US2924795A - Low-loss transmission line - Google Patents

Description

Feb. 9, 1960- H. s. BLACK ETAL Low-Loss TRANSMISSION LINE Filed Dec. 51, 1954 ofuvrfsiw.

f. 044%- AT TURA/EV United States Patent LOW-LOSS TRANSMISSION LINE Harold S. Black, New Providence, and Samuel P. Morgan, Jr., Morristown, NJ., assignors to Bell Telephone Laboratories, Incorporated, New York, N.Y., a corporation of New York Application December '31, 19,54, Serial No. 478,990 1s Claims'. (ci. sas- 96) This invention relates to. conductors of high-frequency v waves, and, more particularly, to conductors of the concentric or coaxial type.

An object'y of this invention is to reduce skin effect in transmission lines operating at frequencies up to predetermined high-frequency limits.

A more specific object is to provide an efiicient yet inexpensive means of improving the attenuation-bandwidth characteristics of insulation lled coaxial cables.

The problem of skin effect is well known to the art and will be outlined here only because the present invention is concerned with this problem. A more complete ex.- planation thereof canflzve found beginning at page 196 of Fields and Waves in Modern Radio by S. Ramo and l. R. Whinnery, John Wiley & Sons, Inc., 1946. Briefiy stated though, skin effect is the increase with frequency of the resistance of a conductor caused by the ltendency of alternating currents to crowd more and more toward the surface of the conductor as'their frequency is increased. The surfaces toward whichthese currents tend to crowd are those surfaces nearest the fields producing them.

Expressed mathematically, the distribution of current density in a semi-infinite plane conductor where z is the direction of current ow and x is the `direction normal tov the surface of the conductor is as follows:

i where io is the density of current flowing in the z direction V rfug where f is frequency, ,u is permeability of the conductor, and g is its conductivity. An example of a semi-infinite planefconductor to which Equation 1 is applicable is a plane conductor of nnitedepth below the surface, infinite width, and infinite length. From Equation 1 it is apparent that at a distance below the surface of the conductor the current iz has decreased to 1/ e of its value at the surface. This distance is called the skin depth of penetration of current into the conductor at a given frequency.

In long distance wire communication two interrelated aspects of skin effect become important. The 'first of these is the increaserin power losses in the transmission lines which necessitates signal amplification at frequent intervals along Vthe lines. The second is the nonuniformity of the transmissioncharacteristics of the lines for differing signal frequencies. A very well known way of dealing with the first aspect of the problem is to plate a thin layer of highly conductive metal such as silver upon a poorly conducting member such as a less expensive base metal. In this way `the power losses may be reduced in the neighborhood of the highest utilized frequency by practicing the procedures described in U.S. Patent 2,052,3l7issued to S. A. Schelkunoff, but at best ICC there is only Vinadequate equalization of these losses at various low frequencies. Conversely, frequency equalization has been achieved at the expense of increased power losses in the way described in United States Patent 1,817,964 to Il R. Carson et al. Several structures disclosed in this patentresembic 4in appearance those to be described-hereinafter in connection with the present invention, but it should be understood that none of the former 'structures succeeds in reducing `power losses while at the same time .achieving frequency equalization. K

So far as is known the most efficient way of dealing with both aspects of the skin effect problem i's disclosed in copending application to A. M. Clogston tiled March 7, 1951, Serial No. 214,393 (now United States Patent 2,769,148, issued October 30, 1956). The structures disclosed in that application utilize as a means of reducing wave atenuation a number of thin, closely spaced conductors spaced apart and parallel to-each other by insulating material. In order for high frequency waves to penetrate throughout such a laminated conducting medium, which isa conditionfor most efficient operation, it is necessary that each individual conductor be at least as thin as the skin depth of penetration of waves in the conductorfmetal at the frequency of the waves, It is also necessary that the velocity of propagation of waves in the region surrounding the 'laminated medium be made substantially the sarne as the velocity within this medium. When these requirements are satisfied it is then possible to have a cablein which the power loss |in the laminated lconductor is appreciably less'than the loss in a solid conductor of the same size and, Vfrom very low frequencies up to frequencies at whichthe skin depth becomes conn parable tothe thickness o f the individual conductors, wave attenuation is almost uniform. By"increasing the number of thin conductors used while at the same time making each conductor thinner, the attenuation-bandwidth characteristics of the, laminated medium can be improved, within certain limits, in any required degree. Thus, one long distance cable built according to the above Clogston disclosure can theoretically transmit all the signals vnow being transmitted by a very large nurnber of conventional long distance lines. In many applicaitons, however, it is not economical to employ such a high-transmission-capacity cable. For this reason it would be desirable to have available a transmission line possessing attenuation-bandwidth characteristics substantially superior to those of conventional transmission lines previously known, but yet being only slightly more difficult to manufacture than these lines. The present invention, prompted by `this need, is based upon the discovery that a two-conductor insulated transmission line can be improved substantially by the proper insertion into the electromagnetic field between these conductors of a singie thin conductor together with the right kind of insulating material.

In accordance with the'present invention in one specific embodiment thereof, a hollow cylindrical conductor having a wall ythicknessiless than the skin depth at a predetermined frequency is suitably placed between and axially aligned with the inner and outer conductors of a coaxial cable. Insulating material having a low dielectric constant is used to separate this thin conductor from the inner conductor and different insulating `material'having asomewhat higher dielectric constant is used toseparate it from the outer conductor. The exact value of the-dielectric constant of thisl latter material and the thickness loffthe lthin'conductor together with certain other physical Adimensions and relationships in this embodiment are critical in -reducing cable attenuation. Theseroptimum dimensions Aand relationships will Yappear in thehfollowingV morecomplete description of the invention rand it'rsufiices here tosay that they exist.

When a structureis made satisfying these requirements its attenuation-bandwidth characteristics will be substantially better than those fora conventional non-airflled coaxial cable of the same outer diameter.

TheV advantages of thepresent invention will be gathered from and a better understanding of its general nature will best be gained by the 'careful study of the following detailed description given in connection with the accompanying drawings, in which: n

Fig. 1 is a sectional view of a preferred embodiment of ythe invention taken along the line 1`1 of Fig. 2;

Fig. 2 is a cross-sectional view of a preferred embodif ment of the invention;

Fig. 3 is a cross-sectional view of another preferred embodiment; p

Fig. 4 is a plot of the attenuation vs. frequency characteristic of the cable of Figs. l and 2 asy compared with a standard coaxial cable; and

Fig. 5 is a plot of the attenuation'vs. frequency char- 'acteristic of the cable of Fig. 3 as compared with a standard coaxial cable.

In explanation of the invention it is necessary to give a brief, mathematical treatment of a transmission system consisting of three coaxial cylindrical conductors separated by two insulating members. An analysis of a system of n coaxial conductors may be found in Transmission Characteristics of the. Submarine Cable, by John R. Carson and J. J. Gilbert, in The Journal of the Franklin Institute, vol. 192, pp. 705-735, December 1921. case of a system of n conductors, with a more thorough study of the effect of the proportions and materials of the cable on the transmission characteristics thereof. The principles of the present invention may be more fully understood in connection with a detailed treatment of the three conductor cable. In the following treatment, the MKS Rational System of units is used throughout except where specified otherwise.

Turning now to the drawings, there is shown in Figs.

l and 2 a three conductor coaxial cable 11 having an l inner cylindrical conducting shell 1, an intermediate cylindrical conducting shell 2 coaxial with shell 1,' and an outer cylindrical conducting shell 3, coaxial with shells 1 and 2. Shells 1, Z, and 3 are made of suitable conducting material, such as copper, andshell 1 may be advantageously formed by copper plating an iron, steel, or other suitable material core, not shown. In addition, shell 3 may be surrounded by a reasonably high impedance shield,.not shown, without detrimentally affecting the operation or the characteristics of the cable. 2 is spaced from and maintained in coaxial relationship with shell 1 by insulating material 4 having a dielectric constant e1 and shell 3 is spaced from shell 2 by insulating material 5 having a dielectric constant e2. Materials which are suitable for insulator 4 are to some extent determinative of what constitutes a suitable material for insulator 5, as will be explained hereinafter, hence a discussion of these materials is postponed until later.

In Figs. l and 2, the inner radius of the ith conducting member (==l, 2, 3) is denoted by ai, its outer lradius by b1, and its thickness by :Fbi-ai. For purposes of this analysis, we consider electromagnetic fields` which propagate along the cable according tothe factor exp -Fz-l-jwT) v(2) where z is distance along the axial direction, I is the propagation constant, w is 21|- times the cyclic frequency, and T is time. Furthermore, let I1 be the current in amperes flowing in the positive z direction inconductor 1, and let I3 Abe the current in amperes owing in. the positivel z direction in conductor 3, in which case the current in the positive z direction-in conductor 2 is The instant analysis may be termed a special Shell l2'=-(l1|-I3), neglecting axial displacementfcurrents in the insulators. vIt may be shown, as inthe aforemenf tioned Carson and Gilbert paper, Ithat the axial electric n tric constants and pernleabilities',"v

theV insulators are 2 17L(aa/b2) i and l is the permeability of inner insulator 4 in henries per meter, n2 is the permeability of outer insulator 5, e1 is the dielectric constant of the inner insulator 4 in farads per meter, e2l is the dielectric constantA of, the outer insulator 5 and'E.('p) isy thecom'ponentof electric eld in volts per meter parallel to the axisat a distance p therefrom. In the present analysis; it is assumed that the conductivities of the dielectricsare zero, "but both dielectric 'and magnetic dissipation, if present, can be accounted for by assigning complexyalues 'to the dielec- When ahollow cylindrical conductorjoff'inner radius a and outer radius b carries a'given ,total current which returns on one or more conductors coaxiafwith it, the

longitudinal electric field intensities *zafitsjsuriace arey where Za, and Zbb are surface impedances in ohms and Zb=Z7m is the transfer impedance. While exact formulae for the impedances may be obtained from the aforementioned Schelkunoff article, .they are.- somewhat unwieldy and require' access totables of Besselafunctionsgin computing the values of the impedances. 'Usefulapproximations sutlicient for the present analysis are contained in a paper entitled ber den Wechselstromwiders'tand von Geraden Drhten by S. Ekelf appearing in Electrische Nachrichtentechnik,vol. 10, No. 3,'p'p.' 1l5T-l22,-l933. In that paper,'Ekelf gives equations which refer to alconducting cylinder whose inner and outer radii are both large compared to Ivthe skin depth, and Whose thickness t=ba is small compared to the mean'radius'l/z(z-l-b). In the present notation these formulae read:

3t2 eoth et 1 Jfmil-FT Sta 5 coth t 1 ,ameter at the same frequency.

In the three conductor cable shown in Figs. 1 and 2, the impedances of the ith conductor are denoted by Z22, Zi?, and Z233 which are a pair of homogeneous -linear equations in terms of the currents I1 and I3. These equations may be satisfied by values of Il and I3 which are not both zero if and only if the determinant of the coefficients vanishes. Setting the determinant equal Ito zero gives a quadratic equaltion in I2:

Equation 18 is a perfectly general relation which must` be satisfied by the propagation constants of the transmission line modes on any system of three coaxial cylindrical conductors separated by two insulators. It 'has two roots, which may be denoted by 11 and F2. (The roots 41, and F2 which correspond to backward traveling waves also satisfy the equation.) The propagation constants may be separated into real and imaginary parts:

11-01-1-31 and I`2=2+l32 (19) i which represent attenuation and phase constants respectively.

One purpose of the present invention is to obtain, with a three-conductor transmission system of predetermined outside diameter, a lower attenuation constant at a specified frequency than may be obtained with a conventional two-conductor coaxial system of the same outside di- Inasmuch as there are two transmission-line modes in the three conductor s ystem, as shown by Equations 18 and 19, it is necessary that that mode which has the smaller attenuation constant be utilized, which, for convenience, may be designated as mode l. The corresponding attenuation constant a1' may be minimized by proper choice of materialsand proportions in the three-conductor cable.

AAs an example, assume that, in the cable of Figs; l and 2, the outside diameter and the design frequency are given, While the proportions and materials used' may be varied within broad limits set by engineering considera-` tions, such asl mechanical strength, dielectrics available, and the range of 'permeabilities available.` Inasmuch as the attenuation"constantt1` is dependent on a great number of parameters, it is impractical to Write out the mathematical expression for up Instead, optimizing of the parameters to achieve a minimum a1 Ymay be conveniently accomplished by a process of successive approximations, as follows:

When allA ofthe parameters are held 'constant except one, such as, for example,.lthe `dielectric constant e2 of insulator 5, s2 is varied until a minimum a1 is reached. The process is then repeated, varying one of the other parameters, until all o f the parameters have been optimized to the first approximation. The process is then repeated until successive approximations cease to have any appreciable elfect on the attenuation constant.

A more eicient procedure for minimizing al than the above method is found in On the Experimental Attainment of Optimum Conditions, by G. E. P. Box and K. B. Wilson, Journal ofthe Royal Statistical Society, Series B, vol. 13, No. l, pp. l-45, 1951. In that paper, it is shown that `the quantity to be lminimized should be evaluated for several different choices of the variables in the neighborhood of the expected minimum. A second degree function of the variables is then fitted, by the method of leastsquares, tothe computed points. By wayof illustration, if there were only one variable factor,

a, would be evaluated at three or more points and a parabolic approximating curve fitted to the points. Setting the rst partial derivatives of the approximating function equal' to zero, a set of simultaneous linear equations is obtained which, when solved, yield the minimum of the approximating function. lf this minimum lies outside of the region which contains the computed points, the variables are adjusted in the direction of the minimum and a new approximating function is tted. This process is repeated until theminimum of the approximating function lies within the region of computed points, which point is then thev minimum value of a1, and the values of the variables may be, in effect, read off.

As an example of 'the application of the foregoing, assume that all conductors have' the conductivity of copper, namely g=5 .8 X 1'07 mhos per meter, that henries per meter, and that el is fixed. Since attenuation `is proportional to the square root of the dielectric constant, it is obviously desirable to select a material having the lowest possible dielectric constant. In the instant case, we are dealing with two dielectric materials having different dielectric constants, `one of which (el) will always be less` than the other (s2). By selecting a material with as low a dielectric constantV as is available, Iand designating this as e1, we are then assured that by holding eyconstant, ye2 will also be minimized for the particular case under consideration. The remaining parameters are combined `in dimensionless ratios defined as follows:

f attenuation a. It can be seen that bandwidth as here used does not refer to a range of frequencies, but to a ratio of'frequencies which defines the improved attenuation characteristics of the cable of the invention relative to an ordinary coaxialacable;v By using the foregoing `-method of optimizing, the `optimum relationships were found for different-values of the ratiok 'Ihe results are shown in the following table: I

` "Tablet attenuation at the design frequency is seen to decrease to as little as 75 percent of that of a conventional coaxial cable within the range of calculations performed in the example, while bandwidth increases by as much as 75 percent within the same range. It is obviousfrom Table I lthat the three conductor cable of Figs. l and;2 offers greatly improved performance over that of the conventional coaxial cable. In Fig. 4 there is shown aplot of the attenuation-frequency characteristic of thecable of Figs. 1 and 2 (i.e.,. the thin shell embodiment) for D/ 60:400, and, for comparison purposes, the equivalent characteristic of a standard coaxial cable,.where Aqc-is-the attenuation constant of the standard coaxial cable with dielectric constant e1, at the design frequency fo. It can be seen from an examination of Fig. 4 that the cable of Figs. 1 and 2 gives a tremendously improved attenuation vs. frequency characteristic, as manifested by the exceptional bandwidth wherein the attenuation remains substantially constant. l

In Fig. 3 there is shown a second preferred embodiment of the present invention. For simplicity in applying the mathematical relations, elementsV and dimensions in Fig. 3 are designated by the same referencecharatcers as like elements and dimensions in Fig. 2. The cable of Fig. 3 differs 'from that of Fig. 2 in that it has a center conductor of solid wire and an outer conductor made of an electrically thick tube, thus providing both mechanical strength and shielding for the cable.` For the cable of Fig. 3, the foregoing mathematical development is applicable except in -the equations of Zag and Zbb. When the radius b of a solid cylindrical conductor is large compared to the skin depth, the surface impedance is given by:

Using the optimizing process explained in the foregoing, the following results are obtained for the cable of Fig. 3, where D is now the inside diameter of the outer conductor.

Table Il 20o 40o 600 5u bz/as 0. 3280 0. 3047 0. 2955 0. 2125 0. 2166 0. 2191 0. 7002 0. 8020 0. 8071 0. 0736 0. 05092 0. 03995 0. 8475 0. 8076 0. 7913 1. 3922 1. 533 1. 5970 Since the cable of Fig. 3 is substantially like a coaxial Acable with the addition of a thin walled intermediate conductor, the advantageous effect of the intermediate conductor can be readily appreciated by an examination of Table II. It is evident that the third conductor, used with the required two dielectrics in an optimally proportioned cable, adds roughly 50 percent to the bandwidth of the coaxial cable. In the case of the cable of Figs. l and 2, another 15 percent increase is obtained. A study of Table II reveals certain facts which were evident in the study of Table I. Thus, the thickness of the intermediate conductor is again within the range of 70-80 percent of the skin depth. Also, the dielectric constants e1 and e2 must diier by a small amount. In Fig. 5 there is shown a plot of the attenuation versus frequency characteristic of the cable of Fig. 3 for D/0=400, and, for comparison purposes, the equivalent characteirstic of the standard coaxial cable having the same constants as the standard coaxial cable of Fig. 4. It can readily be seen that the cable of Fig. 3 givens an increased bandwidth over the standard coaxial cable.

Comparison of the curves of Figs. 4 and 5 reveals that the cable of Figs. 1 and 2 gives an improved performance over the cable of Fig. 3. In practice, Where both mechanical strength and adequate shielding are highly desirable, kthe performance characteristics of the cable of Figs. l and 2 may be achieved by making bothv the inner and outer conductors of some appropriate material such as, for example, iron, and plating the outer surface of the inner member and the inner surface of the outer. member with a highly conductive material such as'copper to the required thickness for the cable of Figs. 1 and 2.

The foregoing optimizations were based upon most of the important parameters being variable. In practice, it might be necessary to conne the insulating materials, for instance, to easily obtainable materials, such as polyethylene and polystyrene. Thus e1 could be 2.26 (polyethylene) and e2 could be 2.45 (polystyrene). In this case, A would have the value 0.084. Furthermore, in applications where the center conductor is to carry D.C. power current or where vthe center conductor is copperplated steel for mechanical strength, it may become necessary to make the center conductor approximately equal in size to the center conductor of a coaxial cable. Thus, for example, the inner and outer conductors may have the same outside diameters as a coaxial cable, and

for the cable of Figs. 1 and 2, and y bllaa= 0.2785

9s for the cable of Fig. 3. Withithese limitations on vthe proportions of the cable, optimizingyieldsthe-following results:

Table III (cable lof Figs. '1 and 2) While the results are not as good as the results obtainable when A may be varied freely, nonetheless, as a practical matter, the results obtainable are much better than the performance of a conventional coaxial cable. As was the case with Tables I and II, the thickness of the intermediate conductor varies in the neighborhood of 75 percent of the skin depth, while the outer and inner cylindrical shells in the cable of Figs. 1 and 2 are approximately 1.5 times the skin depth.

Throughout the analysis of the characteristics of the embodiments shown in the figures, the permeabilities of the insulating materials have been taken to -be equal to each other andrto the permeability of air. Examination of the equations, and particularly Equation 18, reveals that n is a factor equally as important as the dielectric constant e. The same or similar results can be obtained by varying the permeabilities instead of the dielectric constants, or, where such materials may be available, both factors may be made to differ. Applicants do not intend to limit themselves to the case where only the dielectric constants of the insulators are made to differ,

. but intend to include within the scope of the invention the case where the permeabilities are made to differ, and also the case Where both the permeabilites and the dielectric constants are made to diier. Inasmuch as the characteristic wave propagation velocity of a material is proportional to where n is the permeability of the material and e is the dielectric constant thereof, it can readily be seen that by making the permeabilities or the dielectric constants of the insulating materials differ, the insulating materials will have different characteristic wave propagation velocities.

Since in practice all proportions of the cable are likely to deviate from their optimum Values, it is of interest to note that fairly reasonable tolerances are permissible. For example, in the second column of Table I, if only A were variable, for a 0.5 percent variation in a/ao the ratio e2/e1 could lie anywhere between 1.040 and 1.053. In general, the increase in a/ao for a small variation of any one of the cable parameters laway from its optimum value is proportional to the square ofthe variation of the parameter.

While applicants have shown and described two embodiments of their invention, it is obvious to those skilled in the art that numerous other embodiments are possible without departing from the spirit and scope of the appended claims.

What'is claimedjis:4

1. A low-loss :transmission line for electromagnetic waves comprising inner and outer members of conducting material, a single thin member of conducting material between said inner and said outer members, said thin member `being separated from said inner member by first insulating material and being separated from said outer member by second 'insulating material, the characteristic wave propagation velocity of said first insulating material being greater than that of said second insulating material, and the thickness of said thin member is between one-half and one skin depth at the highest frequency of operation of the transmission line.

2. A low-loss transmission line for electromagnetic Waves as claimed in claim 1 wherein the dielectric constant of said iirst insulating material is different from the dielectric constant of said second insulating material.

3. A low-loss transmission line for electromagnetic waves as claimed in claim 1 wherein the permeability of the first insulating material is different from the permeability of the second insulating material.

4. A low-loss Ytransmission line for electromagnetic Waves as claimed in claim 1 wherein both the dielectric constant and the permeability of the first insulating material differ from the corresponding constants of said sec ond insulating material.

5. A low-loss transmission line for electromagnetic waves comprising an inner cylindrical member of con'- ducting material, and an outer cylindrical member of conducting material coaxial with said inner member, a single thin member of conducting material between said inner and outer members and coaxial therewith, said thin member being separated from said inner member of lirst insulating material and being separated from said outer member by a second insulating material, the intrinsic wave propagation velocity of said first insulating material being greater than that of said second insulating material, said thin member having a thickness greater than onehalf and less than one skin depth at the highest frequency of waves to be transmitted.

6. A low-loss transmission line for electromagnetic waves as claimed in claim 5 wherein the dielectric constant of said rst insulating material is different from the dielectric constant of said second insulating material.

7. A low-loss transmission line for electromagnetic waves as claimed in claim 5 wherein the permeability of the rst insulating material is different from the permeability of the second insulating material.

8. A low-loss transmission line for electromagnetic waves as claimed in claim 5 wherein both the dielectric constant and the permeability of the rst insulating material diler from the ycorresponding constants of said second insulating material.

9. A low-loss transmission line for electromagnetic waves as claimed in claim 5 wherein the inner conducting member is a solid cylindrical conductor and the outer conducting member is a hollow cylinder.

10. A low-loss transmission line for electromagnetic waves as claimed in claim 5 wherein both the inner and outer conducting members are hollow cylindrical conductors.

l1. A low-loss transmission line for electromagnetic waves according to claim 5 wherein the spacing between said thin member and said inner conducting member is less than the spacing between said thin member and said outer conducting member.

l2. A low-loss transmission line for electromagnetic waves comprising an inner hollow cylindrical member of conducting material, an outer cylindrical member of conducting material coaxial with said inner member, a single thin intermediate member of conducting material between said inner and outer members and coaxial therewith, said thin member being separated from said inner member by a first insulating material and being separated from said outer member by a second insulating material,

1 l.`l the intrinsic wave propagation velocity ofisaid 'first insulating wave material being .greater than that of said second insulating material, saidthin memberhaving-a thickness greater than one-half 'and less than one skin depth at the highest frequency of waves to be transmitted, said inner member having a thickness greater than one and less than two skin depths thick at said frequency and said outer member having a thickness greater than'oney and less than two skin depths thick at said highest fre` quency. A

13. A low-loss transmissionfline for electromagnetic waves comprising a solid inner member of conducting material, an outer cylindrical member of conducting material coaxial with said inner member, a single thin intermediate member of conducting material between said inner and outer members and coaxial therewith, said thin member being separated from said inner member by a rst insulating material and being separated from said outer member by a second insulating material, the intrinsic wave propagation velocity of said rst insulating material being greater than that of said second insulating material, said thin-member having a thickness greater than one-half and less than one skin depth at the highest frequency of waves to be transmitted, the outside diameter of said intermediate member being greater than one and one-third times the outside diameter of said inner member.

14. A levi/loss transmission line for electromagnetic wavescomprising a soldiinner-vmember of conducting material, the surface of said inner member being coated with a conducting material yof greater conductivity than that of the material of said inner member, angouter cylindrical member of conducting material coaxial with said inner member, the inmner surface of said outer member being coated with a conducting material of greater conductivity than that of. the material of said outer member, a single thin intermediate member of conducting material between said inner and outer members and coaxial therewith, said thin member being separated from said inner member by a first insulating material and being separated from said outer member by a second insulating material, the intrinsic wave propagation velocity of said rst insulating material being greater than that of said second insulating material, said thin member having a thickness greater than one-half and less than one skin depth at the highest frequency of waves to be transmitted.

Yl5. A low-loss transmission line as claimed in claim Y 14 wherein the coatings on the inner and outer members each have a thickness greater than one and less than two skin depths at said highest frequency of operation.

References Cited in the file of this patent FOREIGN PATENTS s 151,466 Australia May 1s, 1953

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