Approximate Frequency Domain Research Articles

Time Domain Expressions for the Current of a Dipole Probe in a Magnetized Plasma

We derive some approximate expressions for the current through an electrically short dipole probe immersed in a cold magnetized plasma. The time-varying current signal due to an applied voltage input to the probe is proportional to plasma parameters such as electron density and electron neutral collision frequency in the ionosphere. By taking Laplace transformations and examining the parallel and perpendicular current contributions, we obtain an approximate theoretical expression for the impedance of the probe. We then infer an even simpler empirical expression based on the approximate theory and frequency domain data obtained from sweeping impedance probes (SIPs) flown on previous sounding rocket missions. The inverse Laplace transform of the expressions will be used to perform direct least mean squares curve fitting against measurements made by a time domain impedance probe (TDIP) flown on a CubeSat. We compare our results with previous analytical results of the impedance of an electrically short dipole in a plasma, and typical sounding rocket impedance data in the ionosphere E-layer. An expression taking into account the appearance of a sheath is also presented. In the frequency domain, our expressions are found to capture the significant features of data from sounding rocket experiments.

Parametric and Coordinate Control of Oscillating Systems: Physics-Based Oscillation Feedback Design

This paper presents and compares two practical implementation schemes based on parametric and coordinate control. The parametric feedback control idea employs a parametric resonance phenomenon. An approximate frequency domain stationarization approach yields the setting for a very simple controller scheme. The application and numerical analysis of the results are given for the pendulum control example, which length varies in a parametric control case. The coordinate and parametric control demonstrate similar damping properties. The study also provides an inventive idea for passive parametric control combined with coordinate control that shows better damping.

Approximate analytical models for cylindrical shear wave propagation in viscoelastic media

Improved approximate frequency domain expressions are derived for cylindrical shear wave propagation in viscoelastic media. These expressions extend prior results that describe cylindrical wave propagation in lossless media. Previously, an analytical expression for a cylindrical wave was obtained in terms of a Hankel function and a large argument approximation was applied to the result. A leading frequency-dependent term was then treated as a constant with respect to frequency. In the improved expression, the frequency-dependence of the leading term is retained. For lossless media, the leading term is a fractional integrator, and for viscoelastic media, the leading term is either a fractional integrator or an integer-order integrator, depending on the frequency range. The lossless and the viscoelastic models are evaluated in the frequency domain for simplified source geometries and compared to numerical results. The comparison shows that the agreement between the analytical and the numerical models is excellent. Implications for time-domain calculations in viscous media will also be discussed. [This work was supported in part by NIH Grant Nos. R01 EB012079 and R01 DK092255.]

Numerical analysis of steady-state operation of three-phase induction machines by an approximate frequency domain technique1

An approximate frequency domain technique is applied to determine the initial values for the transient time-stepping numerical scheme required to take time dependent phenomena like induced voltages, eddy currents and slot ripples in induction machines into account. Using the initial conditions obtained, the steady-state operation of the motor is obtained much faster than by assuming zero initial values. This procedure is employed to the current-fed and voltage-fed 2-D induction motor models and, additionally, to the 2-D multi-slice FEM model of the 1 MW squirrel cage induction motor.

Closed-Form Transmission Line Model for Radiated Susceptibility in Metallic Enclosures

This work presents an approximate frequency domain mathematical model based on the transmission line (TL) theory for field-to-wire coupling in a rectangular metallic enclosure. The currents and voltages at the terminations of a TL induced by known electromagnetic (EM) field sources are expressed in closed form. Validity limits and applicability of the model are discussed by comparing the analytical TL-based predictions with the outputs of a full-wave numerical analysis of the overall structure using a three-dimensional finite integration technique. Deviations from the full-wave solution, due to the scattered field from the TL, have been identified, analyzed, and discussed. The proposed analytical model proves to be generally suited for accurate prediction of radiated susceptibility of single-ended interconnections in closed environments.

Approximate analytical response curve for a parametrically excited highly nonlinear 1-DOF system with an application to ship roll motion prediction

The paper presents a model for a parametrically excited nonlinear 1-DOF damped mass-spring system. An approximate analytical technique is used to obtain the general polynomial whose roots give the response of the system in frequency domain when the parametric excitation acts in the first parametric resonance region. All the details needed for the implementation of the method are given. The model is suitable for the prediction of the parametrically excited roll motion of ships in longitudinal regular waves, thus some examples of application are shown to analyse the behaviour of two different hulls. The proposed approximate frequency domain analysis is shown to be able to disclose some nonlinear features of the ship response still not well known in the field of Naval Architecture.

Modeling NDT piezoelectric ultrasonic transmitters

Ultrasonic NDT applications are frequently based on the spike excitation of piezoelectric transducers by means of efficient pulsers which usually include a power switching device (e.g. SCR or MOS-FET) and some rectifier components. In this paper we present an approximate frequency domain electro-acoustic model for pulsed piezoelectric ultrasonic transmitters which, by integrating partial models of the different stages (driving electronics, tuning/matching networks and broadband piezoelectric transducer), allows the computation of the emission transfer function and output force temporal waveform. An approximate frequency domain model is used for the evaluation of the electrical driving pulse from the spike generator. Tuning circuits, interconnecting cable and mechanical impedance matching layers are modeled by means of transmission lines and the classical quadripole approach. The KLM model is used for the piezoelectric transducer. In addition, a PSPICE scheme is used for an alternative simulation of the broadband driving spike, including the accurate evaluation of non-linear driving effects. Several examples illustrate the capabilities of the specifically developed software.

Various numerical techniques for analysis of longitudinal wave propagation in inhomogeneous one-dimensional waveguides

This paper presents various numerical techniques for the analysis of the one dimensional wave equation with variable coefficients, for governing materials with spatially varying thermal, inertial and elastic properties. Approximate time domain Finite Elements (FE) and frequency domain Spectral Finite Elements (SFE) are formulated, being computationally efficient, accurate and fast convergent compared to any other existing tool. The Sturm-Liouville problem corresponding to this wave equation is discussed and numerically solved using Prufer transformation, and the effect of inhomogeneity on the natural frequencies and mode shapes is elicited. As an application, Functionally Graded Materials (FGM), where the material properties are tailored to vary in spatial directions, are chosen, and the longitudinal wave propagation in an FGM rod due to high frequency impact load is studied. As a possible application of FGM, attenuation of waves reflection at a joint of dissimilar materials is investigated. The notion of inhomogeneous waves, used in dissipative media of more than one dimension, is retained in this one-dimensional approximation.

A Reduced Torque Ripple Controller for Direct Torque Control of Induction Machines

Direct Torque Control (DTC) of induction machines (IM), based on hysteresis comparators and selection table, suffers from variable switching frequency and large torque ripple, especially at low speed. This is because the rate of change of torque and flux and hence the time taken for the torque and flux to reach their upper and lower bands, varies with operating conditions. In this paper a new torque controller with fixed switching frequency is proposed. The structure of the new controller is very simple, with its output similar to that of the conventional three-level hysteresis comparator. The approximate frequency domain analysis of the proposed controller is presented, which served as a guide for the controller's parameters selection. The simulation of the DTC of IM with the proposed torque controller is presented, which is verified by experimental results. The results indicate that the proposed controller is capable of maintaining the torque switching frequency constant and reducing the torque ripple, particularly at low speed.

NOISE IN CONTINUOUS FORCE PRODUCTION 135

The purpose of this experiment was to investigate the long standing hypothesis that the increment in force variability at higher levels of force output is due to increments of noise in the perceptual-motor system. This goal was accomplished by examining the structure of the force variability signal, in addition to, the normal indices of the amount of variability. A group (n = 10) of young adult males performed with the index finger a continuous isometric force production task of matching to a target on a computer screen 10 different levels of force (5 through 85% of maximum) for 15 s trials. There were 10 trials at each force level condition for each subject. The results showed that force variability increased exponentially with increments of force, that the coefficient of variation was a U-shaped function over the force range, and that the complexity of the signal as measured in the time domain [Approximate entropy (Ap En) and frequency domain (spectral analysis] was an inverted U-shaped function. The findings suggest that: a) the signal/noise ratio in force output is directly related to the complexity of the signal; b) that this relation in force output varies as an inverted U-shaped function over the force range; and c) that 50% of maximum force production affords the optimal information transmission. The data provide strong evidence that the concepts of noise and variability are not synonymous in motor control.

Approximate frequency domain analysis for linear damped space structures

A method is presented for the analysis of damped structures in which the structural components are represented by impedance models and analyzed in the frequency domain. Methods are presented to assemble and condense system impedance matrices and then to identify approximate mass, stiffness, and viscous damping matrices for systems whose impedances are complicated functions of frequency. Formulas are derived for determination of approximate values for the natural frequencies and damping of systems represented by mass, stiffness, and viscous damping matrices. The sensitivities of these approximate values to system parameter changes are analyzed. The implementation of these analysis tools is discussed and applied to a simple mechanical system. Nomenclature C = damping matrix E = Young's modulus F = vector of global forces K — stiffness matrix M = mass matrix P = real power T = transformation matrix for reduction of coordinates v = vector of global velocities dv ?= first variation of the velocity mode shape W(s) — complex weighting function X = reactive power Z = impedance matrix &m,pn = viscoelastic material parameters f = damping ratio rj = loss factor a>n = natural frequency Subscripts. E = eliminated degrees of freedom (DOF) EXT = external / = imaginary L = linear NL — nonlinear R = real or retained DOF V = viscoelastic

Time-domain electromagnetic scattering by open ended circular waveguide and related structure

The axial electromagnetic backscattering by four objects characterized in part by either a circular aperture or circular conducting surface is studied. Impulse response waveforms for finite and open circular waveguides, a circular loop and a thin circular disc are synthesized from exact and/or approximate frequency domain scattering data. Complex natural resonances of the four objects are compared to illustrate similar and dissimilar features. For the open circular waveguide it is demonstrated that approximate scattering solutions for loaded guides in the resonance region can be obtained by properly combining low and high frequency estimates.

Use of polarization in electromagnetic inverse scattering

The complete description of electromagnetic scattering processes implies polarization and since an electromagnetic scatterer acts like a polarization transformer we require measurements for the complete description of the target scattering matrices so that the descriptive parameters of a scatterer can be uniquely recovered from the measured field data. For the purpose of introducing the concept of polarization utilization in practice, the radar case is chosen and generalizations to other electromagnetic inverse problems are presented in the conclusions. For example, in radar target discrimination, identification and imaging use of measurement data available over the entire spatial frequency domain of the radar cross section must be made leading to various approximate frequency domain related approaches. Mainly for historical reasons of having had amplitude data available only, in most cases the approximations had been simplified to purely scalar nature; i.e., polarization‐dependent properties were discarded, and the resulting theories are no longer valid or unique. It is the main objective of this analysis to show that because of the vector nature of electromagnetic inverse scattering, theories, if applicable in practice, require incorporation of complete polarization information into their formulation. By applying this approach to existing theories, it is shown that remarkable improvements in fidelity and quality of the reconstructed images are obtained and that indeed there is ample justification for continuing efforts in developing methods and theories of inverse scattering applicable to all those fields of physical sciences where information on the characteristic parameters of a scattering process is to be drawn from remote measurements, be it the electromagnetic vector case or the even more complicated seismic case of s and p wave interactions in elastic media.

FET pulse generator for ultrasonic pulse echo applications

Ultrasonic NDT applications are frequently based on the spike excitation of piezoelectric transducers by means of efficient pulsers which usually include a power switching device (e.g. SCR or MOS-FET) and some rectifier components. In this paper we present an approximate frequency domain electro-acoustic model for pulsed piezoelectric ultrasonic transmitters which, by integrating partial models of the different stages (driving electronics, tuning/matching networks and broadband piezoelectric transducer), allows the computation of the emission transfer function and output force temporal waveform. An approximate frequency domain model is used for the evaluation of the electrical driving pulse from the spike generator. Tuning circuits, interconnecting cable and mechanical impedance matching layers are modeled by means of transmission lines and the classical quadripole approach. The KLM model is used for the piezoelectric transducer. In addition, a PSPICE scheme is used for an alternative simulation of the broadband driving spike, including the accurate evaluation of non-linear driving effects. Several examples illustrate the capabilities of the specifically developed software.