US2052317A - Coaxial conductor transmission system - Google Patents

Description

Aug. 25, 1936.

S. A: SCHELKUNOFF GOAXIAL CONDUCTOR TRANSMISSION SYSTEM Filed Jan. 14, 1932 F/GZ % m z x Q I z 3 Z a O FREQUENCY E m m a:

m Z M 1 E *6 i l I l E l l I I at b 0 cl e qopp THlCl- (NESSOF CONDUCTING SHELL FIG. 4

FREQUENCY 2 Sheets-Sheet 1 1 'INVENTO/P 5. A. SCHELKUNOFF ATTORNZ'V Aug. 25, 1936. s. A. SCHELKUNOFF COAXIAL CONDUCTOR TRANSMISSION SYSTEM Filed Jan. 14, 1932 2 Shets-Sheet 2 FIGS FIG. 7

INVENTOP S A. SCHEL/(UNOFF A TTORNEP Patented Aug. 25, 1936 UNITED STATES COAXIAL CONDUCTOR TRANSMISSION SYSTEM Sergei A. Schelkunoff, East Orange, N. J., assignor to Bell Telephone Laboratories, Incorporated, New York, N. Y., a corporation of New York Application January 14, 1932, Serial No. 586,486

Claims.

This invention relates to conducting systems for the transmission of electrical waves and more particularly to the design of such systems wherein the conductors are in coaxial relation.

An object of the invention is to increase the efiiciency of transmission of a coaxial conductor system.

Another object of the invention is to reduce the attenuation of signaling waves transmitted over a line comprising a pair of coaxial conductors of given diameters.

More particularly the object of the invention is to improve the transmission of waves in a multiplex carrier wave system employing frequencies extending to the order of megacycles per second.

In accordance with the present invention the foregoing objects are attained by observing a critical relation between the thickness of the material comprising the conductors of a coaxial system and the frequencies of the waves transmitted thereover. Where one conductor serves as the return for another conductor coaxial therewith, the current is not uniformly distributed throughout the cross-section of the conductors but tends to concentrate at the inner surface of the outer conductor and at the outer surface of the central conductor. This effect becomes more marked as both the frequency of the waves transmitted and the diameters of the conductors are increased. At high frequencies the waves are practically confined to thin layers at the adjacent surfaces of the conductors and the thickness of the conductors may be reduced without affecting the alternating current resistance.

With continued decrease in conductor thickness, of course, the resistance increases and rapidly approaches infinity as the thickness becomes infinitesimal. Applicant has found, however, that just before the thickness is reached at which the alternating current resistance for a particular frequency begins this rapid increase, the resistance drops to an absolute minimum value, that is, to a value which is less than that obtaining for any other thickness of conductors. Either or both of the conductors may be made of this optimum thickness, a substantial reduction in attennation and in the amount of conducting material required being obtained in each case.

The optimum thickness of conductor depends, as indicated above, on the frequency of the wave transmitted. In general it is less for high frequencies than for low. Where the signaling waves occupy a wide frequency band, the thickness of the conductors is ordinarily to be determined by the highest frequency transmitted, inasmuch as the attenuation of a transmission line is inherently greatest at high frequencies.

The nature of the present invention will more fully appear in the following discussion, reference being made to the accompanying drawings, wherein:

Fig. 1 represents a cross-section of a pair of coaxial conductors;

Fig. 2 shows how the optimum thickness varies with frequency;

Fig. 3 shows diagrammatically the relation between the thickness of the conducting shell and the effective resistance at a particular frequency;

Fig. 4 shows diagrammatically the attenuationfrequency characteristic of a coaxial conductor system for different thicknesses of the conductors; and

Figs. 5, 6 and 7 represent different structural embodiments of applicants invention.

The following is a brief outline of the mathematical analysis leading to the present invention. The various symbols employed, some of which are represented in Fig. 1 of the drawings, have the following significance:

'Ihe conductivity in electromagnetic units @The dielectric constant in electromagnetic units ,u- Ihe magnetic permeability of the conducting material in electromagnetic units aThe inner radius of the central conductor in centimeters aThe inner radius of the outer conductor in centimeters a--The inner radiusof either conductor in centimeters b'The outer radius of the central conductor in centimeters bThe outer radius of the outer conductor in centimeters bThe outer radius of either conductor in centimeters 1*The distance of a typical point from the axis of the coaxial system of conductors f The frequency E-The electric force I-IThe magnetic force IThe total current flowing in the transmis- It is well known that quasi-stationary electromagnetic phenomena obey the following equations formulated by James Clerk Maxwell-- (1) (41rX+1'we)E= curl H (2) iwpH= curl E ods, we have In these equations I is the total current flowmg in the inner conductor of the coaxial pair, Ezl the potential drop on the outer surface of the inner conductor E52 the potential drop on the inner surface of the outer conductor, I (1:) and K0 (3:) the modified Bessel functions as defined by GvN. Watson in his Treatise on the Theory of Bessel Functions, and I0 (11:) and K0 (IE) are their derivatives. The details of the theory of transmission of electric currents over a pair 7 of coaxial conductors may be found in a paper .by S. A. Schelkunoff entitled (Electromagnetic Theory of Coaxial Transmission Lines and Cylindrical Shields published in the Bell System Technical J ournaLOctober, 1934.

The effective resistance 'R' of the central conductor of a coaxial pair is given by the real part of the function Z(o'b', all; 021') Similarly, the effective resistance R. of the outer'conductor is the real part of the function These expressions are valid for all ranges of frequency and diameter.

A- simplified, approximate formula for the effective resistance may be obtained from the asymptotic expansion of each of the foregoing modified Bessel functions:

These latter expressions are accurate to within a fraction of one per cent where the radius of the conductor is one centimeter or greater'and the frequency is ten thousand cycles per second or higher. For conductors of less than one centimeter radius, the same degree of accuracy obtains if the square rootof the frequency involved is at least proportionally greater than ten thousand cycles per second.

The effective resistance of both the central conductor and the outer conductor, it will be observed, is given by essentially the same formula. Varying the quantity h, both the real and the imaginary parts of the functions defined by Equations ('7) and (8) are found to pass through minima for the following values of h:

That is, the eife'ctive resistance of each of the conductors, as defined byrthe real vpart of the functions given by Equations (7.) and (8), possesses an infinite set of maxima and minima. Only the first of these minima, however, i e., the one corresponding to the least value of the electrical thickness h is marked enough to be of practical significance. In this case,

and the physical thickness t of the conductors is 1 (10) t=ba= CHL,

The effective resistance R of the central conductor for this optimum thickness is l E 1 (11) R x tanh and by the analogous formula for the outer conductor,

7 an outer conductor of optimum thickness is approximately two per cent less than that obtaining with an electrically thick conductor.

A physical explanation of this unexpected variation of resistance with thickness involves the fact that there is a difference in. phase between the waves at the surface of each'conductor and the waves within the conductors. There may be, in fact, several complete reversals of phase in the transverse propagation of the waves between the two surfaces of each conductor, alternate layers of conductor in effect carrying oppositely directed waves. In other words, the longitudinal transmission of a wave in'a coaxial conductor system is accompanied by radial propagation or penetration into the conductors at the same frequency but with a much'shorter wave-length.

Where the thickness is such that there is a 90 phase shift between inner and outer surfaces, the resultant current is a maximum, since the current in no part of the conductor has an oppositely directed component; increasing the thickness of the conductors until the phase shift between surfaces is progressively increased to 180, or, in

other words, untilthe thickness of the conductors is one-half a wave-length of the transversely propagatedwaves, reduces the total current, since oppositely directed components are introduced. With a 270 phase shift the current isagain increased, and the resistance thus continues to oscillate about an asymptotic value that is quickly approached as, the thickness ofjthe conductor is increased.

Fig. 3 shows graphically how the effective resistance for a particular frequency varies with.

the thickness of the conducting shell. At b the resistance is a minimum. 'With an increase in the thickness the resistance passes through a maximum value at d. Although theoretically the resistance continues 'to'oscilla te above-and below the asymptotic value represented at 'e,

these variations are negligible. The next minimum point, for example, differs by only twohundredths of one per cent from the asymptotic value obtained with electrically thick conductors.

- The first minimum resistance point for the central conductor is, as hereinbefore stated, of the order of seven per cent below the asymptotic value, and for the outer conductor, two per cent.

Where the radius of the outer conductor is greater than 1 centimeter, the optimum thickness for a frequency of ten thousand cycles per second is approximately 1 millimeter. For higher frequencies it is inversely proportional to the square root of the frequency, as is indicated by Equation (10) and as is represented qualitatively in Fig. 2. Thus, for transmitting a frequency of one million cycles per second, the required thickness is 0.1 millimeter. As a copper shell of this thickness would be mechanically weak, it is preferred that the conductors be formed as a plating on the surface of comparatively heavy pipes or tubes of iron, lead or other suitable material of relatively low conductivity. Suitable designs are shown in Figs. 5, 6 and 7, and are to be described hereinafter,

The present invention is particularly adapted for use in a multiplex carrier wave transmission system, such, for example, as described in L. Espenschied et al. Patent 1,835,031, December 8, 1931. The signals transmitted over such a system may occupy a wide frequency band extending to perhaps a million cycles per second or higher. Inherently the signaling waves of highest frequency are subject to the greatest attenuation, and in general where electrically thick conductors are used, a frequency-attenuation characteristic such as shown at A in Fig. 4 is obtained. By using conductors of optimum thickness as herein described the characteristic shown at D is obtained. Although the attenuation in the latter case is, in the low frequency range. the higher of the two, it will be noted that in the high frequency range, where attenuation is most serious, it is the lower of the two.

As shown in Fig. 4, the attenuation of the conductor system is nearly uniform with frequency for values of conductor thickness below that yielding minimum resistance. Even where the thickness is of the optimum value the attenuation is fairly uniform up to the maximum frequency f2 for which the system is designed. The discovery of this range of conductor thickness for which the attenuation is fairly uniform is not part of applicants invention but is disclosed and claimed in U. S. Patent 1,817,964, issued August 11, 1931 to J. E. Carson and S. P. Mead.

In Fig. 5 is represented a coaxial conductor system in which the central conductor comprises a plating I of copper on the outer surface of an iron pipe 2, and the outer conductor similarly comprises a plating 4 on the inner surface of the larger iron pipe 3. Connected to the conducting system are the terminal circuits G of a multiplex carrier wave or other signaling system. The terminal circuits and other features of the system may be as described, for example, in the Espenschied et a1. patent supra, or of any other suitable type. As the frequencies employed may be of the order of megacycles per second, as little solid dielectric as possible should be placed in the field betwen the conductors. The separators 5 are therefore made of a material having preferably a low dielectric constant and small phase angle.

The thickness of the copper plating is determined in accordance with Equation (10). The dielectric being air, a is unity. The conductivity A depends on the grade of copper employed; in a typical case it may be 0.000625. Assuming for illustration that five hundred thousand cycles per second is the maximum frequency transmitted, the optimum thickness is found to be The thickness thus determined corresponds to the point D on the curve shown in Fig. 3. It

will be observed that the effective resistance is less than that obtaining with thick conductors not only at the optimum thickness represented at point I) but also for a certain range of thickness above and below the optimum value. 7

In Fig. 6 the outer conductor comprises a plating 8 of copper on the inner surface of iron pipe I, while the central conductor is a heavy copper tube 6. In this system the thickness of the outer conductor is the optimum as regards attenuation. As the inner conductor is electrically thick, the resistance of the combination is approximately two percent less than that obtaining were both conductors made of heavy material. A layer of copper 9 on the outer surface of pipe '1 tends to reduce the effect of stray electromagnetic fields on the signals transmitted.

Fig. 7 shows a coaxial conductor system in which the central conductor i0 is plated on the surface of a solid iron wire H. The outer conductor 12. may be formed by passing a thin strip of copper through a circular die, or in any other suitable manner. The insulators 13 in this case are shown as solid beads of porcelain or other suitable material held in position between pinches on the central conductor.

The discovery that for the outer conductor of a concentric return cable there exists an optimum thickness at which the resistance of the combination is a minimum, is due to J. M. Eglin; it is described in his application for patent hearing Serial No. 586,478, filed of even date herewith, which has issued as U. S. Patent 1,972,877, September 11, 1934.

While the present invention has, for purposes of illustration, been described in connection with several of its specific embodiments, it is obvious that the principles herein set forth may be embodied in widely different organizations within the spirit and scope of the appended claims.

In the claims, the expression electrical thickness has the same significance as h and h", h applying to the central conductor and h" to the outer conductor.

What is claimed is:

1. An electrical wave transmission system com prising a pair of coaxial tubular conductors connected one as a return for the other and means for applying high frequency waves thereto, the physical thickness of the inner of said conductors only being one-quarter of the wave-length with which said waves are propagated transversely into said conductors at the maximum frequency of said waves so that the effective resistance of said inner conductor is a minimum.

2. An electrical wave transmission system comprising a pair of tubular conductors arranged in coaxial relation and connected one as the return for the other, means for transmitting over said conductors a band of high frequency waves,

' transverse propagation of said Waves at the maximum signaling frequency but less-than that of electrically thick conductors.

4. An electrical signaling system comprising 'means to generate a broad band of frequencies extending to at least several hundred thousand cycles per second, a pair of conducting shells, said shells being arranged coaxially and separated by a dielectric that is chiefly gaseous, means to apply said band of waves to said conducting pair for transmission thereover, the

thickness of the inner of said shells only being equal to l I Hm where 'x and n are respectivelythe conductivity and magnetic permeability of the material of said inner shell and ,7 is the maximum frequency of said'band.

5. In a multiplex carrier wave signaling system, means to-generate Waves lying in a wide band of frequencies extending to frequencies of the order of megacycles per second, apair of coaxial tubular conductorsseparated by a dielectric that is substantially gaseous, and means to apply said waves to said conductors for transmission thereover, the'thickness of both of said conductors being greater than the fraction where A and ere respectively the conductivity and magnetic permeability of the material of said conductors and f is the maximum frequency of said band, but less than that of electrically thick conductors.

SERGEI A. SCHELKUNOFF.

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