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Proceedings of the IEE  Part IV: Institution Mon...
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Volume 99
Issue 3
Proceedings of the IEE  Part IV: Institution Monographs
Volume 99, Issue 3, July 1952
Volume 99, Issue 3
July 1952
On the current induced in a conducting ribbon by the incidence of a plane electromagnetic wave
 Author(s): E.B. Moullin and F.M. Phillips
 Source: Proceedings of the IEE  Part IV: Institution Monographs, Volume 99, Issue 3, p. 137 –150
 DOI: 10.1049/pi4.1952.0015
 Type: Article
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Morse and Rubenstein did not investigate the induced currents when they published a solution of the problem of the diffraction of waves by ribbons and slits. The authors of the present paper regretted this omission because the diffraction pattern of the scattered wave is directly dependent upon these induced currents and it is very easy to predict the pattern from the distribution of induced current, but not vice versa. Moreover, the distribution of induced current near a bounding edge is a matter of great interest in itself and is likely to serve as a guide in other problems which have not yet been solved. The first two Sections of the paper are devoted to extending the analysis developed by Morse and Rubenstein in terms of Mathieu functions, so as to make possible the calculation of the induced currents. Curves are given which show the distribution of these currents across ribbons whose width is 2λ/π and 4λ/π. The necessary analytical development was very difficult and cumbersome and the evaluation of the results was very troublesome and exacting: the senior author wishes to disclaim any share in this portion of the work, beyond bringing that part of the problem to the attention of the junior author.The senior author had previously obtained an expression for the currents induced in a halfplane and had derived the curve of this distribution. It differed little from the curves derived from the Mathieu function solution for a plane of finite width, thus showing that the disturbance at one edge is very little dependent on the existence of a second parallel edge, provided it is more distant than about ½λ It became clear that the disturbance due to an edge may be considered to be substantially contained within a width of, say, ⅛λ.If this conclusion is accepted as general there is no further necessity to use Mathieu functions in this problem: they are extremely involved and poorly tabulated, and it is advantageous to dismiss them after they have served a useful turn.The third Section of the paper is devoted to predicting the diffraction pattern from the currents induced in the ribbon and to discussing the effect which their distribution will have on the shape of the pattern. It is found that the patterns calculated by Morse and Rubenstein are not compatible with the current distributions derived from the extension of the Morse and Rubenstein analysis. The discrepancy must be due to the inclusion of insufficient terms of an infinite series in the process of numerical evaluation. In evaluating the curves of current distribution given in the paper, the junior author has included as many terms as the published tables of Mathieu functions will permit and is confident that they are adequate. But since there was no direct method of deciding whether the higher degree of accuracy of evaluation was to be credited to the MorseRubenstein patterns or to the current distributions obtained by the junior author, the two authors were led to consider, very closely and generally, the form of current distribution which must obtain to satisfy the essential condition of the problem. This condition is that the current distribution must be such as to produce an electric force which is constant in magnitude and phase all across the ribbon, thereby equilibrating the field of the wave incident normally on it.In Section 7 it is shown, by very simple methods, which are in no way dependent upon either the Mathieu solution or the halfplane solution, that the surface field can be constant over the major portion of the width of a wide ribbon only if the distribution consists of a uniform cophased density together with a second and quadrature distribution which is virtually concentrated in a filament located at each edge, the strength of each filament being equal to the current in a strip of width 0.16λ of the uniform density, and thus independent of the width of the ribbon. It is shown, moreover, that if the uniform cophased density in fact becomes not uniform very near the edges there must be regions, near the edges, over which this density is greater in the one region and less in the other region than the mean density over the width, in such a way that the mean density is unchanged by the lack of uniformity near the edges. But all these properties had already been inferred and derived from the distribution evaluated from the Mathieu functions and for the halfplane. These evaluated distri butions have thus been found to possess the characteristics which are now found to be inherently necessary. In fact this apparently very difficult problem turns out to be a simple one if only it is attacked by examining that distribution which must obtain to produce a uniform force across the ribbon at its surface, in contrast to deriving the currents which must be induced by a given incident field.Once this fact had been recognized, it became apparent that the problem of a very narrow ribbon could now be evaluated, though this is not practicable by the Mathieu process because the limiting values of these functions have not yet been tabulated for small arguments. Section 8 gives the solution for a narrow ribbon, valid within the range such that we may write Y_{0}(z)≃2/π(log z+y).When the ribbon is wide it is obvious that the echoed field must be proportional to width. A curve is given in which the echoed field per unit width is plotted as a function of width, expressed as a multiple of a wavelength: it is substantially constant provided the width of the ribbon exceeds about 0.2λ It is of great interest to find that a result which is obvious for a wide ribbon is still substantially correct even when the width is only ⅕λ; this result is believed to be novel.It is hoped that the paper throws considerable light on the mechanism of the induction of current in a ribbon; it certainly shows the reason why the phase of this current must necessarily change across the width: an effect which was to be expected from general experience of comparable problems, where it had but emerged in the final result of the analysis without disclosing the physical necessity which causes it to exist.Section 10 discusses the case when the direction of propagation of the wave is parallel to the plane of the ribbon. It includes curves showing the distribution of induced currents.An Appendix (Section 12) contains details of the solution for the halfplane, and several formulae are worked out which are required for various computations used in the main part of the paper.
An approximate method for deducing dielectric loss factor from directcurrent measurements
 Author(s): B.V. Hamon
 Source: Proceedings of the IEE  Part IV: Institution Monographs, Volume 99, Issue 3, p. 151 –155
 DOI: 10.1049/pi4.1952.0016
 Type: Article
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An approximate method is developed for deducing the dielectric loss factor of a solid dielectric from the charging current that flows after the sudden application of a direct voltage. It is shown that, subject to certain conditions, the loss factor at a frequency f cycles per second can be deduced from the charging current at a time 0.1/f seconds after applying the direct voltage. The range of application of the method is discussed, and its use in correlating d.c. measurements with a.c. bridge measurements on the same sample is illustrated by experimental results.
The mutual impedance of earthreturn circuits
 Author(s): L.J. Lacey
 Source: Proceedings of the IEE  Part IV: Institution Monographs, Volume 99, Issue 3, p. 156 –167
 DOI: 10.1049/pi4.1952.0017
 Type: Article
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Formulae are developed for the mutual impedance of two finitelength earthreturn circuits, either parallel or at an angle. The new formulae are shown to be generalizations of the CarsonPollaczek formula and of the more recent work of Carter. Numerical results are compared with calculations performed by the methods at present recommended by the Comité Consultatif International Téléphonique.
The impedance of unsymmetrical strips in rectangular waveguides
 Author(s): L. Lewin
 Source: Proceedings of the IEE  Part IV: Institution Monographs, Volume 99, Issue 3, p. 168 –176
 DOI: 10.1049/pi4.1952.0018
 Type: Article
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The radiation from capacitive and inductive strips is calculated in terms of arbitrary currents flowing on the strip surfaces. By requiring the tangential component of the sum of an incident field and the radiated field to vanish at the surface of the strip, an integral equation for the currents is obtained. This integral equation is solved by a transformation of variables due to Schwinger. The integrals involved in the final solution are given in terms of standard elliptic integrals.The following generalizations of the wellknown quasistatic formulae for symmetrically located strips are obtained:(a) Capacitive strip of width D, centre x^{0} from waveguide side; waveguide dimensions a × b (see Fig. 1).Susceptance B=4b/λ_{g} log Θ(β)/(1+s)Θ(0)where cn β = c/(1+s)c = cos(πx_{0}/b) sin(½πD/b).s = sin(πx_{0}/b) cos(½πD/b).The modulus of the elliptic functions is [4s/(1+s)^{2}−c^{2}]^{½}(b) inductive strip of width D, centre Y_{0} from waveguide side; waveguide dimensions a × b (see Fig. 2).Reactance X= a/λ_{g}[−1+K cosec^{2} (πy_{0}/a)/2E − K sin^{2} (½π D/a)]The modulus of the elliptic functions is[1 − sin^{2} (½π D/a) cosec^{2} (πy_{0}/a)]^{½}
The development of a multicathode decade gastube counter
 Author(s): G.H. Hough
 Source: Proceedings of the IEE  Part IV: Institution Monographs, Volume 99, Issue 3, p. 177 –186
 DOI: 10.1049/pi4.1952.0019
 Type: Article
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After the Introduction, which deals briefly with the speed limitations of the present type of coldcathode gastube counter, the mechanism which produces a reduction in the breakdown voltage of a gap adjacent to a discharging gap is outlined and typical curves are given demonstrating the relationship between this reduction in breakdown voltage and other important parameters. A simple type of multicathode tube is described, together with a first development, which has led to the G10/240E, a multielectrode decade counter capable of operating at speeds up to 20 kc/s. Important design features of this multielectrode tube are treated in detail, and a method of computing the d.c. tolerance range of this type of tube is given. After a discussion of the derivation of important limits on the driving pulse and other circuit parameters, typical performance figures are quoted, and reference is made to the exhaustive type of automatic testing to which each tube is subjected in production. In conclusion, a few very general remarks are made concerning the way in which the tube may be used.
A note on the equalarea stability criterion
 Author(s): John E. Parton
 Source: Proceedings of the IEE  Part IV: Institution Monographs, Volume 99, Issue 3, p. 187 –193
 DOI: 10.1049/pi4.1952.0020
 Type: Article
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In the application of the equalarea stability criterion to the case of a synchronous machine connected via a transmission line to either an infinite busbar or another synchronous machine, the limiting load angle θ_{1} is related to the initial loadangle θ_{0} by the equation(π−θ_{1}−θ_{0})sinθ_{1}=cosθ_{0}+cosθ_{1}if resistances are neglected.This equation is not soluble analytically, and it is usual to employ empirical solutions.By advancing the origin of the displacement angle by π/2 and writing (π/2−θ_{0}=α and (π/2−θ_{0}=γ, the equation becomes(α + γ) cos α = sin α + sin γa very good approximate solution of which is α=γ/2.The paper applies this simple approximation, both graphically and algebraically, to the two problems considered, and shows that over the normal practical range the errors introduced are not likely to exceed about 1%.
Observations on the electrical breakdown of gases at 2800 Mc/s. Part 2: Relative breakdown stresses, statistical lags and formative lags
 Author(s): W.A. Prowse and W. Jasinski
 Source: Proceedings of the IEE  Part IV: Institution Monographs, Volume 99, Issue 3, p. 194 –203
 DOI: 10.1049/pi4.1952.0021
 Type: Article
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Gas confined in a nosedincavity type of resonator is subjected to individual pulses of electric stress of frequency 2 800 Mc/s, and the variation of the field amplitude with time is recorded oscillographically. The study of the oscillograms deals with the statistical and formative timelags preceding breakdown and with the relative breakdown stresses of various gases. In all experiments the gas in the resonator is irradiated by means of an auxiliary spark fired just before the beginning of the microwave pulse. The effect on the timelags of the flux of radiation and, separately, of the distance between the irradiating spark and the resonator are examined.The formative time is found to be zero, within the limits of experimental error, for air, nitrogen, oxygen and hydrogen in all conditions examined. It is appreciable, however, in neon, argon and helium. The statistical timelags are much greater in air and nitrogen than in oxygen and hydrogen. A study of these timelags suggests that electrons are present in the gap throughout the pulse and that break down occurs as a consequence of a single event in the life of an electron, rather than by a progressive growth of ionization.The formative times in neon agree with the hypothesis that in this gas electrons are not removed during the pulse.
Transient analysis of synchronous machines
 Author(s): R.E. Vowels
 Source: Proceedings of the IEE  Part IV: Institution Monographs, Volume 99, Issue 3, p. 204 –216
 DOI: 10.1049/pi4.1952.0022
 Type: Article
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The paper reviews the transient theory of synchronous machines and sets out the tworeaction transformation in matrix notation. The advantages of the matrixtransformation theory and the Laplace transform method are demonstrated.It is shown that Park's transformation is equivalent to a change from a synchronous machine to a d.c. machine with brushes in the direct and quadrature axes and, in addition, an independent stationary zero sequence circuit. An equivalent circuit is established for this d.c. machine (metadyne) and it is evident that transient faultcurrents of a synchronous machine are intimately connected with those of a d.c. machine. Solutions are given for transient currents and torque.
The ionospheric propagation of radio waves of frequency 16 kc/s over distances of about 200 km
 Author(s): R.N. Bracewell
 Source: Proceedings of the IEE  Part IV: Institution Monographs, Volume 99, Issue 3, p. 217 –228
 DOI: 10.1049/pi4.1952.0023
 Type: Article
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The detailed information previously obtained at Cambridge of the propagation of waves of frequency 16 kc/s over a distance of 90 km has been extended by investigation of distances up to 200 km. Measurement of phase, the essential feature of the experiments, was achieved by comparison with a reference signal sent from the trans mitter to the receiver by land line.Behaviour over the two ranges is much the same, the chief difference being that multiple reflections are more evident over the greater distance.The background common to this and companion papers is presented.
An investigation of polarization errors in an HAdcock directionfinder
 Author(s): F. Horner
 Source: Proceedings of the IEE  Part IV: Institution Monographs, Volume 99, Issue 3, p. 229 –240
 DOI: 10.1049/pi4.1952.0024
 Type: Article
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The polarizationerror characteristics of Htype Adcock direction finders operating in the v.h.f. band and in the upper part of the h.f. band are controlled to a large extent by resonance phenomena. A theoretical and experimental investigation of a rotating system for very high frequencies has demonstrated the feasibility of calculating, from the physical dimensions of the aerial system, the frequencies at which large errors are liable to occur, and also the magnitudes of the maximum errors. The lowest resonant frequency is that for which the product of aerial length and spacing is onetwentieth of a square wavelength. A second resonance occurs when the spacing is half the wavelength and, if the aerial length is approximately equal to the spacing, the third resonance occurs when the spacing is 0.8 times the wavelength.Three major causes of polarization errors are discussed and formulae are given for calculating these errors. The agreement between the calculated and measured errors at the resonant frequencies suggests that the three causes discussed account for nearly all the errors. Various methods of minimizing errors are examined theoretically and experimentally.Although the instrument used for the experimental investigation was designed for very high frequencies, the results have application to a wider band of frequencies and to instruments of both fixed and rotating types.
An automaticallycontrolled Knudsentype vacuum gauge
 Author(s): C.N.W. Litting and W.K. Taylor
 Source: Proceedings of the IEE  Part IV: Institution Monographs, Volume 99, Issue 3, p. 241 –249
 DOI: 10.1049/pi4.1952.0025
 Type: Article
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A vacuum gauge of the Knudsen^{1} type is described, by which pressures from 10^{−8} mm to 10 mm of mercury are indicated on a movingcoil instrument used in conjunction with a rangechange switch.The advantages and disadvantages of the Knudsen gauge have been listed elsewhere, the main criticisms being of its delicacy and slowness of response. The paper describes an instrument in which these disadvantages are eliminated and several additional advantages provided.The new gauge operates on the principle of balancing the pressuredependent radiometric force by an electrostatic force, the pressure then being calculated from a measured potential difference and the dimensions of the gauge.The principal units of the instrument control system are described in detail and an overall analysis is developed.
The ionospheric propagation of radio waves of frequency 16 kc/s over distances of about 540 km
 Author(s): W.C. Bain ; R.N. Bracewell ; T.W. Straker ; C.H. Westcott
 Source: Proceedings of the IEE  Part IV: Institution Monographs, Volume 99, Issue 3, p. 250 –259
 DOI: 10.1049/pi4.1952.0026
 Type: Article
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The paper describes an investigation of the ionospheric propagation of waves of frequency 16 kc/s over a distance of 535 km. It represents an extension of other investigations in which the propagation over distances of 90 and 200 km was studied.^{1, 3, 4, 13}A long series of measurements of signal amplitude covering the period 1940–44 has been used to study regular diurnal and seasonal variations, and anomalous effects associated with sudden ionospheric disturbances and severe magnetic disturbances. In another series of experiments from May to October, 1949, measurements of phase were made by using the method, previously employed at 200 km, of sending a reference signal from transmitter to receiver by land line. In this way the phase and amplitude of the downcoming wave could be deduced separately.The observations showed that reflection took place from an apparent height of about 74 km by day and 92 km at night; the downcoming wave was of approximately linear polarization during morning twilight, the plane of polarization being rotated clockwise from the normal through an angle of 40°, as seen by an observer looking in the direction of propagation; the effective reflection coefficient in the summer of 1949 was about 0.27 by day and 0.55 at night; the sunrise effects on the height of reflection and the amplitude of the downcoming wave regularly occurred when the zenith distance of the sun was 97° 50′. The effects of sudden ionospheric disturbances on the signal amplitude were explicable in terms of a change of reflection height with little change in the amplitude of the downcoming wave. During and after severe magnetic storms the diurnal variation of the signal amplitude. was abnormal, the abnormality persisting for as long as 38 days.It is clearly evident that there is a marked change in the propagation characteristics of the reflected wave in passing from short (90–200 km) to long (535 km) distances from the transmitter. At short distances the downcoming wave is of approximately circular polarization with a lefthand sense of rotation, while the reflection coefficient in summer is about 0.15 by day and 0.5 at night. The most striking evidence of the change in propagation characteristics is given by the markedly different ways in which the height of reflection varies with the inclina tion of the sun's rays. These conclusions concerning the change of reflection conditions confirm the deductions made by Weekes5 from measurements on the ground interference pattern.
The solution of waveguide and cavityresonator problems with the resistancenetwork analogue
 Author(s): G. Liebmann
 Source: Proceedings of the IEE  Part IV: Institution Monographs, Volume 99, Issue 3, p. 260 –272
 DOI: 10.1049/pi4.1952.0027
 Type: Article
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An experimental iteration process is described for the solution of waveguide and cavityresonator problems. In this process, models of the waveguide crosssection or cavity resonator are set up on resistance networks as previously described elsewhere, and currents are fed into the network junctions according to certain prescribed relations; the fedin currents are then adjusted cyclically until “selfconsistency” is reached. The paper sets out the basic mathematical relations required, and describes the apparatus and its mode of operation. Several examples are given of waveguides having various crosssections and of cavity resonators of axial symmetry. it is shown that the error in favourable cases can be smaller than 0.1%.
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