Showing papers in "International Journal of Electronics in 1964"

Theory of a Class of Discrete Optimal Control Systems

Abstract: The problem considered in this paper is that of finding optimal controls for a class of fixed duration processes in systems described by non-linear difference equations. The discrete versions of the adjoint system and the Hamiltonian are used in conjunction with the original techniques found in the proofs of the Pontryagin maximum principle to derive conditions necessary for a control to be optimal. These necessary conditions are shown to be related to the Pontryagin conditions for continuous systems in the following manner: the requirement of a global maximum of a Hamiltonian becomes a condition of a local maximum or of stationarity, while the transversality conditions remain identical.

Sensitivity in Dynamical System Analysis

Abstract: A few of several possible sets of system condition numbers or sensitivity coefficients are defined relating small changes in system parameters to such measures of system performance as state variables, eigensystems and state variable fuiictionals. Sensitivity functionals are defined also for use in cases where anticipated but undesirable system perturbations occur. The linear or approximately linear dynamical system is of special interest and for these systems it is shown that the condition numbers of all eigenvalues with respect to all elements of the n × n system matrix A are expressible by n 1-term dyads of the form v i X i T, the reciprocal vectors and eigenvectors of A respectively. These matrices are particularly useful in design processes based upon eigenvalue configurations, and it is shown also how they may be employed in the evaluation of a particular class of time weighted functional of the form a of free, stationary, linear systems. Finally it is noted how these matrices are modified ...

Hermite Functional Expansions and the Calculation of Output Autocorrelation and Spectrum for any Time-invariant Non-linear System with Noise Input†

Abstract: By expansion of the input-output relation of an arbitrary non-linear system into a series of Hermite functionals, it is shown that if the input is Gaussian noise, it is possible to derive convenient theoretical expressions for the output autocorrelation function and spectrum.

The Amplification and Transit Time of an Electron Avalanche Traversing a Uniform Electric Field Gap

Abstract: The amplification (A) and transit time (T) of an electron avalanche whilst crossing a gap have been calculated in terms of the electron ionization coefficient (α) and the electron drift velocity (v) with allowance for both electron diffusion and electrode effects. It has been shown that when both α and v are calculated from experimental values for A and T, that errors greater than the experimental error may occur if diffusion and electrode effects are neglected.

A Reappraisal of Certain Aspects of Transistor Theory

Abstract: In the usual analyses of transistor action various assumptions are frequently made; for example, that space charge neutrality exists in the base region, that pn junctions are depleted of mobile carriers, that minority carrier densities next to reverse biased junctions arc near zero, etc. It is shown that none of these assumptions is strictly valid. A now examination of the problem, in which those assumptions are put in better perspective, leads to: (a) a complete, partially numerical, analysis of abrupt pn junctions in equilibrium showing the spatial distribution of holes, electrons and field; (6) a qualitative discussion of these distributions when current is flowing; (c) a revised expression for the small signal capacitance of abrupt pn junctions; (d) a now space-charge-neutral solution for the complex current gain of transistors (this is compared with Shockley's solution). Finally a preliminary numerical solution of the carrier and field distribution in a collector junction, under conditions o...

The Dynamic Behaviour of Magnetic Thin Films

Abstract: The effective damping constant 𝛌eff is measured as a function of frequency by U.H.F. ferromagnetic resonance. The results are compared with those obtained by using a small angle free oscillations technique. In addition, both methods offer a means of determining the gyromagnetic ratio γ. The damping factor 𝛌eff is measured as a function of the anisotropy field Hk, and also of the composition of the nickel—iron film. A possible dispersion of 𝛌eff within the film is discussed. 𝛌eff is also deduced from the exponential decay times of the damped oscillations which occur in experimental hard direction switching waveforms. Such waveforms agree qualitatively with coherent rotational theory. Experimental switching waveforms obtained with large amplitude pulsed reversing fields, applied at 135° to the easy direction, also agree qualitatively with theoretical predictions. Small observed deviations from theory are, perhaps, related to local inhomogeneities of both the anisotropy field and the easy direction. For 135 ...

Ion-Ion Recombination in Iodine Afterglows†

Abstract: Recombination coefficients, in afterglows following pulsed radio-frequency discharges in iodine vapour, are determined by a radio-frequency probing method, which uses the variation of the dielectric constant to measure the ion concentration A small linear radio-frequency mass spectrometer is used to identify the ions present The results show that the recombination coefficient, α, for the mutual neutralization process I2 ++I−→I2'+I'' is independent of pressure between 023 and 10 torr, and is dependent on ion temperature At ion temperatures of 296±3, 328±5 and 338±5°k, the mean values of α are l22( ± 003) × 10−7, l04( ± 005) × 10−7, and 101 (±008) × 10−7 cm3sec−2, respectively Diffusion becomes noticeable at pressures lower than 023 torr From the limited information available the product of diffusion coefficient and pressure, Dap, is estimated to be 10± 3 cm2 sec−1 torr Now at AEI Research Laboratory, Rugby, Warwickshire

A General Minimum Principle for End-point Control Problems†

Abstract: A very brood class of end-point control problems is formulated in general terms, and correspondingly general procedures in the calculus of variations are developed for their solution The generality of the treatment lies in a systematic application of the point of view of functional analysis. The state of the system being controlled is described by an abstract vector in a suitable linear space ; the evolution of the system state with time is described in terms of an operator on the state vector ; the measure of system performance to be maximized or minimized is taken as a functional of the final state. The linearized system operator and its adjoint with respect to an inner product in the state space play central roles in the variational arguments The variational methods are in the spirit of those leading to the familiar Pontrjagin maximum principle, and indeed this principle appears as the finite-dimensional case of the present results. These results however apply equally to infinite-dimensional c...

Impedance of a Coil Placed Near to a Conducting Sheet

Abstract: Mathematical expressions are derived for the changes in resistance and inductance of a single turn of thin wire, due to the presence of a conducting sheet of finite thickness with its surfaces parallel to the plane of the coil Computed results from these expressions are presented, for the case of a non-ferromagnetic sheet, illustrating the effects of variations in sheet thickness and conductivity, the separation of coil and sheet and in frequency of the coil current. These results are relevant to the design and operation of instruments for lead cable-sheath testing.

Direct determination of all the minimal prime implicant covers of switching functions

Abstract: A method of direct determination of all the minimal prime implicant covers of switching functions has been presented in the paper. It has been shown that some of the difficulties encountered in finding directly all the minimal prime implicant covers of the function for which the columns of the cover table cannot be arranged in a single connected cover term matrix or in a number of connected cover term matrices with mutually disjoint sots of prime implicants can be overcome by first dividing the cover table into a number of sub-tables such that the columns of one of the sub-tables can be arranged to form a connected cover term matrix by ignoring the presence of some of the prime implicants from some of its columns. Next by associating the different irredundant covers of the other sub-tables with this connected cover term matrix, all the minimal prime implicant covers of the function can be found out.

The Gradient in the Sampling of N-dimensional Band-limited Functions†

Abstract: Two previous generalizations of the Whittaker-Shannon sampling theorem are combined in a -way which emphasizes the value of the gradient of a function defined on a space of N dimensions. The band-limited functions are sampled, with their gradient, on a sampling lattice which results from an appropriate choice of the corresponding reciprocal lattice. Necessary and sufficient conditions, for a particular synthesis of the functions, are given which govern the relationship between the reciprocal lattice and the bounded support of the Fourier transforms of the functions in question. These conditions are satisfied by the corresponding conditions of the N-dimensional theory when the gradient is not sampled. When the gradient is sampled the conditions are loss stringent and thus allow for an additional economy in the sampling. Two two-dimensional examples are worked out in detail to illustrate the results of the theory.

Further Study of an Optimum Non-linear Control System†

Abstract: This paper is the second of two in which the system studied has a plant which consists of two integrators with a saturable control input, and the performance criterion which is to be minimized is integral-error-squared. In the first paper the known optimum controller was shown to satisfy Pontryagin's maximum principle. In the present paper further verification of the optimum system is obtained by showing that the best performance function satisfies Bellman's partial differential equation. It is found that Bellman's equation is even satisfied for points on the switching curve, Results are also given for other performance criteria.

Experimental Studies of Spinwaves Excited by Parallel Pumping

Abstract: The excitation of spinwaves by a microwave magnetic field in the parallel-pump configuration is described. A swept magnetic field technique for detecting the absorption of microwave energy is employed. Values for the acoustic Q -factor, the magnetoelastic coupling coefficient and exchange constant are obtained for single-crystal yttrium-iron garnet. Verification of Morgenthaler's theory of spinwave-phonon interaction is provided. Experiments employing superimposed r.f. modulation of the magnetic field are in general agreement with Suhl's theory. Observations of relaxation oscillations have been made which differ from those previously reported.

On the Optimum Switching Function of a Certain Class of Third-order Contactor Servomechanism. I†

Abstract: In this paper the optimum switching function of a certain class of linear third-order contactor servomechaniams has been studied in detail.

The Appearance of the Self-cut-off Phenomenon in the Cylindrical Diode†

Abstract: The influence of the filament heating current on the characteristics of a cylindrical diode system has been investigated. In this structure with a radial electric field and a tangential magnetic field, produced by the heating filament current, similarly as in a magnetron geometry, an electron moves in crossed fields. It has been found that in such a structure the condition for the anode current cut-off exists although no external magnetic field is applied. The criterion for the cut-off (self-cut-off( in this structure has been calculated. The critical anode voltage is where If is the filament heating current and li the anode radius. In the experimental part of this work the self-cut-off phenomenon has been confirmed by characteristics Ip= f(If), where Ip is the anode current, and by waveforms of the anode current.

Distribution Function for Output of Certain Linear Filters for Random Input Events

Abstract: Statistical properties of the response of a linear filter to discrete stationary time series are analysed. The input time series consist of discrete random events having a known amplitude distribution. The analysis is carried out for a number of response functions of linear filters especially of interest in pulse.height spectrometry and in pulse signal detection The probability density function of the output stochastic process is calculated and plotted as a function of both the response function parameters, and the average rate and amplitude distribution of the input events. Attention is paid to the moan value, the standard deviation and the factors of skowness and excess of the output process. The normalized form of the calculated curves suitable for direct application on amplitude sensitive systems excited by random events is given. The theoretical results are confirmed by the experiments.

A Frequency-selective RC Feedback Circuit with Relatively Low Component Tolerance Sensitivity†

Abstract: The ‘ total Q sensitivity ’, ΣQ, is presented as a useful figure of merit, for quantitative comparisons of the relative stability of different frequency-selective feedback networks. Physically, ΣQ gives the percentage change in Q which would result if each parameter of the network were changed by 1 % in a direction such that the effects are additive. A very simple selective feedback circuit using a distributed RC network is analysed and compared with other well-known selective networks. It is shown that ΣQ for this network (including the effects of the active element) is considerably less than that for other comparable active feedback networks (for which the active elements are not included). Therefore this network has significant advantages wherever it is not practical to use an LC tank circuit for tuning.

Klystrons with double-gap bunchers

Abstract: The use of double-gap bunching in klystrons is investigated theoretically and it is shown that under suitable conditions the beam coupling coefficient may be 40% higher than for a single gap. Also, the loading of the buncher by the beam under these conditions may be eliminated. It is estimated that the double-gap buncher can improve the overall gain by about 6 dB. The theoretical results have been confirmed in a positive-ion klystron operating at a frequency of 5 Mc/s.

The Effect of a Random Noise Background upon the Amplitude Distribution Function of Random Events

Abstract: Statistical properties of a sum of continuous noise and random discrete events having gamma and Gaussian amplitude distributions, respectively, have been analysed. An expression is derived for the probability density function of this sum as a function of gamma and Gaussian distribution parameters. Attention is paid to the mode value, especially interesting in pulse-height spectrometry. The probability density function of the sum and its mode values are calculated and plotted in a normalized dimensionless form, suitable to direct application. The results can be applied for evaluation of errors in pulse-height spectrometry, especially when multi-channel pulse-height analysers are used.

The Correlation Function of Gaussian Noise after Error-function Limiting!

Abstract: Baum's formula for the correlation function of Gaussian noise after error-function limiting is obtained by a new, simple and relatively direct approach. It sheds some light on the case in which a half-wave linear rectifier precedes the limiter but is not able to simplify the work of Kaufman and Roberts on this problem.

RESEARCH NOTE Laser Induced Electron Emission from Tungsten Points

Abstract: (1964). RESEARCH NOTE Laser Induced Electron Emission from Tungsten Points † Journal of Electronics and Control: Vol. 16, No. 1, pp. 75-75.

An Approximately Optimal Extremul Regulator

Abstract: Many chemical and mineral processing plants are extremal systems, that is they have a best control setting from which deviation in any direction lowers the product yield. The model for such systems has u peaked nonlinear characteristic in the output. Previous empirieal controllers have estimated the slope of the characteristic at the current working point, and then adjusted the control for maximum yield. This paper demonstrates the theory of optimal control of extremal systems. Detailed results are given for a one-dimensional model with (i) random fluctuations in the non-linear characteristic, (ii) noise on the output measurements, (iii) noise in the control path, (iv) dynamics in the control path. Only approximate computations are feasible on a small digital computer, the approximation here incorporates certain features of tho empirical method. Comparisons between the empirical and optimal controller are made.

Wave propagation in an anisotropic column with ring source excitation

Abstract: Propagation of electromagnetic waves through a homogeneous anisotropic column of a medium of infinite length is studied. The anisotropy of the medium is characterized by the dyadic form of the permittivity e and the permeability μ. This anisotropic column is surrounded coaxially by a homogeneous isotropic medium characterized by the scalars e2 and μ2, the complete structure being enclosed by a perfectly conducting metallic circular-cylindrical wave-guide. A magnetic current ring source of arbitrary angular variation is introduced symmetrically in the isotropic medium. For this general problem, the complete expressions for fields (due to the source), the average power flow, and the dispersion relation have been obtained. Dispersion relations for various special cases are also derived. To solve the source problem, dyadic Green functions for both point electric current source and point magnetic current source have been constructed in a formal way from the source-free solutions of the appropriate Max...

The Absolute Optimality of a Non-linear Control System with Integral-square-error Criterion†

Abstract: For a plant consisting of two integrators with saturable control input, a controller is known which gives a minimum value of integral-error-squared. In the present paper it is shown that this value is the absolute minimum (not merely a local minimum), and that the control input which gives it is unique.

Work Function Patches on Oxide-coated Cathodes†

Abstract: Variations in the electron emission from different regions of the surface of sprayed barium oxide cathodes have been observed using electron emission microscopes. A method involving magnetic collimation of the electron flux from the cathode has been applied to measure the Richardson work functions of areas of about 2-5 × 10-5 and to perform a one-dimensional scan of part of the cathode surface. Major emitting areas were found to be separated by distances of from 0-1 to 0-3 mm, of the same order as the separation of irregularities in the cathode surface. The variations in work function on this scale are attributed to the surface roughness of the cathode. A correlation between the logarithm of the emission constant in the Richardson equation and the Richardson work function was found to exist for the small areas investigated.

The Temperature Variation of the Parameters of Silicon Controlled Rectifiers

Abstract: The parameters of silicon controlled rectifiers carrying two base contacts are measured as a function of temperature in the range from room temperature to the normal limits of operation (140-160°c). The values of current gain of the two basic transistor sections of the device are measured as functions of emitter current over the same range of temperatures. The switching condition is found to be independent of temperature and the experimental results are explained in terms of normal transistor theory.

On the Hollow Cathode Effect

Abstract: In this paper the hollow cathode effect is discussed in connection with the derivation of some simple laws which relate the current density, j, the gas pressure, p, and the current amplification factor, q. Thus one may conclude that, under the conditions of a fully developed hollow cathode effect, the product I2p does not depend on the gas pressure, and the graph (log q, logp) has a universal slope given by —2·5. In addition, are presented original experimental data obtained in krypton and xenon.

Transformation of Fluctuations in an Injected-beam Crossed-field Device†

Abstract: Appropriate Llewellyn-Peterson type equations are derived by taking into account the two current-density components in the beam. The final noise transport coefficients are obtained in terms of the initial and tangential velocity components and their time derivatives. Two sets of these coefficients are written in a general form so that the noise transport can be evaluated for several perturbation frequencies and different physical models for which the two velocity components and their time derivatives are specified. These coefficients are evaluated in the gun region for three physical models and in the interaction region for arbitrary input conditions. For non-cycloiding beams in the interaction region these coefficients are also evaluated for several values of ωp/ ωc and ω/ ωc. The velocity fluctuations are decreased while the current fluctuations are increased as ω/ ωc is increased and the perturbation amplitude increases as ωp/ ωc is increased which is in agreement with other results. The pertu...

The Cut-off Characteristics of Plane Magnetrons†

Abstract: The present paper presents the cut-off characteristics of plane magnetrons obtained experimentally by applying an improved measuring method in which the effect of the ‘ marginal’ inhomogeneity of the electric field is reduced by the introduction of a guard anode. However, these characteristics are not in satisfactory agreement with the predictions of the theory which takes into account the initial velocity distribution of the electrons. It is shown that the ‘ marginal’ inhomogeneity of the electric field does not, as such, affect too much the shape of the cut-off curve; also, that a considerable number of electrons are captured by a collector, placed in the same piano as the cathode, only for positive potentials of the collector with respect to the cathode. When the collector and the cathode surfaces are at the same potential these electrons are collected by the guard-ring anode. The existence of these electrons probably accounts for the difference in shape of the cut-off curve of the central ano...

An Electron Beam-plasma Amplifier at Microwave Frequencies†

Abstract: Wave propagation through cut-off waveguide filled with plasma and immersed in an axial magnetic field is considered, extending some results of Trivolpiece and Gould. Synchronous electron beam interactions with respect to forward waves in this system resulting in the amplification of microwave signals are analysed theoretically, and an expression for the gain is derived. An experiment is described where an electron beam interacts with the plasma it produces in passing through a metal tube filled with deuterium at ~0·2 torr, a magnetic field ~4 KG being applied. Analysis of the gains recorded at frequencies around 8 GC/s shows that provided lateral non-uniformity of the plasma distribution is taken into account, the theoretical model used to describe the system is a reasonable one. No effects ascribable to backward wave interactions could be detected.