Showing papers in "Bell System Technical Journal in 1970"

An efficient heuristic procedure for partitioning graphs

Abstract: We consider the problem of partitioning the nodes of a graph with costs on its edges into subsets of given sizes so as to minimize the sum of the costs on all edges cut. This problem arises in several physical situations — for example, in assigning the components of electronic circuits to circuit boards to minimize the number of connections between boards. This paper presents a heuristic method for partitioning arbitrary graphs which is both effective in finding optimal partitions, and fast enough to be practical in solving large problems.

Charge coupled semiconductor devices

Abstract: In this paper we describe a new semiconductor device concept. Basically, it consists of storing charge in potential wells created at the surface of a semiconductor and moving the charge (representing information) over the surface by moving the potential minima. We discuss schemes for creating, transferring, and detecting the presence or absence of the charge. In particular, we consider minority carrier charge storage at the Si-SiO 2 interface of a MOS capacitor. This charge may be transferred to a closely adjacent capacitor on the same substrate by appropriate manipulation of electrode potentials. Examples of possible applications are as a shift register, as an imaging device, as a display device, and in performing logic.

An integral charge control model of bipolar transistors

Abstract: We present in this paper a compact model of bipolar transistors, suitable for network analysis computer programs. Through the use of a new charge control relation linking junction voltages, collector current, and base charge, the model includes high injection effects. The performance substantially exceeds that of existing models of comparable complexity. For low bias and with some additional idealization, the model reduces to the conventional Ebers-Moll model.

Use of the discrete fourier transform in the measurement of frequencies and levels of tones

Abstract: This paper considers the application of a digital computer and discrete Fourier transform (DFT) techniques to the measurement of signals known to comprise only single-frequency tones. We discuss the use of weighting functions to improve the effective selectivity of a measurement system that estimates the frequencies and levels of tones from the coefficients of their DFT. We present three classes of weighting functions which may be used to improve the inherent accuracy of such a system. The form of the weighting functions was chosen to minimize the amount of computer memory required, without using too much computer time. Several formulas are derived for estimating the frequency and level of a tone from its DFT coefficients. We chose the formulas to minimize computation time. Simulation results indicate that, through the use of a proper weighting function, a DFT measurement system that uses 512 samples taken at a sampling frequency of 7040 Hz can be designed so that the maximum error in the frequency estimates of two tones near 1000 Hz and separated by approximately 50 Hz is about 0.03 Hz. The corresponding maximum error in the level estimate is on the order of 0.03 dB.

Adaptive predictive coding of speech signals

Abstract: We describe in this paper a method for efficient encoding of speech signals, based on predictive coding. In this coding method, both the transmitter and the receiver estimate the signal's current value by linear prediction on the previously transmitted signal. The difference between this estimate and the true value of the signal is quantized, coded and transmitted to the receiver. At the receiver, the decoded difference signal is added to the predicted signal to reproduce the input speech signal. Because of the nonstationary nature of the speech signals, an adaptive linear predictor is used, which is readjusted periodically to minimize the mean-square error between the predicted and the true value of the signals. The predictive coding system was simulated on a digital computer. The predictor parameters, comprising one delay and nine other coefficients related to the signal spectrum, were readjusted every 5 milliseconds. The speech signal was sampled at a rate of 6.67 kHz, and the difference signal was quantized by a two-level quantizer with variable step size. Subjective comparisons with speech from a logarithmic PCM encoder (log-PCM) indicate that the quality of the synthesized speech signal from the predictive coding system is approximately equal to that of log-PCM speech encoded at 6 bits/sample. Preliminary studies suggest that the binary difference signal and the predictor parameters together can be transmitted at approximately 10 kilobits/second which is several times less than the bit rate required for log-PCM encoding with comparable speech quality.

On the interaction of roundoff noise and dynamic range in digital filters

Abstract: The interaction between the roundoff-noise output from a digital filter and the associated dynamic-range limitations is investigated for the case of uncorrelated rounding errors from sample to sample and from one error source to another. The required dynamic-range constraints are derived in terms of L p norms of the input-signal spectrum and the transfer responses to selected nodes within the filter. The concept of “transpose configurations” is introduced and is found to be quite useful in digital-filter synthesis; for although such configurations have identical transfer functions, their roundoff-noise outputs and dynamic-range limitations can be quite different, in general. Two transpose configurations for the direct form of a digital filter are used to illustrate these results.

Radiation losses of tapered dielectric slab waveguides

Abstract: In this paper we calculate radiation losses of a single mode dielectric slab waveguide for TE and TM modes. The theory is based on the determination of the radiation losses of one abrupt step. We obtain the losses of arbitrarily deformed waveguides by regarding the arbitrary deformations as a succession of infinitely many infinitesimal steps. This method yields the same results as a very different method presented earlier. It allows us to calculate the losses of TM modes that were hard to obtain by the earlier method. The radiation losses of single mode slab waveguides with abrupt steps of a 2:1 ratio are surprisingly low and can be kept below 1 percent by dimensioning the guide properly. The loss advantage of linear tapers becomes noticeable only when the tapers are very long. An optimized taper changes more rapidly in its wider portion and becomes more gradual in its narrow part.

Queues served in cyclic order: Waiting times

Abstract: This paper extends the results of a previous paper in which two models of a system of queues served in cyclic order were studied. One model is an exhaustive service model, in which the server waits on all customers in a queue before proceeding to the next queue in cyclic order. The other is a gating model, in which a gate closes behind the waiting units when the server arrives, and the server waits on only those customers in front of the gate, deferring service of later arrivals until the next cycle. In the present paper, the Laplace-Stieltjes transforms of the order-of-arrival waiting time distribution functions and, for the exhaustive service model, the mean waiting time for a unit arriving at a queue, are obtained.

Experimental verification of the charge coupled device concept

Abstract: Structures have been fabricated consisting of closely spaced MOS capacitors on an n-type silicon substrate. By forming a depletion region under one of the electrodes, minority carriers (holes) may be stored in the resulting potential well. This charge may then be transferred to an adjacent electrode by proper manipulation of electrode potentials. The assumption that this transfer will take place in reasonable times with a small fractional loss of charge is the basis of the charge coupled devices described in the preceding paper,1 To test this assumption, devices were fabricated and measurements made. Charge transfer efficiencies greater than 98 percent for transfer times less than 100 nsec were observed.

A charge control relation for bipolar transistors

Abstract: We give a relation which links emitter and collector junction voltages, V eb and V eb , collector current I c , and the total charge Q b of carriers that enter through the base terminal (electrons in a pnp transistor): $I_{c} = const{e^(aV_{eb / kT}) - e^(aV_{eb / kT})\over Q_{b}}.$ This relation is valid for high injection conditions, subject only to minor restrictions. The significance for device modeling is discussed.

Adaptive delta modulation with a one-bit memory

Abstract: We propose a delta modulator which, at every sampling instant r, adapts its step-size (for a staircase approximation to the input signal) on the basis of a comparison between the two latest channel symbols, C r and C r-1 Specifically, the ratio of the modified step-size m r to the previous step size m r-1 is either +P or — Q depending on whether C r and C r-1 are equal or not (We recall that, in delta modulation, C r represents the polarity of the difference, at the sampling instant r, between the input signal X r and the latest staircase approximation to it, Y r-1 ) A simulation of the delta modulator with a band-limited speech input has revealed that PQ = 1 and P ⋍ 15 represent optimal adaptation characteristics, on the basis of signal-to-error ratios, over an important range of sampling frequencies; and that at 60 kHz, delta modulation with these adaptation parameters compares favorably with 7-bit logarithmic PCM, which reproduces speech with good telephone quality We present several graphical results from this simulation, and include an evaluation of the effect of independent channel errors on the adaptive delta modulator We proceed to suggest a heuristic theory of the delta modulator which explains the optimality of the condition PQ = 1, and develops an upper bound of 2 for the optimum value of P We conclude with a summary of results from a video simulation which revealed that aforementioned optima for P and Q apply to a video signal

Holographic thin film couplers

Abstract: Recently P. K. Tien and his co-workers have described a prism coupler as a convenient means to feed light into a single mode of a guiding thin optical film.1 Distributed couplers of this kind are of great interest for integrated optical devices. In this brief we describe thin

On the distribution of numbers

Abstract: This paper examines the distribution of the mantissas of floating point numbers and shows how the arithmetic operations of a computer transform various distributions toward the limiting distribution $r(x) = {1 \over x \ln b} \quad (1/b \leqq x \leqq 1)$ (where b is the base of the number system). The paper also gives a number of applications to hardware, software, and general computing which show that this distribution is not merely an amusing curiosity. A brief examination of the distribution of exponents is included.

A new approach for evaluating the error probability in the presence of intersymbol interference and additive Gaussian noise

Abstract: The determination of the error probability of a data transmission system in the presence of intersymbol interference and additive gaussian noise is a major goal in the analysis of such systems. The exhaustive method for finding the error probability calculates all the possible states of the received signal using an N-sample approximation of the true channel impulse response. This method is too time-consuming because the computation involved grows exponentially with N. The worst-case sequence bound avoids the lengthy computation problem but is generally too loose. In this paper, we have developed a new method∗ which yields the error probability in terms of the first 2k moments of the intersymbol interference. A recurrence relation for the moments is derived. Therefore, a good approximation to the error probability of the true channel can be obtained by choosing N large enough, and the amount of computation involved increases only linearly with N. The series expansion is shown to be absolutely convergent, and an upper bound on the series truncation error is given. In order to show the improvement provided in this new method, it is compared with the Chernoff bound technique in three representative cases. An order of magnitude improvement in accuracy is obtained.

Nonorthogonal optical waveguides and resonators

Abstract: The modes of propagation in optical systems which do not possess meridional planes of symmetry (nonorthogonal systems) are investigated in the case where the effect of apertures and losses can be neglected. The fundamental mode of propagation is obtained with the help of a complex ray pencil concept. An integral transformation of the field, based on a quasi-geometrical optics approximation and a first-order expansion of the point characteristic of the optical system, is given; it shows that the complex (three-dimensional) wavefront of the fundamental mode is transformed according to a generalized “ABCD law.” A simple expression is also obtained for the phase-shift experienced by the beam. The higher order modes of propagation are obtained from a power series expansion of the fundamental mode. These higher order modes are expressed, in oblique coordinates, as the product of the fundamental solution and finite series of Hermite polynomials with real arguments. In the special case of systems with rotational symmetry, these series reduce to the well-known generalized Laguerre polynomials. The theory is applicable to media such as helical gas lenses and optical waveguides suffering from slowly varying deformations in three dimensions. Nonorthogonal resonant systems are also investigated. An expression for the resonant frequencies, applicable to any three-dimensional resonator, is derived. Numerical results are given for the resonant frequencies and the resonant field of a twisted path cavity which exhibits interesting properties: the usual polarization degeneracy is lifted and the intensity pattern of all of the modes possesses a rotational symmetry.

Electrochemically controlled thinning of silicon

Abstract: A method for precision thinning silicon integrated circuit slices has been developed whereby either n or p type regions may be selectively removed from material of opposite conductivity. The existence of a simple and economical means to attain precise thickness control permits more complete advantage to be taken of many silicon IC structures. For example, precise thickness control, together with anisotropic1 etching of isolation/separation slots, is expected to permit economical fabrication of high component density, air-isolated monolithic2 integrated circuits.

Optical resonators with variable reflectivity mirrors

Abstract: In this paper we investigate circular optical resonators with gaussian profiles of the mirror reflectivities. Closed form solution to the integral equations for such resonators are obtained. The dominant TEM o,o mode characteristics of a resonator consisting of one variable reflectivity mirror (VRM) and one uniform reflectivity mirror (URM) are considered in detail for a variety of parameters. This resonator is particularly suitable for high-gain lasers. Its advantages in comparison to the conventional type are: (i) there is larger mode volume utilization, and (ii) the power transmitted at the variable reflectivity mirror can in principle be utilized as the power output. We discuss dependence of the spot sizes on laser gain and mirror-curvature tolerances and present a specific design of a Fabry-Perot resonator for fundamental mode operation and the expected performance.

Computed transmission through rain at microwave and visible frequencies

Abstract: In this paper we present tables which contain the Mie scattering coefficient, absorption coefficient, extinction coefficient, equivalent medium index of refraction and phase delay for rains conforming to the Laws and Parsons drop-size distribution. These transmission characteristics have been calculated for microwave frequencies of interest in common carrier radio relay systems, 300 to 1.43 GHz, that is, 0.1 to 21.0 cm, at rain rates from 0.25 to 150.0 mm/hr. We also include the extinction coefficients for the visible wavelength 0.6328 μ. The microwave tables were generated by using a Mie scattering computer program similar to that designed and previously reported by Deirmendjian. The calculations at 0.6328 μ were made separately by employing the usual assumptions for droplets with very large circumference to wavelength ratios.

A unified formulation of segment companding laws and synthesis of codecs and digital compandors

Abstract: Segment companding laws are being considered for use in PCM to cater to the possibility of digital processing of uniformly quantized signals. A unified formulation of the segment companding laws is presented, which permits the detailed structure of quantization to be explicitly characterized. Most important, it is shown that this formulation yields algorithms for the systematic synthesis of coders, decoders, and digital compandors. Examples of circuits synthesized from the algorithms are shown for two segment law companding families — the μ-law and the A-law.

Binary codes which are ideals in the group algebra of an abelian group

Abstract: A cyclic code is an ideal in the group algebra of a special kind of Abelian group, namely a cyclic group Many properties of cyclic codes are special cases of properties of ideals in an Abelian group algebra A character of an Abelian group G of order v is, for our purposes, a homomorphism of G into the group of vth roots of unity over GF(2) If G is cyclic with generator x, the character is entirely determined by what it does to x; this effect is kept, and the characters are discarded If G is not cyclic it is necessary to rehabilitate the characters Without them the notation is impossible; with them one can prove a number of theorems which reduce in the special case to well-known properties of cyclic codes Moreover the writer thinks that the general proof is often easier and more suggestive than the proof for the special case To support this point of view we produce a new theorem, which of course also applies to cyclic codes

The capacity of the Gaussian channel with feedback

Abstract: In this paper we provide a rigorous proof that feedback cannot increase the capacity of the channel with additive colored gaussian noise by more than a factor of two. We also give a tighter bound showing that any increase in capacity is less than the normalized correlation between the signal and noise. It is further shown that gaussian signals and linear feedback processing will achieve capacity. The practical implications are that (i) feedback should be used to simplify encoding and decoding since there is little to be gained in the way of increased capacity and (ii) the various proposed schemes which use linear feedback are doing the correct thing.

Excitation of the dominant mode of a round fiber by a Gaussian beam

Abstract: The excitation of the dominant HE 11 mode of a round optical fiber by a gaussian beam has been calculated. The calculation is based on the assumption that reflected waves can be neglected. It is thus applicable only to fibers with low index difference between core and cladding. It is found that optimum excitation of the HE 11 mode is achieved for loosely guided beams if the product of the beam half-width w times the radial decay constant γ of the HE 11 mode outside of the guide is unity, γw = 1. For tightly coupled modes 2½w must be equal to the core radius in order to achieve optimum excitation. As much as 99 percent of the power can be transferred to the HE 11 mode. Also investigated are the effects of an off-set or tilted beam on the mode excitation. The mode excitation drops to 36 percent if the amount of off-set equals the beam half-width. The effect of tilts depends on the parameter kd, free space propagation constant times core radius of the fiber. For small values of kd or loosely guided modes, the mode excitation is very sensitive to tilts of the gaussian beam. As long as the HE 11 mode is the only mode that can propagate, increasing values of kd lead to less sensitivity with respect to tilts. For multimode operation of the fiber, the sensitivity to tilts increases with increasing values of kd. The minimum of tilt sensitivity coincides with the minimum spot size of the guided mode.

Radiation losses of the dominant mode in round dielectric waveguides

Abstract: The radiation loss theory that has been developed in a series of earlier papers is extended to the dominant mode of the round dielectric waveguide. The theory is applied to the calculation of radiation losses of abrupt steps, gradual tapers, and random wall perturbations of the round dielectric waveguide. The radiation losses caused by an abrupt step, and consequently the losses of tapers, are far higher for the dominant mode of the round dielectric waveguide than they are for corresponding steps and tapers of the dielectric slab waveguide. However, the losses caused by infinitesimal random wall perturbations of the round waveguide are nearly equal to the random wall losses predicted on the basis of the slab waveguide theory. In fact the losses of the dominate mode as well as the circular electric TE 01 mode of the round rod due to random wall perturbations are very nearly the same. The theory is limited to circular symmetric distortions of the round dielectric rod (diameter changes). The radiation losses caused by steps of the round dielectric waveguide that carries the dominate guided mode have been verified by experiments at millimeter wave frequencies.

Determination of the shape of the human vocal tract from acoustical measurements

Abstract: In this paper we describe methods for determining the cross-sectional area function of the human vocal tract from acoustical measurements made at one end. The pressure and volume velocity are assumed to obey Webster's horn equation, which is valid for frequencies below 3.5 kHz. Acoustical properties below 3.5 kHz do not uniquely specify the area function. This paper shows how high frequency information may be incorporated into the mathematical model in a manner consistent with a priori information about the vocal tract. Some results of application of the methods by computer simulation are presented. It is interesting to see from the figures that nine numbers (namely, length, four formants, and four residues) specify the area function quite well for practical purposes.

The potential due to a charged metallic strip on a semiconductor surface

Abstract: We solve numerically the problem of finding the potential and electric field around a negatively charged metallic contact on the surface of an n-type semiconductor. The semiconductor, which has permittivity ∊ 1 , fills the half-space y 0 is vacuum with permittivity ∊ 0 . In suitable dimensionless coordinates the potential ϕ satisfies Laplace's equation in y > 0 and the equation ▽2ϕ = eϕ − 1 in y 0 0 | » 1 and η = ∊ 0 /∊ 1 > « 1. We examine in considerable detail the limiting case η = 0, first for the less practical situation where |ϕ 0 | « 1 and then for |ϕ 0 | » 1. In case the |ϕ 0 | « 1 we show that our numerical solution agrees well with the exact analytical solution of a linearized version of the problem. For |ϕ 0 | » 1, we give plots of the equipotential curves, curves of equal charge density, and curves of constant electric field amplitude. These results also yield expressions for the capacitance of both a strip and a circular electrode. The modifications of these results when η > 0 are also given in some detail. Finally, we discuss the numerical calculations at some length.

Image storage and display devices using fine-grain, ferroelectric ceramics

Abstract: Thin plates of ferroelectric ceramic in combination with transparent conductive and photoconductive films have been used to form device structures that can store a real image as a spatial variation in birefringence. This image can be viewed directly by suitably polarized transmitted light or projected onto a viewing screen. The stored image is erasable by the application of appropriate combinations of light and electric fields.

Upper bound on the efficiency of dc-constrained codes

Abstract: We derive the limiting efficiencies of dc-constrained codes. Given bounds on the running digital sum (RDS), the best possible coding efficiency η, for a K-ary transmission alphabet, is η = log 2 λ max /log 2 K, where λ max is the largest eigenvalue of a matrix which represents the transitions of the allowable states of RDS. Numerical results are presented for the three special cases of binary, ternary and quaternary alphabets.

Lead-acid battery: Tetrabasic lead sulfate as a paste material for positive plates

Abstract: We present a reproducible method of synthesizing tetrabasic lead sulfate (4PbO · PbSO 4 ) which produces discrete elongated crystals approximately 22 microns long. Tetrabasic lead sulfate undergoes anodic conversion to PbO 2 while maintaining the characteristic morphology of the 4PbO · PbSO 4 crystals. This results in lead-acid battery positive plates having performance characteristics superior to those fabricated from conventional paste formulations. We furnish data showing the performance of 4PbO · PbSO 4 positive plates as a function of plate porosity and present stress cycling data, comparing it with the behavior of typical conventional positive plates.

Lead-acid battery: Positive grid design principles

Abstract: In this paper, we present accelerated test data which show the superior anodic corrosion and growth behavior of pure lead as compared to lead calcium and lead-antimony positive grids for lead-acid batteries in float service. We relate differences in growth behavior to differences in metallurgy for these three alloy systems. Pure lead has been incorporated into circular grid designs and tests show these to be a substantial improvement over conventional rectangular grids. A novel grid design concept has been developed and applied to the design of pure lead circular grids. The rate and direction of growth in the grids are controlled by appropriate geometrical design of the grid members. Batteries incorporating these circular grids increase in capacity with age rather than decrease in capacity as do rectangular grids. The circular grids can be designed to provide lifetimes of several centuries.

Theorems on the computation of the transient response of nonlinear networks containing transistors and diodes

Abstract: We consider in detail the nonlinear equations encountered at each time step when certain implicit numerical-integration algorithms are used. In terms of only the properties of the Jacobian matrix of the pertinent set of differential equations, we present necessary and sufficient conditions for the existence and uniqueness of the solution of the nonlinear equations for all continuous forcing functions and any given step size. Since engineers often think about dynamic nonlinear transistor network problems in terms of the eigenvalues of the relevant Jacobian matrix, the results described are of immediate conceptual value. In particular, it is possible to carry out the algorithms whenever the conditions presented are satisfied. Several other types of results are also presented. For example, for a special but significant and useful numerical-integration formula, theorems are proved concerning properties of the computed sequence such as the extent to which the sequence is relatively immune to small local errors introduced at each step as a result of the fact that it is ordinarily not possible to compute the solution of a certain equation exactly. All of the results are concerned with network models that are often used in computer simulations. In fact, we heavily exploit some special properties possessed by the nonlinear functions associated with such models.