US 2086629 A Abstract available in Claims available in Description (OCR text may contain errors) HIP July 13, 1937. s. P. MEAD 2,086,629 SHIELDED CABLE SYSTEM Filed April 14, 1956 2 Sheets-Sheet l F/G/ 7'77 7' 7 .2 FRANSM/TT/NG RECEIVING TELEVISION TELEVISION TERMINAL TERM/MAL N A QQZM IN [/5 N TOR SRMEAD A TTORNEV VALUES or July 13, 1937,, S. P. MEAD SHIELDED CABLE SYSTEM Filed April 14, 1936 FIG? RAD/O MANSH/ 775R u z VALUES OF 2 I l2 l4 VALUES OF F 2-38 VALUES OF /5 VALUE? OF 2 a 2 Sheets-Sheet 2 VALUES OF c/A //v VE/V TOR ATTORNEY Patented July 13, 1937 Ni'iiifi lhtihiii iCii- FME Z,8fi,629 SliliElLlB ED @AELE SYSTEM Sallie ll. Mead, New orlr, if assignor to Bell Telephone Lahore s, incorporated, New York, N. a corpora ion or New Yorlr Application April i i, i936, No. 74,269 9 (Cl. S e l) This invention relates to electrical transmis- Fig. 8 is a family of curves showing the relation sion systems and more particularly to high irebetween attenuation and the geometric proporquency signaling systems comprising several contioning of a shielded two-pair cable in which the ductors disposed within a metallic shield. conducting wires and the shield have the same For the transmission of high frequency signals conductivity; 5 such as employed in wide band carrier telephone Fig. 9 shows the relation, optimum with reand television systems shielded conducting sysspect to low attenuation, between the dimensional terns comprising one or more pairs of conductors ratios of a shielded two-pair cable and the rabalanced with respect to ground have heretofore tio of the respective conductivities of the shield 10 been proposed. Such shielded systems are charand the conducting wires; and 10 \acterized by low susceptibility to interference Fig. 7.0 is a graph showing the relation between arising from external sources, this being due in mimmum attenuation and the conductivity ratio part to the shield surrounding the conductors and in shielded two-pair cables of optimum configin part to the electrical balance of the pairs with uration. respect to ground. Conversely, and for the same Referring now to the drawin s, there is shown 15 reasons, waves transmitted through the shieldin Fig. l a typiwl tIEVHSmiSSiOH Sy t in a ed system have little or no disturbing effect on ance with the invention comprising television teradjacent external signaling circuits. A further "ials TTI TTQ, connected by a transmission characteristic is, or may be, moderate attenuar-in s f ur c n or sy m ri lly tion even at frequencies of several hundred or 'osed within a copper tube and substantially 20 several thousand kilocycles per second and high- 1' insulated therefrom. iwo diagonally opposite er. As with all familiar types of conducting sysconductors comprise a circuit and of the two cirtems, however, the attenuation increases as the cults shown one may be utilized for transmission frequency rises and this becomes a limiting factor in the east-west direction and the other for transin the design of the entire system. mission in the west-east direction. Repeaters may 25 A particular object of the present invention is be installed in the line at suitable intervals. In to reduce the attenuation of signals in a shieldthis embodiment it is presumed that both circuits ed high frequency transmission system comprisare operated in the same frequency range and that ing two pairs of conductors. More specifically, this may be as much as a megacycle in width. the object is to provide a conducting system of ilternatively, transmission in two directions may 30 this type in which the dimensions and spacing be effected over each circuit utilizing different i of the conductors are optimum with respect to portions of the frequency range for separation signal attenuation. of the oppositely directed signals. The optimum design in accordance with the Another typical embodiment of the present inpresent invention is dependent on several varivention is represented in Fig. 2 where a radio 35 able factors. Applicant has discovered the crititransmitter RTi is connected to two independent cal relationships that must exist between the sevdipole antennas R'lz over a shielded two-pair v eral variables and these are set forth in mathecable similar to that represented in Fig. 1 and m i l formulae that pp n a subsequent utilized in substantially the same manner for 40 portion of this sloecificatifillone-way transmission, diagonally opposite con- 40 The nature of the present inl'ention and 05191 ductors again comprising each of the two cirebjects and features thereof will appear more suits. ! fully in the detailed description that follows, ref- Figs 3, 4 and 5 Show cable structures Suitable erence being made to the accompanying drawfor use in transmission systems such as shown in show typical four-wire transmisa In 3 h Conductors are 45 sion Systems embodying the present inventign; maintained in spaced relation with respect to the Figs. 3, 4) and 5 Shaw in partial section shie1d copper tube 5 by means of perforated insulating ed twomair cables in accordance with the washers c spaced at intervals such that the divention. electric between the conductors and the sheath 50 Fig 6 is a cmss sectiona1 View f a typical substantially gaseous. Fig. 3 shows also how shielded twmpair cablv; four signaling circuits may be derived from the Figs. 7 and 7A are diagrams used in conngcfour conductors and sheaths. Two side circuits tion with the mathematical demonstration and S1 and S2 are obtained simply by connection to description of applicants invention; each pair of diagonally opposite conductors. A 55 phantom circuit P is derived by connections to the mid-point of the two side circuits, in this case each pair of diagonally opposite conductors being utilized as one side of the phantom circuit. A fourth, ghost circuit G is derived by means of a connection to the mid-point of the phantom circuit and a connection to the sheath, the four conductors in parallel being utilized as one side of the circuit. The four conductors may be laid parallel to the axis as shown in Fig. 3 or disposed. with a slight helical twist as shown in Fig. i. The two-pair cable represented in Fig. 4: is characterized chiefly by the fact that a solid dielectric material 6 is utilized to maintain the four conductors in their relative positions with respect to each other and the sheath S. The shielded two-pair cable illustrated in Fig. comprises a sheath made up of a number of interengaging profiled strips '5 up with a slight helical twist and bound together by an external helical Wrapping of iron or brass tape 9. Each of the four conductors has applied to it a helical cord 8 of any suitable insulating material and an over-all wrapping of paper to. Another insulating cord H is wrapped around the four insulated conductors holding them in position with respect to the shield. In any of the cables hereinbefore described the conductors may be of such type that currents of frequencies well above the audible range travel substantially on the outer surfaces of the conductors. They may be, for example, either olid or tubular. In the latter case the thickness of the walls of the tube may be small compared to the diameter. The conductors may alternatively consist of a cylindrical assembly of conducting strips, tapes, ribbons, uninsulated wires or the like. The latter form of construction might be particularly desirable if the conductors are large and if a flexible structure is required. The four conductors comprising the cable may be either parallel or transposed at frequent intervals. In either case the conductors may be considered parallel for mathematical purposes and the optimum diameter and spacing ratios will be the same in either case. One method of transposing is to twist the conductors helically around the axis of the shield as illustrated. The shield, in addition to performing an electrical function by protecting the circuit from external induction, may be useful in affording mechanical protection to the circuit and thereby permitting the use of an air dielectric to a considerable extent. As the high frequency current penetrates into the shield and conductors very little because of skin effect, the electrical requirements are satisfied by a thin shield and thin walled conductors. Consequently, the thickness of the shield and the thickness of the walls of the conductors will ordinarily be determined by mechanical considerations. The thickness of the shield will usually be such that it does not enter into the problem of dete minin the optimum configuration of conductors and shield. The use of the shield will ordinarily make it possible where desired to allow the signals transmitted over the path to drop down to a minimum level determined by the noise due to thermal agitation in the conductors. Hence the use of a shield may allow the spacing of intermediate amplifiers at wider intervals: in the circuits than would otherwise be possible. Fig. 6 is a cross-section of a shielded two-pair cable, on which are indicated the principal variables: the radius a of the individual conductors, the internal radius 19 of the sheath, and the distance c from the axis of each conductor to the axis of the sheath. The last-mentioned dimension will hereinafter he sometimes referred to as the interaxial separation of the conductors and the sheath. Our object is to determine the ratio of the inner diameter of the shield to the diameter of the conductors and the ratio of the diagonal interaxial separation of the conductors to the inner diameter of the shield that makes the high frequency attenuation a minimum for any given inner diameter of shield. This will be done by first developing a general expression for the attenuation of such a system as a function of these ratios and then determining the value of these ratios which will make the attenuation a minimum for any predetermined size of shield. The attenuation is also a function of the conductivity of conductors and shield. Therefore, the values of the aforementioned ratios will be found for values of the ratio, l/0'0, of the conductivity of the wires to that of the shield, varyfor specific example, from 1 to 13. The ratio (Tl/60:1, for example, may correspond to a system of copper conductors with copper shield, and the ratio (Ii/00:13, to copper conductors with lead shield. Thus, a formula will be derived for the attenuation of a wave of frequency above the audible range propagated in a pair of long straight parallel wires of circular cross-section, with a similar pair at right angles to the first and with the two pairs enclosed symmetrically in a hollow conducting shield of circular cross-section the axis of which is parallel to and equally distant from the axes of the four wires. The system, therefore, consists of two balanced pairs. While the attenuation depends only upon the dimenions and electrical constants of the system, nevertheless arbitrary currents I1 and I2 will be assumed in the two pairs. The current I2 might, of course, be zero. That is, the second circuit may or may not be energized. In the shielded four-wire system there are two circuits available in addition to the two-side circuits. One of these is the phantom of the fourwire circuit, in which, of course, the two wires of each of the two side circuit pairs are used in parallel to form the sides of the phantom circuit. The other available circuit is that formed by the four wires in multiple with the shield as the return, the latter being sometimes called the ghost or wraith circuit. These circuits correspond to the three possible modes of propagation in a system of balanced pairs; that is, side circuit, phantom circuit, and sheath (or ground) return. Each mode may exist alone, or theoretically, any two or all three may exist simultaneously without cross-talk from one another. (See Propagation of periodic currents over a system of parallel wires by John R. Carson and Ray S. I-Ioyt, Bell System Technical Journal, July, 1927.) Formulae may be developed for the phantom and sheath-return circuits by mathematical analyses similar to that for the side circuit, and the proportioning determined to provide minimum attenuation for these circuits independently. Were all three of these circuits orany two of them to be used simultaneously the proportioning might be on the basis of the maximum total frequency range obtainable for agiven size of shield and any given maximum allowable attenuations for the circuits used. The shielded phantom circuit has an advantage over the other four-wire circuits and over the shielded pair on the score of the reduction which it affords in cross induction with neighboring circuits. On the other hand, in systems of the proportions of cable configurations, the attenuation in the phantom is about twice that in the pair for the same size of shield owing to the comparatively large ratio of the diameter of the wires to the spacing. In other words, in order to obtain the same attenuation for the phantom as for the pair or side circuit, the system must be twice as large as for the latter. As for the sheath-return circuit, while the attenuation is of the same order of magnitude as in the side circuit, the induction with neighboring circuits would be large. This circuit might, however, have special uses such as signaling. In the schematic cross-section of the configuration shown in Fig. 'l, conductors No. i and No. 3 form the first pair and No. 2 and No. 1, the second pair. The notation for coordinate systems and dimensions will be clear from Fig. '7. For convenience, the shield is assumed of infinite extent, its thickness being of no significance in the present problem. The conductors are assumed nonmagnetic and the leakage conductance is as sumed to be zero. It is well known that the attenuation, or, per unit length of a conducting system, when the leakage is zero and the irequency is so high that w L is large compared with R is given by where R, L, and C are the eiiective resistance, inductance and capacity of the system per unit length. Denoting by Z the impedance of the system per unit length, we have Z=R+iwL=2Z +4iw10g (2c/a)+AZ, (2) where Z1 is the internal impedance of the wire per unit length with concentric return and AZ the impedance increment or proximity efiect correction due to the presence of the shield and second pair of wires and the reaction of the wires of the first pair upon each other. The inductance L may be written i-i' e where Li is the internal inductance of wires and sheath and Le the external inductance of the system. By external inductance is meant that portion of the inductance which is independent of the conductivity of the conductors and which may therefore be determined by assuming infinite conductivity. Hence, we have With the notation, )WZIZ/ZC, ezC/b, a:radius of wires in cms., b radius of sheath in cms., c interaxial separation of wires and sheath in cms., lc specific inductive capacity of dielectric in electrostatic c. g. s. units, :1 for air, o velocity oi light=3 l0 cms. per second, ao conductivity of sheath in electromagnetic c. g. s. units, ai conductivity of wires in electromagnetic c. g. s. units, zi internal impedance of wire with concentric return, Zo=internal impedance of sheath with concentrio return, the impedance Z may be written, Upon the assumption of circular symmetry in the current distribution in the wires (equivalent to the concentration of current on the axes) the 5s in Formula (4) are all zero; that is, 2 1 z=2z sag -#4110 log (5) A Z representing the impedance increment due to the loss in the shield. Thus Formula (5) gives the total impedance when the Wires are very thin (filamentary) or when they are composed of insulated strands, and it is the same with or without the second pair. When the wires are solid, tubular or composed of uninsulated strands, 51, 50', and 612 represent the effect of the presence of the second pair of wires. Without the second pair of wires Z is given by putting 5i=60'=612=0. When the conductors are solid, tubular or composed of uninsulated strands, however, we may ignore the internal inductance, Li, of the conductors as compared to the external inductance Le of the system. In that case, that is, when Li/Le 1, Equation (1) may be written R/zL (6) On this basis the required attenuation is given by Where high frequency resistance of shield high frequency resistance of Wire For two pairs without the sheath, obtained by putting 22: or 6 0, in (I), We have the formula 0: R F' Where 1 1 F and The formula for a single pair shielded is obtained from Equation (I) simply by putting 50': 61'=512'=0 and Without the shield, by then putting :0. I proceed to the derivation of the impedance Z from the geometry and electrical constants of the system. The method is as follows (referring to the cross-sectional diagram of Fig. 7) The axial electric force Ez and the tangential magnetic force H0 (which will be represented by E and H. respectively) at any point in the dielectric are given in terms of a vector potential A and a scalar potential V by the relations, H :curl A (7) Putting F=iwA and 'y= 2, we have which must hold at the surfaces of the conductors. Representing by K and 'y the characteristic impedance and propagation constant per unit length, by V1 and V1 the potential at r1=a and 13:11, respectively, and by I1 the current in wire No. 1, we have 1) a K= I1'- 1 (a) 7K=R+iwL U Thus we have (1)+ (1) 3)+ (3) R+1wL-- (10) the Superscripts (l) and (3) indicating the values of E and F at the surfaces 11:61 and r3=a, respectively. We must now express E and F in terms of Ii. Inside the conductors, E must satisfy the wave equation. It may, therefore, be written ni Sin 9 i]: Ona inside conductor No. j and E Emma/ u cos n+ n i mm] inside the sheath where gm, am, he and hn are arbitrary constants and where and A110, Am, BnO, and Bnj are arbitrary constants to be determined by boundary conditions. We may immediately reduce the number of arbitrary constants by considering that the field at any point (Tmqbc) is the negative of the field at the point (10,=0+1r) 01' that We have, therefore, on revising the constants to avoid double subscripts, A cos min-i-B sin nqi F Z iwl log 11+ 2 (15) F 2u1'wI log 1 2-- Z Sm (16) F =2 iwI log 13" i COS Sm ms (17) F4: 21111012 log 14'' 2- COS g? Sin 11. n=1 The boundary conditions at ri a and 12:0. are DF MOE Tr Mar.- (19 and BF OE 1, 2 20 4 1' Wu J and at 70:1), @F MOE "670 was 21) and BF OE E0- "6E (22) To apply these boundary conditions, E and F must be transformed to the coordinate systems r1,1; T2,2; and T0,0. Performing this transformation, as we shall show below, gives for F in the neighborhood of r1=a, where Gn and H11 are expressible in I1, I2 and the arbitrary constants An, Bn, Cn, Dn, Wn and Wm. A similar expression is obtainable for F at rz a with, we may say, G11 and En corresponding to Gm and En. In the neighborhood of ro=b, F is given by 21 %)"0, sin nzto (24) n: where On and Nn are expressible in terms of An, Bn, Cn, Dn, I1 and I2. Introducing Equations (11), (12) (23), and (24) in the boundary relations GED-(22) and equating harmonic coefficients will give 12 simultaneous equations to determine the arbitrary constants An, Bn, Cm, 1311, Wu, Wn' and the six constants pertaining to the interior of the wires and sheath. Now turning back to Equation (10), it is apparent from the boundary relations that the harmonic terms in the expressions E +F vanish, leaving only the fundamental. From symmetry it is also evident, then, that We thus obtain (with I1=1) R+iwL 2(E +F )=2Z +4iw log :+AZ (25) where m 1 nr 42 D, sin I n=l C2 4- co 2 2n--l This completes the formal solution of the problem. However, as a straightforward solution of the doubly infinite set of equations for the arbitrary constants is not possible, the method of approximation which has been applied to analogous problems in Wave propagation over parallel conductors to obtain the correction due to proximity effect, will be given below. We shall first add the details which were omitted in the outline of the formal solution. The following relations among the coordinate systems are used to express G11, H, Gn, Hm, On, and Nu in the arbitrary constants An, B11, Cn, Dn, Wn, and Wm. These are derived in Note II of the paper Transmission Characteristics of the Submarine Cable, by Carson and Gilbert, Jour. Franklin Institute, Dec, 1921. Refering to Fig. 7A, we have cos no, (1)" 111- 12 n L 11 C05 log r =log 0 news 2 cos )(4 o s)+ i '1 722:1 COS 11(153 r2 2G) n -C l 2 C2 TB 0 Qn J& 2 I 2)".' Pl gsm mp S +2 1 n C2 sin 4 Q,, (35a) 15 Where n 1 n+2 n 1 n 2 n+3 Qn 1)7|[ n n+iwl l n+z ,y %l n+sw Qn=( n+( CL+1 .1 c and. So, So, TA, and TB will be clear from the log rS 1g 5 COS (Was similar expressions in Equation (35). 1 c 2 A Applying relations (32(34), F, in the neigh- 5(3 COS (3 borhood of 70:17 is given by, w 1 F: 2 21L- [W COS (217.1) +W2 1 sin (2n-l)gl+ m 211-1 I 2 3 cos (2n1) 4w 1 +2P/f i (-1)"2M 1 3 272-1 (9 1\ 4120A +21% 1 "2M ,0- ro Sm in o c B (36) In the present problem, Where a A1 211" 2A2 or 2 1! 0 (2n-2)(2n3) A A 011 0, 2=% 3 5 4 2! l +C2'P1 B 2 2B 40 and 1VIB= 5+ c 1! c TE Z (2 2 (2 3 Bin-1 3 or M2! 63 C- 68) :3, 53:0, Z We are new in a position to introduce E and F 4 4 in the boundary relations (19)(22) to obtain Applying Formulas (26)-(31), F, in the neighthe arbitrary constants. Putting ILIMOZ/LIZI, borhood. or r1=a, becomes equating harmonic coefiicients and solving, gives l i F--2,u 1w1' 1og 2c A,,+ where the equations (remembering that \=a/2c and (B C/b), aoeaezo .211 11;- when Z w 3; 1 R2752 QT;- 4120) But we have Simplifying, we get (When the arguments of the Bessel functions e) 20 are omittted 21 is to be understood with Jn and 2C fl"j 5 i with Kn.) The following method of successive 2m 4 approximations is found applicable to the solu- T z i tion of Equations (SW-(39). 8 4" .8 We represent AZ by the sum i J (1) 2 2 AZ:A Z+A Z+A Z+ D1 9 f 20 1+ 1W where the increments A Z, M Z, are ob- Z 4 2& tained by the following procedure. (ii-H 1+ e 1. Neglecting the summations in An and Dn a q A,,i 4 5 ..v 42 in Equation (39), to determine a first approxild- OE e matlon to We have, far 11:1 3. Now returning to the surface of the shield, 41-, we include the An and D11 series in boundary 2n-1=mmn-1 Equation (39). Then, putting N Since A 1) 0 u) Z 21 wK0 h B.) CD lm 2C 0- ZOKOI Z0 w en Z0 and d) We may write Z0 20 n2n-1= to obtain W1 in terms of Ai and D1 we have and 1) (1) w) 2 2 z1 (o) n=1 2 1 0 Now we may approximate AZ more closely by 42' j (4 addin the increment, 3 8Z0l e +410 log 1+6 .0) (07 L310) L (1) This impedance increment is exactly the same A 20 7 2c 2W1 (43) as that obtained when the second pair is absent, and writing 0 as is to be expected since the ignoring of the AZ:A Z-|-A Z (44) 0 2?\2 4e 8X2 2& d 2 #w 2 (1 w 25 H 6 2x 6 1 86 e 4X e 26 1e 1-x (1-e 1+i '1+e 55 +(1-2e )(13e +5e series in An and D11 is equivalent to the assump 0 tion of uniform current distribution over the surfaces of the wires (i. e., circular symmetry about the axes). Thus A Z represents the impedance increment if the wires are filamentary or if they are composed of insulated strands. 5 2. Proceeding to the boundary relations at T120, and i'z a, and putting We however, that the terms An /(20W, L n /(20 CW /3 may be appreciable. These are obtained from Equations (SW-(39) by putting Thus, a more exact value of M Z is given by (1) l o) Mug: 2% .1. 422 g t 31 (1) 4. Proceeding to the next increment in AZ we have e) (2) (2 o r (45) This degree of approximation includes all terms containing x Terms containing higher powers of A may be ignored. m2: 2 +4 2cW Thus we have Where F0, F1 and Le are given by Equation (4). Finally, Introducing R and Le in Equation (3) gives a as 'abscissae c/b for the case of a conductivity ratio 01/00, of unity. To obtain the attenuation, 0c, in decibels per mile, the ordinates, F, are to be multiplied by the factor 0.0466 1?? 1.96 Q 7;)- b Alp/Rf for copper wires with a'1=0.565 10 where :frequency in megacycles, b :radius of shield in centimeters, lc :specific inductive capacity of dielectric in electrostatic c. g. s. units (:1 for air), ao=conductivity of shield in electromagnetic c. g. s. units, 0'1 :conductivity of wires in electromagnetic c. g. s. units. The optimum dimensional ratios are thus seen to be c/b=0.49 and a/2c=0.15, giving b/a=6.8. Fig. 9 shows the optimum values of c/ b and b/a for values of 01/00 from 1 to 13, the dotted curves representing the corresponding optimum dimensional ratios for a single pair cable. These are the conditions for minimum attenuation when the inner diameter of the shield is fixed. It may be observed that the optimum proportioning ratios are independent of the frequency, dielectric con stant and absolute size of conductors. Fig. 8 shows the minimum value of attenuation in decibels per mile, when cri/ao l, to be or for a system of copper conductors, (1.9o /1 r/b)(1.475) The solid curve of Fig. 10 represents the minimum attenuation for the two pair shielded cable for values of al/ao from 1 to 13. To obtain decibels per mile, multiply the ordinates by the factor T 7 Ka for copper wires. The dotted curve represents the minimum attenuation in a single pair shielded cable. It is obvious that the attenuation of the system can be reduced by increasing the size of the shield, keeping the ratios b/a and 0/1) fixed. The diameter of the shield would probably be determined by such considerations as the maximum frequency to be transmitted over the system and the maximum allowable attenuation at that frequency. It will be noted that the attenuation in the two pair shielded cable may be made equal to that in the single pair shielded cable by increasing the radius of the shield about 10 per cent. It is interesting to note that the fixed ratios give fixed values of inductance, capacity and characteristic impedance regardless of the actual size of the system. Thus, by substituting the ratios 11/4; and 0/2) as given by Fig. 9 into Expressions (3) and i) and changing to practical units, the inductance and capacity can be obtained. They are, respectively, L:0.733 milhenry per mile and 0:0.0393 microfarad per mile when cri/o'o:l and k:1. The value of the high frequency characteristic impedance for the optimum configuration becomes K=Jm= 137 ohms Obviously, the data for the solution of the converse problem of the optimum size and proportioning of a cable to have a predetermined attenuation is also provided by Figs. 9 and 10. Thus, to design a two-pair cable of conductivity 0'1 with a shield of conductivity 00 to have a given attenuation 0c, introduce the appropriate F from Fig. 10 in Equation (I) to obtain 1) (in centimeters) ccrresponding to the given value of a (in decibels per mile). Then determine a and c from the ratios 0/?) and 17/6; in Fig. 9. It is interesting to note that the ratio a/c is practically constant with respect to the conductivity ratio. For example, suppose we require the optimum dimensions for an attenuation of 6 decibels in a system of copper wires within a copper sheath for a frequency of one million cycles per second when lc:1.0'7. We then have f l, (1:6, 7c:1.07. From Fig. 10, F=1. l75. From Equation (I), 20.50 cm.=0.19'7 in. From Fig. 9, c/b=0.49 and b/a:6.8 Thus, 0:0.0965 in. and 2a:0.058 in. In the determination of the configuration for minimum attenuation it was assumed that the value of leakage conductance was zero. However, in practice it will be necessary to support the two conductors and to keep them in the desired relative position with respect to the shield. This will require the use of a certain amount of dielectric mate ial inside the shield which will consequent introd. amount of leakthe average dielectric constant of s By making such supports out of materials having low loss and lov d electric constant and by spacing th as far apart as possible, it is possible to m" the effect on the attenuation, and conseque' by on configuration for minimum attenuation, negligible. However, if for any r ason is desired to st? port the conductors with respect the snield in a manner which introduces a relatively large amount of leakage loss, it is still poss ble in many cases to determine the values of 12/6; and for minimum attenuation. Thus it will. be shown that the configuration which results in minimum attenuation is independent of the dielectric loss and the average dielectric constant, provided that the value of the average dielectric constant is independent of the configuration of the conductors and sheath. At frequencies high enough so that 14 is large compared with R and w C is large compared with G2 the attenuation of a tra...smission system in which the leakage loss is not negliwhere the leakage loss, :ZTfpC, p being tn power factor and C k/L. Therefore, the high frequency attenuation is D 7 gape/ w/ T C is the capacity per unit length of the independent where system. This also is substantially of the dielectric loss. These conditions would be met by completely filling the space between the conductors and shield with a material, such as oil or a solid rubber insulation or else by using insulators made of thin flat discs of an appropriate insulation, such as porcelain or glass. A suitable insulator might also consist of a solid dielec ric, such as rubber in which ir has been entrapped. It the air bubbles are small and evenly distributed through the non-gaseous portion. of the dielectric, the average dielectric constant and the dielectrio loss can be made nearly independent of the diameter and spacing ratios of the system. If the value of the average dielectric constant varies with changes in diameter and spacing ratios of the conductors and shield, it becomes extremely difficult to obtain mathematical solution for the diameter and spacing ratios which give minimum attenuation for any fixed diameter of shield. However, when gaseous and nongaseous dielectrics are arranged in any desirable manner, the ratio of the inner diameter of the shield to the diameter of the conductors and the ratio of the interaxial spacing of the conductors to the inner radius of the shield will not differ much from the values given by Fig. 9. If both non gaseous and gaseous dielectrics are used, and are disposed in such a in nner that the boundary irfaces between different dielectrics lie along llowed by the flux in a homogeneous dielectric, "n configuration will apparently be the a gaseous dielectric. s of construction as those described involving the use of a partly or wholly non-gaseous dielectric may be desirable for either mechanical or electrical reasons. e conditions t must be satisfied for maxi- 1 high frequency characteristic impedance for either pair or a hielded quad can also be de termined. The high frequency characteristic impedance of shielded solid pair when the conductors are small compared to the shield is: the same as when the second pair is absent. For any given ratio of inner diameter of shield to diameter oi conductor the characteristic impedance becomes: For maximum characteristic impedance the expression must be maximized. This can be accomplished by talzirg its derivative with respect to E and putting it equal to zero. Thus we find that 6 .4186 for maximum characteristic impedance for any ratio of inner diameter of shield to diameter of conductor, providing the latter ratio is large. Ir", however, the conductors are large with respect to the shield, Equation (53) no longer holds. However, the position of the conductors with respect to the shield must be such as to minimize the capacity, since the capacity and high frequency characteristic impedance are in versely proportional to each other. t can be seen that as the diameters of the conductors approach. in size the inner radius of the shield, c approaches .5 for minimum capacity and hence maximum high frequency characteristic impedance. Thus, for any given ratio of inner diameter of shield to diameter of conductor, the ratio of the interaxial separation of the conductors to the inner diameter or" the shield should be between the limits and .590. For practical purposes a value of about .49 may generally be used to secure maximum impedance. t will be obvious that the general principles herein disclosed may be embodied in many other organizations widely difierent from. those illustrated without departing from the spirit of the invention as defined in the following claims. What is claimed is: 1. A transmission system comprising tour cylindrical conductors, a cylindrical conducting shield of predetermined diameter surrounding said conductors, one of said conductors being connected as a return for another to form a transmission circuit, said conductors and shield being insulated from one another, the relative dimensions and spacings of said conductors and shield being such that the high frequency attenuation of said circuit will be a minimum. 2. A transmission system comprising four cylindrical conductors, a cylindrical conducting shield of predetermined diameter surrounding said conductors, one of said conductors being connected as a return for another to form a transmission circuit, said conductors and shield being insulated from one another by a substantially gaseous dielectric, the relative dimensions spacings of said conductors and shield being such that the high frequency attenuation of said circuit will be a minimum. 3. A transmission system comprising four cylindrical conductors, a cylindrical conducting shield of predetermined diameter surrounding said conductors, said conductors being helically twisted around the axis of said shield, one of said conductors being connected as a return for another to form a transmission circuit, said conductors and shield being insulated from one another, the relative dimensions and spacings of said conductors and shield being such that the high frequency attenuation of said circuit Will be a n nirnum. i. A transmission system comprising four cylindrical conductors, a cylindrical conducting shield of predetermined diameter surrounding said conductors, one of said conductors being connected as a return for another to form a transmission circuit, said conductors and shield being insulated from one another, said conductors being of such a type that conduction of currents whose frequencies are substantially above the audible range takes place substantially on th surface of said conductors, the relative dimensions and spacings of said conductors and shield being such that the high frequency attenuation of said circuit Will be a minimum. 5. A. transmission system comprising four solid cylindrical conductors, a cylindrical conducting shield of predetermined diameter surrounding said conductors, one of said conductors being connected as a return for another to form a transmission circuit, said conductors and shield being insulated from one another, the relative dimensions and spacings of said conductors and shield being such that the high frequency attenuation of said circuit will be a minimum. 6. A transmission system comprising four hollow cylindrical conductors, a cylindrical conducting shield of predetermined diameter surrounding said conductors, one of said conductors being connected as a return for another to form a transmission circuit, said conductors and shield being insulated from one another, said conductors having walls of substantial thickness as compared with their diameters, the relative dimensions and spacings of said conductors and shield being such that the high frequency attenuation of said circuit will be a minimum. 7. A transmission system comprising four cylindrical conductors, a cylindrical conducting shield of predetermined diameter surrounding said conductors, one of said conductors being connected as a return for another to form a transmission circuit, said conductors and shield being insulated from one another by a substantially gaseous dielectric, said conductors being of such a type that conduction of currents Whose frequencies are substantially above the audible range takes place substantially on the surface of said conductors, the relative dimensions and spacings of said conductors and shield being such that the high frequency attenuation of said circuit Will be a minimum. 8. A transmission system comprising four cylindrical conductors, a cylindrical conducting shield of predetermined diameter surrounding said conductors, said conductors being helically twisted around the axis of said shield, one of said conductors being connected as a return for another to form a transmission circuit, said conductors and shield being insulated from one another, said conductors being of such a type that conduction of currents Whose frequencies are substantially above the audible range takes place substantially on the surface of said conductors, the relative dimensions and spacings of said conductors and shield being such that the high frequency attenuation of said circuit will be a minimum. 9. A transmission system comprising four cylindrical conductors, a cylindrical conducting shield of predetermined diameter surrounding said conductors, one of said conductors being connected as a return for another to form a transmission circuit, said conductors and shield being insulated from one another, the ratio of the interaXial separation of said conductors to the inner diameter of said shield and the ratio of the inner diameter of said shield to the diameter of each of said conductors being such that the high frequency attenuation of the circuit will be a minimum. SALLIE P. MEAD. Referenced by
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