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Study of remote probing of inhomogeneous media making use of the known reflection coefficient of the medium as a function of the varied incident angle of the probing plane wave. An analytical method is developed for processing these reflection coefficient data. A critical evaluation of the numerical aspects of the method is presented.
This work addresses the problem of excitation of a parallel plate waveguide by an array of rectangular waveguides that arises in applications such as the continuous transverse stub (CTS) antenna and dual-polarized parabolic cylindrical reflector antennas excited by a scanning line source. In order to design the junction region between the parallel plate waveguide and the linear array of rectangular waveguides, waveguide sizes have to be chosen so that the input match is adequate for the range of scan angles for both polarizations. Electromagnetic wave scattered by the junction of a parallel plate waveguide by an array of rectangular waveguides is analyzed by formulating coupled integral equations for the aperture electric field at the junction. The integral equations are solved by the method of moments. In order to make the computational process efficient and accurate, the method of weighted averaging was used to evaluate rapidly oscillating integrals encountered in the moment matrix. In addition, the real axis spectral integral is evaluated in a deformed contour for speed and accuracy. The MoM results for a large finite array have been validated by comparing its reflection coefficients with corresponding results for an infinite array generated by the commercial finite element code, HFSS. Once the aperture electric field is determined by MoM, the input reflection coefficients at each waveguide port, and coupling for each polarization over the range of useful scan angles, are easily obtained. Results for the input impedance and coupling characteristics for both the vertical and horizontal polarizations are presented over a range of scan angles. It is shown that the scan range is limited to about 35 for both polarizations and therefore the optimum waveguide is a square of size equal to about 0.62 free space wavelength.
Here, we present PyOECP, a Python-based flexible open-source software for estimating and modeling the complex permittivity obtained from the open-ended coaxial probe (OECP) technique. The transformation of the measured reflection coefficient to complex permittivity is performed based on three different methods. The software library contains the dielectric spectra of common reference liquids, which can be used to transform the reflection coefficient into the dielectric spectra. Several Python routines that are commonly employed (e.g., SciPy and NumPy) in the field of science and engineering are required only so that the users can alter the software structure depending on their needs. The modeling algorithm exploits the Markov Chain Monte Carlo method for the data regression. The discrete relaxation models can be built by a proper combination of well-known relaxation models. In addition to these models, electrode polarization, a typical measurement artifact for interpreting dielectric spectra, can be incorporated into the modeling algorithm. A continuous relaxation model, which solves the Fredholm integral equation of the first kind (a mathematically ill-posed problem), is also included. This open-source software enables users to freely adjust the physical parameters to obtain physical insight into their materials under test and will be consistently updated for more accurate measurement and interpretation of dielectric spectra in an automated manner. This work describes the theoretical and mathematical background of the software, lays out the workflow, and validates the software functionality based on both synthetic and empirical data included in the software.
The reflection and transmission characteristics of plane waves scattered by a finite-thickness shear layer having a linear velocity profile and bounded by two otherwise uniform parallel flows is examined using the pressure perturbation equation solutions in the shear layer shown previously to be in terms of Whittaker M functions. In addition to the angle of plane wave incidence and the relative Mach number of the flows bounding the shear layer, it is found that the scattering properties of the shear layer depend crucially upon a parameter tau in such a manner that the case tau approaching zero characterizes the long wavelength properties of the layer and the case tau approaching infinity characterizes the short wavelength properties of the layer. In contrast to the region of ordinary reflection in the cases where the corresponding vortex sheet does not have a Brewster angle, the values of the reflection coefficient up to tau of 2 follow those of the vortex sheet; for the case for which the corresponding vortex sheet has a Brewster angle, the magnitude of the reflection coefficient may be sensitive to even small changes in tau in certain cases.
When radiometric equipment is available, noise temperature measurement techniques provide a convenient and accurate means for determining the dissipative component of the insertion loss of a two-port network. It is increasingly becoming the practice to ignore mismatch errors caused by multiple reflections between the source, the receiver, and the component whose dissipative loss is being measured. Mismatch errors are difficult to determine in practice because of the requirements of having full knowledge of the magnitudes of reflection coefficients and S-parameters. This article shows it is permissible to neglect the effects of mismatch errors if special conditions are met. These special conditions only require that the reflection coefficients of the source and load be made negligibly small and that the two-port network being evaluated has reciprocal and symmetrical properties.
An approximate method to determine the index of refraction of a dielectric obstacle is presented. For simplicity one dimensional models of electromagnetic scattering are treated. The governing equations yield a second order boundary value problem, in which the index of refraction appears as a functional parameter. The availability of reflection coefficients yield two additional boundary conditions. The index of refraction by a k-th order spline which can be written as a linear combination of B-splines is approximated. For N distinct reflection coefficients, the resulting N boundary value problems yield a system of N nonlinear equations in N unknowns which are the coefficients of the B-splines.
An approximate method to determine the index of refraction of a dielectric obstacle is presented. For simplicity one dimensional models of electromagnetic scattering are treated. The governing equations yield a second order boundary value problem, in which the index of refraction appears as a functional parameter. The availability of reflection coefficients yield two additional boundary conditions. The index of refraction by a k-th order spline which can be written as a linear combination of B-splines is approximated. For N distinct reflection coefficients, the resulting N boundary value problems yield a system of N nonlinear equations in N unknowns which are the coefficients of the B-splines.
A practical technique for measuring the dielectric constant of vegetation leaves and similarly thin materials is presented. A rectangular section of the leaf is placed in the tranverse plane in a rectangular waveguide and the magnitude and phase of the reflection coefficient are measured over the desired frequency band using a vector network analyzer. By treating the leaf as an infinitesimally thin resistive sheet, an explicit expression for its dielectric constant is obtained in terms of the reflection coefficient. Because of the thin-sheet approximation, however, this approach is valid only at frequencies below 1.5 GHz. To extend the technique to higher frequencies, higher order approximations are derived and their accuracies are compared to the exact dielectric-slab solution. For a material whose thickness is 0.5 mm or less, the proposed technique was found to provide accurate values of its dielectric constant up to frequencies of 12 GHz or higher. The technique was used to measure the 8 to 12 GHz dielectric spectrum for vegetation leaves, teflon and rock samples.
The reflection coefficient of a microphone support structure used insist noise testing is documented through tests performed in the anechoic AeroAcoustic Propulsion Laboratory. The tests involve the acquisition of acoustic data from a microphone mounted in the support structure while noise is generated from a known broadband source. The ratio of reflected signal amplitude to the original signal amplitude is determined by performing an auto-correlation function on the data. The documentation of the reflection coefficients is one component of the validation of jet noise data acquired using the given microphone support structure. Finally. two forms of acoustic material were applied to the microphone support structure to determine their effectiveness in reducing reflections which give rise to bias errors in the microphone measurements.
Several methods for computing the reflection coefficients from mesh surfaces are discussed. Some methods mentioned have severe limitations, and the spectral approach appears to be the most attractive alternative. In spite of some inherent problems, the solutions obtained with this method will offer not only the reflection coefficients but also the currents carried on the mesh. This would allow separation of the power lost to resistive terms from that due to transmission loss. Overall, good results and rapid convergence should be obtained from this method when proper care is applied.
The effect of random and systematic errors associated with the measurement of normal incidence acoustic impedance in a zero-mean-flow environment was investigated by the transmission line method. The influence of random measurement errors in the reflection coefficients and pressure minima positions was investigated by computing fractional standard deviations of the normalized impedance. Both the standard techniques of random process theory and a simplified technique were used. Over a wavelength range of 68 to 10 cm random measurement errors in the reflection coefficients and pressure minima positions could be described adequately by normal probability distributions with standard deviations of 0.001 and 0.0098 cm, respectively. An error propagation technique based on the observed concentration of the probability density functions was found to give essentially the same results but with a computation time of about 1 percent of that required for the standard technique. The results suggest that careful experimental design reduces the effect of random measurement errors to insignificant levels for moderate ranges of test specimen impedance component magnitudes. Most of the observed random scatter can be attributed to lack of control by the mounting arrangement over mechanical boundary conditions of the test sample.
There is great interest in the application of thin film high temperature superconductors in high frequency electronic circuits. A ring resonator provides a good test vehicle for assessing the microwave losses in the superconductor and for comparing films made by different techniques. Ring resonators made of YBa2Cu3O(7-x) have been investigated on LaAlO3 substrates. The superconducting thin films were deposited by sequential electron beam evaporation of Cu, Y, and BaF2 with a post anneal. Patterning of the superconducting film was done using negative photolithography. A ring resonator was also fabricated from a thin gold film as a control. Both resonators had a gold ground plane on the backside of the substrate. The ring resonators' reflection coefficients were measured as a function of frequency from 33 to 37 GHz at temperatures ranging from 20 K to 68 K. The resonator exhibited two resonances which were at 34.5 and 35.7 GHz at 68 K. The resonant frequencies increased with decreasing temperature. The magnitude of the reflection coefficients was in the calculation of the unloaded Q-values. The performance of the evaporated and gold resonator are compared with the performance of a laser ablated YBa2Cu3O(7-x) resonator. The causes of the double resonance are discussed.
Pioneer Venus high-angle radar imaging data are used here to correct values of the specular power reflection coefficient for the effects of diffusely scattering small-scale surface roughness. A value of 5.0 + or - 0.9 is found for the average dielectric permittivity of the rolling plains and lowlands, suggesting that most of the Venus surface is overlain by at most only a few cm of soil or dust. The unexpectedly high values of power reflection coefficient are confirmed by observations of correspondingly low values of radiothermal emission. Thus there can be little doubt that most of the highlands contain significant amounts of a conducting mineral near the surface.
A solution is presented to the problem of an infinite array of microstrip patches fed by idealized current probes. The input reflection coefficient is calculated versus scan angle in an arbitrary scan plane, and the effects of substrate parameters and grid spacing are considered. It is pointed out that even when a Galerkin method is used the impedance matrix is not symmetric due to phasing through a unit cell, as required for scanning. The mechanism by which scan blindness can occur is discussed. Measurement results are presented for the reflection coefficient magnitude variation with angle for E-plane, H-plane, and D-plane scans, for various substrate parameters. Measured results from waveguide simulators are also presented, and the scan blindness phenomenon is observed and discussed in terms of forced surface waves and a modified grating lobe diagram.
This paper presents measurements and simulations of a linearly polarized VHF folded dipole operating at 60 MHz for NASA’s upcoming Europa Clipper mission. The spacecraft contains a ground penetrating radar, consisting of an array of four VHF antennas, that will characterize the surface of Jupiter’s icy moon Europa. Measured far-field radiation patterns and reflection coefficients above a 50×80m perfect ground plane are compared to predicted results using commercial software. Normalized Far-Field radiation pattern cuts are measured utilizing a biconical antenna and receiver mounted on a flying drone. Simulations of the radiation pattern show that the number of lobes increases with the distance of the antenna from the ground due to the ground-bounce phenomenon. In addition, the measured and simulated reflection coefficients stay unchanged for height above 2 meters, which matches the predicted calculation of the reactive-near field region of this antenna. However, the antenna electrical parameters are optimized for use on the spacecraft and become detuned in the presence of a ground plane. Simulated and measured return loss discrepancy less than 0.5 dB is presented. Radiation pattern comparisons show similar agreement when taking into account the effect of far-field measurement uncertainties.
It is required to find the reflection and transmission coefficients for a tapered waveguide. It is assumed that the taper is very long and gradual such that no higher order modes are excited from the discontinuity of the waveguide. Three different methods are presented for finding the reflection coefficient and two methods are presented for finding the transmission coefficient. A traditional differential equation method which finds only the reflection coefficient is presented. An additional set of differential equations are presented which finds both the reflection and transmission coefficients. A FEM (finite element method), which solves for both the reflection and transmission coefficients, is presented with its limitations. An example of a tapered coaxial line and waveguide is presented with the different methods compared and contrasted.
A water body s surface can be modeled as a horizontal mirror. Water detection based on sky reflections and color variation are complementary. A reflection coefficient model suggests sky reflections dominate the color of water at ranges > 12 meters. Water detection based on sky reflections: (1) geometrically locates the pixel in the sky that is reflecting on a candidate water pixel on the ground (2) predicts if the ground pixel is water based on color similarity and local terrain features. Water detection has been integrated on XUVs.
We evaluate the feasibility of spectral time domain reflectometry (STDR) and spread spectrum time domain reflectometry (SSTDR) as a new modality for impedance measurement to test energized/noisy systems over a very broad frequency spectrum (near dc to gigahertz) as well as multiple channels in parallel. We simulate how the S/SSTDR signal parameters (signal-to-noise ratio (SNR) frequency and length of the pseudo-noise (PN) signals) affect the accuracy and usable frequency band for reflection coefficient and impedance measurement. An initial measurement validation is included. Here, we conclude with a recommendation of what will be required for a viable multichannel impedance (and reflection, transmission coefficient) measurement system for either energized or nonenergized systems, in noisy environments, that can test multiple channels simultaneously.