, mechanism size, and workspace volume, we pose the design problem as a multiobjective optimization. We first calculate the Pareto frontier, which can then be used to select the desired design parameters based on secondary criteria, such as performance sensitivity and dynamic characteristics. To facilitate design iteration, we apply the pseudo rigid-body approach with a lumped approximation of the flexure joints. A planar mechanism is used to illustrate the analysis and design techniques.

Analysis of Dynamic Behavior of an Absorption Chiller Heater. 1st Report, Simulation Model of Dynamic Characteristics of Evaporator and Absorber.

A mathematical model for evaporator and absorber, which are components of a double-effect, water/lithium-bromide absorption chiller heater, is developed. The purposes of this model are to discribe the dynamic behavior of the machine, and to investigate optimum control method and internal configuration of the machine. In order to satisfy these demands, the model is constructed, based on the internal configuration of the machine which is currently manufactured. The evaporator and the absorber of the machine take the form of a shell and tube heat exchanger. There is a sprinkler inside the evaporator and the absorber, and thus there is falling film. Therefore, both these two components feature the following elements : vapor, liquid refrigerant or solution, heat-transfer tubes, and circulating water. Each of these parameters is classified according to its flow direction. A lumped approximation is adopted for these elements, and the heat capacity of heat-transfer tubes is taken into account. A time lag of the system given by the circulating water in the tubes can be estimated with this model.

Groundwater quality management of a low inertia basin: Application to the San Mateo Basin, California

A two-dimensional finite element model is applied to the San Mateo Basin, California in order to investigate feasible and efficient management alternatives to enhance the basin yield and preserve the basin water quality. The model utilizes lumped approximation methods for the determination of its subsurface boundary conditions, and incorporates a variety of hydrological processes. The model solves uncoupled flow and transport equations using a nodal domain integration technique for the flow model and an integrated finite difference method for the transport model. The model incorporates the basin inputs and outputs as ocean flux, well and phreatophyte extractions, subsurface inflow, precipitation and streambed percolation. Modeling results indicate that the substained yield may be maximized by interception of ocean outflow from the basin. An improvement of about four times of the historical sustained yield was achieved. This strategy required relocation of existing wastewater recharge ponds and increasing basin extractions. In order to intercept most of the ocean outflow by increasing basin extractions, simulated subsurface seawater intrusion was observed. The water quality study indicated that the basin yield could be increased significantly by moderately relaxing the water quality criteria near the ocean.

Assessing the validity of the unireactant lumped approximation in multireactant systems following first-order kinetics

Assessing the validity of the unireactant lumped approximation in multireactant systems following first-order kinetics.

PCG methods in transient FE analysis. Part II: Second order problems

AbstractIn the Part I companion paper, various PCG (preconditioned conjugate gradient) strategies for solving the first order time dependent problem Mu̇ + Ku = f were compared. In all cases M was assumed to be the consistent ‘mass’ matrix arising out of conventional finite element semi‐discretization of the partial differential equation, and not its lumped approximation. In the present paper, similar PCG strategies are applied to the second order time dependent problem Mü + Cu̇ + Ku = f. Again consistent M and C can be retained. Various global and element level preconditioners are compared and optimized.

Optimal emission control of a transient air pollution source by the method of finite difference

Following Butkovskiy (1969) an approach is made in solving distributed optimal control problem of air pollution by the use of lumped approximation based on finite difference representations of the spatial derivatives yielding a set of differential difference equations, In this paper the diffusion of a horizontally homogeneous concentration distribution is considered, when the ground level source is taken as a control with respect such that the system will reach a desired state from an Initial state In a lowest possible time.

Signal and noise theory for a dc SQUID amplifier

A theory is presented for the gain and noise in an amplifier based on a dc SQUID. In the lumped circuit approximation, the total inductance of the input circuitL T is coupled to the SQUID inductanceL via a mutual inductanceMii=α e (LL T )1/2 and is in series with a voltage source with a resistanceR i and a capacitanceC i . The results are expressed in terms of parameters for a SQUID with reduced inductance (1−α e 2 )L. The voltage gain of the amplifier at frequency ω/2π isM i V Ф r /Z T * (ω), while the total voltage noise at the output of the SQUID isV N r (ω)+M i 2 V Ф r J N r (ω) (R i + 1/jωC i )/LTZ T * (ω). Here,Z T * (ω)=Z T (ω)−J Ф r M i 2 (R i + 1/jωC i )/L i , whereZ T (ω) is the total impedance of the unloaded input circuit,V Ф r andJ Ф r are the flux-to-voltage and flux-to-circulating current transfer functions of the reduced SQUID, andV N r (ω) andJ N r (ω) are the noise voltage and noise current of the reduced SQUID.

Comments on "The modeling of resistive interconnects for integrated circuits" by R.J. Antonine and G.W. Brown

For original paper see ibid, vol.SC-18, no.2, p.200 (1983). It is shown that by using the exact time-dependent analytical solution, the validity of the lumped circuit approximation of a resistive interconnect given by Antonine and Brown can be better appreciated. Their study is extended here to short-circuited and capacitively loaded lines.

On controlling an autothermal fixed-bed reactor at an unstable state—III: Model reduction and control strategies which avoid sstate estimation

A simplified approach for the control of fixed-bed reactors is discussed. Key elements include: (i) careful modeling of the reactor to obtain a lumped approximation with good internal structure (i.e. appropriate coupling between inputs and state variables through the different response modes); (ii) a major reduction in model size to an accurate, low-order form; (iii) derivation of a control algorithm for the low-order model; and (iv) direct application to the full-order system without the use of state estimation. The success of this approach is rooted in the choice of modeling techniques and of a model reduction procedure. The powerful new reduction method of Litz is evaluated here. Applications of the technique to a simulated unstable autothermal reactor are demonstrated for the case of modal control with incomplete state feedback. Results point to a high probability of success in subsequent experimental tests.

A generalized approach to the solution of variable systems subjected to arbitrary source functions and boundary conditions

Under study are layered inhomogeneous systems with or without forcing functions as represented by sources and boundary conditions. Under a forced or unforced state, such systems pervade the fields of sound and vibration. A common formulation to the constraints and physical laws that apply is given by using the Fredholm integral equation. A unified and versatile solution is developed analytically to treat these problems under forced or unforced conditions. Then the approach is dissected to implement the results on the computer or to treat, at the outset, the lumped approximation of the distributed system. This development modifies, extends, and generalizes previous studies that have been applied to a restricted class of systems. Here the treated systems need not be limited to those describable by a strictly bilinear or symmetric Green function. Also, the source function and boundary conditions are not limited to those of special type or form. Throughout, examples are given to introduce, motivate and illustrate the analysis.

Lumped approximation to distributed RC notch networks for linear integrated circuits

Handling of the transcedental equations arising in distributed networks is rather cumbersome. Therefore, in this paper, a lumped approximation to the RC network has been examined. Generalized expressions have been derived for the open circuit voltage transfer function valid for n-lumped sections. This is a rational polynomial and as such easier to handle for analytical purposes. Application has been made to the cases of n = 2 to seven sections and the results obtained have been compared with the ones from exact analysis of the RC notch network. Root-locus graphs have also been derived and plotted for three and seven sections.

Equivalent circuit and gain of MOS field effect transistors

A single lumped approximation to the linear equivalent circuit of the MOS field effect transistor is presented, which describes its characteristics within the entire useful frequency range. The y-parameters are expressed as a function of the lumped circuit elements. The power gain for maximum output power and the maximum voltage gain for cascaded transistors are calculated.