Proceedings of the IEE  Part C: Monographs
Volume 105, Issue 7, March 1958
Volumes & issues:
Volume 105, Issue 7
March 1958
The concept of heterogeneous surface impedance and its application to cylindrical cavity resonators
 Author(s): A.E. Karbowiak
 Source: Proceedings of the IEE  Part C: Monographs, Volume 105, Issue 7, p. 1 –12
 DOI: 10.1049/pic.1958.0003
 Type: Article
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The concept of heterogeneous surface impedance is introduced. This is defined as an impedance sheet whose surface impedance varies from point to point in an arbitrary manner. The approach is found yield useful results in a variety of physical situations, and a few applications are illustrated by numerical examples.Physical heterogeneous impedance sheets are extremely common. Typical examples are provided by resonators which are built up of several pieces of metals of various conductivities, resonators imperfectly assembled (e.g. by having small gaps between various parts), effects of imperfect machining or annealing, etc.The formulae developed relate the Qfactor and the resonant frequency of a cavity to its dimensions and the Fourier components the surface impedance function, which, in general, may be anisotropic. The analysis is kept as general as possible, and the formulae developed do not exclude any of the practical cases.In the case of circumferential heterogeneity it is shown that all E_{m, n, l} and H_{m, n, l}modes (other than E_{0} and H_{0}modes) are unstable unless the 2mth harmonic of the heterogeneous surface impedance is absent. It is further concluded that such cavities are characterized by doublehumped resonance curve, but so far as the E_{0} and H_{0}modes are concerned, the cavity may be regarded as homogeneous with surface impedance equal to the mean value of the surfaceimpedance function.With the exception of a few isolated cases (discussed in detail) an axially heterogeneous cavity, when supporting any E_{m, n, l} or H_{m, n, l}mode, may be regarded as a homogeneous one whose axial anisotropic component is the sum of the mean value of the surfaceimpedance function and onehalf of its lth harmonic, and whose circumferential component is given by the difference between the mean value of the surfaceimpedance function and onehalf of its lth harmonic.It is shown that, in general, a unique value of the surface impedance cannot be ascribed to an unbounded periodic sheet, but if its period is sufficiently small (in comparison with the wavelength), the heterogeneous sheet behaves as if it were homogeneous of surface impedance equal to the mean value of the surfaceimpedance function.
The approximate calculation of the electric field between a rod and a concentric ring by means of toroidal functions
 Author(s): G.W. Carter and S.C. Loh
 Source: Proceedings of the IEE  Part C: Monographs, Volume 105, Issue 7, p. 13 –17
 DOI: 10.1049/pic.1958.0004
 Type: Article
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The electric field set up when a live conductor in the form of a rod passes through the centre of an earthed ring of circular section is approximately calculated by replacing the rod by an hourglassshaped conductor of the same minimum radius. The resulting field is found terms of toroidal functions, numerical Tables of which are given. To find how closely the calculated results approach the true values for rod and ring, a systematic electrolytictank study is undertaken, and charts of the differences between theory and experiment are given. is found that the theoretical attack is successful in predicting the smallest figure to which the voltage gradient on the electrodes can be reduced, but that the conductor radii which will enable that figure to be realized are somewhat different in practice from those suggested by the theory.
A spectrometer method for measuring the electrical constants of lossy materials
 Author(s): J.S. Seeley
 Source: Proceedings of the IEE  Part C: Monographs, Volume 105, Issue 7, page: 18 –18
 DOI: 10.1049/pic.1958.0005
 Type: Article
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The analysis of the propagation of a plane wave at oblique incidence through a strip of lossy material is stated, the behaviour of the lossy material being completely represented by the use of a complex refractive index and a complex reflection coefficient. A measurement technique is described whereby these constants can be measured from a strip of material used in a 1 cm parallelplate spectrometer. The analysis and measurement technique are checked by the application of the spectrometer method and the established waveguide method to the measurement of two ordinary lossy dielectrics. The spectrometer method may be used for the measurement of any homogeneous material, and is especially suitable for the examination of anisotropic artificial dielectrics. The accuracy of the method is discussed for the measurement of the electrical constants of mediumloss materials with refractive indices between 0.5 and 2.0.
The statistical basis of impulse testing
 Author(s): T.J. Lewis
 Source: Proceedings of the IEE  Part C: Monographs, Volume 105, Issue 7, p. 27 –35
 DOI: 10.1049/pic.1958.0006
 Type: Article
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The normal procedure of impulsetesting insulation involves the average of a series of similar tests and the determination of the percentage breakdown at a given impulse ratio. The basis of this procedure involves the properties of a series of Bernoulli trials, the outcome of each trial being either breakdown or nonbreakdown of the insulation tested. These properties, which are of a statistical nature, are analysed, and the results expected for various types of insulation and impulse waveshape are given and compared with existing experimental data where possible. The probable outcome of a series of N impulse trials is shown to have a binomial distribution, and estimates of the errors involved are given. The effect of sample variation which applies particularly to tests on solid insulation is also treated briefly.The paper provides a statistical background against which the results of impulse voltage experiments may be judged.
The thermal properties of highvoltage insulants
 Author(s): P.H.G. Allen
 Source: Proceedings of the IEE  Part C: Monographs, Volume 105, Issue 7, p. 35 –45
 DOI: 10.1049/pic.1958.0007
 Type: Article
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Lack of agreement between published values of the thermal properties of highvoltage insulants necessitates the development of relatively simple methods for their measurement. Transient methods for the determination of the thermal diffusivity of solids and thermal conductivity of fluids are described, with examples of their use and an estimate of their accuracy. Allowance is made for anisotropy in the case of solids. Suitable methods for determination of specific heat are discussed, and the importance of the rate of change of density of liquids with temperature is stressed.
The calculation of cyclic rating factors and emergency loading for one or more cables laid direct or in ducts
 Author(s): H. Goldenberg
 Source: Proceedings of the IEE  Part C: Monographs, Volume 105, Issue 7, p. 46 –54
 DOI: 10.1049/pic.1958.0008
 Type: Article
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The knowledge of the loss load factor of a load cyclically applied to a cable laid direct in the ground or in a duct, together with the detail of the load current for the six hours prior to maximum core temperature, is shown to be adequate for cyclicratingfactor calculations. If the loss load factor is known without further calculation, the method is shorter than an earlier one described by the author. The method is extended to deal with shortterm emergency loads within accepted temperature limits and with groups of cables carrying diverse cyclic loads.
Coefficients for ‘decomposition’ of functions into Laguerrefunction series
 Author(s): J.W. Head and Gwynneth M. Oulton
 Source: Proceedings of the IEE  Part C: Monographs, Volume 105, Issue 7, p. 55 –56
 DOI: 10.1049/pic.1958.0009
 Type: Article
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Given a function of time which behaves arbitrarily up to a certain time and is thereafter negligible, a satisfactory 10term Laguerreseries approximation to the function can in general be written down in terms of the values of the function (obtained by graphical interpolation if necessary) at times proportional to the 10 zeros of the Laguerre function of order 10. The way in which the approximation fails when the procedure is deliberately applied to an unsuitable function is considered.
Transient heating of buried cables
 Author(s): J.C. Jaeger and Gordon H. Newstead
 Source: Proceedings of the IEE  Part C: Monographs, Volume 105, Issue 7, p. 57 –60
 DOI: 10.1049/pic.1958.0010
 Type: Article
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The paper develops exact methods of computing the thermal performance of buried cables, based on a solution of the relevant differential equations given by Jaeger in 1956.The approach differs from that of other workers, who have used approximate methods of calculation. It is shown that the integrals occurring in the exact solution only require a small amount of computation, and if there is very great demand for this information, it could easily be codified by one of the national computing organizations.The results obtained by the exact method are compared with those of other workers, particularly Whitehead and Hutchings (1938), and it is shown that, although their methods are generally satisfactory, they can lead to large discrepancies in particular cases, especially for small heating times. Calculations are made for a particular cable to show the application of the method.
An approximate transient analysis of a secondorder positioncontrol system when backlash is present
 Author(s): E.A. Freeman
 Source: Proceedings of the IEE  Part C: Monographs, Volume 105, Issue 7, p. 61 –68
 DOI: 10.1049/pic.1958.0011
 Type: Article
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An approximate transient analysis is derived for a secondorderpositioncontrol system with backlash. The general characteristics of the transient oscillations are discussed, and the relationship between the amplitude of overshoot and time is given explicitly. It is shownthat there is a best choice for the ratio of the moments of inertia onopposite sides of the backlash if a maximum decrement of the transientoscillations is required. Furthermore, the conditions for which thesettling time for the system is a minimum are also derived. The effectof derivative of input on the transient response is considered. Resultsfrom an electronic analogue of the system confirm the theoretical work.
The measurement of inductionmotor stray loss and its effect on performance
 Author(s): T.H. Barton and V. Ahmad
 Source: Proceedings of the IEE  Part C: Monographs, Volume 105, Issue 7, p. 69 –75
 DOI: 10.1049/pic.1958.0012
 Type: Article
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Stray losses are shown to affect the performance of induction motors to a very considerable extent—far greater than is indicated in B.S. 269. The sources of loss and methods for isolating the contribution of each to the whole are discussed. It is suggested that the total loss should be taken as the sum of the components, and this proposal is shown to be accurate except at small negative slips when the loss is much greater than such a calculation indicates. A single easy test, the reverserotation test, extrapolated according to simple rules, is shown to be sufficient to predict the stray loss under all conditions (including d.c. excitation) with sufficient accuracy for the majority of purposes, and it is proposed that such a test should replace the existing recommendations of B.S. 269.
Generalized operators for the approximate steadystate analysis of linear and nonlinear circuits
 Author(s): A.J.O. Cruickshank
 Source: Proceedings of the IEE  Part C: Monographs, Volume 105, Issue 7, p. 76 –87
 DOI: 10.1049/pic.1958.0013
 Type: Article
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A method of approximate analysis is given for linear and nonlinear circuits subjected to sinusoidal or nonsinusoidal applied voltages. In brief, the method may be said to be a periodic analogue of the technique of time series. Waveforms are represented by an ncomponent operator giving the values of the wave at each of n ordinates. For waves containing only odd harmonics, the halfcycle is divided into n parts, while for those containing even harmonics the complete cycle is divided into n parts. The central feature of the method is the use of a shift operator, u, which translates any waveform to the right by l/nth of a halfcycle or of a complete cycle as the case may be. The fundamental relations u^{n} = − 1 and u^{n} = 1 are obtained in the two cases respectively.For linear circuit work the method is advantageous where the periodic input is numerically or graphically specified and where a similar description of the output is required. The procedure is then to form, according to certain rules, an impedance operator for the circuit and to operate on the inverse of the impedance operator, i.e. the admittance operator, by the input wave of applied voltage. The waveform of the current, or the output in the case of a transferfunction operator, is then obtained. From this, r.m.s. values and powers are easily computed. Since the method relates basically to operations on nonsinusoidal waveforms displaced with respect to each other, it is also suitable for e.m.f. calculations in distributed coil groups moving in nonsinusoidal fields.In the solution of nonlinear circuits, e.g. those containing ironcored coils or nonlinear resistors, the current is obtained by a process of continued approximation. This can be done very simply. An initial solution is assumed or a very rough calculation made in order to start the procedure. One particular method of doing this is to assume that all of the applied voltage acts across the nonlinearity. From the static characteristic of the nonlinearity a second estimation can then be made of the voltage acting across the nonlinearity using the imposed circuit equation. The two estimations are averaged and the procedure is repeated until there is only a small change in any of the waveforms. The method appears to be of fairly general application. Both sinusoidal and nonsinusoidal applied voltages may be handled with the same amount of work. It is suitable for instantaneous and noninstantaneous nonlinearities, and since it provides a response waveform, r.m.s. currents and powers may be obtained. It is also suitable for circuits containing more than one nonlinearity.The method, however, is approximate, numerical and relates to a fixed frequency. The accuracy is generally within 5% of the maximum ordinate in the waveform with the normal ordinate spacings employed. R.M.S. values and powers, however, may be obtained more accurately, the error in these seldom exceeding 2%.
A note on the evaluation of the response of a nonlinear element to sinusoidal and random signals
 Author(s): J.L. Douce
 Source: Proceedings of the IEE  Part C: Monographs, Volume 105, Issue 7, p. 88 –92
 DOI: 10.1049/pic.1958.0014
 Type: Article
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A simple method is developed for analysing the response of nonlinear elements to sinusoidal and random signals. Special cursors are presented which enable the effective gain of the nonlinear unit to be determined quickly.For sinusoidal signals the technique provides a rapid means for rinding the Fourier components of fundamental frequency of the output waveform, for both singlevalued and for hysteretic forms of nonlinearity. The gain of any singlevalued nonlinearity when subject to a random signal is also evaluated. The amplitude probability distribution of the signal can be any known function.The method of analysis is invaluable for deriving the response of nonlinear control systems subjected to random or sinusoidal inputs.
The design of automaticgaincontrol systems for autotracking radar receivers
 Author(s): J.C.G. Field
 Source: Proceedings of the IEE  Part C: Monographs, Volume 105, Issue 7, p. 93 –108
 DOI: 10.1049/pic.1958.0015
 Type: Article
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A survey is presented of the automaticgaincontrol requirements for targettracking radars of the conicalscanning type. A simple analysis of linear closedloop a.g.c. systems is given, from which the required performance can be related to circuit parameters. Practical considerations regarding methods of controlling i.f. amplifier gain, number and position of controlled stages, and means of extracting the conicalscan modulation are briefly reviewed.The frequencyresponse characteristics of the a.g.c. loop, as governed by the conflicting requirements of stability, speed of response, and faithful reproduction of the scan modulation, are discussed from the Bode and Nyquistdiagram points of view. A simple graphical method of allowing for the sampling process in a pulsed radar system is given.The design methods are illustrated by a description of the development of an a.g.c. system for a particular naval firecontrol radar. This system employs suppressorgrid i.f. amplifier control, the control voltage being developed by a special d.c. amplifier having an exponential characteristic obtained by negative feedback via a series of biased diodes. A filter embodying a twinT network is employed to achieve maximum speed of response consistentAwith minimum modulation phase shift.Targettracking trials with this system demonstrated that a significant increase in aiming error can be produced by fastacting automatic gain control unless the receiver noise level is sufficient to keep the loop closed during deep fades.
A contribution to the theory of probes in waveguides
 Author(s): L. Lewin
 Source: Proceedings of the IEE  Part C: Monographs, Volume 105, Issue 7, p. 109 –116
 DOI: 10.1049/pic.1958.0016
 Type: Article
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An account is given of some of the difficulties which beset the calculation of the impedance of the finitesize probe in a waveguide. In the particular case of a probe completely spanning a rectangular guide and fed by a coaxial line, a solution is set up in which the line is represented by an arbitrary loading impedance terminating the probe. An integral equation for the current in the probe is solved by a Fourier series in the waveguide modes, and an approximate summation of the double series involved is achieved using Poisson's formula. An expression is derived for the probe impedance from which an equivalent circuit with determinate parameters is obtained. The quasistatic antenna solution is derived as a limiting case for small probe radius, and an interpretation is attempted of the physical significance of the individual terms in the expression for the inductance of an inductive post in waveguide. This is a particular case of the probe for which the solution is well known but for which the meaning of the formula is not too clear.
Some tests on a statorfed polyphase shunt commutator motor
 Author(s): C.S. Jha
 Source: Proceedings of the IEE  Part C: Monographs, Volume 105, Issue 7, p. 117 –125
 DOI: 10.1049/pic.1958.0017
 Type: Article
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Based on theory developed in earlier papers, equivalent circuits are established for a statorfed 3phase shunt commutator motor available for tests. Details are given of methods used in the measurement of equivalentcircuit parameters. The measurement and separation of motor noload losses are discussed. Test results obtained in noload and load tests are shown to give fairly good agreement with calculated behaviour.
Outline of a theory of nonuniform transmission lines
 Author(s): Boris G. Kazansky
 Source: Proceedings of the IEE  Part C: Monographs, Volume 105, Issue 7, p. 126 –138
 DOI: 10.1049/pic.1958.0018
 Type: Article
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Complex differential equations relating to nonuniform transmission lines are studied, and the corresponding twoparameter families of solution curves are investigated with the aim of establishing some important properties, e.g. the relationship which exists between the singular points of the differential equation for the normalized impedance and the nonreflective impedances of the corresponding nonuniform line. Because of this relationship it is possible to determine the nonreflective impedances of an arbitrary tapered line by purely algebraical method and to construct the tangents to the impedance loci at a given point of the impedance plane. Moreover, reflection and transmission coefficients are uniquely determined by the singularities, and differential equations can be readily deduced for these coefficients. Methods of synthesis of nonuniform lines are also indicated.
Thermal noise in multisection radio links
 Author(s): B.B. Jacobsen
 Source: Proceedings of the IEE  Part C: Monographs, Volume 105, Issue 7, p. 139 –150
 DOI: 10.1049/pic.1958.0019
 Type: Article
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Microwave radio links are used for the longdistance transmission of large groups of telephone channels and for television signals. Thermal noise effects arise in each section of the link, and the magnitude of the resulting noise in the overall circuit is one of the major parameters of the overall transmission circuit.The paper outlines methods of calculating the thermal noise in a long radio link when the individual radiotransmission sections are subject to fading. Various methods of expressing fading statistics are discussed, and it is proposed that the statistics of the individual path shall be expressed in terms of the three first hourly moments of the fading ratio and the statistics of these moments.A technique is described for combining the effects of fluctuating fading in successive (tandemconnected) paths to obtain the hourly fading moments of the overall circuit. A method is given of converting the overall moments into an overall circuit fading distribution; this is expressed in terms of an ‘augmented lognormal distribution’, which can readily be translated into the distribution of thermal noise in the overall connection.The noise requirements for longdistance telephone circuits are specified for a 2500 km circuit, although any particular project will generally be much shorter. To avoid the difficulties involved in subdividing the noise permitted for 2500 km, it is proposed instead to treat such path performance data as can be made available as if it were representative of all the sections which would enter into a 2500 km circuit (synthetic overall circuit).Thermal noise can be calculated for the synthetic circuit and compared with the requirements; this comparison will show whether the actual paths for which data are available are suitable to form part of an overall connection.
An improved electromagnetic analogue
 Author(s): W.T.J. Atkins
 Source: Proceedings of the IEE  Part C: Monographs, Volume 105, Issue 7, p. 151 –154
 DOI: 10.1049/pic.1958.0020
 Type: Article
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The paper is concerned with the quantitative representation of symmetrical electromagnetic fields by analogue. An improved type of analogue is described, enabling dynamic as well as static effects to be studied. Possible applications are indicated.
The mathematical theory of vibratory angular tachometers
 Author(s): K. Fearnside and P.A.N. Briggs
 Source: Proceedings of the IEE  Part C: Monographs, Volume 105, Issue 7, p. 155 –166
 DOI: 10.1049/pic.1958.0021
 Type: Article
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A mathematical theory for a vibratory rateofturn measuring device is developed in order to bring out the more important characteristics.By using properties of Mathieu's equation it is shown how performance depends on the parameters of the system, particularly the resonant frequency and damping factor of the torsion mechanism. These results are compared with those obtained from the more simplified theory.
A simplified derivation of the Fourier coefficients for Chebyshev patterns
 Author(s): J.L. Brown
 Source: Proceedings of the IEE  Part C: Monographs, Volume 105, Issue 7, p. 167 –168
 DOI: 10.1049/pic.1958.0022
 Type: Article
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In the design of linear arrays containing an odd number of elements with constant element spacing of less than a half wavelength, the mathematical problem reduces to that of finding explicitly the coefficients, b_{m}, in the expansion where a and b are constants, n > 0, and T_{m}(x) is defined as cos (m arc cos x) for m ≥ 0. Such a problem was initially solved by DuHamel and later given by Salzer in a form more convenient for computation. The purpose of this paper is to give an alternative derivation of Salzer's result, making use of the orthogonality properties the Chebyshev polynomials in order to obviate the fairly elaborate series manipulations required in the previous derivation.
Variations of characteristic impedance along short coaxial cables
 Author(s): J. Allison
 Source: Proceedings of the IEE  Part C: Monographs, Volume 105, Issue 7, p. 169 –176
 DOI: 10.1049/pic.1958.0023
 Type: Article
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A method is described for determining the local characteristic impedance at any point on a highfrequency coaxial cable. Measurements are made of the deviations from a harmonic series of the resonant frequencies of a short length of open or shortcircuited cable. It is shown how these deviations can be used to calculate the coefficients of Fourier series describing the impedance variations along the length. Since the measurements are performed at microwave frequencies, the resolution of the impedance changes is considerably better than for lowerfrequency methods.Measurements on an artificially discontinuous cable have allowed the experimental accuracy of the method to be determined, and close agreement has been obtained between the experimentally predicted and the actual impedance changes.Results from short cable samples indicate that the local variations of characteristic impedance are largely due to changes in the diameter over the dielectric filling.
Transformation of the Smith chart through lossless junctions
 Author(s): H.V. Shurmer
 Source: Proceedings of the IEE  Part C: Monographs, Volume 105, Issue 7, p. 177 –182
 DOI: 10.1049/pic.1958.0024
 Type: Article
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It is frequently necessary, when using microwave transmission systems, to determine the impedance on one side of a lossless junction in terms of a known impedance on the other side. The paper provides rigorous analysis of the relation between Smith charts for the two sides of the junction by utilizing the theory of a complex variable. Pairs of reference planes are chosen so that an opencircuit at the first plane corresponds to an opencircuit at the second, which is on the other side of the junction. The transforming section is described in terms of the reflection coefficient at the first plane when the line containing the other is matched. The circles of constant reflection coefficient, etc., which constitute a Smith chart corresponding to the first plane, are transformed mathematically into corresponding circles at the second plane. A universal chart is derived which enables circles of constant voltage standingwave ratio (or reflection coefficient) to be transformed readily from one plane to the other.
The conductivity of oxide cathodes. Part 3: Movements of electrolytic oxygen in a conventional diode system
 Author(s): G.H. Metson
 Source: Proceedings of the IEE  Part C: Monographs, Volume 105, Issue 7, p. 183 –188
 DOI: 10.1049/pic.1958.0025
 Type: Article
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A conventional form of oxidecathode diode can, in appropriate circumstances, evolve a continuous currentdependent stream of electrolytic oxygen. This oxygen emerges from the cathode surface as a negative ion and passes to the anode, where it may or may not be chemically absorbed. If absorption is incomplete, a proportion of the oxygen can be returned to the cathode and give rise to a number of characteristic reactions. These reactions are studied and shown to be analogous to the electrolytic actions of the Stype assembly described in Part 2 of the paper.
The conductivity of oxide cathodes. Part 4: Electron transfer mechanisms
 Author(s): G.H. Metson
 Source: Proceedings of the IEE  Part C: Monographs, Volume 105, Issue 7, p. 189 –195
 DOI: 10.1049/pic.1958.0026
 Type: Article
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The present Part considers the mechanisms of electron transfer through the oxidecathode matrix. In the temperature range 850–1 100° K it is shown experimentally that, effectively, the whole of the electron stream passes through the vacuum interstices of the matrix. Progression is on a startstop basis, with the electrons dissipating energy in the form of heat by successive nonelastic collisions with impeding oxide particles. The whole electron current is emitted thermionically at the cathodic core surface, where the theoretically predicted cooling effect is localized and observed. In the temperature range 290–600° K, electron transfer is on a purely resistive basis and involves no act of thermionic emission, i.e. the electron never emerges from the solid oxide into vacuum.The results of the experimental work are in complete harmony with the hypothesis put forward in 1949 by Loosjes and Vink.
On the amplification factor of a triode valve. Part 2
 Author(s): E.B. Moullin
 Source: Proceedings of the IEE  Part C: Monographs, Volume 105, Issue 7, p. 196 –202
 DOI: 10.1049/pic.1958.0027
 Type: Article
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A recent paper showed that in the wellknown relation I = f(V_{a}+μV_{g}), the parameter μ (commonly called the ‘amplification factor’) should be a constant, and thus independent of the magnitude of I. Though long experience has shown that μ is substantially independent of I, yet the derivation, used in that paper, for calculating the value of μ, appeared to show that it ought to be completely independent of I. The classic derivation of μ, e.g. that used by H.J. Van der Bijl, appeared to show that the classic formula for μ was exact only in the limit when I was vanishingly small.This paper describes measurements designed to test whether really is independent of I. A balance method was devised which was capable of measuring μ to an accuracy of about 1%. The valve which was tested consisted of a separately heated disc cathode, 8 mm diameter and an anode (also 8 mm in diameter) 0.55 mm distant from it. The distance between the grid plane and the cathode was 0.15 mm.Fig. 3 shows the measured values of μ plotted as a function of V_{g} three different constant values of anode current. It shows that, for a given value of V_{g}, μ, in fact, increases by some 20% as I increased from 3 to 11 mA. It also shows that, in fact, μ decreases by about 20% when I is constant, as the negative value of V_{g} is increased from about 2 to 8 volts.Fig. 4 shows that, for constant I, the effect of changing V_{g} is removed by a substantial reduction of cathode temperature; but this reduction does not remove the increase of μ with increase of I. This means that the increase of μ with I is due to the increase of distance between gridplane and barrier—an increase which must be significant for a valve in which the distance between grid plane and cathode is only 0.15 mm. It is argued, it is thought conclusively, that the effect of V_{g} is due the periodic fluctuations, across the plane of the barrier, of the current density crossing it. The author is convinced that, if a valve had been used in which the pitch of the grid wires was small compared with their distance from the barrier plane, μ would be independent of both I and V_{g}. In other words, μ was constant in the early separatelyheated cathode valves.Section 5 points out that the necessary and sufficient condition for constant anode current is that any change in V_{g} must not cause any change in the positive charge on the cathode. Accordingly the positive charge, extracted from the grid to make it more negative, must be handed on, unchanged, to the anode, thereby increasing its potential. If the electric force due to the space charge between grid and anode is ignored as unimportant, and it is shown that this must be true, μ is equal to the product of the capacitance between grid and anode and the capacitance between grid and the barrier plane, both in the absence of space charge—a form which has long been known but whose meaning has always seemed rather obscure. Its validity depends only on (a) ignoring any striation in the stream of anode current, and (b) ignoring the effect of the presence of space charge between grid plane and anode.Section 6 explores the dependence of μ on the ratio of peak gridswing to mean grid potential. Experiment shows that μ is constant, within about 1%, for all peak grid swings which do not exceed the grid bias.
The sliding contact of graphite and copper
 Author(s): W. Davies
 Source: Proceedings of the IEE  Part C: Monographs, Volume 105, Issue 7, p. 203 –211
 DOI: 10.1049/pic.1958.0028
 Type: Article
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Experiments with welldeveloped sliding contacts of graphite and copper have shown the marked influence of atmospheric and electrical conditions on the kinetic friction and contact resistance.Dry oxygen at low pressures appears to be lubricating for currents of any magnitude flowing in either direction through the contact. However, at higher pressures of this gas it is no longer lubricating and its effect on the friction and resistance is markedly dependent upon the direction of the current.Water vapour alone is found to be lubricating, but in company with oxygen its action is complex and it modifies the effect of oxygen profoundly. It lubricates currentless and negative brushes, but increases the kinetic friction of positive brushes, probably as a result of its stabilization of the contact interface.Increase in the pressure of dry oxygen always increases the contact resistance of positive brushes, but an initial increase at moderate pressure with negative brushes is followed by a marked decrease at higher pressures.Water vapour alone has only a slight effect on contact resistance, but it modifies the effect of oxygen quite remarkably, especially in the case of positive brushes. Again its action is complex, but in the main it tends to reduce the contact resistance of positive brushes and to increase that of negative brushes.
The variation with current and inductance of metal transfer between contacts of palladium and silver
 Author(s): R.I.B. Cooper and Janet Riddlestone
 Source: Proceedings of the IEE  Part C: Monographs, Volume 105, Issue 7, p. 212 –217
 DOI: 10.1049/pic.1958.0029
 Type: Article
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The work on transfer between platinum contacts, published by one of the authors in previous papers, has been extended to palladium and silver. Curves of the net transfer in 6volt d.c. circuits are given for currents of a few amperes and inductances ranging from less than 0.1μH up to 110μH. Some measurements have also been made in 12 and 24volt circuits for palladium. The general nature of the transfer for palladium is both qualitatively and quantitatively similar to that for platinum, but in the case of silver, neither residual nor reversed shortarc transfer has been demonstrated. Theoretical analysis of the results shows that the quantity determining transfer in an inductive circuit is the ratio of the charge passed in the arc to the volume of residual transfer at the same break current. Under conditions of constancy of this ratio, transfer is found to be proportional to the square of the break current up to 6.5 amp.
Electromagnetic fields in a ferromagnetic medium, with particular reference to harmonic distortion due to hysteresis
 Author(s): V.G. Welsby
 Source: Proceedings of the IEE  Part C: Monographs, Volume 105, Issue 7, p. 218 –229
 DOI: 10.1049/pic.1958.0030
 Type: Article
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(12)
As a result of magnetic hysteresis, the propagation of electromagnetic waves through a ferromagnetic medium is accompanied by the generation of harmonicfrequency fields. An approximate theoretical method of treating the problem is developed and applied to study the thirdorder voltage distortion factor of an inductor as a function of frequency. An analogue method is also described which enables the study to be extended experimentally to cases where the theoretical analysis is not applicable; e.g. for large flux densities or for complex input waveforms.
A theoretical investigation of the form assumed by a submarine cable during laying or recovery
 Author(s): V.G. Welsby
 Source: Proceedings of the IEE  Part C: Monographs, Volume 105, Issue 7, p. 230 –239
 DOI: 10.1049/pic.1958.0031
 Type: Article
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The increasing use of submerged repeaters and the introduction of new cable types have drawn attention to the hydrodynamic problems involved in the laying and recovery of deepsea cables. The paper deals with the case of a uniform cable being laid or picked up at a constant speed. A method is described whereby the shape of the curve assumed by the cable under given conditions can be estimated and the maximum tension in the cable predicted.
Two theorems concerning group delay with practical application to delay correction
 Author(s): G.G. Gouriet
 Source: Proceedings of the IEE  Part C: Monographs, Volume 105, Issue 7, p. 240 –244
 DOI: 10.1049/pic.1958.0032
 Type: Article
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Two theorems are stated which enable properties of group delay to be expressed directly in terms of the transfer function of a linear transmission system. Examples are given to show how the results mightbe usefully applied to certain problems of delay correction.
Conditions for the impedance and admittance matrices of nports without ideal transformers
 Author(s): I. Cederbaum
 Source: Proceedings of the IEE  Part C: Monographs, Volume 105, Issue 7, p. 245 –251
 DOI: 10.1049/pic.1958.0033
 Type: Article
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The matrices relating two adequate systems of simple network coordinates of the same network, e.g. nodepair voltages or loop currents, are shown to have all their elements and subdeterminants equal to +1, −1 or 0. Any nport may be looked upon as a part of an adequate system of independent node pairs described on the network or loops inscribed into the network. In the former case the additional node pairs, not included in the nport, ought to be considered as opencircuited and in the latter case the additional loops ought to be looked on as shortcircuited. The conditions for cutset and loopincidence matrices are discussed, and then the conditions for impedance and admittance matrices of nports without ideal transformers are defined in terms of those incidence matrices. The discussion of the conditions thus derived leads, among other things, to a conclusion that matrices representing pureresistance nports are necessarily such that each principal minor of such a matrix is greater than the modulus of any minor built from the same rows (or columns).
Excitation of surface waves
 Author(s): B. Friedman and W. Elwyn Williams
 Source: Proceedings of the IEE  Part C: Monographs, Volume 105, Issue 7, p. 252 –258
 DOI: 10.1049/pic.1958.0034
 Type: Article
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It is shown how to locate a dipole source above a dielectric surface so as either to produce as pure a surface wave as possible or to maximize the amount of energy carried by the surface wave.
The network synthesis on the insertionloss basis
 Author(s): J. Zdunek
 Source: Proceedings of the IEE  Part C: Monographs, Volume 105, Issue 7, p. 259 –291
 DOI: 10.1049/pic.1958.0035
 Type: Article
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A unified and concise exposition is provided of the general insertionloss filter theory. Methods of synthesis of most important network functions are derived in terms of the prescribed steadystate network performance; also realization procedures are explained and expressed in terms of explicit formulae for direct application to the design of conventional ladder structures with an arbitrary number of branches.Two particular cases are solved in detail, namely the symmetrical and the inverseimpedance, lowpass networks, which are both unified in a single mathematical treatment. Such unification enables one to consider both of them as one general case of a lowpass analogue ladder structure.Special emphasis is given to the CauerDarlington method of synthesis of networks whose insertionloss response approximates, in Chebyshev's sense, to that of the ideal wave filter; however, Taylor's approximation (maximally flat response) and the constantk filters are also included.In the case of the maximally flat and the Cheby̅shev passband approximation, important explicit formulae for the ladder components are derived for a network with an arbitrary number of branches and an arbitrary termination ratio. These components (ladder coefficients) are thus directly computable from the required discrimination characteristics or the reflection factor, and from the bandwidth specifications.
The effect of the ground constants, and of an earth system, on the performance of a vertical mediumwave aerial
 Author(s): G.D. Monteath
 Source: Proceedings of the IEE  Part C: Monographs, Volume 105, Issue 7, p. 292 –306
 DOI: 10.1049/pic.1958.0036
 Type: Article
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The compensation theorem is used to determine the effect of finite ground conductivity, and of an earth system, on the performance of a vertical aerial, such as is used for mediumfrequency broadcasting.The characteristics affected are the input impedance, the groundwave field strength for a given aerial current and the vertical radiation pattern. The first two of these together determine the efficiency, which is the most important consideration in the design of earth systems. When the effective height of the aerial exceeds 0.1λ, little can be gained by the use of an earth system exceeding 0.2λ in radius when the ground is highly conducting and 0.3 or 0.4λ when it is poorly conducting. The effect of the earth system on the vertical radiation pattern is shown to be unimportant practically, but results are given for one case in order to compare with experimental radiation patterns. The agreement is quite good.
A rapid method of analysing the m.m.f. wave of a single or polyphase winding
 Author(s): R.F. Burbidge
 Source: Proceedings of the IEE  Part C: Monographs, Volume 105, Issue 7, p. 307 –311
 DOI: 10.1049/pic.1958.0037
 Type: Article
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The usual method of evaluating the harmonic components of the m.m.f. wave of a polyphase winding is to perform a Fourier analysis. This can, however, be a long and tedious process, especially for stepped waveforms, and further it is common practice to perform the analysis for two limiting currentvector positions, to provide a check on the results.The method described here is exceptionally simple to apply, and makes use of the wellknown standard winding factors. It is shown that, by simple substitution, the magnitudes of the Fourier fundamental and harmonic components of the m.m.f. in the airgap can be found directly, although no indication is given of their relative phase angles. The mathematics of the proof has been fitted as closely as possible to the conditions prevailing in a real machine winding, whilst at the same time maintaining generality of treatment.The value of the method is exemplified in the last Section of the paper, by carrying out the analysis for an m.m.f. wave of some complexity. The ease of the method is at once apparent.
Diffraction by cylindrical reflectors
 Author(s): Robert Plonsey
 Source: Proceedings of the IEE  Part C: Monographs, Volume 105, Issue 7, p. 312 –318
 DOI: 10.1049/pic.1958.0038
 Type: Article
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p.
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(7)
The electromagnetic diffraction problem is formulated in terms of the determination of the currents induced on a refiectorscatterer by a primary source. All field quantities are readily determined therefrom.An approximate solution ignores the interaction of currents on the refiectorscatterer in that it relates the surface current to the incident magnetic field. This is the geometricaloptics current. For the strip and circular reflector with line source at its centre, corrections to the geometricaloptics currents are obtained by an approximate analytic technique. In each case this yields an equivalent line current at the edges.The field of the line current is nonisotropic; its directional gain is determined by appealing to the Sommerfeld halfplane solution. The line currents do not greatly affect the total pattern; this indicates that the main character of the diffraction can be obtained from the geometricaloptics currents.Measurements of the diffracted field of a circular cylindrical reflector with line feed at its centre were made in a parallelplane device. A description of some of the features of the equipment is given. The results confirm that geometricaloptics currents are themselves satisfactory, but are inconclusive with respect to the correction line currents.
Discussion on “The effect of magnetic saturation on the d.c. dynamic braking characteristics of a.c. motors”
 Source: Proceedings of the IEE  Part C: Monographs, Volume 105, Issue 7, page: 318 –318
 DOI: 10.1049/pic.1958.0039
 Type: Article
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The inherent instability of induction motors under conditions of double supply
 Author(s): J.C. Prescott and B.P. Raju
 Source: Proceedings of the IEE  Part C: Monographs, Volume 105, Issue 7, p. 319 –329
 DOI: 10.1049/pic.1958.0040
 Type: Article
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p.
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A polyphase induction motor provided with balanced windings on both stator and rotor can operate as a synchronous motor at a certain specified speed if each of these windings is connected to a balanced polyphase supply. Under the conditions of such double supply it can maintain this specified speed over a range of mechanical power output, thus exhibiting a synchronizing torque similar to that associated with the conventional synchronous machine.In addition to this synchronizing torque, there are present also torques which, being proportional to the speed of rotation, may be regarded as damping torques and which under certain circumstancesmay be negative, i.e. they may act in such a direction that a deviation from synchronous speed, though initially very small, will increase exponentially, thus making synchronous operation impossible. It is to the investigation of these damping torques that the discussion in this paper is directed, and they are considered in relation to the case which seems to present the greatest practical interest—that in which the stator and rotor are connected to the same busbars and in such sense as to give a synchronous speed which is twice that corresponding to the busbar frequency. Operating in this way the machine exhibits a negative damping torque which, in general, decreases with increase in rotor or stator leakage reactance but becomes positive over a small range of values of the coupling coefficient. It appears from the investigation that it is possible to design a motor for operation at the double synchronous speed which shall have a large positive damping torque and which will therefore be stable in operation.
Discussion on “The measurement and prediction of induction motor stray loss at large slips”
 Source: Proceedings of the IEE  Part C: Monographs, Volume 105, Issue 7, page: 330 –330
 DOI: 10.1049/pic.1958.0041
 Type: Article
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p.
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