An experimental study of the insulated dipole antenna immersed in a conducting medium

The driving-point admittance and the amplitude and phase distributions of the current referred to the driving-point were measured for an insulated cylindrical antenna immersed in a conducting medium. The ratiosigma/omegaepsilon_{r}epsilon_{0}of the conducting medium was varied fromsigma/omegaepsilon_{r}epsilon_{0}= 0.036to 8.8, a range which includes a variety of media such as poor insulators, the ionosphere, plasmas, dry earth, wet earth, lake water and sea water. The antenna heightbeta hin radians was varied frombeta h=0.1throughbeta h=2piat intervals of 0.1. The thickness of the insulator was varied fromb/a = 1.25tob/a = 12.0whereais the radius of the antenna andbthe radius of the insulator. Measurements have also been made of the admittance, current and phase distributions along an insulated antenna with a conductive top load, that is, one whose tip is in direct contact with the conducting medium. It is found that when the tip of the antenna is in direct contact with the conducting medium, the current increases almost linearly as the end of the antenna is approached. This is quite unlike the decaying sinusoidal distribution on the completely insulated antenna. In a general sense, the experimental results are in fair agreement with an approximate theoretical expression for the admittance of an insulated antenna immersed in a highly conducting solution. The approximate theory is based on the driving-point admittance of a coaxial line whose outer conductor is imperfectly conducting and infinite in extent.     

Dipole antenna in space-time periodic media

The problem of dipole radiation in sinusoidally spacetime periodic media is studied and solved. The space-time periodicity can be considered as due to a strong pump wave and is expressed as a traveling-wave type change in the dielectric constant or the plasma density (i.e.,epsilon(z,t) = epsilon_{0}epsilon_{r}[1 + epsilon_{1} cos (Kz - Omega t)]andN(z,t) = N_{0}[1 + N_{1} cos (Kz - Omega t)]). The solution also covers the limit case of a sinusoidally stratified medium (Omega = 0). The solution is formulated in a matrix form, such that the basic results and diagrams apply, with minor changes, to the different cases studied: electric and magnetic dipole in a dielectric, plasma, and uniaxial plasma. The wave-vector diagram is used extensively in studying and presenting the different properties of the solution: caustics, effect of the disturbance (pump wave) motion, harmonics, radiation outside the allowed cone in a uniaxial plasma. Many dipole radiation patterns are given and their features explained physically. Finally, our solution and results are extended to the generally space-time periodic media whereepsilon(z,t)andN(z,t)behave aseta(z,t) = eta_{0}[1 + eta_{1}f(Kz - Omega t)]wheref(xi)is any periodic function.     

Flush mounted rectangular cavity slot antennas--Theory and design

The loaded rectangular cavity slot antenna is analyzed using variational methods in conjunction with simplified equivalent circuit techniques to derive accurate design guides for efficiency, bandwidth, and resonant frequency. The aperture admittance is computed and the effects of a compound aperture plane iris and of material loading are analyzed. The aperture admittance of all such loaded cavity antennas is proportional tomu_{r},sqrt{mu_{r}/epsilon_{r}}, or1/epsilon_{r}, which characteristic lends to a common method of optimization of|T|^{2}(transmission cofficient). Experimental results include: 1) measurements of aperture field; 2) a comparison of theoretical and experimental value of bandwidth, efficiency, resonant frequency, and beam pattern for several experimental models; and 3) the measurement of the effect of applied dc magnetic field.     

Construction of de Bruijn sequences of minimal complexity

It is well known that the linear complexity of a de Bruijn sequenceSof length2^{n}is bounded below by2^{n- 1} + nforn geq 3. It is shown that this lower bound is attainable for alln.     

The weight-distribution of a coset of a linear code (Corresp.)

The coseta + Aof the linear codeAhas weight distribution related to that ofA^{perp}and ofA^{perp} cap a^{perp}.     

The small bare loop antenna immersed in a dissipative medium

The input admittance of a small thin-wire circular loop antenna, driven by a slice generator, immersed in a dissipative medium, is considered. It is found that the solution given by Storer for the loop antenna in a lossless medium can be carded over readily by replacingzeta_{0}byzeta, andk_{0}byk. The numerical values of the normalized input conductance and input susceptance of a small loop antenna, namelybeta b leq 0.3,Omega = 10, are calculated. It is to be noted that the input susceptance is practically independent ofkwhile the input conductance changes as much as seventeen times in this special case.     

On the distribution of de Bruijn sequences of given complexity

The distributiongamma (c, n)of de Bruijn sequences of ordernand linear complexitycis investigated. It is shown that forn geq 4, gamma (2^{n} - 1, n) equiv 0 pmod{8}, and fork geq 3, gamma (2^{2k} - 1,2k) equiv 0 pmod{l6}. It is also shown thatgamma (c, n) equiv 0 pmod{4}for allc, andn geq 3such thatcnis even.     

Linear binary shift register circuits utilizing a minimum number of mod-2 adders

A family of linear binary shift register circuits is described in terms of generator polynomialsg(x)which require fewer mod-2adders than those derived from the companion matrices. These circuits are derived from various combinations of the functionsa(x), b(x), andx^{d}ing(x) = 1 + a(x)x^{d}b(x)andc(D), e(D), andD^{m}of the reciprocal polynomialg^{ast}(x) = f(D) = 1 + c(D)D^{m}e(D). Tables are provided for all simplifications thus achievable for primitive polynomial of degrees5through9, and for some nonprimitive polynomials.     

Mutual admittance characteristics for two-element parallel prolate spheroidal antenna systems

Spheroidal dipole antenna systems consisting of two thin center-fed parallel prolate spheroids in various configurations (side-by-side and collinear) are considered, The resultant EM fields are represented as modal expansions in terms of spheroidal vector eigenfunctions. The translational addition theorems for spheroidal functions developed by the authors in a previous paper play the central role in the formulation of a system matrix [G] which transforms the primary. EM excitations of the fed dipoles into their scattered responses. From the knowledge of the [G] matrix, the mutual admittances of the dipole system are obtained and plotted against center-to-center separation of the dipoles for side-by-side and collinear dipole configurations. The major to minor axial ratios of 10:1 and 100:1 of the prolate spheroidal dipoles are considered for presenting various curves. However, for the side-by-side configuration, due to a radius of convergence of the translational relation for outgoing wave to incoming wave transformation, the separationdof the spheroids is restricted tod > {a_{1}, a_{2}}_{max}, whosea_{1}anda_{2}are the semimajor axial lengths of the two spheroids.     

On the quality factor of strip and line source antennas and its relationship to superdirectivity ratio

Exact formulas are derived for the quality factorQof strip and line source antennas. Contrary to popular opinion, none of them is equal to Taylor's superdirectivity ratiogammaor togamma - 1. But in the case ofE-plane strip sources (the complement of the type of strip source treated by Woodward and Lawson) the value ofQis precisely equal togamma_{alpha}^{-1/2}- 1, wheregamma_{alpha}^{beta}is a generalized superdirectivity ratio that reduces to Taylor'sgammawhen the edge exponentalphaand the pattern weighting exponentbetaare both zero. In the case ofH-plane strip sources the value ofQis approximately equal togamma_{alpha}^{1/2} - 1, and forH-plane line sources of vanishing widthait is approximately equal to[(2/pi) ln (2.516lambda/pi a)]gamma_{alpha}^{1}.     

A bound on lightweight sequences with application to definite decoding (Corresp.)

It is shown that the numberMof binary-valuedn-tuples having fractional weightdeltaor less,0 < delta leq frac{1}{3}, such that no twon-tuples agree in anyLconsecutive positions, is bounded by2^{2LH(delta)+1}. A set ofn-tuples is constructed to show that this bound is not likely to be improved upon by any significant factor. This bound is used to show that the ratiod_{DD}/n_{DD}of definite-decoding minimum distance to definite-decoding constraint length is lower bounded byH^{-l}[frac{1}{6} cdot (1 - R)/ (1+R)]asn_{DD}grows without bound.     

Impedance of a finite insulated antenna in a cold plasma with a perpendicular magnetic field

A variational formulation is developed for the impedance of a finite strip antenna embedded in a planar dielectric slab which is surrounded by a magnetoionic medium (cold electron plasma) with a static magnetic field impressed in a direction perpendicular to the antenna surface. Closed form expressions are obtained in the limit of low frequencies, and for a short antenna in a uniaxial medium. The impedance becomes large at the plasma frequency, near the upper hybrid resonance frequency, and further resonances are observed near the gyro-frequency if the gyro-frequency exceeds the plasma frequency. The reactance of a short antenna is inductive at low frequencies, but becomes capacitive as the thickness of the insulation around the antenna is increased. For very thin insulating layers the wave number of the variationally approximated current distribution exceedssqrt{sqrt{epsilon_{1}} sqrt{epsilon_{3}}} k_{0}(epsilon_{1}andepsilon_{3}are the two diagonal elements of the permittivity matrix), whereepsilon_{1}andepsilon_{3}may have positive or negative real parts. However, this approximation does not apply to current distributions along an insulated antenna. The present calculations are also compared with earlier work on antenna impedances.     

Theoretical and experimental study of a finite cylindrical antenna in a plasma column

A numerical technique has been used to solve the integral equation determining the current distribution on a finite cylindrical antenna in a long plasma column; a "cold" isotropic plasma model with a relative dielectric constantepsilon_{r} = 1 - omega_{p}^{2}/omega^{2}is used in the analysis. Collision losses and inhomogeneities in the plasma have been ignored for the sake of mathematical simplicity. It is found that when0 < epsilon_{r} < 1, the plasma column tends to behave like a dielectric and reduces the effective electrical length of the antenna. The current distribution is still somewhat sinusoidal but with a longer wavelength. In the range-1 < epsilon_{r} < 0, the antenna characteristics undergo a drastic change; the current decays very rapidly along the antenna and, for antennas longer than a quarter wavelength, the input admittance remains almost constant and independent of the length. Extensive experimental measurements have been made to verify the theory. The plasma sheath surrounding the antenna was produced by an active, hot.cathode, helium discharge; the plasma diagnostic measurements were made by using Langmuir probes and cavity perturbation techniques. The theoretical and experimental results show a significant degree of qualitative agreement.     

General theory of doubly periodic arrays over an arbitrary finite field and its applications

A general theory of doubly periodic (DP) arrays over an arbitrary finite field GF(q)is presented. First the basic properties of DP arrays are examined. Next modules of linear recurring (LR) arrays are defined and their algebraic properties discussed in connection with ideals in an extension ringtilde{R}of the ringRof bivariate polynomials with coefficients in GF(q). A finitetilde{R}-module of DP arrays is shown to coincide with thetilde{R}-module of LR arrays dermed by a zero-dimensional ideal intilde{R}. Equivalence relations between DP arrays are explored, i.e., rearrangements of arrays by means of unimodular transformations. Decimation and interleaving of arrays are defined in a two-dimensional sense. The general theory is followed by application to irreducible LR arrays. Among irreducible arrays,M-arrays are a two-dimensional analog ofM-sequences and may be constructed fromM-sequences by means of unimodular transformations. The results of this paper are also important in studying properties of Abelian codes.     

The biconical antenna in a radially stratified medium

The theory of a transmitting biconical antenna in a radially and continuously stratified medium is developed; its input impedance is computed and plotted vs. its length for various media and cone angles. The medium extends to infinity and is characterized by a complex dielectric factorxi=epsilon-isigma/omega=epsilon_{0}f(r), whereris the radial distance from the center of the antenna. For the "stratification function" the formf(r)= (kr+a)/(kr+b)is considered, whereaandbare constant parameters, in general complex. The plots clearly exhibit all effects of dissipation and stratification expected on physical grounds and observed experimentally for dipole antennas.     

The two-to-one rule in data smoothing (Corresp.)

If a signal is estimated by a weighted average of the data in the interval(t - c, t + c ), then the variancesigma^{2}of the estimate decreases, but its bias b increases, with increasing c. It is shown that in high accuracy estimates, the mean-square error e is minimum ifcis such thatsigma = 2b, regardless of the formh (t)of the smoothing weight. Furthermore, the resultinge_{m}is minimum ifh(t)is a truncated parabola.     

Diffraction by a circular aperture in a unidirectionally conducting screen

The diffraction of a normally incident plane electromagnetic wave with wave numberkby a circular aperture of radiusain a unidirectionally conducting plane screen of zero thickness and infinite extent is considered. In the limit of largeka, the ratio of the transmission cross section to the geometrical optics valuepi a^{2}, is found up to the order(ka)^{-3/2}.     

A Phase-Adaptive Echo Canceller with Reduced Sensitivity to Power Variations

In a previous correspondence [1], we have studied an echo canceller (EC) compensating far-end echos affected by frequency offset. It has been shown that the sensitivity of the loop gain versus the powerPof the echo and the powerSof the signal, can be reduced by adoption of a normalized gain multiplied by the echo power. In this correspondence a novel and very simple algorithm is described that further reduces this sensitivity and yields an optimum phase loop gain proportional to(S/ p)^{1/6}.     

A class of composite codes (Corresp.)

Certain useful properties of the cyclic codeVare discussed with wordsV(x)=V_{1}(x)(l+x^{n})/(l+x^{n_{1}})+V_{2}(x)(l+x^{n})/(l+x^{n_{2}}), where fori=1,2,V_{i}(x)belongs to a binary codeV_{i}of lengthn_{i}.     

A fundamental inequality between the probabilities of binary subgroups and cosets

The probability of a set of binaryn-tuples is defined to be the sum of the probabilities of the individualn-tuples when each digit is chosen independently with the same probabilitypof being a "one." It is shown that, under such a definition, the ratio between the probability of a subgroup of order2^{k}and any of its proper cosets is always greater than or equal to a functionF_{k}(p), whereF_{k}(p) geq 1forp leq frac{1}{2}with equality when and only whenp = frac{1}{2}. It is further shown thatF_{k}(p)is the greatest lower bound on this ratio, since a subgroup and proper coset of order2^{k}can always be found such that the ratio between their probabilities is exactlyF_{k}(p). It is then demonstrated that for a linear code on a binary symmetric channel the "tall-zero" syndrome is more probable than any other syndrome. This result is applied to the problem of error propagation in convolutional codes.