Transmission Formula Research Articles

Simple formulas for transmission through periodic metal grids or plates

A simple closed-form approximate solution is given for the transmission coefficient of a normally incident electromagnetic plane wave through a screen made of periodic metal grids (inductive screen), or made of metal plates (the complementary capacitive screen). Explicit formulas are also presented for cascading screens and dielectric slabs. When compared with the exact solution, our approximate simple formulas show good numerical accuracy.

Centers of structures in electromagnetism--a critical analysis

Some principles for finding reference points or centers of structures in electromagnetism are outlined. It is pointed out that the centers which are found depend on arbitrary choices. Since some of the principles are based on Friis's transmission formula and the radar equation, these are given in forms suitable for finding centers. The use of correction factors and near-field parameters are outlined. In particular, proper use of different near-field radar cross sections for plates and spheres are outlined.

Gain of corrugated conical horns

The absolute gain of a corrugated horn which is designed as a 100-GHz gain standard for the Crawford Hill 7-Meter offset reflector has been calculated and measured. The measured gain is determined from "three horn" transmission measurements. The other two horns are a TRG Model W869 corrugated horn and a dual mode horn. Correction factors were computed from the near field power transmission formula. The measured gain of the gain standard is <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">30.8 \pm 0.16 dB</tex> . Comparison between measured and calculated gains indicate very low ohmic loss in a corrugated horn. The condition of maximum gain for a given length has been found to be a half wavelength phase deviation in the horn aperture. Calculated gain data as well as near field correction factors for two identical corrugated conical horns are given here as reference information.

Electromagnetic transmission through narrow slots in thick conducting screens

The general formulas for electromagnetic transmission through an infinitely long slot in a perfectly conducting screen of finite thickness are specialized to the case of a narrow slot. The slot may be filled with a homogeneous isotropic material. A simple equivalent circuit for the narrow slot is developed. It is found that for certain screen thicknesses the slot becomes resonant, and exceptionally large transmission of energy may occur. In fact, as the slot width approaches zero, the transmission width at resonance becomes 1/\pi wavelengths regardless of the actual slot width. The effect of loading the slot with a lossy dielectric is also considered. Computations are given to illustrate the validity of the equivalent circuit model and the accuracy of transmission characteristics computed from it.

Reflection and transmission coefficients for transversely isotropic media

abstract It has become necessary in seismology to consider more complicated models of the Earth's structure in order to obtain synthetic seismograms that are more consistent with actual field data. Gassmann (1964) and Postma (1955) have presented results dealing with travel-time methods in anisotropic media—in particular, transversely isotropic media. Kinematic properties alone, however, are not enough to conclusively interpret seismic records. Consequently, dynamic properties must be considered producing a need for synthetic seismograms. One of the most efficient methods for obtaining synthetic seismograms is through the use of asymptotic ray theory (Hron and Kanasewich, 1971; Hron, 1973; Hron, Kanasewich and Alpaslan, 1974). A necessary step in the implementation for layered media displaying transverse isotropy is the computation of reflection and transmission coefficients at the interface between two such layers. Reflection coefficients for a free interface and the corresponding surface conversion coefficients must be computed, as well. Theoretical formulas for reflection, transmission, and surface conversion coefficients corresponding to the zero-order approximation of asymptotic theory are presented for the above-mentioned media.

Near-Field Gain Correction for Transmission between Horn Antennas

When the gain of a horn antenna is to be measured from the power transmission loss between it and a standard horn, the Friis transmission formula must be corrected if the horn separation is not considerably greater than 2d2/?. Expressions for the correction between a pyramidal horn and a conical horn, and between dissimilar pyramidal horns, are presented with sample results. A method of applying these corrections to minimize the errors in the horn gain measurements is described.

“Total” internal reflection of a beam-wave at a curved interface

The partial transmission of a cylindrical wave at a cylindrical interface between two different media is discussed, and is used as the basis for a new derivation of a power transmission formula previously derived for locally-planewaves by Snyder and Love. The formula is applied to the case of a Gaussian beam wave, and the relevant power transmission coefficient is obtained. The power transmission coefficient for a beam wave incident on a plane interface is also derived. It is shown that leakage due to spread of the angular plane-wave spectrum beyond the critical angle may well be much greater than that due to curvature when the radius of the curvature is large.

Use of semiliquid greases in closed gearboxes

1. Semiliquid greases have a number of advantages over liquid transmission oils. The use of the semiliquid greases eliminates the need for complex seals, gives a considerable reduction in lubricant consumption, and simplifies the maintenance of the mechanisms lubricated. Moreover, the semiliquid greases are better in preventing corrosion and are effective in reducing the levels of noise, vibration, and shock loading; they are better in lubricity, particularly during startup and shutdown. The disadvantage of these products, in comparison with liquid lube oils, is that they are not as effective in removing heat. 2. The present [USSR] product line of semiliquid greases is limited. Hence the matter of developing domestic semiliquid greases for enclosed gearboxes is very urgent. 3. In the development or selection of formulas for semiliquid transmission greases, the following considerations may be used as rough guidelines. a) For multifunctional semiliquid greases, petroleum oils are the logical choice as the dispersion medium, in view of their relatively good availability. b) The most promising materials should be considered to be greases thickened with lithium soaps of 12-hydroxystearic acid; these greases are high in mechanical stability. Also very promising are greases thickened with complex calcium and aluminum soaps. c) The properties of greases can be improved markedly by the use of antioxidant, anticorrosion, antiscoring, adhesion, and other additives.

Relaxation effects in Mössbauer transmission and scattering. I general formulas

In this first part (I) we derive some general formulae for Mossbauer transmission and scattering in the absence of relaxation. Emphasis is put on the influence of the linewidth of the incident radiation on physical observables. We also examine the angular selection rules for scattering by a powder. In the second part (II) we will introduce relaxation and compare the advantages and limitations of the different Mossbauer techniques in relaxation studies.

Numerical solution for the near-field transmission between two H-plane sectoral electromagnetic horns

The effect of higher order interactions in the coupling between two H -plane sectoral electromagnetic horns on the field distribution at the aperture of the transmitting horn is calculated using the point matching technique. A nonsingular integral equation for the induced current in the receiving horn, due to the initially incident wave from the transmitting horn, is formulated using a conformal transformation which maps the cross sectional contour of the receiving horn onto two circles on which the induced currents are finite. The solution leads to a modified field distribution in the transmitting aperture which is then employed in Hu's near-zone power transmission formula to compute a gain correction factor for H -plane sectoral horns. It is shown that the correction factor oscillates about that reported by Chu and Semplak with an amplitude which increases for smaller separation distances.

Extension of Wolter's multilayer reflection and transmission formulae for orthorhombic absorbing media

Wolter's multilayer reflection and transmission formulae are extended for the case, that the multilayer system is composed of orthorhombic media. These are oriented in such a way, that two of their principal dielectric axes lie in the surface of a layer. The third axis forms with a second one the plane of incidence. An analysis of the complex roots in the formulae, always present when dealing with absorbing media, is given to choose the correct solutions. The extended formulae are well suited for a computer program. They allow e.g. the computation of Attenuated Total Reflection (ATR)-spectra of anisotropic crystals.

The effects of sample imperfections on optical spectra

AbstractThe results of the theory of light reflection from rough surfaces have been extended to cover the case of light transmission through a sample with rough surfaces, as well as reflection and transmission for inhomogeneous samples. A concept of “Inhomogeneity Induced Roughness” of the constant phase plane has been introduced to describe the specular reflection from inhomogeneous media. The drastic influence of the multiple scattering effect on the optical spectra has been demonstrated for a simple model. The generalized formulae for reflection and transmission of light for imperfect samples are given. Finally, several peculiar experimental observations concerning exciton spectra in II–VI compounds, light scattering at the plasma frequency in metals, electroreflection, and other effects are discussed.

Introduction to radio and radio antennas

Electromagnetic wave propagation is a simple and beautiful phenomenon, but its rigorous mathematical derivation from Maxwell's equations is formidable. This article makes many of the concepts visible and plausible using only mathematics available to college freshmen and taught today in most high schools. Those who are familiar with the subject will appreciate the simple and direct way in which Dr. Friis' transmission formula is derived. This derivation is new and is published here for the first time.

Satellite Power Determination for a given Ground Station

The link calculations for transmission between Satellite and Ground Station has been done using the transmission formula which has been derived and its salient features explained in course of its derivation. The Satellite power has been determined using the formula to provide usefully detectable signal for a given modulation technique and ground station (Satellite Telemetry Station at the Physical Research Laboratory, Ahmedabad). The nature of the signal from a known Satellite [Naval Research Laboratory (USA)'s Solar X-Ray Monitoring Satellite]. has been explained with the help of transmission formula and the power level, diagram has been drawn. The variation of Satellite power with slant range has been plotted.

Optical reflection and transmission formulae for thin films

The very complicated formulae which relate the components of the complex refractive index of a thin film to the measurable optical reflection and transmission coefficients have been put into a much simpler form. This greatly simplifies the programming for a computer solution of the equations, and also leads to some useful approximate formulae.

Pulse Shapes of Spherical Waves Reflected and Refracted at a Plane Interface Separating Two Homogeneous Fluids

A review is given of Cagniard's method for determining the shapes of the reflected and transmitted waves resulting from a point source of spherical waves of arbitrary waveform located in one of two homogeneous fluids separated by a plane interface. Symmetry relations enable the basic Cagniard solutions for reflection to be obtained from those or transmission, and a reciprocity relation shows that the formulas for transmission when the source is located in one of the two fluids can easily be obtained from the formulas for transmission when the source is located in the other fluid. An Appendix lists explicit solutions for all cases (reflection or transmission with the source located in the fluid of higher or lower sound velocity). The propagation of jump discontinuities the Cagniard solution is shown to be in agreement with geometrical ray theory. Impulse reflection and transmission coefficients are obtained from the asymptotic values of the basic Cagniard solutions. It is then demonstrated that these same coefficients can be deduced from a solution to Laplace's equation.

On ladder networks and continued fractions

Driving-point immittance of general ladder network can always be put in the form of a continued-fraction expansion, where all the quotient terms are positive-real functions. Recursion formulas for transmission (ABCD) parameters lead us to another form of continued fraction. These fractions, whose terms are not (in general) positive-real functions, are chained by means of negative signs. It is not the purpose of this letter to develop one special realization technique. The intention is only to show that driving-point immittance of ladder network can be represented as an expansion of negative-sign fractions, and thatt his expansion can be used, more or less successfully, for the realization of ladder networks.

Measurement of Gamma Ray Induced Secondary Electron Current from Various Elements

Knowledge of the angular distribution and absolute efficiency for gamma ray induced secondary electron currents is necessary in the development of fast radiation detectors, in dosimetry and in transient radiation effects studies. The angular distribution of the emergent forward electron current and the absolute quantum efficiency for 1.25 MeV gamma ray induced secondary electron current has been measured for elements having atomic number 6, 13, 29, 48, and 82. To ensure electron equilibrium, targets of thickness about equal to the extrapolated range of a 1.25-MeV photoelectron were used. The non-equilibrium thickness of one-tenth the extrapolated range was also used. A significant difference between the total target current and the total forward current was observed. This difference increased with atomic number and target thickness, as would be expected from results of electron backscattering experiments. Forward currents, calculated as a function of atomic number and target thickness, using Mar' s universal electron transmission formula and taking into account both Compton and photoelectric effects, agree well with experimental results.

Comments on H. Volland's remarks on Austin's formula

In a recent paper (publis hed in Nachr. T echn. Zeitschr.) Volland proposes an analyti cal model of the earth· ionos phe re waveguid e which is claimed to be in basic agreeme nt with the predictions of t he semi e mpirical transmission formula of L W. Austin for frequ e ncies less than 300 kc/s. In this note, the Rat·earth ass umptions made by Volland are question e d an d any agreement of hi s res u lt with Austin's formula is a ttribut ed to a fortuitou s cancell ation of e rrors. It is rathe r interestin g to n ote that H . Volland [1964] has r ecently publi shed a pa per under th e title Bemer­ kungen zur Aus tin'schen Forme] (Re marks on Austin' s formula). This basic radio transmission formula was proposed b y L. W. Austin and pub]jshe d in the Bulletin of th e Bureau of Standards over 50 ye ars ago [Aus tin , 191 5]_ Volland proposes an analyti­ cal model of th e earth-ionospher e waveguid e whi c h i s claimed to be in basic agreement with the predictions of the semi-empirical A us tin formula for frequ en cies less than 300 kc /s. At the same time, Volland sta tes that a fl at-earth ass umption is adequate and he asserts that the curvature of th e earth leads onl y to second­ order correc tion s and, thus, may be neglected. Sin ce this latter state ment is in violent co ntradi c ti on to most of the r ecent th eoreti cal work on VLF and LF mode theory of propagati on, so me comments on Volland's paper are call ed for. To pro perly orient the reader , a bri ef survey of Vol­ land's formulation is giv e n. His model consists of a flat homoge neo us earth with a di electri c constant Ee and conductivity (Te. The ionos phere is r e presented by a reflecting level at a height h above the earth's surface_ His formula, in cylindrical coordinates (p, cp , z), for the vector potential of a vertical dipole source of moment II is given by

Gain of Electromagnetic Horns

The absolute gain of a standard horn is often measured by determining the transmission loss versus separation between two identical standard horns. Correction ratios are needed because the usual criterion for separation (2a2λ) may not justify the use of the far-zone power transmission formula. Using the near-field power transmission formula, the ratio between the Fraunhofer and Fresnel gain of a pyramidal electromagnetic horn has been computed as a function of horn dimensions and separation distance. The calculated corrections have been applied in the absolute gain measurement of a standard horn which was used as a calibration reference in a recent 4080-mc gain measurement of a large horn-reflector antenna. The measured gain of the standard horn at 4080 mc is 20.11 db with an accuracy of ±0.035 db. The calculated gain is 20.15 db.