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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
NASA NTRS1977

Prediction of pilot reserve attention capacity during air-to-air target tracking

Reserve attention capacity of a pilot was calculated using a pilot model that allocates exclusive model attention according to the ranking of task urgency functions whose variables are tracking error and error rate. The modeled task consisted of tracking a maneuvering target aircraft both vertically and horizontally, and when possible, performing a diverting side task which was simulated by the precise positioning of an electrical stylus and modeled as a task of constant urgency in the attention allocation algorithm. The urgency of the single loop vertical task is simply the magnitude of the vertical tracking error, while the multiloop horizontal task requires a nonlinear urgency measure of error and error rate terms. Comparison of model results with flight simulation data verified the computed model statistics of tracking error of both axes, lateral and longitudinal stick amplitude and rate, and side task episodes. Full data for the simulation tracking statistics as well as the explicit equations and structure of the urgency function multiaxis pilot model are presented.

Onstott, E. D.↗
NASA NTRS1981

Software models: A Bayesian approach to parameter estimation in the Jelenski-Moranda software reliability model

Maximum likelihood estimation procedures for the Jelinski-Moranda software reliability model often give misleading answers. A reparameterization and a Bayesian analysis eliminate some of the problems incurred by MLE methods and often give better predictions on sets of real and simulated data. Practical difficulties in estimating the initial number of errors N and the failure rate of each error phi by the method of maximum likelihood are: N, the MLE of N, is occasionally infinite (i.e., the routines for calculating N and phi do not converge). It is shown that N is finite sub i only if the regression line of the interevent times t sub i vs. i has positive slope. A serious problem is that often N approximates n, the sample size, and sometimes N = n. Thus the MLE predicts that the program is perfect even when it is far from being so. Only when almost all failures have been removed can N and phi be trusted near the end of debugging.

Littlewood, B.↗
DOE OSTI2021

Search for CPT and Lorentz invariance violation in the muon $g -2$ experiment at Fermilab

The Muon g-2 experiment at Fermilab (E989) aims to measure the anomalous magnetic moment of the muon, $a_{\mu}= (g-2)/2$, to a groundbreaking precision of $140$ ppb, obtaining a near four-fold increase in precision over the previous experiment, E821, at the Brookhaven National Laboratory (BNL). The value of $a_{\mu}$ from BNL currently differs from the Standard Model prediction by $\sim 3.7$ standard deviations, suggesting the potential for new physics and therefore, motivating a new experiment.Because the theory predicts this number with high precision, testing the g-factor through experiment provides a stringent test of the SM and can suggest physics beyond the Standard Model. The goal of the Fermilab Muon $g-2$ experiment is to increase the statistical precision by more than a factor of 20 and reduce systematic errors by a factor of 3. By measuring muon precession rate ($\omega_a$) in an external magnetic field, the anomalous magnetic moment will be calculated. This is an incredibly challenging experiment with a unique opportunity to provide new insight into nature. \\ The $g-2$ data also provides a great opportunity for setting the most stringent limits on some of the Standard Model Extension CPT Lorentz violating (LV) parameters in the muon sector. One of the CPT and Lorentz violating signatures that we can look for using $g-2$ data is a sidereal variation of $\omega_a(t)$. Extensive simulation studies confirm that the sensitivity regarding the sidereal varation roughly scales with $\omega_a$ uncertainty. Hence, the $g-2$ experiment at FNAL should be able to reach limits of $\sim 5\times10^{-25}$ GeV. Because the CPT and LV analyses are essentially studies of variations in $\omega_a$ as a function of time and charge, performing an $\omega_a$ analysis sets the stage for the CPT and LV measurement. This dissertation focuses on the methodology of a fully functioning framework and analyzing the Fermilab Muon $g - 2$ Run 2 data containing $\sim 11$ billion events above an energy threshold of $1.7$~GeV.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Spherically expanding flame in silane–hydrogen–nitrous oxide–argon mixtures

The effect of silane addition on the laminar flame speed ($S^0_u$) of flames propagating in hydrogen–nitrous oxide–argon mixtures has been investigated experimentally for the first time using the spherically expanding flame technique in a constant volume combustion chamber. Replacing hydrogen by silane and maintaining the equivalence ratio constant, much higher flame speeds, explosion peak pressures, and pressure rise coefficients were measured. A previously developed detailed reaction model has been updated based on ab initio thermodynamic properties calculations and collision limit violation analysis. The improved reaction model demonstrates encouraging performance in predicting the flame speed, with a mean absolute error below 11%. To explain the effect of silane addition on the flame dynamics, a number of parameters have been calculated including OH and H rate of production, heat release rate per reaction, and sensitivity coefficient on . The dynamics of freely propagating flames in SiH 4 –H 2 –N 2 O–Ar mixtures is essentially controlled by reactions of the H–O–N chemical system: N 2 O+H=N 2 +OH, OH+H 2 =H 2 O+H, and N 2 O(+M)=N 2 +O(+M). Whereas silane addition does not influence much the rate of production of OH, it significantly modifies that of H with a number of pyrolytic chemical pathways of silicon hydrides, such as SiH+H 2 =SiH 2 +H and Si+H 2 =SiH+H, which act as sink of H atom as they proceed in the backward direction. The reactions forming SiO(s) and SiO 2 (s), such as SiO+OH=SiO 2 (s)+H and 2SiO=2SiO(s), are exothermic and significantly contribute to the temperature increase. The adiabatic, constant pressure flame temperature for mixture containing silane is significantly higher, up to several 100’s K. The increase of induced by silane addition seems to be mostly related to the large increase of the flame temperature which leads to higher energy release rate.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Novel application of neutrinos to evaluate U.S. nuclear weapons performance

There is a growing realization that neutrinos can be used as a diagnostic tool to better understand the inner workings of a nuclear weapon. Robust estimates demonstrate that an Inverse Beta Decay (IBD) neutrino scintillation detector built at the Nevada Test Site with a 1000-ton active target mass at a standoff distance of 500 m would detect thousands of antineutrino events per nuclear test. This would provide less than 4% statistical error on the measured antineutrino rate and 5% error on antineutrino energy. Extrapolating this to an error on the test device explosive yield requires knowledge from evaluated nuclear databases, non-equilibrium fission rates, and assumptions on internal neutron fluxes. Initial calculations demonstrate that the total number of neutrinos emitted per fission in the first 10 3 s after a short pulse of 239 Pu fission is about a factor of two less than that from Pu fissioning under steady state conditions. Furthermore, there are significant energy spectral differences as a function of time after the pulse that must be considered. These and other model dependencies will be discussed in the paper. In the absence of nuclear weapons testing, many of the technical and theoretical challenges of a full nuclear test could be mitigated with a low cost smaller scale 20 ton fiducial mass IBD demonstration detector placed near a pulsed reactor. Potential reactors include the Texas A&M University TRIGA 1 GW–10 ms pulsed facility or the Sandia Annular Core Research Reactor. The short duty cycle and repeatability of pulses would provide critical real environment testing and measurements, which would be valuable for planning a possible real test shot in the future. Furthermore, the antineutrino rate as a function of time data would provide unique constraints on fission databases and model assumptions. Finally, there are impactful science drivers such as sensitive searches for ∼1 eV 2 sterile neutrinos and ∼MeV scale axions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Updating PV and Battery Bill Savings Calculations for Net Billing: New Best Practices for Input Data and Uncertainty

Jurisdictions are increasingly adopting compensation structures for distributed PV and PV-battery systems that price exported energy lower than energy consumed onsite (net billing rates). Standard methods for calculating the bill savings from PV and PV-battery systems were developed for net metering structures, and applying these same methods to net billing structures (such as using Typical Meteorological Year weather with actual year load) introduces bias errors that underestimate PV-battery system bill savings by between 1.5\% and 9\%, depending on the utility rate. We assess the magnitude of these errors and compare them to other sources of uncertainty when estimating the bill savings from PV and PV-battery systems under more complex utility rates.

14 SOLAR ENERGY↗
NASA NTRS1987

Analysis of counting errors in the phase/Doppler particle analyzer

NASA is investigating the application of the Phase Doppler measurement technique to provide improved drop sizing and liquid water content measurements in icing research. The magnitude of counting errors were analyzed because these errors contribute to inaccurate liquid water content measurements. The Phase Doppler Particle Analyzer counting errors due to data transfer losses and coincidence losses were analyzed for data input rates from 10 samples/sec to 70,000 samples/sec. Coincidence losses were calculated by determining the Poisson probability of having more than one event occurring during the droplet signal time. The magnitude of the coincidence loss can be determined, and for less than a 15 percent loss, corrections can be made. The data transfer losses were estimated for representative data transfer rates. With direct memory access enabled, data transfer losses are less than 5 percent for input rates below 2000 samples/sec. With direct memory access disabled losses exceeded 20 percent at a rate of 50 samples/sec preventing accurate number density or mass flux measurements. The data transfer losses of a new signal processor were analyzed and found to be less than 1 percent for rates under 65,000 samples/sec.

Oldenburg, John R.↗
NASA NTRS1993

Random errors of oceanic monthly rainfall derived from SSM/I using probability distribution functions

Global averages and random errors associated with the monthly oceanic rain rates derived from the Special Sensor Microwave/Imager (SSM/I) data using the technique developed by Wilheit et al. (1991) are computed. Accounting for the beam-filling bias, a global annual average rain rate of 1.26 m is computed. The error estimation scheme is based on the existence of independent (morning and afternoon) estimates of the monthly mean. Calculations show overall random errors of about 50-60 percent for each 5 deg x 5 deg box. The results are insensitive to different sampling strategy (odd and even days of the month). Comparison of the SSM/I estimates with raingage data collected at the Pacific atoll stations showed a low bias of about 8 percent, a correlation of 0.7, and an rms difference of 55 percent.

Chang, Alfred T. C.↗
NASA NTRS2000

Modeling Oceanic Primary Production: Photoacclimation and Nutrient Effects on Light-saturated Photosynthesis

In this report, we describe a new model (the 'PhotoAcc' model) for estimating changes in the light-saturated rate of chlorophyll-normalized phytoplankton carbon fixation (Pbmax). The model is based on measurements conducted during the Atlantic Meridional Transect studies and the Bermuda Time Series program. The PhotoAcc model explained 64% to 82% of the observed variability in Pbmax for our data set, whereas none of the previously published Pbmax models described over the past 44 years explained any of the variance. The significance of this result is that a primary limiting factor for extracting ocean carbon fixation rates from satellite measurements of near surface chlorophyll has been errors in the estimate of Pbmax. Our new model should thus result in much improved calculations of oceanic photosynthesis and thus the role of the oceans in the global carbon cycle.

Behrenfeld, Michael J.↗
NASA NTRS2021

Power Operations of the Mars Exploration Rovers

The rovers of the National Aeronautics and Space Administration’s (NASA) Mars Exploration Rovers (MER) project, Spirit (MER-A) and Opportunity (MER-B), safely landed on the surface of Mars three weeks apart during January 2004. Spirit and Opportunity were built and operated by the Jet Propulsion Laboratory (JPL), which is managed by the California Institute of Technology (Caltech) for NASA. Spirit landed at Gusev Crater, 14.8 degrees south of the equator, and operated continuously on the surface of Mars from January 4, 2004 until last contact from Spirit on March 22, 2010. Opportunity landed at Meridiani Planum, a location 2.5 degrees south of the Martian equator. Opportunity operated continuously on the Martian surface from January 25, 2004 until the last received transmission from Opportunity on June 10, 2018. The goal of the MER project was to determine if Mars ever had a habitable environment, in particular, if it ever had water. During their missions, both Spirit and Opportunity found evidence that liquid water once flowed on the surface of Mars. Both Spirit and Opportunity used a 1.33 m2 triple-junction solar array as their power sources. Based on observations of the original Mars rover, the Sojourner rover of the Mars Pathfinder mission that landed on Mars on July 4, 1997, the expectation was that the Martian dust would rapidly accumulate on the solar arrays of Spirit and Opportunity, and that the rovers would not have enough energy to continue operations after 90 Martian days (sols). Instead, due in part to lower dust accumulation rates than expected and numerous dust cleaning events, the Spirit and Opportunity rovers continued to operate on the Martian surface for over 2000 sols (MER-A) and 5000 sols (MER-B), respectively. During this time, the rovers experienced multiple Martian winters and several dust storms. Because the sources of solar array energy loss were known, the solar array energy output offered a method to scientifically estimate the loading and aeolian removal of dust from the solar arrays each sol. The MER Power operations team called this value that they calculated the solar array Dust Factor (DF). Dust Factor was defined as the fraction of sunlight that penetrates the accumulated dust on the surface of the solar array. A Dust Factor of 1.0 would indicate that the solar array was perfectly clean. A Dust Factor of 0.6 would indicate that only 60% of the available sunlight was able to penetrate the accumulated dust on the solar arrays. The MER Power subsystem operations team used the Multi-Mission Power Analysis Tool (MMPAT) to perform these Dust Factor calculations. The MMPAT software tool modeled the behavior of the solar arrays and the batteries as they interacted with the spacecraft power loads over the mission timeline. MMPAT also had knowledge (through telemetry and user inputs) of telemetered Power subsystem voltages and currents, atmospheric opacity (Tau), rover surface location, rover attitude, the planetary tilt and distance of Mars from the sun based on day of year, the instantaneous elevation of the sun based on time of day, temperatures (internal and external), terrain masking, and shadowing (due to the camera mast and antennas). Once all of the known sources of array energy loss are accounted, the remaining difference between the expected array energy and the actual array energy determines the solar array Dust Factor. The assumptions made while determining the Dust Factor are 1) that the single measured atmospheric opacity value (Tau) is constant over the course of the entire sol, 2) there is no measurable solar cell degradation, 3) there are no shorted strings and therefore, 4) all unexpected solar array energy losses are due to accumulated dust on the solar array. Although it cannot provide an absolute measure of dust loading, the determination of solar array Dust Factor provides a useful way of tracking dust accumulation and aeolian dust removal trends on Martian spacecraft. Any spacecraft on the Martian surface is vulnerable to dust, especially solar-powered spacecraft. The Spirit and Opportunity rovers were operational on the Martian surface for much longer than expected due in part to aeolian removal of dust from their solar arrays. The first few dust removal events were a pleasant surprise to the MER operations teams; however, over time a pattern began to arise. In over three Mars Years on the surface, the Power operations team tracked the solar array Dust Factor at Gusev Crater (location of MER-A) and observed that there were several significant dust removal and deposition events in Mars Year (MY) 27, even in the absence of a large dust storm. In MY 28 at Gusev Crater, the large atmospheric opacity (Tau) increase lagged significant dust removal events. Overall at Gusev Crater, there was a pattern of steady dust accumulation on the solar arrays, with a small number of significant dust cleaning events. At Meridiani Planum, where Opportunity rover operated for over seven Mars Years (late MY 26 to mid MY 34), a clear and consistent pattern of dust movement emerged. Meridiani Planum had a predictable, seasonally dependent pattern of gradual and continuous dust accumulation and removal. In summary, this paper explains the reasons for the development of the solar array Dust Factor and how it was used in mission operations. In particular, this paper describes the MMPAT software package, how it models array energy, including the important assumptions, model inputs and sources of error. And finally, this paper will show how the calculated solar array Dust Factor was used at Gusev Crater and Meridiani Planum to predict dust accumulation rates and weather patterns, and the importance of this generated data set for current and future solar- powered missions to Mars, such as the InSight lander and the planned Mars Sample Return rover.

Chin, Keith B.↗
NASA NTRS1998

Depth dependence of absorbed dose, dose equivalent and linear energy transfer spectra of galactic and trapped particles in polyethylene and comparison with calculations of models

A matched set of five tissue-equivalent proportional counters (TEPCs), embedded at the centers of 0 (bare), 3, 5, 8 and 12-inch-diameter polyethylene spheres, were flown on the Shuttle flight STS-81 (inclination 51.65 degrees, altitude approximately 400 km). The data obtained were separated into contributions from trapped protons and galactic cosmic radiation (GCR). From the measured linear energy transfer (LET) spectra, the absorbed dose and dose-equivalent rates were calculated. The results were compared to calculations made with the radiation transport model HZETRN/NUCFRG2, using the GCR free-space spectra, orbit-averaged geomagnetic transmission function and Shuttle shielding distributions. The comparison shows that the model fits the dose rates to a root mean square (rms) error of 5%, and dose-equivalent rates to an rms error of 10%. Fairly good agreement between the LET spectra was found; however, differences are seen at both low and high LET. These differences can be understood as due to the combined effects of chord-length variation and detector response function. These results rule out a number of radiation transport/nuclear fragmentation models. Similar comparisons of trapped-proton dose rates were made between calculations made with the proton transport model BRYNTRN using the AP-8 MIN trapped-proton model and Shuttle shielding distributions. The predictions of absorbed dose and dose-equivalent rates are fairly good. However, the prediction of the LET spectra below approximately 30 keV/microm shows the need to improve the AP-8 model. These results have strong implications for shielding requirements for an interplanetary manned mission.

Flight Experiment↗
NASA NTRS2007

Determining a Method of Enabling and Disabling the Integral Torque in the SDO Science and Inertial Mode Controllers

During design of the SDO Science and Inertial mode PID controllers, the decision was made to disable the integral torque whenever system stability was in question. Three different schemes were developed to determine when to disable or enable the integral torque, and a trade study was performed to determine which scheme to implement. The trade study compared complexity of the control logic, risk of not reenabling the integral gain in time to reject steady-state error, and the amount of integral torque space used. The first scheme calculated a simplified Routh criterion to determine when to disable the integral torque. The second scheme calculates the PD part of the torque and looked to see if that torque would cause actuator saturation. If so, only the PD torque is used. If not, the integral torque is added. Finally, the third scheme compares the attitude and rate errors to limits and disables the integral torque if either of the errors is greater than the limit. Based on the trade study results, the third scheme was selected. Once it was decided when to disable the integral torque, analysis was performed to determine how to disable the integral torque and whether or not to reset the integrator once the integral torque was reenabled. Three ways to disable the integral torque were investigated: zero the input into the integrator, which causes the integral part of the PID control torque to be held constant; zero the integral torque directly but allow the integrator to continue integrating; or zero the integral torque directly and reset the integrator on integral torque reactivation. The analysis looked at complexity of the control logic, slew time plus settling time between each calibration maneuver step, and ability to reject steady-state error. Based on the results of the analysis, the decision was made to zero the input into the integrator without resetting it. Throughout the analysis, a high fidelity simulation was used to test the various implementation methods.

Vess, Melissa F.↗
DOE OSTI2025

2025 Review and Revision of Federal Guidance Report 15

Federal Guidance Report No. 15 (FGR 15), External Exposure to Radionuclides in Air, Water and Soil, published in 2019 and referred to below as FGR 2019, provides age-specific effective dose rate coefficients for reference persons externally exposed to each of 1252 radionuclides homogenously distributed in environmental media. Soon after completion of FGR 2019, the International Commission on Radiological Protection (ICRP) published a similar report (ICRP Publication 144, 2020) addressing the same radionuclides and many of the external exposure scenarios addressed in FGR 2019. In 2023 Argonne National Laboratory (ANL) published a review of dose coefficients in FGR 2019, concluding that “The external effective dose from beta radiation is not appropriately accounted for in FGR 15 for both low- and high-energy beta emitters in air, in soil, and on soil surfaces.” That conclusion was based largely on comparisons of dose coefficients in FGR 2019 with values in ICRP Publication 144 but also on consideration of some unexpected patterns of equivalent dose rate coefficients across tissues and of effective dose rate coefficients across different soil depths, for a selected set of low-energy beta emitters. In response to the ANL report, the Center for Radiation Protection Knowledge (CRPK) at Oak Ridge National Laboratory (ORNL) performed an extensive reexamination of the methods and published values of FGR 2019. CRPK found that coding errors had resulted in inaccurate estimates, primarily overestimates, in many of the dose coefficients tabulated in FGR 2019 but that many of the differences between results in FGR 2019 and ICRP Publication 144 could be traced to differences in methodology. CRPK has corrected all errors in FGR 2019 associated with the coding errors and has taken the opportunity to improve a major portion of the remaining dose coefficients in FGR 2019, primarily through additional Monte Carlo calculations resulting in improved statistics for tissue equivalent dose rate coefficients for exposure to monoenergetic sources. This has eliminated the need for extrapolation of results from high and medium energies to low energies, as was done in FGR 2019. In addition, inconsistencies in the methodology identified in the review, such as computational representation of the adult female, were eliminated. The revised effective dose rate coefficients are consistent with values in ICRP Publication 144 except for differences in values clearly arising from differences in methodology; and differences in values for a relatively small set of very low-energy radionuclides with highly uncertain dose coefficients regardless of methodology.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1989

Quantization effects in Viterbi decoding rate 1/n convolutional codes

A Viterbi decoder's performance loss due to quantizing data from the additive white Gaussian noise (AWGN) channel is studied. An optimal quantization scheme and branch metric calculation method are presented. The uniformly quantized channel capacity C(sub u)(q) is used to determine the smallest number of quantization bits q that does not cause a significant loss. The quantizer stepsize which maximizes C(sub u)(q) almost minimizes the decoder bit error rate (BER). However, a slightly larger stepsize is better, like the value that minimizes the Bhattacharyya bound. The range and renormalization of state metrics is analyzed, in particular for K = 15 decoders such as the Big Viterbi Decoder (BVD) for the Galileo mission. These results are required to design reduced hardware complexity Viterbi decoders with a negligible quantization loss.

Onyszchuk, I. M.↗
NASA NTRS1987

Three dimensional numerical scattering from ocean-like surfaces

A new method of calculating the electric field scattered from two-dimensional conducting rough surfaces is presented. This method uses the operator conjugate gradients technique and the extended boundary condition equation. This avoids the build-up of round-off errors encountered in the inversion of large matrices. It also avoids the singularities of the integral kernels usually encountered in the method of moments. Techniques for improving the rate of convergence by applying physical constraints are discussed. This method is presently being used to calculate the polarization signatures from simulated ocean-like surfaces.

Rodriguez, Ernesto↗
DOE OSTI2024

Direct, simple and efficient computation of all components of the virtual-casing magnetic field in axisymmetric geometries with Kapur–Rokhlin quadrature

In a recent publication (Toler et al., J. Plasma Phys., vol. 89, issue 2, 2023, p. 905890210), we demonstrated that for axisymmetric geometries, the Kapur–Rokhlin quadrature rule provided an efficient and high-order accurate method for computing the normal component, on the plasma surface, of the magnetic field due to the toroidal current flowing in the plasma, via the virtual-casing principle. The calculation was indirect, as it required the prior computation of the magnetic vector potential from the virtual-casing principle, followed by the computation of its tangential derivative by Fourier differentiation, to obtain the normal component of the magnetic field. Our approach did not provide the other components of the virtual-casing magnetic field. In this letter, we show that a more direct and more general approach is available for the computation of the virtual-casing magnetic field. The Kapur–Rokhlin quadrature rule accurately calculates the principal value integrals in the expression for all the components of the magnetic field on the plasma boundary, and the numerical error converges at a rate nearly as high as the indirect method we presented previously.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1990

Flat plate at incidence as a waverider in rarefied hypersonic flow

The physical validity of continuum models and their ability to predict the critical aerothermodynamic properties of a waverider at high altitudes are examined using a flat plate at angle of attack as a generic hypersonic lifting vehicle. For a shock layer far from local translational equilibrium, a theoretical study based on Grad's thirteen-moment equations shows that the Navier-Stokes based solutions can correctly predict the drag, lift, and surface heat transfer rate, with the prediction error comparable to that of the standard shock-layer theory. The conclusion is supported by a comparison with direct simulation Monte Carlo calculations.

Cheng, H. K.↗
NASA NTRS1991

Optical phase-locked loop (OPLL) for free-space laser communications with heterodyne detection

Several advantages of coherent free-space optical communications are outlined. Theoretical analysis is formulated for an OPLL disturbed by shot noise, modulation noise, and frequency noise consisting of a white component, a 1/f component, and a 1/f-squared component. Each of the noise components is characterized by its associated power spectral density. It is shown that the effect of modulation depends only on the ratio of loop bandwidth and data rate, and is negligible for an OPLL with loop bandwidth smaller than one fourth the data rate. Total phase error variance as a function of loop bandwidth is displayed for several values of carrier signal to noise ratio. Optimal loop bandwidth is also calculated as a function of carrier signal to noise ratio. An OPLL experiment is performed, where it is shown that the measured phase error variance closely matches the theoretical predictions.

Win, Moe Z.↗