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At least 73 records · Page 4

Modified fast frequency acquisition via adaptive least squares algorithm

A method and the associated apparatus for estimating the amplitude, frequency, and phase of a signal of interest are presented. The method comprises the following steps: (1) inputting the signal of interest; (2) generating a reference signal with adjustable amplitude, frequency and phase at an output thereof; (3) mixing the signal of interest with the reference signal and a signal 90 deg out of phase with the reference signal to provide a pair of quadrature sample signals comprising respectively a difference between the signal of interest and the reference signal and a difference between the signal of interest and the signal 90 deg out of phase with the reference signal; (4) using the pair of quadrature sample signals to compute estimates of the amplitude, frequency, and phase of an error signal comprising the difference between the signal of interest and the reference signal employing a least squares estimation; (5) adjusting the amplitude, frequency, and phase of the reference signal from the numerically controlled oscillator in a manner which drives the error signal towards zero; and (6) outputting the estimates of the amplitude, frequency, and phase of the error signal in combination with the reference signal to produce a best estimate of the amplitude, frequency, and phase of the signal of interest. The preferred method includes the step of providing the error signal as a real time confidence measure as to the accuracy of the estimates wherein the closer the error signal is to zero, the higher the probability that the estimates are accurate. A matrix in the estimation algorithm provides an estimate of the variance of the estimation error.

Kumar, Rajendra↗

Reducing Spurious Output Of NCO's

Spurious frequency components in output of numerically controlled oscillator (NCO) reduced by dithering appropriate digital signals with small random noise signal prior to truncation. Enables reduction of word length without increasing spurious signal power.

Zimmerman, George A.↗

Wide Tuning Capability for Spacecraft Transponders

A document presents additional information on the means of implementing a capability for wide tuning of microwave receiver and transmitter frequencies in the development reported in the immediately preceding article, VCO PLL Frequency Synthesizers for Spacecraft Transponders (NPO- 42909). The reference frequency for a PLL-based frequency synthesizer is derived from a numerically controlled oscillator (NCO) implemented in digital logic, such that almost any reference frequency can be derived from a fixed crystal reference oscillator with microhertz precision. The frequency of the NCO is adjusted to track the received signal, then used to create another NCO frequency used to synthesize the transmitted signal coherent with, and at a specified frequency ratio to, the received signal. The frequencies can be changed, even during operation, through suitable digital programming. The NCOs and the related tracking loops and coherent turnaround logic are implemented in a field-programmable gate array (FPGA). The interface between the analog microwave receiver and transmitter circuits and the FPGA includes analog-to-digital and digital-toanalog converters, the sampling rates of which are chosen to minimize spurious signals and otherwise optimize performance. Several mixers and filters are used to properly route various signals.

Lux, James↗

All-Digital Baseband 65nm PLL/FPLL Clock Multiplier using 10-cell Library

PLLs for clock generation are essential for modern circuits, to generate specialized frequencies for many interfaces and high frequencies for chip internal operation. These circuits depend on analog circuits and careful tailoring for each new process, and making them fault tolerant is an incompletely solved problem. Until now, all digital PLLs have been restricted to sampled data DSP techniques and not available for the highest frequency baseband applications. This paper presents the design and preliminary evaluation of an all-digital baseband technique built entirely with an easily portable 10-cell digital library. The library is also described, as it aids in research and low volume design porting to new processes. The advantages of the digital approach are the wide variety of techniques available to give varying degrees of fault tolerance, and the simplicity of porting the design to new processes, even to exotic processes that may not have analog capability. The only tuning parameter is digital gate delay. An all-digital approach presents unique problems and standard analog loop stability design criteria cannot be directly used. Because of the quantization of frequency, there is effectively infinite gain for very small loop error feedback. The numerically controlled oscillator (NCO) based on a tapped delay line cannot be reliably updated while a pulse is active in the delay line, and ordinarily does not have enough frequency resolution for a low-jitter output.

Shuler, Robert L., Jr.↗

ALL-Digital Baseband 65nm PLL/FPLL Clock Multiplier Using 10-Cell Library

PLLs for clock generation are essential for modern circuits, to generate specialized frequencies for many interfaces and high frequencies for chip internal operation. These circuits depend on analog circuits and careful tailoring for each new process, and making them fault tolerant is an incompletely solved problem. Until now, all digital PLLs have been restricted to sampled data DSP techniques and not available for the highest frequency baseband applications. This paper presents the design and preliminary evaluation of an all-digital baseband technique built entirely with an easily portable 10-cell digital library. The library is also described, as it aids in research and low volume design porting to new processes. The advantages of the digital approach are the wide variety of techniques available to give varying degrees of fault tolerance, and the simplicity of porting the design to new processes, even to exotic processes that may not have analog capability. The only tuning parameter is digital gate delay. An all-digital approach presents unique problems and standard analog loop stability design criteria cannot be directly used. Because of the quantization of frequency, there is effectively infinite gain for very small loop error feedback. The numerically controlled oscillator (NCO) based on a tapped delay line cannot be reliably updated while a pulse is active in the delay line, and ordinarily does not have enough frequency resolution for a low-jitter output.

Schuler, Robert L., Jr.↗

Higher-Order Approximations for Stabilizing Zero-Energy Modes in Peridynamics Crystal Plasticity Models with Large Horizon Interactions

The non-ordinary state-based peridynamics theory combines non-local dynamic techniques with a desirable correspondence material principle, allowing for the use of continuum mechanics constitutive models. Such an approach presents a unique capability for solving problems involving discontinuities (e.g., strain localization, fracture, and fragmentation). However, the correspondence-based peridynamics models often suffer from zero-energy mode instabilities in numerical implementation, primarily due to the approximations of the non-local deformation gradient tensor. This paper focuses on a computational scheme for eliminating the zero-energy mode oscillations using a choice of influence functions that improve the truncation error in a higher-order Taylor series expansion of the deformation gradient. The novelty here is a tensor-based derivation of the linear constraint equations, which can be used to systematically identify the particle interaction weight functions for various user-specified horizon radii. In this paper, the proposed higher-order stabilization scheme is demonstrated for multi-dimensional examples involving polycrystalline and composite microstructures, along with comparisons against conventional finite element methods. The proposed stabilization scheme is shown to be highly effective in suppressing the spurious zero-energy mode oscillations in all numerical examples while enabling efficient simulations of strain localizations across material interfaces.

Non-Ordinary State-Based Peridynamics↗

Numerical simulation and comparison with experiment for self-excited oscillations in a diffuser flow

This paper describes numerical simulations of self-excited oscillations in a two-dimensional transonic diffuser flow obtained by solving the Navier-Stokes equations with a two-equation turbulence model. Comparisons were made between the computational results and experimental data. For the mean flowfields, the agreement between computation and experiment is good for the wall pressures, shock location, and the separation and reattachment points. However, the thickness of the computed recirculation zone is about 50 percent of the measured thickness. For the fluctuating flowfields, a great deal of qualitative similarity exists between the computation and experiment; however, the predicted oscillation frequency is about 50 percent higher than the measured value. The formation of a succession of downstream-traveling counter-rotating vortices, as seen experimentally, is also vividly displayed in the numerical results.

Hsieh, T.↗

Inertial oscillation of a vertical rotating draft with application to a supercell storm

An analytic model (vertical rotating draft) which includes the gross features of a supercell storm on an f-plane, undergoes an inertial oscillation that appears to have been overlooked in previous analytic and numerical models. The oscillation is nonlinear and consists of a long quiescent phase and a short intense phase. During the intense phase, the rotating draft has the following features of a supercell: the diameter of the core contracts as it spins up and expands as it spins down; if vertical wind shear is included, the track of the rotating draft turns to the right (an anticyclonic rotating draft turns to the left); this turning point is followed by a predominantly upward flow; and the horizontal pressure gradient is very small (a property of most tornadoless supercells). The rapid spin-up during the intense phase and the high Rossby numbers obtainable establish the ability of the Coriolis force to spin up single cyclonic or anticyclonic supercells by means of this inertial oscillation. This surprising result has implications for numerical supercell simulations, which generally do not rely on the Coriolis force as a source of rotation. The physics and mathematics of the inertial oscillation are given, and the solution is applied to a documented supercell.

Supercell thunderstorm↗

Discrete Kinetic Eigenmode Spectra of Electron Plasma Oscillations in Weakly Collisional Plasma: A Numerical Study

It has been demonstrated that in the presence of weak collisions, described by the Lenard-Bernstein collision operator, the Landau-damped solutions become true eigenmodes of the system and constitute a complete set. We present numerical results from an Eulerian Vlasov code that incorporates the Lenard-Bernstein collision operator. The effect of the collisions on the numerical recursion phenomenon seen in Vlasov codes is discussed. The code is benchmarked against exact linear eigenmode solutions in the presence of weak collisions, and a spectrum of Landau-damped solutions is determined within the limits of numerical resolution. Tests of the orthogonality and the completeness relation are presented.

Kinetic Eigenmode Spectra↗

Numerical simulations of supersonic flow through oscillating cascade sections

A finite difference code was developed for modeling inviscid, unsteady supersonic flow by solution of the compressible Euler equations. The code uses a deforming grid technique to capture the motion of the airfoils and can model oscillating cascades with any arbitrary interblade phase angle. A flat plate cascade is analyzed, and results are compared with results from a small perturbation theory. The results show very good agreement for both the unsteady pressure distributions and the integrated force predictions. The reason for using the numerical Euler code over a small perturbation theory is the ability to model real airfoils that have thickness and camber. Sample predictions are presented for a cascade of loaded airfoils and show appreciable differences in the unsteady surface pressure distributions when compared with the flat plate results.

Huff, Dennis L.↗

Numerical analysis of supersonic flow through oscillating cascade sections by using a deforming grid

A finite difference code was developed for modeling inviscid, unsteady supersonic flow by solution of the compressible Euler equations. The code uses a deforming grid technique to capture the motion of the airfoils and can model oscillating cascades with any arbitrary interblade phase angle. A flat plate cascade is analyzed, and results are compared with results from a small-perturbation theory. The results show very good agreement for both the unsteady pressure distributions and the integrated force predictions. The reason for using the numerical Euler code over a small-perturbation theory is the ability to model real airfoils that have thickness and camber. Sample predictions are presented for a section of the rotor on a supersonic throughflow compressor designed at NASA Lewis Research Center. Preliminary results indicate that two-dimensional, flat plate analysis predicts conservative flutter boundaries.

Huff, Dennis L.↗

Numerical analysis of supersonic flow through oscillating cascade sections by using a deforming grid

A finite difference code was developed for modeling inviscid, unsteady supersonic flow by solution of the compressible Euler equations. The code uses a deforming grid technique to capture the motion of the airfoils and can model oscillating cascades with any arbitrary interblade phase angle. A flat plate cascade is analyzed, and results are compared with results from a small-perturbation theory. The results show very good agreement for both the unsteady pressure distributions and the integrated force predictions. The reason for using the numerical Euler code over a small-perturbation theory is the ability to model real airfoils that have thickness and camber. Sample predictions are presented for a section of the rotor on a supersonic throughflow compressor designed at NASA Lewis Research Center. Preliminary results indicate that two-dimensional, flat plate analysis predicts conservative flutter boundaries.

Huff, Dennis L.↗

Numerical simulations of supersonic flow through oscillating cascade sections

A finite difference code has been developed for modeling inviscid, unsteady supersonic flow by solution of the compressible Euler equations. The code uses a deforming grid technique to capture the motion of the airfoils and can model oscillating cascades with any arbitrary interblade phase angle. A flat plate cascade is analyzed, and results are compared with results from a small-perturbation theory. The results show very good agreement for both the unsteady pressure distributions and the integrated force predictions. The reason for using the numerical Euler code over a small-perturbation theory is the ability to model 'real' airfoils that have thickness and camber. Sample predictions are presented for a cascade of loaded airfoils and show appreciable differences in the unsteady surface pressure distributions when compared with the flat plate results.

Huff, Dennis L.↗

Numerical calculations of velocity and pressure distribution around oscillating airfoils

An analytical procedure based on the Navier-Stokes equations was developed for analyzing and representing properties of unsteady viscous flow around oscillating obstacles. A variational formulation of the vorticity transport equation was discretized in finite element form and integrated numerically. At each time step of the numerical integration, the velocity field around the obstacle was determined for the instantaneous vorticity distribution from the finite element solution of Poisson's equation. The time-dependent boundary conditions around the oscillating obstacle were introduced as external constraints, using the Lagrangian Multiplier Technique, at each time step of the numerical integration. The procedure was then applied for determining pressures around obstacles oscillating in unsteady flow. The obtained results for a cylinder and an airfoil were illustrated in the form of streamlines and vorticity and pressure distributions.

Bratanow, T.↗

High order accurate solutions of viscous problems

We consider a fourth order extension to MacCormack's scheme. The original extension was fourth order only for the inviscid terms but was second order for the viscous terms. We show how to modify the viscous terms so that the scheme is uniformly fourth order in the spatial derivatives. Applications are given to some boundary layer flows. In addition, for applications to shear flows the effect of the outflow boundary conditions are very important. We compare the accuracy of several of these different boundary conditions for both boundary layer and shear flows. Stretching at the outflow usually increases the oscillations in the numerical solution but the addition of a filtered sponge layer (with or without stretching) reduces such oscillations. The oscillations are generated by insufficient resolution of the shear layer. When the shear layer is sufficiently resolved then oscillations are not generated and there is less of a need for a nonreflecting boundary condition.

Hayder, M. E.↗

High order accurate solutions of viscous problems

We consider a fourth order extension to MacCormack's scheme. The original extension was fourth order only for the inviscid terms but was second order for the viscous terms. We show how to modify the viscous terms so that the scheme is uniformly fourth order in the spatial derivatives. Applications are given to some boundary layer flows. In addition, for applications to shear flows the effect of the outflow boundary conditions are very important. We compare the accuracy of several of these different boundary conditions for both boundary layer and shear flows. Stretching at the outflow usually increases the oscillations in the numerical solution but the addition of a filtered sponge layer (with or without stretching) reduces such oscillations. The oscillations are generated by insufficient resolution of the shear layer. When the shear layer is sufficiently resolved then oscillations are not generated and there is less of a need for a nonreflecting boundary condition.

Hayder, M. Ehtesham↗

Line narrowing of AgGaSe2 optical parametric oscillator by injection seeding

Solid-state lasers are developed for atmospheric applications. Optical parametric oscillators (OPO) are being investigated as sources of tunable radiation in the 2.5-12 micron range where development of conventional lasers is subject to numerous difficulties. Parametric oscillation is a nonlinear optical technique for converting laser output to longer wavelengths. Incident photons, typically from a pulsed pump laser, are converted into two photons of longer wavelength, while satisfying energy conservation. The particular split of energy is determined by momentum conservation; the wavelength of interest is usually selected by angle orientation of the nonlinear material with respect to the direction of propagation of the pump beam. An OPO based on AgGaSe2 was considered.

Watson, George H.↗