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At least 325 records · Page 18

Numerical analysis of unsteady flow in a converging-diverging nozzle

This study investigates the physics of jet noise by the numerical solution of the three dimensional unsteady Navier-Stokes equations for a low-supersonic jet (Mach numbers on the order of 1.4) from a converging-diverging (C-D) nozzle and mixing with a subsonic surrounding flow. The numerical method used for the solution of these equations is the second order accurate MacCormack explicit predictor-corrector scheme. The numerical results are compared to the experimental results of Yamamoto for the same C-D nozzle geometry and similar operating conditions. The goal of the study is to use numerical simulation techniques to resolve accurately physical processes which contribute to jet noise, and to assess whether performing these simulations in a three dimensional geometry is worth the additional cost in computing resources as compared to a comparable simulation on a two dimensional planar or axisymmetric geometry. Scientific visualization is used to observe the spreading characteristics of the jet, as well as to examine the structure of the shocks within the jet core. The time average velocity and turbulence intensity level at various locations are computed and compared with experimental results. A two point space-time cross correlation is used to compute the mean convection speed through the shear layer, and these predictions are compared with results from theory.

James N Scott↗

Experimental Observations on a Low Strain Counter-Flow Diffusion Flame: Flow and Bouyancy Effects

Diffusion flames are of great interest in fire safety and many industrial processes. The counter-flow configuration provides a constant strain flow, and therefore is ideal to study the structure of diffusion flames. Most studies have concentrated on the high velocity, high strain limit, since buoyantly induced instabilities will disintegrate the planar flame as the velocity decreases. Only recently, experimental studies in microgravity conditions have begun to explore the low strain regimes. Numerical work has shown the coupling between gas phase reaction rates, soot reaction rates, and radiation. For these programs, size, geometry and experimental conditions have been chosen to keep the flame unaffected by the physical boundaries. When the physical boundaries can not be considered infinitely far from the reaction zone discrepancies arise. A computational study that includes boundary effects and accounts for the deviations occurring when the major potential flow assumptions are relaxed was presented by Borlik et al. This development properly incorporates all heat loss terms and shows the possibility of extinction in the low strain regime. A major constraint of studying the low strain regime is buoyancy. Buoyant instabilities have been shown to have a significant effect on the nature of reactants and heat transport, and can introduce instabilities on the flow that result in phenomena such as flickering or fingering. The counter-flow configuration has been shown to provide a flame with no symmetry disrupting instabilities for inlet velocities greater than 50 mm/s. As the velocity approaches this limit, the characteristic length of the experiment has to be reduced to a few millimetres so as to keep the Rayleigh number (Ra L = (β g 0 L 3 ∆T)/(𝑎v)) below 2000. In this work, a rectangular counter-flow burner was used to study a two-dimensional counter-flow diffusion flame. Flow visualisation and Particle Image Velocimetry served to describe the nature of the stagnation plane for strain rates smaller than 100 (1/s). These experiments were conducted with a non-reacting flow. Video images of a propane air diffusion flame were used to describe the behaviour of a diffusion flame in this regime. Flame geometry and pulsation frequency are described.

J. A. Sutula↗

Improved Method of Manufacturing SiC Devices

The phrase, "common-layered architecture for semiconductor silicon carbide" ("CLASSiC") denotes a method of batch fabrication of microelectromechanical and semiconductor devices from bulk silicon carbide. CLASSiC is the latest in a series of related methods developed in recent years in continuing efforts to standardize SiC-fabrication processes. CLASSiC encompasses both institutional and technological innovations that can be exploited separately or in combination to make the manufacture of SiC devices more economical. Examples of such devices are piezoresistive pressure sensors, strain gauges, vibration sensors, and turbulence-intensity sensors for use in harsh environments (e.g., high-temperature, high-pressure, corrosive atmospheres). The institutional innovation is to manufacture devices for different customers (individuals, companies, and/or other entities) simultaneously in the same batch. This innovation is based on utilization of the capability for fabrication, on the same substrate, of multiple SiC devices having different functionalities (see figure). Multiple customers can purchase shares of the area on the same substrate, each customer s share being apportioned according to the customer s production-volume requirement. This makes it possible for multiple customers to share costs in a common foundry, so that the capital equipment cost per customer in the inherently low-volume SiC-product market can be reduced significantly. One of the technological innovations is a five-mask process that is based on an established set of process design rules. The rules provide for standardization of the fabrication process, yet are flexible enough to enable multiple customers to lay out masks for their portions of the SiC substrate to provide for simultaneous batch fabrication of their various devices. In a related prior method, denoted multi-user fabrication in silicon carbide (MUSiC), the fabrication process is based largely on surface micromachining of poly SiC. However, in MUSiC one cannot exploit the superior sensing, thermomechanical, and electrical properties of single-crystal 6H-SiC or 4H-SiC. As a complement to MUSiC, the CLASSiC five-mask process can be utilized to fabricate multiple devices in bulk single-crystal SiC of any polytype. The five-mask process makes fabrication less complex because it eliminates the need for large-area deposition and removal of sacrificial material. Other innovations in CLASSiC pertain to selective etching of indium tin oxide and aluminum in connection with multilayer metallization. One major characteristic of bulk micromachined microelectromechanical devices is the presence of three-dimensional (3D) structures. Any 3D recesses that already exist at a given step in a fabrication process usually make it difficult to apply a planar coat of photoresist for metallization and other subsequent process steps. To overcome this difficulty, the CLASSiC process includes a reversal of part of the conventional flow: Metallization is performed before the recesses are etched.

Okojie, Robert S.↗

Micro-Textured Black Silicon Wick for Silicon Heat Pipe Array

Planar, semiconductor heat arrays have been previously proposed and developed; however, this design makes use of a novel, microscale black silicon wick structure that provides increased capillary pumping pressure of the internal working fluid, resulting in increased effective thermal conductivity of the device, and also enables operation of the device in any orientation with respect to the gravity vector. In a heat pipe, the efficiency of thermal transfer from the case to the working fluid is directly proportional to the surface area of the wick in contact with the fluid. Also, the primary failure mechanism for heat pipes operating within the temperature range of interest is inadequate capillary pressure for the return of fluid from the condenser to the wick. This is also what makes the operation of heat pipes orientation-sensitive. Thus, the two primary requirements for a good wick design are a large surface area and high capillary pressure. Surface area can be maximized through nanomachined surface roughening. Capillary pressure is largely driven by the working fluid and wick structure. The proposed nanostructure wick has characteristic dimensions on the order of tens of microns, which promotes menisci of very small radii. This results in the possibility of enormous pumping potential due to the inverse proportionality with radius. Wetting, which also enhances capillary pumping, can be maximized through growth of an oxide layer or material deposition (e.g. TiO2) to create a superhydrophilic surface.

Yee, Karl Y.↗

Hypersonic Boundary-Layer Instabilities over Ogive-Cylinder Models

Computational investigations of an ogive-cylinder geometry with varying nosetips at zero degrees angle of attack are presented. The model geometry and conditions are selected to match experiments conducted in the Air Force Research Laboratory (AFRL) Mach 6 Ludwieg Tube. Five nosetips of interest were selected for the computational studies herein: two sharp ogives, two blunt ogives, and one hemispherical nosetip. Computations are performed at a freestream Reynolds number of 7.01 × 10 6 m -1 . Each sharp and blunt tip ogives had a 14 and 28 degree version for the tip angles. A cylindrical section follows the nosetip, resulting in a meter long model such as in the experiments. The laminar flow solutions are analyzed. The boundary-layer-edge properties and the velocity and temperature profiles are compared across streamwise locations aft of the ogive-cylinder junction. The blunt nosetips induce an entropy layer that envelopes the boundary-layer profiles. Modal stability analysis identifies most amplified frequencies corresponding to Mack’s second modes that agree with experimental results for the sharp tips. Similar to the experimental measurements based on wall-mounted pressure sensors, no unstable modes are found for the blunt models. Nonmodal analysis revealed a broadband set of disturbances present for the blunter tips, in agreement with experimental observations. Flow perturbation contours of most amplified planar and oblique disturbances are shown to qualitatively match wind tunnel Schlieren images, with a switch from rope-like to elongated structures, i.e., from high frequency Mack’s second modes to low frequency Mack’s first modes, as the nosetip angle is increased for the sharp tip, and from boundary-layer to entropy-layer disturbances as the bluntness is increased.

Boundary layer transition↗

Hypersonic Boundary-Layer Instabilities over Ogive-Cylinder Models

Computational investigations of an ogive-cylinder geometry with varying nosetips at zero degrees angle of attack are presented. The model geometry and conditions are selected to match experiments conducted in the Air Force Research Laboratory (AFRL) Mach 6 Ludwieg Tube. Five nosetips of interest were selected for the computational studies herein: two sharp ogives, two blunt ogives, and one hemispherical nosetip. Computations are performed at a freestream Reynolds number of 7.01 × 10 6 m -1 . Each sharp and blunt tip ogives had a 14 and 28 degree version for the tip angles. A cylindrical section follows the nosetip, resulting in a meter long model such as in the experiments. The laminar flow solutions are analyzed. The boundary-layer-edge properties and the velocity and temperature profiles are compared across streamwise locations aft of the ogive-cylinder junction. The blunt nosetips induce an entropy layer that envelopes the boundary-layer profiles. Modal stability analysis identifies most amplified frequencies corresponding to Mack’s second modes that agree with experimental results for the sharp tips. Similar to the experimental measurements based on wall-mounted pressure sensors, no unstable modes are found for the blunt models. Nonmodal analysis revealed a broadband set of disturbances present for the blunter tips, in agreement with experimental observations. Flow perturbation contours of most amplified planar and oblique disturbances are shown to qualitatively match wind tunnel Schlieren images, with a switch from rope-like to elongated structures, i.e., from high frequency Mack’s second modes to low frequency Mack’s first modes, as the nosetip angle is increased for the sharp tip, and from boundary-layer to entropy-layer disturbances as the bluntness is increased.

Boundary layer transition↗

LPE growth of 1.3 micron InGaAsP CW lasers on /110/ InP substrates

A description is presented of the liquid-phase epitaxial (LPE) growth of high-quality InGaAsP/InP continuous-wave (CW) laser structures on (110) InP substrates using conventional LPE without the need for special growth procedures. Double heterojunction laser structures were grown using the LPE supercooling method with a horizontal sliding boat. Low broad-area current densities (970 A/sq cm) and CW operation achieved at room temperature indicate that results comparable to up-to-date devices may be achieved. The inherent tendency for surface planarity maintenance due to the perfect surface stoichiometry of the (110) surface is a feature that may lend itself to the generation of improved interface growth in quaternary III-V and related semiconductor alloy systems. The similar cross-sectional appearance of structures grown on (110) and (100) orientations show that conventional LPE can be used with (110) surface planes without introducing special growth procedures.

Hawrylo, F. Z.↗

Modulation Collimator Fine Grids for HESP

The proposed High Engergy-Solar Physics (HESP) million will require fine, precise, high aspect ratio modulation collimators for the High Energy Imagin Spectrometer (HEISPEC). The fabrication approach described here rests on the proven precision of semiconductor lithography - the ability to replicate extremely accurate patterns onto different planar substrateds.

LIGA HESP pitch structures solar x-rays gamma rays↗

Phenocryst fabric in lunar basalt sample 12052 from the Ocean of Storms.

Pyroxene phenocrysts in Apollo 12 sample 12052, a porphyritic basalt, have a weak, planar preferred orientation and a lineation as determined by crystal-elongation measurements and universal-stage measurements in orthogonal thin sections. The structures are probably the result of laminar flow. Numerous vugs and the flow foliation in sample 12052 suggest crystallization as a surface flow or a near-surface sill. Flowage appears to have ceased by the time of crystallization of the variolitic groundmass of the sample. The fabric data suggest a two-stage crystallization of sample 12052.

Greenwood, W. R.↗

A study of compressible mixing layers using filtered Rayleigh scattering

High Reynolds number compressible planar free shear layers were studied using a planar laser visualization technique. Two convective Mach numbers, M(c) = 0.51 and 0.86, were studied in the developing and fully developed regions. The structures in the M(c) = 0.51 case were characterized by 2D core and roller regions, similar to subsonic shear layers. Also for the M(c) = 0.51 case, plan views in the developing region showed the existence of streamwise streaks, possibly indicating the presence of organized streamwise vorticity. The M(c) = 0.86 flow was much less organized than the lower convective Mach number case and highly three dimensional.

Elliott, Gregory S.↗

Thermal conductivity of zirconia thermal barrier coatings

Thermal barrier coatings (TBC's) applied to the hot gas components of turbine engines lead to enhanced fuel efficiency and component reliability. Understanding the mechanisms which control the thermal transport behavior of the TBC's is of primary importance. Physical vapor description (PVD) and plasma spraying (PS) are the two most commonly used coating techniques. These techniques produce coatings with unique microstructures which control their performance and stability. The PS coatings were applied with either standard power or hollow sphere particles. The hollow sphere particles yielded a lower density and lower thermal conductivity coating. The thermal conductivity of both fully and partially stabilized zirconia, before and after thermal aging, will be compared. The thermal conductivity of the coatings permanently increase upon being exposed to high temperatures. These increases are attributed to microstructural changes within the coatings. Sintering of the as fabricated plasma sprayed lamellar structure is observed by scanning electron microscopy of coatings isothermally heat treated at temperatures greater than 1100 C. During this sintering process the planar porosity between lamella is converted to a series of small spherical pores. The change in pore morphology is the primary reason for the observed increase in thermal conductivity. This increase in thermal conductivity can be modeled using a relationship which depends on both the temperature and time of exposure. Although the PVD coatings are less susceptible to thermal aging effects, preliminary results suggest that they have a higher thermal conductivity than PS coatings, both before and after thermal aging. The increases in thermal conductivity due to thermal aging for partially stabilized plasma sprayed zirconia have been found to be less than for fully stabilized plasma sprayed zirconia coatings. The high temperature thermal diffusivity data indicates that if these coatings reach a temperature above 1100 C during operation, they will begin to lose their effectiveness as a thermal barrier.

Dinwiddie, R. B.↗

Thermal conductivity of zirconia thermal barrier coatings

Thermal barrier coatings (TBC's) applied to the hot gas components of turbine engines lead to enhanced fuel efficiency and component reliability. Understanding the mechanisms which control the thermal transport behavior of the TBC's is of primary importance. Physical vapor deposition (PVD) and plasma spraying (PS) are the two most commonly used coating techniques. These techniques produce coatings with unique microstructures which control their performance and stability. The PS coatings were applied with either standard powder or hollow sphere particles. The hollow sphere particles yielded a lower density and lower thermal conductivity coating. The thermal conductivity of both fully and partially stabilized zirconia, before and after thermal aging, will be compared. The thermal conductivity of the coatings permanently increases upon exposed to high temperatures. These increases are attributed to microstructural changes within the coatings. Sintering of the as-fabricated plasma sprayed lamellar structure is observed by scanning electron microscopy of coatings isothermally heat treated at temperatures greater than 1100 C. During this sintering process the planar porosity between lamella is converted to a series of small spherical pores. The change in pore morphology is the primary reason for the observed increase in thermal conductivity. This increase in thermal conductivity can be modeled using a relationship which depends on both the temperature and time of exposure. Although the PVD coatings are less susceptible to thermal aging effects, preliminary results suggest that they have a higher thermal conductivity than PS coatings, both before and after thermal aging. The increases in thermal conductivity due to thermal aging for partially stabilized plasma sprayed zirconia have been found to be less than for fully stabilized plasma sprayed zirconia coatings. The high temperature thermal diffusivity data indicate that if these coatings reach a temperature above 1100 C during operation, they will begin to lose their effectiveness as a thermal barrier.

Dinwiddie, R. B.↗

Large Eddy Simulation Of Gravitational Effects In Transitional And Turbulent Gas-Jet Diffusion Flames

The influence of gravity on the spatial and the compositional structures of transitional and turbulent hydrocarbon diffusion flames are studies via large eddy simulation (LES) and direct numerical simulation (DNS) of round and planar jets. The subgrid-scale (SGS) closures in LES are based on the filtered mass density function (FMDF) methodology. The FMDF represents the joint probability density function (PDF) of the SGS scalars, and is obtained by solving its transport equation. The fundamental advantage of LES/FMDF is that it accounts for the effects of chemical reaction and buoyancy exactly. The methodology is employed for capturing some of the fundamental influences of gravity in equilibrium flames via realistic chemical kinetic schemes. Some preliminary investigation of the gravity effects in non-equilibrium flames is also conducted, but with idealized chemical kinetics models.

Jaberi, Farhad A.↗

Carbon Nanofiber-Based, High-Frequency, High-Q, Miniaturized Mechanical Resonators

High Q resonators are a critical component of stable, low-noise communication systems, radar, and precise timing applications such as atomic clocks. In electronic resonators based on Si integrated circuits, resistive losses increase as a result of the continued reduction in device dimensions, which decreases their Q values. On the other hand, due to the mechanical construct of bulk acoustic wave (BAW) and surface acoustic wave (SAW) resonators, such loss mechanisms are absent, enabling higher Q-values for both BAW and SAW resonators compared to their electronic counterparts. The other advantages of mechanical resonators are their inherently higher radiation tolerance, a factor that makes them attractive for NASA s extreme environment planetary missions, for example to the Jovian environments where the radiation doses are at hostile levels. Despite these advantages, both BAW and SAW resonators suffer from low resonant frequencies and they are also physically large, which precludes their integration into miniaturized electronic systems. Because there is a need to move the resonant frequency of oscillators to the order of gigahertz, new technologies and materials are being investigated that will make performance at those frequencies attainable. By moving to nanoscale structures, in this case vertically oriented, cantilevered carbon nanotubes (CNTs), that have larger aspect ratios (length/thickness) and extremely high elastic moduli, it is possible to overcome the two disadvantages of both bulk acoustic wave (BAW) and surface acoustic wave (SAW) resonators. Nano-electro-mechanical systems (NEMS) that utilize high aspect ratio nanomaterials exhibiting high elastic moduli (e.g., carbon-based nanomaterials) benefit from high Qs, operate at high frequency, and have small force constants that translate to high responsivity that results in improved sensitivity, lower power consumption, and im - proved tunablity. NEMS resonators have recently been demonstrated using topdown, lithographically fabricated ap - proaches to form cantilever or bridgetype structures. Top-down approaches, however, rely on complicated and expensive e-beam lithography, and often require a release mechanism. Reso - nance effects in structures synthesized using bottom-up approaches have also recently been reported based on carbon nanotubes, but such approaches have relied on a planar two-dimensional (2D) geometry. In this innovation, vertically aligned tubes synthesized using a bottom- up approach have been considered, where the vertical orientation of the tubes has the potential to increase integration density even further. The simulation of a vertically oriented, cantilevered carbon nanotube was performed using COMSOL Multi - physics, a finite element simulation package. All simulations were performed in a 2D geometry that provided consistent results and minimized computational complexity. The simulations assumed a vertically oriented, cantilevered nanotube of uniform density (1.5 g/cu cm). An elastic modulus was assumed to be 600 GPa, relative permittivity of the nanotube was assumed to be 5.0, and Poisson s ratio was assumed to be 0.2. It should be noted that the relative permittivity and Poisson s ratio for the nanotubes of interest are not known accurately. However, as in previous simulations, the relative permittivity and Poisson s ratios were treated as weak variables in the simulation, and no significant changes were recognized when these variables were varied.

Kaul, Anupama B.↗

Synthesis, Structure, Characterization, and Decomposition of Nickel Dithiocarbamates: Effect of Precursor Structure and Processing Conditions on Solid-State Products

Single-crystal X-ray structures of four nickel dithiocarbamate complexes, the homoleptic mixed-organic bis-dithiocarbamates Ni[S2CN(isopropyl)(benzyl)]2, Ni[S2CN(ethyl)(n-butyl)]2, and Ni[S2CN(phenyl)(benzyl)]2, as well as the heteroleptic mixed-ligand complex NiCl[P(phenyl)3][(S2CN(phenyl)(benzyl)], were determined. Synthetic, spectroscopic, structural, thermal, and sulfide materials studies are discussed in light of prior literature. The spectroscopic results are routine. A slightly distorted square-planar nickel coordination environment was observed for all four complexes. The organic residues adopt conformations to minimize steric interactions. Steric effects also may determine puckering, if any, about the nickel and nitrogen atoms, both of which are planar or nearly so. A trans-influence affects the Ni-S bond distances. Nitrogen atoms interact with the CS2 carbons with a bond order of about 1.5, and the other substituents on nitrogen display transoid conformations. There are no strong intermolecular interactions, consistent with prior observations of the volatility of nickel dithiocarbamate complexes. Thermogravimetric analysis of the homoleptic species under inert atmosphere is consistent with production of 1:1 nickel sulfide phases. Thermolysis of nickel dithiocarbamates under flowing nitrogen produced hexagonal or -NiS as the major phase; thermolysis under flowing forming gas produced millerite (-NiS) at 300 C, godlevskite (Ni9S8) at 325 and 350 C, and heazlewoodite (Ni3S2) at 400 and 450 C. Failure to exclude oxygen results in production of nickel oxide. Nickel sulfide phases produced seem to be primarily influenced by processing conditions, in agreement with prior literature. Nickel dithiocarbamate complexes demonstrate significant promise to serve as single-source precursors to nickel sulfides, a quite interesting family of materials with numerous potential applications.

microscopy↗

TriTruss Packaging and Deployment Trade Study

An architecture and feasibility study of next generation In-Space Assembled Telescopes (iSAT) concluded that robotic in-space assembly of modular components is necessary to enable large (>15-meter diameter) primary apertures. The iSAT study recommended that the foundational structure be assembled from modular TriTruss modules that are packaged for launch, deployed on-orbit and robotically assembled into the final configuration. This paper will describe and summarize the results of a trade study that investigated viable concept of operations (ConOps) for the packaging and deployment (P&D) of individual planar TriTruss modules that could be assembled to form a large aperture iSAT. The ideal TriTruss P&D concept is defined as one that: allows for efficient packaging; has sufficient geometric versatility to be launch vehicle independent; provides a stiff and lightweight structure; has low mechanical complexity; and has component modularity. The P&D concept should allow for prelaunch subsystem or utility integration if required. The concept would be kinematically simple and be robotically deployed using a minimum number of specialized tools. In this first phase of an ongoing more comprehensive trade study, concepts were proposed and then evaluated based on initial metrics representing features of an ideal P&D concept. The P&D concepts evaluated are categorized as: core collapse, face collapse, and erectable structures. Sub-scale models were constructed to help understand the kinematics and mechanical complexity required to enable P&D. Based on a weighting scale, the most promising candidate P&D concepts have selected and will undergo more rigorous structural design, analysis, and testing in the study’s next phase. The ultimate goal of the comprehensive trade study will be to recommend a single TriTruss design and associated P&D concept that will be built and evaluated at NASA Langley Research Center’s In-Space Assembly Laboratory.

in-space assembly (ISA)↗

Extended-Range Ultrarefractive 1D Photonic Crystal Prisms

A proposal has been made to exploit the special wavelength-dispersive characteristics of devices of the type described in One-Dimensional Photonic Crystal Superprisms (NPO-30232) NASA Tech Briefs, Vol. 29, No. 4 (April 2005), page 10a. A photonic crystal is an optical component that has a periodic structure comprising two dielectric materials with high dielectric contrast (e.g., a semiconductor and air), with geometrical feature sizes comparable to or smaller than light wavelengths of interest. Experimental superprisms have been realized as photonic crystals having three-dimensional (3D) structures comprising regions of amorphous Si alternating with regions of SiO2, fabricated in a complex process that included sputtering. A photonic crystal of the type to be exploited according to the present proposal is said to be one-dimensional (1D) because its contrasting dielectric materials would be stacked in parallel planar layers; in other words, there would be spatial periodicity in one dimension only. The processes of designing and fabricating 1D photonic crystal superprisms would be simpler and, hence, would cost less than do those for 3D photonic crystal superprisms. As in 3D structures, 1D photonic crystals may be used in applications such as wavelength-division multiplexing. In the extended-range configuration, it is also suitable for spectrometry applications. As an engineered structure or artificially engineered material, a photonic crystal can exhibit optical properties not commonly found in natural substances. Prior research had revealed several classes of photonic crystal structures for which the propagation of electromagnetic radiation is forbidden in certain frequency ranges, denoted photonic bandgaps. It had also been found that in narrow frequency bands just outside the photonic bandgaps, the angular wavelength dispersion of electromagnetic waves propagating in photonic crystal superprisms is much stronger than is the angular wavelength dispersion obtained by use of conventional prisms and diffraction gratings and is highly nonlinear.

Ting, David Z.↗

Recent advances in antenna synthesis.

A technique for the synthesis of planar aperture antennas has been developed. It applies equally well to continuous or array type apertures. Patterns with shaped main beams and complex sidelobe structures can be synthesized. The method involves applying corrections iteratively and converging toward the desired pattern. The iteration process terminates when the synthesized pattern approximates the desired pattern to within a specified tolerance. A computer program has been written to perform all calculations. The source distribution which is required to produce the synthesized pattern is provided as output. The method is such that patterns requiring complex source distributions will not be synthesized (such as superdirective patterns).

Stutzman, W. L.↗