On the accuracy of physical optics

The first-order correction to the physical optics (PO) solution for the axial radiation field from parabolic reflector antennas is found. The correction is of orderk^{-1}and is in quadrature with the PO solution. By means of the correction term the accuracy of the PO surface integral is round to be better than0.22(lambda/D)^{2}dB on axis, whereDis the diameter of the reflector. Thus, the PO solution for the directivity is extremely accurate for commun reflector sizes of several wavelengthslambda.     

Boresight-gain loss and gore-related sidelobes of an umbrella reflector

It is shown that energy in the gore-related sidelobes of an umbrella reflector comes from energy lost from the main beam. Both boresight gore-loss and sidelobe level correlate directly with cyclic aperture phase error caused by the geometry. The gore-sidelobe peak is located neartheta_{p}, wheresin theta_{p} = 1.2N_{G} (pi/Dlambda)whereN_{G}is the number of gores andDis the reflector diameter. An expression is also derived for the amplitude of the gore-related sidelobe.     

Short-channel MOSFET VT-VDScharacteristics model based on a point charge and its mirror images

Short-channel MOS transistordV_{T}/dV_{DS}characteristics are expressed by an analytic function of fundamental device parameters. The expression is derived from a simple model of short-channel MOS transistors in threshold condition, which is based on a point charge and its mirror images. With this expression,dV_{T}/dV_{DS}is found to be proportional to1/L^{2}-1/L^{4}, whereLis channel length. Following factors are also found, wherein the source and drain junction depth effect is only logarithmic ondV_{T}/dV_{DS}characteristics,dV_{T}/dV_{SUB}anddV_{T}/dV_{DS}are closely related in short-channel MOS transistors, and short-channel effects are expected to be smaller in MOS transistors on SOS than on bulk silicon, due to a large number of Si/sapphire interface states. This model is simple, and it can be applied to short-channel MOS transistor designing and circuit simulations.     

The analysis of deployable umbrella parabolic reflectors

The radiation characteristics of an umbrella-type reflector are studied in detail. When the supporting ribs of the quasiparabolic reflector are parabolic in shape and the surface between any two adjacent ribs is the surface of a parabolic cylinder, the deviation of the surface from the true parabolic shape has the effect of spreading the focal point of the parabolic reflector into a focal region, the limits of which can be calculated from the knowledge of the reflector parameters. The best feed position can be accurately determined by requiring that the phase error over the surface be minimized. For the cosine to the powernillumination, numerical results showing the gain degradation, the shift in optimum focal point, and the change in secondary patterns, due to the deviation of the reflector surface from the true parabolic surface, are presented.     

Electromagnetic reflection from an extended turbulent medium: Cumulative forward-scatter single-backscatter approximation

The backscatter cross sectionQfor high-frequency irradiated turbulent dielectric media, many mean free pathsL_{1}wide, is computed. The lengthL_{1}is the distance into the medium over which the mean electric field decreases in amplitude by a factore^{-1}. Previous calculations have always been restricted toL ll L_{1}. It is found thatQincreases from the Born approximationQ = Q_{1}for medium widthL ll L_{1}toQ = 2Q_{1}forL gg L_{1}, and the theory is valid as long asL ll (kL_{0})^{5/3} L_{1}, a significant improvement over the Born approximation, when the macroscaleL_{0}is much larger than the wavelength2_{pi}k^{-1}. The improvement is due to incorporation of the dominant effects of cumulative forward scattering in the local electric field in the medium. A rigorous and a heuristic derivation are given. The transitional behavior is discussed and a simple physical interpretation is given.     

A technique to estimate the relative gains, tuning phases, and RE phase shifts of the elements of a phased-array radar

An in-situ technique to estimate the following parameters of a phased-array antenna is described: 1) the relative array-element excitation voltages, 2) the array-element tuning phases, and 3) the RF phase shifts at the array elements. This technique has several significant features. First, it involves the use of two auxiliary antennas. One is a remote continuous wave (CW) source directed at the phased-array antenna. The other is a passive antenna mounted close to the phased-array antenna. Its output is used to produce a reference phase for phase measurements. Second, it contains a technique to reduce the errors in phase estimates. Third, it takes note that beam steering uses phase sums of the form (phi_{k} + beta_{kl}), wherephi_{k}is the tuning phase for thekth array elemenet andbeta_{kl}, is an RF phase shift of the array element, and pays special attention to reduce the errors associated with the estimates of these sums. Fourth, it assumes the use of a reasonably stable and strong CW source of commerically available quality. No other assumptions are made. Experimental results obtained with a 295-elementS-band space-fed phased-array antenna are given.     

Some periodic convolutional codes better than any fixed code (Corresp.)

Some(n_{o}=2; k_{o}=1)noncatastrophic periodic convolutional codes with memoryM=4are given that have the same free distance,d_{infty}, as the best fixed code but have both a smaller number of paths of weightd_{infty}per time instant and a smaller average number of information bit errors per such path for periodsT=2, 3, 4, and5. It is also shown that an(n_{0}, k_{0})code of periodTis equivalent to a fixed code with parameters(Tn_{0}, Tk_{0}).     

The fast decoding of Reed-Solomon codes using Fermat transforms (Corresp.)

It is shown thatsqrt[8]{2}is an element of order2^{n+4}inGF(F_{n}), whereF_{n}=2^{2^{n}}+1is a Fermat prime forn=3,4. Hence it can be used to define a fast Fourier transform (FFT) of as many as2^{n+4}symbols inGF(F_{n}). Sincesqrt[8]{2}is a root of unity of order2^{n+4}inGF(F_{n}), this transform requires fewer muitiplications than the conventional FFT algorithm. Moreover, as Justesen points out [1], such an FFT can be used to decode certain Reed-Solomon codes. An example of such a transform decoder for the casen=2, wheresqrt{2}is inGF(F_{2})=GF(17), is given.     

Propagation of current on bent wire antennas-an experimental study

The results of precise measurements of the driving point responses to a 200 ps input pulse of bent wire antennas of circular cross section mounted above a ground plane are presented. Transmission and reflection coefficients (plotted as functions of frequency to 3 GHz) describing the propagation and reflection of monochromatic current waves on the bent wires are inferred from the measurements. The results show that the current pulse reflected from a sharp bend (rtheta ll ctau_{1}), whereris the bend radius,thetais the bend angle,cis the speed of light, andtau_{1}is the pulse duration) is a compressed replica of the incident pulse, and that a current pulse propagating around a gradual bend (rtheta approx ctau_{1}) is continuously reflected from the whole length of the bend. The time domain measurements and the inferred frequency domain data give a clear physical picture of the mechanism of current propagation on bent-wire antennas.     

Hypothesis testing with multiterminal data compression

The multiterminal hypothesis testingH: XYagainstH̄: X̄Ȳis considered whereX^{n} (X̄^{n})andY^{n} (Ȳ^{n})are separately encoded at ratesR_{1}andR_{2}, respectively. The problem is to determine the minimumbeta_{n}of the second kind of error probability, under the condition that the first kind of error probabilityalpha_{n} leq epsilonfor a prescribed0 < epsilon < 1. A good lower boundtheta_{L}(R_{1}, R_{2})on the power exponenttheta (R_{1}, R_{2},epsilon)= lim inf_{n rightarrow infty}(-1/n log beta_{n})is given and several interesting properties are revealed. The lower bound is tighter than that of Ahlswede and Csiszár. Furthermore, in the special case of testing against independence, this bound turns out to coincide with that given by them. The main arguments are devoted to the special case withR_{2} = inftycorresponding to full side information forY^{n}(Ȳ^{n}). In particular, the compact solution is established to the complete data compression cases, which are useful in statistics from the practical point of view.     

Description of image information content and image transfer efficiency by single parameters

It is proposed that the numberN*, given byN*=4ab[intmin{0}max{infin}T(f) df]^{2}, is equal to the number of picture elements in an image within which the noise-free modulation transfer functionT(f)of the image device (display) is uniform and isotropic;aandbare the edge lengths (mm) of a rectangular format, andfis the spatial frequency (cycles/mm). An equation forN*, that applies to nonuniform and anisotropic modulation transfer functions is also given. A picture element transfer efficiencyE*is defined as (N*/N*'), whereN*'is the number of picture elements transferred to the image (display) by an "ideal" device.     

Far-field approximations to the Kirchoff-Helmholtz representations of scattered fields

The standard far-field approximation to the Kirchhoff formula for the field scattered by a flat metallic plateSof arbitrary shape is given by a certain surface (double) integral. This double integral can be reduced to a line integral evaluated around the boundary of S. Moreover, ifSis a polygon, this line integral can be reduced to a closed form expression involving no integrations at all. The use of such line integral representations can easily reduce the costs of numerical calculation by orders of magnitude. If the integrands are to be sampledptimes per wavelength to achieve an acceptable degree of precision, and ifAis the area ofS, then the numerical evaluation of the double integral requiresp^{2}A/lambda^{2}functional evaluations whereas the line integral only requirespsqrt{A/lambda^{2}}. IfSis a polygon withNvertices, then only2Nfunctional evaluations are required to evaluate the closed form expression with no quadrature error at all.     

A method for computing addition tables inGF(p^n)(Corresp.)

Conway showed that a table of Zech's logarithms is useful to perform addition in GF(p^{n})when the elements are represented as powers of a primitive element. The Zech's logarithmZ(x)ofxis defined by the equationalpha^{z(x)}=alpha^{x} + 1, wherealphais a primitive element, zero is written asalpha^{ast}, andx=ast,O,1, cdots ,p^{n}-2. A simple algorithm for making a table of Zech's logarithms is presented.     

Writing on dirty paper (Corresp.)

A channel with outputY = X + S + Zis examined, The stateS sim N(0, QI)and the noiseZ sim N(0, NI)are multivariate Gaussian random variables (Iis the identity matrix.). The inputX in R^{n}satisfies the power constraint(l/n) sum_{i=1}^{n}X_{i}^{2} leq P. IfSis unknown to both transmitter and receiver then the capacity isfrac{1}{2} ln (1 + P/( N + Q))nats per channel use. However, if the stateSis known to the encoder, the capacity is shown to beC^{ast} =frac{1}{2} ln (1 + P/N), independent ofQ. This is also the capacity of a standard Gaussian channel with signal-to-noise power ratioP/N. Therefore, the stateSdoes not affect the capacity of the channel, even thoughSis unknown to the receiver. It is shown that the optimal transmitter adapts its signal to the stateSrather than attempting to cancel it.     

Studies of the Focal Region of a Spherical Reflector: Polarization Effects

The polarization of the reflection of a uniform plane wave incident on a spherical reflector is analyzed using the current distribution method for scattered fields. The current distribution on the reflector is derived. For reflectors subtending about60degor less, the radiation scattered in the direction of the circle of least confusion has essentially the same polarization as that reflected specularly from the tangent plane. The effective current, the component of surface current density radiating toward the focal region, is derived in several representations. Assuminghat{i}incident polarization, contour plots are provided forhat{i},hat{j}, andhat{k}components in spherical coordinates. Next, general formulas are derived for thehat{i},hat{j},hat{k}components of the reflected fields, in terms of the direction cosines of the normal to the reflecting surface. These are displayed in terms of projections, and apply directly to the spherical reflector.     

Concentration-dependent diffusion of boron and phosphorus in silicon

A calculation is made of the tail of the impurity concentration profile resulting from concentration-dependent diffusion from a constant surface concentration into a semi-infinite medium. The calculation predicts that if the concentration dependence at low impurity concentrations is negligible, the low concentration portion of the doping profile should still take the familiar form,C = C'_{s} erfc (x/2 D_{i^{frac{1}{2}}}t^{frac{1}{2}}). Diis the commonly known diffusion coefficient at low impurity concentrations, whileC'_{s}is the "apparent" surface concentration.C'_{s}depends on the actual surface concentration and also depends on how the diffusion coefficient varies with impurity concentration at high concentrations. It is a constant for a given diffusion system but could be orders of magnitude higher than the actual surface concentration. Empirical data have been obtained for boron and phosphorus diffusions in silicon and found to be in good agreement with this prediction.     

Some important geometrical features of conic-section-generated offset refelector antennas

Geometrical characteristics of conic-section-generated offset reflectors are studied in a unified fashion. Some unique geometrical features of the reflector rim constructed from the intersection of the reflector surface and a cone or cylinder are explored in detail. It is found that the intersection curve (rim) of the rotationally generated conic-section reflector surface and a circular cone with its tip at the focal point is always a planar curve and has a circular projection on the focal plane only for the offset parabolic reflector. Furthermore, in this case, the line going through the center of the circle, parallel to the focal axis, and the central axis of the cone do not intersect the reflector surface at the same point. Numerical results are presented to demonstrate some unique features of offset parabolic reflectors.     

The imperfectly conducting cylindrical transmitting antenna: Numerical results

The complex wave number, the distribution of current, the admittance, and the radiating efficiency of cylindrical antennas made of imperfect conductors are evaluated numerically from a previously derived theory[1]. The quantity2lambda r^{i}/zeta_{0}(wherer^{i}is the resistance per unit length,lambdais the free-space wavelength, andzeta_{0} = 377ohms) is used as the parameter in a range that extends from zero to 200. Extensive graphs and tables are given.