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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 73 records · Page 4

Accuracy Assessment of Response Surface Approximations for Supersonic Turbine Design

There is a growing trend to employ CFD tools to supply the necessary information for design optimization of fluid dynamics components/systems. Such results are prone to uncertainties due to reasons including discretization. errors, incomplete convergence of computational procedures, and errors associated with physical models such as turbulence closures. Based on this type of information, gradient-based optimization algorithms often suffer from the noisy calculations, which can seriously compromise the outcome. Similar problems arise from the experimental measurements. Global optimization techniques, such as those based on the response surface (RS) concept are becoming popular in part because they can overcome some of these barriers. However, there are also fundamental issues related to such global optimization technique such as RS. For example, in high dimensional design spaces, typically only a small number of function evaluations are available due to computational and experimental costs. On the other hand, complex features of the design variables do not allow one to model the global characteristics of the design space with simple quadratic polynomials. Consequently a main challenge is to reduce the size of the region where we fit the RS, or make it more accurate in the regions where the optimum is likely to reside. Response Surface techniques using either polynomials or and Neural Network (NN) methods offer designers alternatives to conduct design optimization. The RS technique employs statistical and numerical techniques to establish the relationship between design variables and objective/constraint functions, typically using polynomials. In this study, we aim at addressing issues related to the following questions: (1) How to identify outliers associated with a given RS representation and improve the RS model via appropriate treatments? (2) How to focus on selected design data so that RS can give better performance in regions critical to design optimization? (3) How to combine NN and polynomial techniques for improving the accuracy of the RS model?

Papila, Nilay↗

Do nonlinearities play a significant role in short term, beat-to-beat variability?

Numerous studies of short-term beat-to-beat variability in cardiovascular signals have not resolved the debate about the completeness of linear analysis techniques. This aim of this paper is to evaluate further the role of nonlinearities in short-term, beat-to-beat variability. We compared linear autoregressive moving average (ARMA) and nonlinear neural network (NN) models for predicting instantaneous heart rate (HR) and mean arterial blood pressure (BP) from past HR and BP. To evaluate these models, we used HR and BP time series from the MIMIC database. Experimental results indicate that NN-based nonlinearities do not play a significant role and suggest that ARMA linear analysis techniques provide adequate characterization of the system dynamics responsible for generating short-term, beat-to-beat variability.

NASA Discipline Cardiopulmonary↗

Microscopic optical model calculations of 4He, 12C-nucleus absorption cross sections

Calculations of absorption cross sections using a microscopic first-order optical potential for heavy-ion scattering are compared with experiments. In-medium nucleon-nucleon (NN) cross sections were used to calculate the two-body scattering amplitude. A medium-modified first-order optical potential was obtained for heavy-ion scattering using the in-medium two-body scattering amplitude. A partial wave expansion of the Lippmann-Schwinger equation in momentum space was used to calculate the absorption cross sections for various systems. The results are presented for the absorption cross sections for 4He-nucleus and 12C-nucleus scattering systems and are compared with the experimental values in the energy range 18-83A MeV. The use of the in-medium NN cross sections is found to result in significant reduction of the free space absorption cross sections in agreement with experiment.

NASA Discipline Radiation Health↗

Lessons Learned and Flight Results from the F15 Intelligent Flight Control System Project

A viewgraph presentation on the lessons learned and flight results from the F15 Intelligent Flight Control System (IFCS) project is shown. The topics include: 1) F-15 IFCS Project Goals; 2) Motivation; 3) IFCS Approach; 4) NASA F-15 #837 Aircraft Description; 5) Flight Envelope; 6) Limited Authority System; 7) NN Floating Limiter; 8) Flight Experiment; 9) Adaptation Goals; 10) Handling Qualities Performance Metric; 11) Project Phases; 12) Indirect Adaptive Control Architecture; 13) Indirect Adaptive Experience and Lessons Learned; 14) Gen II Direct Adaptive Control Architecture; 15) Current Status; 16) Effect of Canard Multiplier; 17) Simulated Canard Failure Stab Open Loop; 18) Canard Multiplier Effect Closed Loop Freq. Resp.; 19) Simulated Canard Failure Stab Open Loop with Adaptation; 20) Canard Multiplier Effect Closed Loop with Adaptation; 21) Gen 2 NN Wts from Simulation; 22) Direct Adaptive Experience and Lessons Learned; and 23) Conclusions

Bosworth, John↗

Intelligent Vision Systems Independent Research and Development (IR&D) 2006

This report summarizes results in conduct of research sponsored by the 2006 Independent Research and Development (IR&D) program at Marshall Space Flight Center (MSFC) at Redstone Arsenal, Alabama. The focus of this IR&D is neural network (NN) technology provided by Imagination Engines, Incorporated (IEI) of St. Louis, Missouri. The technology already has many commercial, military, and governmental applications, and a rapidly growing list of other potential spin-offs. The goal for this IR&D is implementation and demonstration of the technology for autonomous robotic operations, first in software and ultimately in one or more hardware realizations. Testing is targeted specifically to the MSFC Flat Floor, but may also include other robotic platforms at MSFC, as time and funds permit. For the purpose of this report, the NN technology will be referred to by IEI's designation for a subset configuration of its patented technology suite: Self-Training Autonomous Neural Network Object (STANNO).

Patrick, Clinton↗

Aircraft system modeling error and control error

A method for modeling error-driven adaptive control of an aircraft. Normal aircraft plant dynamics is modeled, using an original plant description in which a controller responds to a tracking error e(k) to drive the component to a normal reference value according to an asymptote curve. Where the system senses that (1) at least one aircraft plant component is experiencing an excursion and (2) the return of this component value toward its reference value is not proceeding according to the expected controller characteristics, neural network (NN) modeling of aircraft plant operation may be changed. However, if (1) is satisfied but the error component is returning toward its reference value according to expected controller characteristics, the NN will continue to model operation of the aircraft plant according to an original description.

Kulkarni, Nilesh V.↗

Optimization of a Multi-Stage ATR System for Small Target Identification

An Automated Target Recognition system (ATR) was developed to locate and target small object in images and videos. The data is preprocessed and sent to a grayscale optical correlator (GOC) filter to identify possible regionsof- interest (ROIs). Next, features are extracted from ROIs based on Principal Component Analysis (PCA) and sent to neural network (NN) to be classified. The features are analyzed by the NN classifier indicating if each ROI contains the desired target or not. The ATR system was found useful in identifying small boats in open sea. However, due to "noisy background," such as weather conditions, background buildings, or water wakes, some false targets are mis-classified. Feedforward backpropagation and Radial Basis neural networks are optimized for generalization of representative features to reduce false-alarm rate. The neural networks are compared for their performance in classification accuracy, classifying time, and training time.

false alarm rate↗

In-Situ and Remote-Sensing Data Fusion Using Machine Learning Techniques to Infer Urban and Fire Related Pollution Plumes

Airmass type characterization is key in understanding the relative contribution of various emission sources to atmospheric composition and air quality and can be useful in bottom-up model validation and emission inventories. However, classification of pollution plumes from space is often not trivial. Sub-orbital campaigns, such as SEAC4RS (Studies of Emissions, Atmospheric Composition, Clouds and Climate Coupling by Regional Surveys) give us a unique opportunity to study atmospheric composition in detail, by using a vast suite of in-situ instruments for the detection of trace gases and aerosols. These measurements allow identification of spatial and temporal atmospheric composition changes due to various pollution plumes resulting from urban, biogenic and smoke emissions. Nevertheless, to transfer the knowledge gathered from such campaigns into a global spatial and temporal context, there is a need to develop workflow that can be applicable to measurements from space. In this work we rely on sub-orbital in-situ and total column remote sensing measurements of various pollution plumes taken aboard the NASA DC-8 during 2013 SEAC4RS campaign, linking them through a neural-network (NN) algorithm to allow inference of pollution plume types by input of columnar aerosol and trace-gas measurements. In particular, we use the 4STAR (Spectrometer for Sky-Scanning, Sun-Tracking Atmospheric Research) airborne measurements of wavelength dependent aerosol optical depth (AOD), particle size proxies, O3, NO2 and water vapor to classify different pollution plumes. Our method relies on assigning a-priori ground-truth labeling to the various plumes, which include urban pollution, different fire types (i.e. forest and agriculture) and fire stage (i.e. fresh and aged) using cluster analysis of aerosol and trace-gases in-situ and auxiliary (e.g. trajectory) data and the training of a NN scheme to fit the best prediction parameters using 4STAR measurements as input. We explore our misclassification rates as related to our ground-truth labels, and with multi-layered pollution plume cases. The next step in our analysis is to optimize parameter selection for a scheme that can be applied to space-borne aerosol and trace-gas observation platforms such as OMI, and future geostationary satellites such as TEMPO and GEO-CAPE.

Neural-network↗

Quantifying Libya-4 Surface Reflectance Heterogeneity With WorldView-1, 2 and EO-1 Hyperion

The land surface imaging (LSI) virtual constellation approach promotes the concept of increasing Earth observations from multiple but disparate satellites. We evaluated this through spectral and spatial domains, by comparing surface reflectance from 30-m Hyperion and 2-m resolution WorldView-2 (WV-2) data in the Libya-4 pseudoinvariant calibration site. We convolved and resampled Hyperion to WV-2 bands using both cubic convolution and nearest neighbor (NN) interpolation. Additionally, WV-2 and WV-1 same-date imagery were processed as a cross-track stereo pair to generate a digital terrain model to evaluate the effects from large (>70 m) linear dunes. Agreement was moderate to low on dune peaks between WV-2 and Hyperion (R2 <; 0.4) but higher in areas of lower elevation and slope (R2 > 0.6). Our results provide a satellite sensor intercomparison protocol for an LSI virtual constellation at high spatial resolution, which should start with geolocation of pixels, followed by NN interpolation to avoid tall dunes that enhance surface reflectance differences across this internationally utilized site.

Hyperion↗

Experimental Demonstration and System Analysis for Plasmonic Force Propulsion

This project developed a higher-fidelity model of a recently envisioned small spacecraft propulsion system for precision pointing and proximity control. Plasmonic force propulsion harnesses solar light focused onto plasmon reactive subwavelength nanostructures to accelerate and expel nanoparticle propellant via strong optical forces. The goal of the project was to show that plasmonic space propulsion can provide the level of proximity and attitude control envisioned for future NASA nano/picosatellite missions, a level that is better than state-of-the-art approaches. We achieved this goal by showing that plasmonic force thrusters are feasible for a range of advanced mission concepts requiring swarm formations in a deep space environment. We performed three case studies that evaluated the performance of the plasmonic force propulsion thruster in a deep space, microsatellite swarm formation. These case studies assumed the propulsion system could generate thrust at the level predicted from our Phase 1 study (1.6 μN). Through these cases we were able to analyze the concept within a mission specific context through detailed orbital dynamics calculations. Results indicate that, with the Phase 1 estimated thrust level, the approach is promising for providing attitude control to swarm formation spacecraft. Further, we achieved goals related to technology development. Specifically, we experimentally demonstrated nanoparticle acceleration due to plasmonic forces with asymmetric nanostructures excited by focused laser light. Additionally, we investigated the thrust sensitivity and nanoparticle propellant injection dependencies upon thermal effects. As a result of our study, plasmonic force propulsion is at an early TRL 3. Active research and design has been conducted analytically and in the laboratory. Furthermore, practical applications such as the three case studies have been identified for the scientific basic principles that were observed. Future efforts related to fundamental understanding of these techniques should focus on 1) developing a standalone array of asymmetric nanostructures that can effectively interact with a stream or reservoir of particles or 2) experimentally evaluate a dielectrophoretic injector for nanoparticle propellant. The main limitation discovered about plasmonic propulsion regards performance estimates significantly below the Phase 1 estimations. Specifically, original assumptions in the Phase 1 project (notably, a linear array of asymmetric nanostructures) is not a viable approach to achieving significant acceleration, high exhaust velocity, of nanoparticles. More specifically, we assumed in Phase 1 that nanoparticles would be accelerated in series by a long linear array of asymmetric nanostructures. That is, the acceleration of the nanoparticle would build and increase with the kick received by each subsequent nanostructure. This is fundamentally flawed. The potential profile of a single nanostructure is such that it prohibits this phenomenon. The potential energy associated with the plasmon-generated dielectrophoretic force is a potential well, which is good for trapping nanoparticles, but cannot provide significant acceleration of particles to expel them out and away from the nanostructure. Further, a nanoparticle expelled from the first nanostructure would need to overcome the potential barrier for entry into the next nanostructure accelerating stage. Fundamentally, this effect means that a linear array of nanostructures is not a viable accelerating structure. Correspondingly then, acceleration can, or should, only be provided by one nanostructure, and the net acceleration and thrust force of a single nanostructure is small (~cm/s exhaust velocities, sub-nN level thrust vs. the 100’s m/s, μN originally envisioned). While our experiments demonstrated acceleration and manipulation of a nanoparticle using laser light in aqueous environment, the achievable energy and momentum addition to the nanoparticle from a single nanostructure stage is too low for useful propulsion. In terms of thrust prediction, the estimated thrust of 1.6 μN in Phase 1 is reduced to a few nN of thrust with this new insight and understanding of the concept. This thrust level is too small to achieve attitude control of swarms as originally envisioned.

Plasmonic Force↗

Direct Measurements of the Mechanical Strength of Carbon Nanotube - Aluminum Interfaces

Interfacial load transfer plays a critical role in the bulk mechanical performance of nanofiber-reinforced metallic-matrix nanocomposites (MMNC). In this paper, we investigate the mechanical strength of interfaces in double-walled carbon nanotube (CNT)-reinforced aluminum (Al) nanocomposites by using in situ electron microscopy nanomechanical single-tube pull-out techniques. The nanomechanical measurements reveal the shear lag effect on the CNT-Al interface that is found to possess an average interfacial shear strength (IFSS) of about 28.7 MPa. The study also shows that thermal annealing results in substantially higher binding strength interfaces between CNTs and Al matrices. The average IFSS of CNT-Al interfaces that were thermally annealed at 400 °C is found to reach about 35.3 MPa, a 23% increase from that of the non-annealed interfaces. The maximum load bearing capacity of the annealed interfaces reaches about 304 nN, a 40.1% increase from that of the non-annealed ones (about 217 nN). The findings are useful to better understand the load transfer mechanism in CNT-reinforced MMNC and the tuning and optimization of the reinforcing performance through thermal processing.

Interfacial strength↗

Investigation of Improved Wall Heat Flux Behavior Observed When Computing Hypersonic Flow Using a Face-averaged Nodal-gradient Approach On Tetrahedral Grids

We investigate the origin of a significant reduction in computed numerical “noise” in the spatial variation of computed wall heat flux observed when using a node-centered weighted least squares(WLSQ) gradient approach when solving the Reynolds-averaged Navier-Stokes (RANS) equations for hypersonic boundary layer flows on highly stretched tetrahedral grids. This investigation is conducted using a 2nd-order, cell-centered, finite-volume, discretization which we employ to contrast results obtained using two WLSQ gradient approaches: a conventional 3-D, cell-centered, node-neighbor, WLSQ gradient (NN-CCG) approach and a 3-D, face-averaged, node-centered gradient (F-ANG)approach. The F-ANG approach, is shown to produce significantly less “noise” in the spatial variation of wall heat flux, than the NN-CCG approach and we demonstrate the cause of this “noise” via a series of numerical experiments where we compute hypersonic laminar and turbulent boundary layer flows.We further investigate the level of grid resolution required for a tetrahedral grid to approach the fidelity of a grid resolved hexahedral grid solution obtained using an equivalent structured grid method.

Jeffery A. White↗

Hailstorm Analyses and Detection Derived from Current and Historical Satellite Data and Convective Environmental Parameters

We seek to demonstrate the extent to which hailstorms can be detected using a combination of geostationary (GEO) visible and infrared metrics of storm intensity and convective environmental parameters from reanalysis. Hailstorm identifications from low-Earth-orbiting (LEO) passive microwave sensors and maximum expected size of hail (MESH) from ground-based radar serve as a proxy for hail events. Data are analyzed for two warm seasons over the contiguous United States (CONUS). A neural network (NN) is trained to predict hailstorm detection dependent on optimal multi-variate weighting of observed and modeled input. The NN results are then applied to a 15-year Meteosat Second Generation climatology over South Africa to depict where hailstorms are most likely to occur. We also explore the impact of GEO imager resolution on our ability to discriminate hailstorms by matching GOES-13 (4 km) and GOES-16 (2 km) storm intensity metrics against hail characteristics using LEO, MESH, and spotter reports over CONUS during 2017, when both satellites were simultaneously imaging. Such analysis allows us to assess the feasibility of assembling a severe storm climate data record back to GOES-8, in the mid-1990’s. Finer spatial resolution of GOES-16 better resolves the updraft characteristics and intensities that are inherently linked to hail formation; however, GOES-13 can be normalized to achieve comparable detection capability. When intelligently combined with model-derived convective environmental parameters, GEO-derived storm intensity metrics enable high-spatial resolution hail risk assessment at hourly intervals throughout the diurnal cycle anywhere around the world and an improved understanding of hailstorms in the climate system.

Kyle F Itterly↗

Direct Comparisons Between GPM-DPR and CloudSat Snowfall Retrievals

Two spaceborne radars currently in orbit enable the sampling of snowfall near the surface and throughout the atmospheric column, namely, CloudSat’s Cloud Profiling Radar (CPR) and the Global Precipitation Measurement mission’s Dual-Frequency Precipitation Radar (GPM-DPR). In this paper, a direct comparison of the CPR’s 2C-SNOW-PROFILE (2CSP), the operational GPM-DPR algorithm (2ADPR) and a neural network (NN) retrieval applied to the GPM-DPR data is performed using coincident observations between both radars. Examination of over 3500 profiles within moderate to strong precipitation (Ka band ≥ 18 dBZ) show that the NN retrieval provides the closest retrieval of liquid equivalent precipitation rate R immediately above the melting level to the R retrieved just below the melting layer, agreeing within 5%. Meanwhile, 2CSP retrieves a maximum value of R at −15°C, decreases by 35% just above the melting layer, and is about 50% smaller than the GPM-DPR retrieved R below the melting layer. CPR-measured reflectivity shows median reduction of 2–3 dB from −15° to −2.5°C, likely the reason for the 2CSP retrieval reduction of R . Two case studies from NASA field campaigns [i.e., Olympic Mountains Experiment (OLYMPEX) and Investigation of Microphysics and Precipitation for Atlantic Coast-Threatening Snowstorms (IMPACTS)] provide analogs to the type of precipitating systems found in the comparison between retrieval products. For the snowfall events that GPM-DPR can observe, this work suggests that the 2CSP retrieval is likely underestimating the unattenuated reflectivity, resulting in a potential negative, or low, bias in R . Future work should investigate how frequently the underestimated reflectivity profiles occur within the CPR record and quantify its potential effects on global snowfall accumulation estimation.

Atmosphere↗

Machine Learning Approaches for Rare-Earth Silicate Environmental Barrier Coating Thermochemical and Thermomechanical Property Predictions

Environmental barrier coatings (EBCs) are a necessary enabling technology for the transition from superalloys to silicon carbide (SiC) ceramic matrix composites (CMCs) in gas turbine engines for increased efficiency and decreased fuel costs. SiC-based CMCs are prone to oxidation-based degradation in the engine hot section, and rare-earth (RE) silicates are promising candidates for EBCs due to their close thermal expansion match to the composite substrate and oxidation resistance. However, the design of EBCs is hindered by the large chemical space of candidate materials and the difficulty in obtaining material properties for engineering optimization. This is especially difficult as research continues into mixed-cation or “high-entropy” RE silicates. First-principles computational methods such as density functional theory (DFT) are highly effective at calculating material properties to guide coating design but are limited by their computational cost. Atomistic simulations have the potential to both accelerate property calculations and expand the properties able to be calculated due to their lower computational compared to DFT. However, they require interatomic potentials (IAPs) specific to the material system of interest, and, to our knowledge, there are no suitable IAPs for RE silicates. Machine learning (ML) is a promising technique to accelerate material property predictions indirectly by generating IAPs for atomistic simulations or via direct prediction. In this work, we present two ML approaches to accelerate the calculation of RE silicate properties relevant to EBC design: 1) a ML-derived interatomic potential (IAP) for atomistic simulations of yttrium disilicate (Y2Si2O7) from DFT training data, and 2) a neural network (NN) model to directly predict thermochemical properties of RE silicates and oxides directly from easily obtainable unit cell parameters. Classical MD simulations using the IAP yield lattice properties and bond lengths in good agreement with both DFT and experimental results from x-ray diffraction. Thermodynamic properties calculated using the finite-displacement phonon method and quasi-harmonic approximation were orders of magnitude faster than DFT with good agreement to the DFT results. The IAP was also used to calculate properties such as coefficient of thermal expansion (CTE) that require large simulation supercells and are therefore difficult with DFT. The IAP correctly predicted the anisotropic nature of the CTE in three different phases of Y2Si2O7. The NN model predicts constant pressure heat capacity, Cp, orders of magnitude faster than DFT calculations, which can enable its use as a surrogate model for multiscale simulations. The two methods presented in this work demonstrate the utility of ML for accelerating the prediction of RE silicate properties, which can in turn accelerate EBC design and optimization.

machine learning↗

AMSR-2 Daily Snow Depth Data Product Using a Neural Network Algorithm Trained by Collocated ICESat-2 Measurements

By using diffusion theory and Monte Carlo lidar radiative transfer simulations, Hu 1 et al. (2022b) has derived snow depth from the first-, second- and third-order moments of the lidar backscattering pathlength distribution. Lu 2 et al. (2022,2024) calculated the snow depth by applying the methods to the satellite ICESat-2 lidar measurements over the Arctic sea ice, as well as land surfaces of Northern Hemisphere. In this paper, a neural network (NN) algorithm, employing several channels from AMSR-2 and the humidity vertical profiles GMAO GEOS-IT, is trained to determine snow depth identified by time and geolocation matched 2019 ICESat-2 snow-depth data during winter months over the Arctic sea ice. The trained NN snow-depth was applied to 2014-2020 AMSR-2 clear pixel data, although the algorithms perform reasonably well in thinner clouds. This paper used AMSR-2 data, a passive microwave instrument to generate a wide range of snow depth data, covering extensive spatial areas in the cross-orbit direction.

Neural Network↗

Cislunar Trajectory Design and Maneuver Autonomy for NASA's Moon to Mars Architecture

NASA’s Moon to Mars architecture is an ambitious roadmap of manned cislunar and deep space exploration. The extensive amount of orbital assets required will place a significant burden on ground-based resources, such as communication networks and operations facilities. Spacecraft autonomy is essential for maintaining a vast number of complex missions beyond Earth orbit. To achieve full autonomy, spacecraft must be able to employ methods of robust maneuver design without an explicit dependence on commands sent from the ground. This level of autonomy is needed not only for stationkeeping, but also for outbound transfers. To address the need of spacecraft maneuver design autonomy, this work investigates the use of neural networks (NNs) in a supervised learning environment. A supervised learning approach for NNs allows for a curated training data set, consisting exclusively of perturbations applied to a desired mission concept of operations (ConOps). The proposed approach allows humans on the ground to design a specific mission ConOps before flight, then employ NNs to fly the mission robustly and autonomously. This investigation numerically tests maneuver autonomy in four highly sensitive regions of flight: orbit raising, translunar injection burns, powered lunar flybys, and invariant manifold insertion burns. These straining cases are contextualized by testing them in a demonstration mission, targeting an Earth-Moon L3 orbit. The study first establishes feasibility by automating impulsive burn maneuvers. However, some guidance algorithms will need more intensive commands, such as inertial pointing and angular rates. To validate this method, NN maneuver autonomy is applied to a finite burn model of the demonstration mission. The use of sequential, mission specific maneuvers provide an appropriate testbed to demonstrate the robustness of a NN trained on feasible perturbed states. Moreover, these scenarios provide preliminary proof-of-concept for fully autonomous missions that execute maneuvers without dependence upon explicit command uplinks. As a result, the technological advancement proposed in this work may significantly ease the strain on ground-based mission operations. This would enable complex and autonomous mission execution in cislunar and deep space regimes, filling a technology gap required to support future manned missions.

NASA↗

Intermodulation characteristics of X-band IMPATT amplifiers.

Measurement of the intermodulation products produced when two equal amplitude signals are applied to the input of an X-band IMPATT diode amplifier. A Si p(+)nn(+) IMPATT diode was operated in a double-slug-tuned reflection amplifier circuit that was tuned to provide 20 dB of small-signal gain at 9.340 GHz. The intermodulation tests consist of measurements of the magnitudes and frequencies of the amplifier output signals as a function of the input signal drive levels and frequency separations. The gain and single-frequency characteristics of the amplifier were also measured and are used along with the theoretical device and circuit admittance characteristics as a basis for explanation of the intermodulation results. A low-frequency dominance mechanism is found to exist in which the low-frequency signals are amplified more than the high-frequency signals. This mechanism becomes more significant as the amplifier drive level is increased.

Trew, R. J.↗