US 2453759 A Description (OCR text may contain errors) Nov. 16, 1948. A. 1.. ROBINSON ,4 ' TAPERED UNION FOR CONCENTRIC CONDUCTOR LINES Filed Dec. 20, 1945 PRIOR ART L-z v A T TORNEY Patented Nov. 16, 1948 TAPERED UNION FOR CONCENTRIC. CONDUCTOR LINES Albert L. Robinson, South Orange, N. .1., assignor to Bell Telephone Laboratories, Incorporated, New York, N; Y., a corporation of New York Application December 20, 1943, Serial No. 514,948 1 Claim. (ohms-44) This invention relates to a concentric conduca tapered union for connecting such two sections. The patent of E. 1. Green, No. 1,341,473 granted January 19, 1932, discloses a concentric conductor line comprising two sections of different physical sizes assembled such that the ratio of the internal diameter of each outer conductor to the external diameter of its associated inner condoctor is substantially the same so that both line sections have substantiallythe same impedance. The patent of A. G. Clavier, No. 1,932,448 granted October 31,- 1933, discloses two concentric conductor sections of different physical sizes connected by aconical adapter arranged such that, at any point therealong, the ratio of the internal diameter of the outer conductor to the external diameter of the inner conductor is substantially equal to the corresponding: ratio of either line section. As a consequence, the characteristic impedance of the conical adapter is substantially equal or matched to that of either line section. It has been found that the conical adapter tends to vary in efiective impedance from point to point with variations in the frequency of the signal waves being transmitted thereover, and that such impedance variation tends to increase with frequency. This tends to introduce an impedance mismatch between the joined line sections and thereby to create reflection efiects which tend to introduce loss in the transmitted signals. The impedance variation of the conical adapter, that is, the impedance mismatch between the joined line sections, tends to attain a maximum when the wavelength of the transmitted signal waves tends to approach the physical length of the conical adapter. This'mismatch may be important in such uses asmaking accurate measurements, for example; The present invention contemplates connecting two concentric conductor sections of different physical sizes, but the same characteristic impedance, by a tapered union whose characteristic impedance from point to point substantially matches that of the individual line sections regardless of the wavelength of the transmitted signals. The object of the invention is to provide a concentric conductor transmission line of at least two sections of different physical sizes, with a substantially uniform impedance irrespective of the wavelength of the signals transmitted thereover. In a concentricconductor transmission line comprising at least two sections having difierent physical sizes and connected by a tapered concentric conductor union as disclosed in the Green patent, supra, a specific embodiment of the 2' present invention comprises a tapered concentric conductor union in which the outer and inner conductors are arranged such that, for a given radius and center, the ratio of the are extending between two diametrically opposite points on the internal surface of. the outer conductor to the are extending between two diametrically opposite points on theexternal surface of the inner conductor is substantially equal to the corresponding ratio of diameters of either of the line sections being joined together. As a consequence, the characteristic impedance of the taperer i union from point to point is substantially equal totha-t of either of the two line sections being connected together, regardless of the dimensional relation between the wavelength of the signals and the physical length of the tapered union. 1 i The invention will. be readily understood from the following description taken together with the accompanying drawing in which: Fig. 1 is a partial cross-sectional viewof a concentric conductor and graphically illustrates the distributionof the electrostatic and electromagnetic fields intervening between the inner and outer conductors and familiar to the prior art; Fig. 2 is a cross-sectional view taken along the lines 2-4 in Fig, .1; Fig. 3 is apartial cross-sectional view of a specific embodiment of the present invention; Fig. 4 is a. partial cross-sectional view similar to Fig. 3 but graphically showing the distribu tion of the electrostatic and: electromagnetic fields in Fig. 3; and' Fig. 5 is a cross-sectional view taken along the line 5-5 of Fig; 4'. a a a In Figs. 1 and 2 an outer conductor I 0. is arranged concentrically with an inner conductor H such that a certain ratio exists. between the inside diameter of the outer conductor andfthe outside diameter of the inner conductor. According to the Green. patent, supra, this ratio provides the assembled outer and inner conductors with a certain characteristic impedance; 1 lOgm a" v in which Zo=is the characteristic impedance in ohms, K isthe dielectric constant of the insulate ing material separating the outer and inner conductors, and D is the inside diameter of the outer conductor, and d is the outside diameter of the inner conductor. Hence, with a given dielectric constant K, the characteristic impedance isdetermined by the ratio In the con-centric conductor section of Fig. 1 the average electrostatic field at successivepoints along thehorizontal axisof the line is graphically thereof; and the electromagnetic field at successive points along the horizontal axis of the line is graphically shown by the vertically disposed characters and At a given point along the longitudinal axis of the concentric conductor line, the average electrostatic field may be further represented graphically like the spokes of a wheel, Fig. 2, while the average electromagnetic field may be graphically shown as a plurality of concentric circles, Fig. 2. A plurality of concentric conductor sections similar to the one shown in Figs. 1 and 2 may be embodied in a concentric conduct-or transmission system illustrated in Fig. 3. Referring to this figure, concentric conductor section l2 comprises outer conductor l3 and inner conductor l4 spaced concentrically, for example, by insulator l5 as illustrated in the patent of P. H. Smith, No. 2,280,- 200 granted April 21, 1942; and concentric conductor section [6 includes outer conductor l l and inner conductor i8 spaced concentrically by insulator l9 inthe manner of the Smith patent, supra. It is evident that the two outer conductors l3 and -.ll have different inside diameters, and the two inner conductors I4 and I8 have different outside diameters. However, the ratios of the inside diameters of the individual outer conductors I3 and I! to their associated inner conductors I4 and I8, respectively, are substantially equal so that the individual concentric conduct-or sections 12 and 16 have substantially the same characteristic impedance as disclosed in Green patent supra. .;Thus, the physical relationship of the outer and inner conductor of the two concentric conductor sections determines the distribution of both the electrostatic and electromagnetic fields therein, and both the latter, in turn, determine the characteristic impedance of the individual concentric conductor sections. Hence, the physical relationship of the outer and inner conductors embodied in the individual concentric conductor sections determines their characteristic impedance. The concentric conductor sections l2 and I6 are connected by a tapered union'25, Fig. 3, comprising a tapered outer conductor 26 and a ta pered inner conductor 21. A suitable wave translating device 28 applied across the outer and inner conductors of the concentric conductor section l2 serves to transmit or receive signal waves of a high order of frequency, including the ultra-high frequency range. Thus, the wave translating device 28, concentric conductor sections l2 and I6, and tapered union 25 comprise a high frequency transmitting or receiving system. In accordance with a specific embodiment of the present invention, the tapered concentric conductor union 25 is arranged to have a characteristic impedance from point to point, which is substantially equal to that of the individual concentric conductor sections l2 and Hi. This is accomplished by designing the tapered union such that, for a given radius and center, the ratio of the length of the are formed between diametrically opposite points on the internal surface of the tapered outer conductor 26 to the length of the are formed between diametrically opposite points on the external surface of the tapered inner conductor 27 is substantially equal to the ratio of the inside diameters of either outer conductor I3 or, ll to the outside diameter of the associated inner conductor M or l8. Thus, the characteristic impedance of the tapered union, from point to point, is substantially equal to the characteristic impedance of either concentric conductor section l2 or it, both of which, as previously pointed out, have substantially the same characteristic impedance. It will be observed that in any tapered union .in which the foregoing geometrical relations obtain, the diameter of the inner tapered conductor 21, in the plane of the larger end of the outer tapered conductor 26, is necessarily smaller than the diameter d of the connected coaxial conductor l8. It is only at some distance X (Fig. 3) beyond that plane that the diameter of the inner tapered conductor becomes equal to the diameter (1. Referring to Fig. 3, the arc A extends between diametrically opposite points on the internal surface of the outer tapered conductor 26; are E between diametrically opposite points on the external surface of the inner tapered conductor 21 the given radius 30 extends between both arcs A and B and. the given point 3! on the horizontal axis of the union 25; and the arc B coincides with a portion of the are A. As graphically illustrated in Fig. 4, the average electrostatic and electromagnetic fields tends to describe arcs. As such fields determine the impedance of the tapered uni-on, Equation 1 can now be written:- At the bottom of page 286 of S. A. Schelkunoffs textbook entitled Electromagnetic Waves published by the D. Van Nostrand Company, Inc. in 1943,mention is made that if two coaxial cones are insulated at their common apex and if an alternating current voltage is maintained between their apices, waves will be generated with electric lines coinciding with meridians and magnetic lines along circles coaxial with the axis. Let I(r) be the total current in the inner cone, and WT) the voltage from the inner cone to the outer cone along a meridian. The voltage is the integral of 1E0 along a meridian and may be expressed as 2 cot i opwhich is the exact formula for the characteristic impedance of a tapered section of coaxial conductor. For small angles, the tangent of an angle is approximately equal to the angle in radians so that the following approximation may be made. (arc length for 0 0 arc length for 0 where the arcs are measured along the same meridian. Equations 1 and 2 may be written 138 D 138 Arc A 138 gic 27 Thus, it is seen when the ratios tions l2 and I6 and tapered union 25 are substantially equal. What is claimed is: A microwave transmission line comprising two sections of coaxial conductor line having different physical sizes and arrangedto have the same ratio of the inside diameter of the outer conductor to the outside diameter of the inner conductor for both said sections, and a tapered union for connecting said two sections, comprising sonically tapered outer and inner conductors extending coaxi-ally in the same direction and proportioned so that the insidesurface of the tapered outer conductor and the outside surface of the tapered inner conductor have a common apex, said tapered conductors being further proportioned so that the ratio of the angle formed between the axis of said union and the inside surface of said tapered outer conductor to the angle formed between said axis and the outside surface of said tapered inner conductor is substantially equal to said diametrical ratio of the two coaxial sections being connected, the length of said tapered union being comparable with the wavelength of the microwaves transmitted therethrough. ALBERT L. ROBINSON. REFERENCES CITED The following references are of record in the file of this patent: UNITED STATES PATENTS Number Name Date 1,841,473 Green Jan. 19, 1932 1,932,448 Clavier Oct. 31, 1933 Patent Citations
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