US 2787656 A Abstract available in Claims available in Description (OCR text may contain errors) A ril 2, 1957 G. RAISBECK 2,737,656 MAGNETICALLY LOADED CONDUCTORS Filed Dec. 30, 1954 2 Sheets-Sheet 1 FIG. 2A LI a uz 0 RH /NVENTOR 'G. RAISBECK ATTORNEY United States Patent O MAGNETICALLY LOADED CONDUCTORS Gordon Raisbeck, Bernards Township, Somerset County, N. J., assignor to Bell Telephone Laboratories, incorporated, New York, N. Y., a corporation of New York Application December 30, 1954, Serial No. 478,680 2 Claims. (Cl. 178 45) v This invention relates to transmission lines for use in the propagation of electromagnetic waves. More particularly, this invention relates to magnetically loaded transmission lines having a low attenuation per unit length as compared to similar, unloaded transmission mes. It is an object of this invention to provide a magnetically loaded transmission line having a low attenuation per unit length. More particularly, it is an object of this invention to provide a transmission line in which the optimum magnetic loading effects are realized for a line of given geometrical configuration. The benefits to be gained from magnetically loading a transmission linev have long been appreciated. In a properly loaded line, the magnetic permeability of the loading material increases the inductance per unit length of the line, resulting in an increase in" the intrinsic impedance thereof and a consequent decrease in attenuation per unit length. Heretofore; efforts to reduce the attenuation of a line by magnetic loading have been only partially successful, since the magnetic material, if conductive, introduces extra losses into the line, or if non-conductive, increases the capacitance of the line. a Several schemes for continuously loading a line have been proposed, but it has been found that where the loading material is continuous, the hysteresis and eddy current losses more than nullify the beneficial results of the loading. In an effortrto eliminate these undesirable effects, suspensions of powdered magneticfiia'te'rial in dielectric material have been roposed, but the" resulting permeabilityof the mass has been too low to be of any appreciable'benefit. I Materials such as ferrites, which have a high magnetic permeability and a high resistance, appear to be the most promising materials' for magnetic loading. However, such r materials, when used in a continuous loading arrangement, exhibit such high hysteresis losses that there is no benefit tobe gained. The hysteresis losses can be minimized by introducing air gaps into the geometry of the loading material, but the presence of air gaps results in an unequal' curire'nt distribution in the conductors. This elfe'ct can be at least partially overcome by imparting to the conductors irregular shapes or configurations, which are reached through trial and error experimentations. In a paper entitled Noyaux et Coquilles dans la Domaine des Telecommunications, in' Cables et Transmissea vol. 6, 1 and 2, 1952, by MrP'raclie, a thorough study is presented of the loading problem in the specialized case of a-coaxial line with a coneentric shell of'loading material between the inner and outer conductor. While the problem is; treated with great detail, and optimized specifications for the numerous parameters are obtained, the solutibn fails to take' into accountthe dielectric loss tangent, it being assumed throughout thatthis parameter is zero, with a result that; optimum loadingvis notattained. - The present inventiion is based upon a; mathematical treatment which, after a change of variables, yields only 2 three parameters, including dielectric losses, possible an optimum proportionin'g of the transmission line variables regardless of the geometry of the line. In a preferred embodiment, the invention comprises a coaxial transmission line having-a concentric shell of magnetic loading material such as ferrite disposed between the inner and e-uterconductors. The dimensionsof the in er and outer conductors and of the Shell of loading mate ial are so proportioned relative to each other and to the other parameters of the line that the attenuation per unit length of the line is considerably less than heretofore obtainable through ma'gneticloading. I 1 Various other illustrative embodiments will be described herein, each of which is characterized by continuous niagnetic loading and an optimum proportioning of the parameters, resulting in a considerable decrease in attenm ation. The invention will be better understood from the following detaileddescription taken in conjunction with the accompanying 'clrawings in which: N Fig. l is a cross-section view of a coaxial cable embodying the principles of the invention; 7 Fig. 2A is an equivalent circuit of the cable of Fig. 1; Fig. 2B is a simplified equivalent circuit of the cable of Fig. l; 4 7 Figs. 3 and 4 are gra hs of the performance characteristics of transmission lines embodying the invention; Fig. 5 is a perspective view of a preferred embodiment of the invention; and I Fig. 6 is a cross seet-ionalview of st ill anothef preferred embodiment. p I Turning now to Fig. 1, there is shown a coaxial cable 11 comprising an inner" conductor 12 having an outer diameter d, anouter conductor 13 having an inner diam eter D, and a dielectric or insulator 14 separating the two conductors. Ahollow eylindr ical'member 15 having an inner diameter a"; and an outer diameter D and made of magnetic material which, for reasons stated in the foregoing, is preferably a high permeability, high resistance material such as ferrite, is interposedgbetweeii the inner and outer conductors concentrically therewith. Dielectric 14 has a permeability no and a dielectric const ant s while the loading member 15 has a tangential permeability ,LL and a radial dielectric constant e. The imaginary components of [L and s are taken int account in the form of figures of merit Q and" Q", which "56 explained more fully hereinafter. i An equivalent circuit of a unit length of line is shown in Fig. 2A, wherein L1 is the inductance due to fields between d and d Ln is the inductance between d and D1, and L111 the inductance between DI and D. R0 is the series conductor resistance and R11 is the loss associated with Ln. In like manner C1 is the capacitance between d'and d C11 the capacitance between d and D1, and C111 the capacitance between D1 and D. In addition, Gn is the loss conductance associated with C11. For purposes of the present analysis;-itzis-fpermissible to assume that the dielectric 14 is free of loss and that the frequency ishighenoughso that all current flow is at the surface of the-conduhtors. The inductance of a coaxial line is given by the expression where D is the inner diameter of the outer conductorand d is the outer diameter of the inner conductor. In addition, for a coaxial line where Q' is the reciprocal of the magnetic loss tangent of the loading material. The loss conductance is given where Q" is the reciprocal of the dielectric loss tangent of the loading material. It is a simple matter to combine the various elements of Fig. 2A into the equivalent circuit of Fig. 2B. It can readily be shown that in such case From the expression for attenuation in a coaxial line it can be shown that, in the case of an unloaded line and combining Equations 6 through 12, we arrive at the expression then 5 k V t/m 1/ V51 15 Regarding Q Q, Q". d, d,, and Di. as independent parameters, it is apparent that all of the variables in Equations 14 through 17 are independent of the dimensions of the line except v. The optimum dimensions of the line may, therefore, be readily obtained by ditferentiating Equation 17 with respect to v and setting the derivative equal to zero, from which we get at which point Figures 3 and 4 are graphs of Equation 19 for dilfering values of m and k. Inspection of the curves of Fig. 3 reveals the effect of dielectric loss, which is included in the parameter m. The family of curves represents fixed values of m and the consequent variation in loss for varying k. It can be seen from Fig. 4 that decreases, the slope of the curve decreases, and the role of m, and consequently, dielectric loss, becomes more important compared to k. The utility of the curves of Figs. 3 and 4 is obvious. They show to what extent one kind of loss may be substituted for another. In addition, for a given line size, it is possible to compute the values of k and m for available magnetic materials, and then determine from Figs. 3 and 4 whether it is feasible to construct such magnetically loaded line. Having arrived at an expression for minimum attenuation, it becomes a simple matter to determine the dimensions of the line which, for a given group of materials, yields the minimum attenuation possible. Rearranging Equation 16, an expression is obtained for the ratio D /d which gives the optimum dimensions for minimum attenuation, thus It can be seen from Equation 20 that the magnitudes of the dimensions D, d, D and d, do not matter so long as the ratio D1/d1 and D/d satisfy the equation. It follows from this, then, that the value of the ratio D/d which minimizes 0C0, which, as is well known, is equal to 3.59, should be used to minimize on also. This fact can be readily verified by inspection of Equation 17. As an illustration of the difference in results reached log shaman when dielectric losses are considered, assume that available materials have the following "set of parameter values: Q=320, and Q"==40. In the aforementioned Prache article, the method there presented assumes .Qf=a and k=0, and the result reached is D, I 1.89 This gives an expected of 0.65. However, because of dielectric loss, the actual value of is 1.02. The method herein proposed leads to the following results It is obvious that failure to consider dielectric losses leads to a result which is not the optimum obtainable, whereas the present method produces optimum dimensioning of the cable and loading material for a given group of materials. The present invention has been set forth in the foregoing in the preferred embodiment of a coaxial cable. Actually, however, the principles of the invention are equally applicable to other types of conductors also, provided that the boundaries of the loading material are surfaces which would be equipotentials if the loading material were removed. When this condition is met, Equations 6 through 9 become, respectively: o X+q-1 where X is a number independent of anything except the geometrical configuration of the loaded line, and for the sake of simplicity shall be referred to as the geometric configuration parameter. In Fig. 5 there is shown a pair of fiat conductors 21 and 22 of infinite extent separated by a distance T. Positioned between the conductors is a member 23 of loading material such as ferrite, having a thickness 1. Inasmuch as the dimensions of length and breadth do notenter into the computations in this case, the parameter X becomes loaded as shown in Fig. 6, the influence of the magnetic field surrounding each wire must be considered, inasmuch as that portion of loading member 33 'n'earest cenduc'tor32 is under the influence of stronger magnetic fields than that portion remote from conductor 32 and vice 'versa. The same conditions apply to member 3 and its relationship to conductor 31. By use of a system of bi-polar coordinates, it becomes a relatively simple matter to take into account the proximity effect in designing and dimensioning the loading members. Anex plan-ation of bi-p'olar coordinates and their relationship to magnetic fields can be found in Electromagnetic Theory" by J. A. Shatton (McGraw-Hill, 1941). Such a system requires the selection of two points a and b with respect to which any circle must satisfy the relationship: ;-:=c0nstant=n (26) where r is the distance from point a to any point on the circle and re is the distance from point b to any point on the circle. It can be seen that for different values of n, a family of circles is described, the centers of which lie on a line joining points a and b and which are asymmetrically disposed with respect to the points a and b. In Fig. 6, this constant is designated for the surface of conduc tor 32, '4 for the inner surface of loading member 34, and ,u, for the outer surface of loading member 34. In like manner t, designates the outer surface of member 33, ,u, the inner surface, and the surface of conductor 7 31. The net result is that the various members are asymmetrical with respect to the point a and b, and are not concentric With each other. In such a case, the geometric configuration parameter becomes: For a symmetrical system, .t,=l/;t,,, n,=l/p,, and ;t,=1/,u, and is not the case, another variable is introduced into the. problem. This, however, does not affect the basic concepts constituting the principles of the invention, although is results in a somewhat more tedious mathematical reduction to the basic formula. While the principles of the invention have been set forth in detail as applied to certain specific embodiments, it is to be understood that these embodiments are by way of illustration. Numerous other arrangements may be devised by those skilled in the art without departing from the spirit and scope of the invention as set forth in the appended claims. What is claimed is: l. A transmission line of the coaxial conductor type having conducting and dielectric portions, magnetic loading material of cylindrical shape interposed between and spaced from the inner and outer conductors, said loading material having with respect to free space a permeability and a dielectric constant e, the ratio of 11/: being greater than unity, said line having a geometrical configuration parameter a log and d, are, respectively, the outside and inside diameters of the loading material, said loading material being dimensioned relative to the conducting and dielectric portions of said line in accordance with the expression X==v(pq) q+l where p is the ratio of the permeability of the loading material to that of the dielectric portion of said line, q is the ratio of the dielectric constant of said dielectric portion to that of said loading material and v is equal to where Q being the figure of merit of the transmission line without the loading material, Q being the reciprocal of the magnetic loss tangent of the loading material, and Q" the reciprocal of the dielectric loss tangent of the loading material. 2. A transmission line as defined in claim 1 wherein the magnetic loading material is ferrite. References Cited in the file of this patent UNITED STATES PATENTS Patent Citations
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