Volume 26, Issue 2, 01 February 1955

Measurement of Microwave Diffraction from a Long Slit in a Thin Conducting Plane
View Description Hide DescriptionThis paper gives the results of measurements of the fields diffracted from a long narrow slit in a large conducting plane, when a uniform plane is incident. The results for two polarizations are shown.

Backscattering from Wide‐Angle and Narrow‐Angle Cones
View Description Hide DescriptionSolutions are obtained for the diffraction of the waves radiated by scalar and vector point sources on the axis of a semi‐infinite cone. The scalar problems are solved by the method of characteristic Green's functions to yield directly various alternative representations whose different convergence properties are discussed; the vector problem is solved by an application of spherical transmission line theory. To evaluate the plane wave scattering observed far from the cone tip, a highly convergent contour integral representation is selected and evaluated approximately for the special case of backscattering from cones having large and small apex angles. The results for the large‐angle cone exhibit the transition from a backscattered spherical wave to a plane wave as the cone degenerates into an infinite plane.

Diffraction by Apertures
View Description Hide DescriptionThe diffraction of plane electromagnetic waves by apertures in a plane screen which is infinitesimally thin and perfectly conducting is studied both theoretically and experimentally. The theoreticalanalysis employs a dyadic Green's function to develop vector formulas for the scattered fields, and from these formulas integral equations are obtained for the aperture distributions. The vector representation makes possible a compact demonstration of the electromagnetic form of Babinet's principle by means of which one may extend the aperture analysis to complementary disks. The integral equations are then used to construct a variational principle for the aperture transmission coefficient.
Detailed analysis and numerical computations are carried out for two configurations. For the circular aperture a first‐order vector trial function with frequency dependent coefficients is chosen for the aperture distribution. The approximate transmission coefficient is found to agree closely with the exact value in the region 2πa/λ≤3. For elliptical apertures a zeroth‐order approximation is evaluated using a one‐component trial function. Numerical results are given for minor‐to‐major axis ratios of ½ and ⅓.
Transmission coefficientmeasurements were carried out in the 24 000 megacycle band (λ=1.25 cm) using an image plane technique. The apparatus was first calibrated with the exact solution of the circular aperture. The approximate results calculated for elliptical apertures are then seen to be in good agreement with the measurements over the accessible range.

Relation of Antimony Transmission and the Photoelectric Yield of Cs–Sb
View Description Hide DescriptionThe relation of transmission of thin films of antimony as a function of thickness expressed in micrograms per cm^{2} has been determined for blue, red, and white illumination. An abrupt change in optical properties of the antimony layer has been noted at the phase change. The transition occurs at a transmission of approximately 30 percent. Photosurfaces have been prepared by activating the deposited antimonyfilms with cesium. The photoelectric yield for both regular and reverse illumination has been determined for different antimony thicknesses. For reverse illumination the peak response occurs between 5.5 and 6.0 micrograms per cm^{2} of antimony. Expressing the photoresponse for reverse illumination of green light with decreasing transmission of the original antimony layer for blue, white, and red light shows peaks at 82, 88, and 92 percent, respectively. The transmission of the photosurface, which is substantially independent of processing or photoelectric efficiency of the surface, is given for blue, green, and white light.

Spin‐Echo Memory Device
View Description Hide DescriptionA proton‐rich sample placed in a strong inhomogeneous magnetic field of mean strength H _{0} was subjected to a pattern of relatively weak radio‐frequency pulses at the Larmor frequency of the protons in the field H _{0}. The pattern was then recalled by applying a strong rf pulse at a later time as in the spin‐echo technique. It is shown both mathematically and experimentally that such a series of pulses, varying in amplitude can be ``memorized'' by the spin system of protons for times as long as one second and then repeated, preserving both shape and relative amplitude.

Theory of Elasticity and Consolidation for a Porous Anisotropic Solid
View Description Hide DescriptionThe author's previous theory of elasticity and consolidation for isotropic materials [J. Appl. Phys. 12, 155–164 (1941)] is extended to the general case of anisotropy. The method of derivation is also different and more direct. The particular cases of transverse isotropy and complete isotropy are discussed.

Radiation of Plasma Noise from Arc Discharge
View Description Hide DescriptionThe mechanism of radiation of plasma noise inherent to arc discharge is studied experimentally. Intense electromagnetic radiation of random noise character is observed at the frequency of plasma oscillation of the ion sheath formed at the cathode drop. Maximum radiation occurs when the external circuit connected to the cathode is in resonance with the plasma frequency. The oscillating current in the external circuit is concluded to be generated by the periodic electron emission from the cathode caused by small perturbation of potential gradient at the cathode surface as a result of the variation in the ion sheath potential. This conclusion is supported by several experiments under various air pressures, electrode materials, current densities, etc.

Measurement of Carrier Lifetimes in Germanium and Silicon
View Description Hide DescriptionThe decay of photoconductivity has been used to measure the lifetime of excess carriers in rectangular samples of germanium and silicon. The sample is illuminated by a short pulse of light and the sample lifetime obtained from an oscilloscope display of the decay of photoconductivity. Analysis of the solution of the diffusion equation yields methods of measuring the bulk lifetime, the surface recombination velocity, and the diffusion constant.

Short‐Time Frequency Measurement of Narrow‐Band Random Signals by Means of a Zero Counting Process
View Description Hide DescriptionAny instrumentation for measuring the mean frequency of a narrow‐band random signal presents an output quantity which inherently fluctuates about that value which represents the true mean frequency, due to the finite measuring time. In comparing the accuracy of various instrumentations for short‐time frequency measurement a useful figure of merit is variance of the output/(sensitivity) ^{2}. In this paper the figure of merit is obtained for an instrumentation which measures frequency by determining the average number of zero crossings of the signal in a short time. The significant problem is the determination of the mean square number of zeros of a random function in time T. The general result is presented in the form of an integral. For an assumed Gaussian power spectrum the integral is integrated graphically to obtain a figure of merit which is compared with previously published figures of merit of an autocorrelator and frequency discriminator.

Internal Friction of Metal Single Crystals
View Description Hide DescriptionSemiquantitative calculations were made of that portion of the internal friction of annealed and moderately cold‐worked metal single crystals which is due to dislocation motion. The calculations were made on the basis of a qualitative theory of Nowick. It is shown that Nowick's theory leads to reasonable orders of magnitude of the observed internal friction and changes of the modulus of elasticity. At low temperature or at high frequencies (megacycle range) Nowick's hysteresis mechanism becomes inoperative and theories of Koehler and of Eshelby have to be considered to calculate the internal friction.

Anomalous Forward Switching Transient in p‐n Junction Diodes
View Description Hide DescriptionA delay in the flow of forward current when a grown‐crystal p‐n junction diode is switched from reverse to forward bias is explained on the basis of an extra p‐n barrier in the grown‐crystal bar. This effect was observed in 10 out of 24 production units, while no such anomaly was found in fused‐junction diodes. A mathematical theory of the effect gives good agreement with the experimental results.

Methods of Measuring Dielectric Constants Based upon a Microwave Network Viewpoint
View Description Hide DescriptionDielectric samples located in wave guide are represented by network four‐poles whose admittance determinant is related simply to the dielectric constant. The four‐pole viewpoint, which has heretofore not been adequately exploited, makes possible the utilization of the whole body of transmission line four‐pole measurement techniques, including those of precision and invariance. New measurement procedures based on these techniques have been formulated which are either length invariant or location invariant; that is, the dielectric constant is determinable without the knowledge of either the length or the location of the sample. Four specific measurement procedures are presented which incorporate the precision as well as the invariance aspects.

Information Theory Aspects of Propagation through Time‐Varying Media
View Description Hide DescriptionThe channel capacity of a communications system which utilizes wave propagation through a time‐varying medium such as the ionosphere or troposphere is evaluated in terms of the statistical properties of the medium and of the noise. The signal fading in such a system reduces the capacity. Rayleigh fading is found to give rise to an equivalent signal to noise ratio of 1.72, while shallow fading of the Gaussian type augments the noise in the channel by a fraction of the signal power proportional to the fading depth. An optimum manner of band width subdivision is shown to exist when selective fading is present.
Information theory concepts are broadened to include the possibility of multiple reception at spaced receiving sites, and the consequent increase in theoreticalchannel capacity is computed as a function of the number of such sites and the signal statistics. The method of maximum liklihood is utilized to obtain optimum combinatorial laws for the multiple signals. The commonly employed maximum signal selection diversity system is shown to perform as well as the optimum system in the presence of Rayleigh fading, for a small number of receiving sites.

Analog Computer Construction of Conformal Maps in Fluid Dynamics
View Description Hide DescriptionA general‐purpose electronic analog computer has been used extensively to construct the streamlines around two‐dimensional airfoil shapes immersed in an incompressible, nonrotating, nonviscous fluid. The computer generates a circular Lissajous pattern on a plotting table, and then transforms the coordinates of the circle into the airfoil shape by a conformal transformation. Two samples of the variety of airfoil shapes so constructed are shown. The accuracy of the process, which has been checked by a digital computer and a desk calculator, is quite satisfactory; the speed of the actual mapping process is highly advantageous to thorough exploration of a variety of airfoil shapes.

On the Diffusion of Decaying Particles
View Description Hide DescriptionThe probability of neutron absorption on a spherical surface for a radial source in a medium for which the particle has prescribed lifetime and rate of diffusion is calculated. This helps illuminate the more intricate, related problem for a charged particle diffusing in the presence of a radial inverse‐square electric field to the extent that an explicit relation for the relative absorption probabilities that accompany changes in the direction of the drift field is secured. An asymptotic solution for the absorption probability is also provided which in first‐order approximation may be applied in the range of interest for transistors.

On Power Spectra and the Minimum Detectable Signal in Measurement Systems
View Description Hide DescriptionA least upper bound for the minimum detectable signal of a receiving system whose input is a periodic wave form plus interference is specified in terms of the first and second moments of the rectified output. Also, it is shown that the power spectrum of the rectified output (together with the impedance characteristic of the output meter) serves to establish the first and second moments of the meter deflection for either of the following two cases:
(1) The rectified output operates a meter, and the difference in meter readings with the signal on and off constitutes the observation from which the message is inferred.
(2) The rectified output feeds a synchronous detector whose meter reading is directly proportional to the message. Here we require that there be no input noise which is modulated at the synchronous frequency.

Patch Effect for the Thermionic Emission from Polycrystalline Tantalum
View Description Hide DescriptionThe slope modifications for the Schottky line implied by simple patch theory have been obtained at high fields for thermally etchedtantalum filaments. For ac‐aged filaments, only the usual low field patch modification was obtained. For dc‐aged filaments an additional anomaly at higher fields was obtained, simultaneous with the appearance of the dc etch pattern on certain faces of the crystal grains. This high field anomaly, consisted of a double break in slope, and appeared at an average patch field about 50 times the patch field due to the distribution of crystal faces.

Inertial Impaction of Aerosol Particles on Cylinders
View Description Hide DescriptionThe inertial impaction of aerosol particles on cylinders was investigated to determine the relationship between the efficiency of impaction and the inertial parameter, the Reynolds number of flow, and the effect of interception. The impaction of sulfuric acidaerosols of nearly uniform size ranging from 0.6 to 1.4 microns diameter, on two platinum wires, 29 and 83 microns diameter, and two tungsten wires, 53 and 106 microns diameter, was measured at several velocities of flow past the wires. Reynolds numbers ranged from 13 to 330. For values of the square root of the inertial parameter Ψ^{½} below 1.4, the experimental efficiencies of impaction agree with those predicted by Langmuir and Blodgett for potential flow and by Landahl and Herrmann for a Reynolds number of 10. The experimental values are higher than the calculated values for Ψ^{½} greater than 1.4. The theoretical prediction that a critical value of Ψ^{½} exists at approximately ¼, below which inertial impaction does not occur, was verified.
 LETTERS TO THE EDITOR


Wall Effects on Microwave Measurements of Ferrite Spheres
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The Transition Structure of Nickel
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