US1817964A - Concentric conductor transmission system - Google Patents

Description

Aug. 11, 1931.

J. R. CARSON ETAL 1,817,964

CONCENTRI'CONDUCTOR TRANSMISSION SYSTEU med may 2s. 1929 2 sheets-met 1 Jgwmwsgmad Aug. Il, 1931.

J. R. CARSON ETAL CONCBNTRIC CONDUCTOR TRANSMISSION SYSTEM Filed May 23. 1929 2 Sheets-Sheet 2 www? www y Carson v BY ATTORNEY y Patented Aug. 11,1931

UNITED sTATEs PATENT OFFICE v.Toma n. cansoN, or NEW Horn. PENNSYLVANIA, Nn snm r. nnen, or maw ironic,I N. Y., assumons Iro enmarcan runrnoim AND 'rnnnamn conm.

A CORPORATION OFNEW YORK CONCENTRIG OONDUCTOB TRANSMISSION SYSTEI Application -led lay 28,

Ihis invention relates to a novel form of conductor structure employing concentric cylindrical conductors for the transmission of a wide band of frequencies with relatively v low attenuation. The invention particularly relates to an arrangement of the conductors such that a fairl uniform attenuation may be E obtained for a and of frequencies below a preassigned limit.

If a solid cylindrical conductor or a hollow cylindrical conductor having relatively thick walls is provided, ,with a returnconductor `comprising a hollow cylindrical conductor concentrically arranged with res t to the first conductor, and the two con uctors are separated by a dielectric consisting largely of air or other gaseous medium, the transmission line thus formed will have a number of desirable characteristics. Its attenuation at all .20 fr uencies will be quite low as compared wi the corresponding attenuation of open wire lines and cable circuits such as are now commonly used for telephone transmission. Such a transmission circuit may, therefore, be em lo ed for the transmission of a much wi er and of frequencies than has been posc sible with types 0f transmission circuits heretofore used. It also has the advantage that it is substantially free from interference from neighboring conducting systems and in itself tends to produce but llttle interference into adjacent transmission circuits.

The present invention is, however, more particularly concerned with the type of conducting system in which the two concentric conductors are either thin copper hellslor i else comprise two concentric cylindrical structures of 4relatively low conductivity with o a thinlskin of good conductingm'aterial on the outer surface of the inner conductor and the inner surface of the outer conductor. The last mentioned arrangement is based upon the fact that in a concentric conductor system v415 the current at'the higher frequencies tends to crowd to the outer. surface of the inner conductor and the inner surface of the outer conductor. Applicantshave discovered that ifv the walls of the concentric conducting cylinders are made sufficiently thin, the attenualtransmitted over the 'outer conductor wi I 4cordance with the other mode the intermedi- 1929. Serial No. 365,515.

tion will be substantially uniform over awide range of fre uencies up to an upper limitin frequenc w ich is dependent u n the thiciness of t e conducting walls. n en- .eral, the system may be deslgned'so that V1f it is desired to obtain uniform attenuation up to a preassigned frequency, the thickness of the conductin walls will bear a definite relation to that requency. For exam le, Vwith a conductor having conductivity ,i the -frequency f and the thickness d of the wall 1n centimeters be approximately related in accordance with the formula `the attenuation will be substantially uniformV be emI loyed., In other'words,if the thick- 76 nessjo the walls d is so chosen that the attenuation will be substantially uniform up to a' frequency f, the increase in attenuation from frequency f up to frequency 4f will be quite tolerable.

As .an alternative varrangement itis proposed, in accordance with t e present invention, to Vobtain a fair degree of equalization to a concentric conductor stem b employing three or more concentrlc cylin rical conductors@ For example, a concentric conduc.- tor system may comprise an inner, an intermediate and an outer cylindrical conductor, and a frequency band ma be s lit. up into two sub-bands,- oneof whic will e, in eect, transmitted over a circuit vcomprising the inner conductor with the intermediate con-l ductor as a return, the other sub-band bei the intermediate conductor as a return. Such a system will have in general two modes of propagationA-In accordance with one m'ode the intermediate and outer conductors act as a return for the 'inner conductor, whilein acl l'oo ate and inner conductors act as a return for the outer conductor.

Applicants have found that the attenuation in accordance with these two modes of 5 propagation will be substantially the same as though the system were treated as two inde-` pendent conducting systems, one of which comprises the inner and intermediate conductors and the other of which comprises the intermediate and outer conductors. At the higher frequencies ,the return currents, in accordance with the two modes of propagation, tend to concentrate respectively at the two surfaces of the intermediate conductor, and it is unnecessary that these two surfaces of the intermediate conductor be separated by an insulating material. It is, therefore, quite feasible to so connect the conductors at the terminals that one band of frequencies will be'transmitted over the inner conduct-or with the intermediate conductor as a return, and the other band of frequencies (the higher band) will be transmitted overthe outerlconductor with the intermediate conductor as a return, thus attaining a substantial degree of equalization as between the two bands by reason of the fact that the amount of conducting material employed in the intermediate and outer conductors for the transmission of the higher frequency band will be much greater than that employed for the lower frequency band.

The invention will now be more fully understood from the Y following description when read in connection with the accompanying drawings, in which Figure l shows curves illustrating the transmission characteristics of a conducting system comprising two thinwalled concentric cylindrical conductors; Fig. 2 shows curves illustrating the transmission characteristics of a concentric conducting system comprising two concentric cylindrical members of relatively low conductivity with a thin skin of high conductive material upon the inner surface of the outer cylinder and upon the outer surface of the inner cylinder; Fig. 3 shows the transmission characteristics of a system similar to that of Fig. 2 arranged to attain a substantial degree of equalization of attenuation by the emv ployment of more than two concentric conductors; while Fig. 4 shows the transmission characteristics of a system of multiple transmission conductors each of which comprises a c lindrical conductor with thin walls.

n order to understand the principles of the invention it is desirable to give a general mathematical treatment from which may be derived four general formul applying to four general cases,as follows:

System I. A thick copper core and return sheath:

System II. Two thin-walled copper shells. System III. Two lead conductors with copper skins.

System IV. Three co per shells.

It will be understoo of course, that the mathematical treatment is general and the invention is not limited to the use of copper and lead as -relatively good and relatively poor conducting materials, these particular materials being merely chosen for purposes of illustration. l

Consider a long cylindrical conductor or core surrounded by another cylindrical conductor (the return conductor) coaxial with the first and separated from it by a layer of dielectric. The transmission of periodic currents over a system of n such coaxial cylinders is analyzed in detail in the paper Transmission characteristic of the submarine cable by John R. Carson and J. J

Gilbert, Journal Franklin Institute, December, 1921.

In the present case, denote by E2 and El the electric forces per unit length at the inner surface (radius=b) of the return conductor, and the outer surface (radius=a) of the core, respectively, and let I represent the current in the core and y the propagation constant. Then, in accordance with formula (l5) of the paper referred to above,

and w=2r times frequency, f. Now, Writing so that Z1 and Z2 represent the internal impedance of the core and return, respectively, and putting G=O, Equation (l) becomes and wemywz' But theterm (Z1+Z,)/1L is usually small in comparison to unity. In that case,

a proximately, or substitutin for L and t eir values from llquation (1%, K

System I Thick copper'core and sheath eration may comprise either a solid cylindrical conductor or a hollow cylindrical conductor whose walls are comparatively thick with a return or sheath of suitable conducting ma. terial, the sheath being cylindrical and arranged concentrically with respect to the core, and its walls being of suicient thickness to approximate the effect of a wall of infinite thickness. The two conductors (the lcore and the sheath) will preferably be separated in such a manner that the intervening dielectric will be equivalent to a gaseous dielectric.

It is well known that the internal imped- '25 ance of a long cylindrical wire .is given by A Jo(zl) Z "2"%J'.e. 4) where so 21-=W tal,

ai s 41I1', pf=permeability of the conductor, klgconductivity of the conductor,

J,(:c|) =Besse1 function of the irstkind of zeroth order, l A dJ(zl) i o #1,(21) "-T- i y y See,`for instance, Jahnke and Emde Funktionentafelnp. 143; also p. 717 of paper by Carson and 1lbertabove referred to. 5 Similarly (p. 717, Carson and Gilbert paper), the internal impedance of the outer or return conductor of such electrical thickness that it may be assumed infinite in extent, is given by Y '50 50G/2) where i v ys'ibJ-ar i 2:4'm`al2,

p,=permeability of conducting material, y f o0 )l,=conductivity of conducting material,

lKy l2) I=Bessel function off second kind Qf zeroth order,

'ft-.1 l Kay c dy At the vefy high. frequencies considered- The conducting system here under consid-y here, w1 and y, are so large that the values of the Bessel functions for very large ar ents maybe substituted in Equations (gnaliid (5), namely:

These give, after simplifying,

l Z2 b I, (7)

Now, putting p1a2=a=1 (since we are concerned with non-magnetic substances) andA 1=A3=A and remembering that d=thick ness of shell, p=b/a, t=/v2 and n=41rd y/ fh, then substituting (6) and (7) in (3) gives Formula I.

System Il.' Taba thin copper shells y The conductor arrangement here considered comprises two hollow cylindrical shells with thm walls of copper or other ood conductin material, the two shells eing arrange concentrically and one actingas a return for the other. In the following mathematical treatment the outer cylindrical shell will be treated as a return for the inner shell, although this is purely conventional. As both the inner and outer 'radius of each conductor is of importance here,fin the following formul a1=a is theouter radius and bi the inner 105 radius of the inner shell, while afis the outer rradius and b2=b is the inner radius of the outer shell. The impedance of a tubular conductor with concentric return outside is given by no Z ziieMa (3l) l. I l x'l Ml (il) where l MJI) =Jo (3x) +3Ko (5Fl) l M'.(r1) =J' (w1) +8K. (mi) s J' (yi) K'. (1li) In :ian/'E y; f v l (See formula (19), Wave propagation over parallel tubular conductors by S. P. Mead, Bell System vTechnica-l Journal,` April, 1925.)

- When the return is inside, the internal impedance 1s given by interchanging :vand y 13 and reversing the sign, or, for the inner conductor ZllQiwMo (y2) y Z 'aya (9) Equations (8) and (9) may be written,

. Zl-:ZolFl and Z2=IZ2F2 (11) Where Z"1 and Z"2 are ZL and ZL of System I. Now, upon writing the limiting Values,

i701@ Il afb' 1+1 /v; Jill/l .leeft te p Jaz) Klo E /b/)(1+1)'N; K0 Ico) H/ae Kee) JoQl/l f-bl)(1 i] (12) Jaa* te a W K10 E -n )(m a' )H2 Klvcy) (Le Where a=a\/ and b =b\/ (when :A )u y2=1) Fx and F2 become 1 2 l 1 -I- m F1 =F2=1 m (13) Where m e-v; (af-bouw,

L: (l'li) Thus, Formula II follows immediately from Equations (10) to (13) and (3) ,/EijLpMHQHm (y gp 10g p 4nd i-wLti/"w/v (H) Note that when m- O, which would be the case When n is large, i. e., when the shell is electrically thick, F1=F2 1 and Formula II reduces to Formula I. (From the relation n 4in-dw it is of course evident that n will be large whenever the frequency f, the conductivity A, or the thickness d of the shell is large.)

System III: Two lead conductors with copper skins ofthe inner lead core. The copper skins are A applied to these two`surfac'es because at high frequencies the current tends to crowd to theinner surface of the outer conductor and to the outer surface of the inner conductor, where a2 and bz'are the outer and inne!` radii of thecopper skin, while a, and b, are

due to the so-called skin effect.

on its inner surface. p ance Z2 of the outer bi-metallic conductor is defined as before by the relation Consider the outer lui-metallic conductor comprising a lead sheath with a copper skin The internal imped- Eg: -z2l, (14) I being the current in the core or inner bimetallic conductor and E2 the electric force Where ug and og are complicated expressions in Bessel functions involving the constants and dimensions of the copper skin. The ratio Ig/I is required. Expressions analogous to (14) for E2, the electric force at the outer surface of the copper skin and for E3 at the inner surface of the lead sheath, are

Where I3 is the current in the lead sheath. But I+I2+I3=0, as there is no current outside of the lead sheath and, by the lawof the continuity of the tangential electric force at the surface of separation of two conductors,

EzzEa.

Thus I I 'lL/3+'U2 and, from (14), (15) and (17),

For the very high frequencies which We are considering,

r lILV-b, 41rhd 1--m (1+i) 15eme the corresponding dimensions of the sheath. Here, as before, l

l I. tI-41am ,-nductivity of copper skin d =thickness of copperskin msc-(144) )mL-constants'of outer sheath (permeability and conductivity) is Note that when 'zo Equation (i7) gives l ,5 or the current is confined to the copper skin and f Wheif n is so l'arge, i. e.,/the frequency so high, that 1ra-0, the current is confined to the copper akin and Z1='v which is identical with is very man with w lz. ma al,

respect v with negligible error, we have also,

Thus, from (21) and (18),

Z1=P Z2, (22) and, we may write where and, as in (19),

` u, i n(1,+ i+1.

Thus, on substituting Z1 andZ, from tions (22) and (23) in Formula (3), mula III follows immediately; ynamel 1 i3 n(1+'i) 1+m logp 47M 1m mwN/v (iii) If, however, the bi-metallic core is replaced by a copper shell alone, Z1- is given by 'Z1='v1=pu, l I Z,+Z,=(F+p)u', andr F III should be replaced by so that It isinterestingto note that when fmO,

v Formula III becomes Formula I, indicating that when the freiuency is so high that ,the current is confine entirely tothe copper,

the `thinness of the copper itself is no longer l vis significant, that is, the copper skin itsel electricall thick. When Ao=0, Formula III becomes ormula II.

System IV: Three copper shells ioo 'y The system here considered involves three concentric cylindrical conductors, an inner conductor, an intermediate conductor and an outer conductor, se arated by two dielectric spaces which shol d be practically equivalent to air, or other gaseous dielectric. The three conductors, as will be shown later, may be treated as equivalent to two conducting systems, vone involving the outer conductor as a return for the intermediate conductor and the other involving the intermediate con-i v ductor as a return for the inner` conductor;

From this standpoint the intermediate condnctor may be formed of an inner and outer skin of good conducting material upon a shell of some low conductingmaterial such BS lead, or the two skins may kbe separated .the outer conductor may comprise a skin upon the inner surface of a lead sheath and the inner conductor may comprise a conducting skin upon a core of lead. At high frequencies, however, as will more clearly ap. pear later, the inner and outer skins of the mtermediate conductor may not be separated but may merge together w1thout in any way interfering with the normal transmission characteristics of the system.

In this system of three conductors separated from one another by two dielectric spaces, an equation analogous to (l) holds for each dielectric space. Referring to the conductors, beginning with the innermost, by subscripts 1 2 and 3 respectively, and distinguishing the potentials at the inner surfaces from those at outer surfaces by primes,

,Y2 i60 012 and Here, if b1, b2 and b3 designate the inner radii of conductors l, 2 and 3, and if a1, a2 and a3 designate the outer radii, then by putting ba/az: 2vMal-:Pa

2 10g p and x 10g p.

Introducing in (25) and (26) the linear expressions in terms of I1 and I2 for E1, E2, E2 and E3, gives two equations to be solved simultaneously for Iz/I1 and A2. Eliminating Iz/I1 gives a quadratic in y2, the two solutions y. and yb corresponding to the two possible modes of propagation in the system. The mode of propagation accordin to y. involves the conception of the interme' iate and outer conductors acting in parallel as a return for the inner. conductor, while the mode of propagation in accordance with yb involves the idea of the inner and intermediate conductors acting in parallel as a returnl for the outermost conductor.

Solvin (25) and (26) for w2==y2+w2L0 instead o directly for y gives,

where, as above, using the general subscript i in place of 1, 2 or 3 as the case may be Fl 1 +1) Lirica,

b, 4nd i-m bi Then 2 2 ew x 1: *e* 1 "wel and, to a good approximation,

1/Ew 1 272 'Y- v (l 2 wz/v2 (28) Then, from Equations (27) and (28)', Formula IV follows immediately; namely,

Where 1 b3 b3 2 16m *p G ail if# 1 E JFT ffii 12 1 +p 2l Note that when the frequency is high so that m 0, G approaches either of two values,

l .b2 or 1. Therefore si miei@ Lt@ 74b2vlogp 4nd l-mdMl'/E w/v an i l+p n(1+'i)1+m 7-4b3v log p 41nd 1-m Transmission characteristics (IVa) We have now develo ed general Formul I, II, III and IV for our different cases of concentric conductor systems. We w1ll now show how from these equations the attenuation and phase distortion may be plotted with respect to a function of the frequency 'tofproduce curves which are perfectly general or a. conductor system of each type, regardless of its dimensions.

Considering first System I, it is well known that y, the propagation constant per unit length of any conducting system, may be expressed A y=a+i (29) where a is the attenuation constant per unit length and the phase constant per unit length. For convenience, the phase constant may be. separated into two components,d one of which proportional to uency and the other of which is a much smal er component:

repmenting the phase distortion. Thus, v Y

where l. is the phase distortion and is lthe component proportional to frequency which may be expressed 'Ba-41e; (29) we have i v=a+i(|+=) (32) From Eqiliation (32) and Equation (I) assumlng t at =1, as will be the case w ere the dielectric is air or an equivalent material, q.

.,dynein) Hg- (as) it is evident from Equation (33) that we may I write Equatin the real arts and the imaginary parts of quation 34) we havel L 1 P. ,1 l a 4 bvlogp m n (35) and 51" 4b log p'4fil)" (36) From Equations (35) and (36) it is clearthat a and ,81 may be plotted as the same straight line, as shown for example by the solid line of Fig. 1. The curve of Fig. 1- may betaken as representing the values proportional to either a or 1 plotted as ordinates against the various values of (mlm which is common to both a and ,81, as shown I by Equations (35) and (36)'. The actual ordinates used in plotting the curve 10 were obtained by first dividi out this factor;

The values of a and 1 wi be in c. g. s. lunits mile.

and, therefore, to obtain the attenuation and phase distortion per mile it is necessary to multiply the ascertained values of a and 1 by .161X10, the number of centimeters in a It' isrinteresting to note that the `factor 1+p) /log p has 4a minimum when p=3.59.

onsequentl'y, both the attenuation and phase distortion will be a minimum when the ratio b/a=3.59. Assuming this optimum ratio and 2% inches for the inside dlameter of the sheath or outer conductorz when f=10 we have a=0.756 TU per` m1le, 1=0.07 and 2=33.7 radians per mile. Hence, the hase distortion is practically negligible an the attenuation is comparatively small for a freuency of 10 cycles. This value of attenuation, it will be seen, gives a current'ratio of 1/10th in about 35 mlles.

Coming now to System'II, it is evident that an equation in terms of a and l may be obtained from Equation (II in a manner lanalogous to that by which quation' (34) was o tained from Equation (I), This equation is as follows; I i 'i `[gl-i-pn-t'i) 1lm y 10g p 41|' 11n.l ail-'wl (37) Equating the real part of the left-hand terni of Equation (37) to a and the imaginary part to zl, it will be found that will be a common factor to both a and ,81.

Dividing both a and ,B1 by this factor and Aplotting curves corresponding to a and l We obtain the dotted curves 11 and 12 of Fig. l, `these curves representin the case of two thin shells. As in the case o curve 10, the values of a and 1L as given by the dotted line curves must be multiplied by the above factor to give the true values of the attenuation infTU and the phase distortion in radians.

It will be noted that thedotted curve 11 (which shows how the attenuation a varies with respect to frequency) departs but little from constant attenuation up to v alue of n=.51r, soA that we have as a characteristic of the thin shell type of circuit substantial attenuation equalization up to the frequency corresponding to the value n=.51r. Remembering Athat s 'It 41rd1ff), and setting .5=4d1/f 6.06 x10-4, where for copper A=6.06X10, we have 25 s f=a ap roxixnately as the frequency up to which su tantial equalization is obtained. This relation is the criterion for determining the thickness of copper conductor necessary to equalize up to any given frequency.

Again noting the shape of the curve 1l, it will be found that even up to a value of n=1r the increase in attenuation is quite tolerable. On the assumption that we will tolerate the amount of increase in attenuation indicated at 1r, we have approximately becomes the criterion for determining the thickness of copper conductor (,\=6.06 104) necessary to equalize within the assumed limits of variation up to a given frequency. For example, for the case where f=10", we have d Tf1-06 centimeters approximately.

If in Fig. 1 the curves 11 and 12 were plotted for higher values of n, it would be found that at a value of about n= 1.51r the curves 11 and 12 reached their common asymptote,

walls, Aand a return conductor or sheath likey wise comprising a thick-Walled hollow cylinder of lead or other material of low conductivity, with a thin skin of copper or other good conducting material upon the inner surface of the outer lead sheath and upon the outer surface of the lead core. From Equation (III) it will be evident, by analogy to the treatment already applied to Equations (I) and (II), that the factor is' again common to both the attenuation a and the phase distortion l, as lobtained from Equation (III). With this factor out, the

corresponding values proportional to a and v ,81 may be plotted as shown by the curves 11 and 12 in Fig. 2. Comparing these curves with the curves 11 and 12 for the case of thin shells without the lead sheath and core, it will be seen that there is some increase in the phase distortion due to the lead, and that the equalization of attenuation at different fre'-V quencies is not so good as in the? case of the thin copper shells.

If, however, the lead core with outer skin of proximating those of system II, as is indicated by the curve 12 of Fig. 2. The curves 11. and 12" are obtained by substituting for F 1n Equation (III) the factor Frlp 1 -ip as was previously indicated in the neral mathematical treatment relating to ystem III (see particularly the comments immediately following Equation III).

Inthe case where the lead is employed in connection with both the inner and outer conductors, as well as in the case where it is only employed in the outer conductor, the values of a and ,B1 approach their values for thin copper shells alone when 'n is in the neighborhood of 1r, as will be clear from the curves of Fig. 2. At this point, however, the current is practically confined to the copper, so that a and ,L rapidly approach thelr values for thick copper conductors. If the curves were plotted for higher values of n, it would be found that they all reach their common asymptote, a straight line corresponding to 10 of Fig. 1, at about 1.51. v

At frequencies as high as those we are here considering (from the neighborhood of 100,000 cycles to 1,000,000 cycles or more), a lead sheath of the ordinary thickness, which is about l/Sth of an inch, will serve as a shield from interference. For a frequency of 10 cycles and a thickness of 1/8th inch,

(In the foregoing expression 2.54 is the number of centimeters in an inch and .444)(10 is the conductivity of lead.) The ratio of the electric force E at the outer surface of the lead to the electric force E at the inner surface, which is roughl a measure of the protection against inter erence, is proportional to en/z, which is less than 2 per cent. in this case, and'rapidly decreases for higher frequencies.

When for mechanical or other reasons it is necessary to make the copper skin somewhat thicker than is required for good equalization, as described in connection with systems II and III, or when it is desired to extend the frequency range over which equalization is obtained so that th'e corresponding' values of a no longer lie on the equalized portion of the curve, the attenuation may be substantially equalized by employing a multiple concentric conductor system such as outlined System IV. As has been under the headitl out, the intermediate conpx'eviouely poin meen curve ab is (over the ran ductor may lead or some exible insulatmg material with a skin of high conductivity on both sides, or it maybe composed entirely of a ood. conductin material, such as copen, by dividing the frequencyrange inner conductor with the intermediate conductor as a return and the intermediate conductor with the outer conductor as a return) considerable attenuation equalization is obtainable. This is due to the fact that the attenuation is inversely proportional to the inner radius of the outerof the two conductors (see factor b in Equations (I), (II) and and factors b2' and b, in Equations IVa) and (IVb)). If, .for example, the

cuit having the larger b. This is illustrated. t in F' 3. The three-conductor s stem'is in this figure shown as comprisin t ree cylindrical members, No. 1, No. 2 an No. 3. The lower frequency band 'is symbolically represented at G. as being applied between conductor No. 1 and lguonuctor lio.1 2,a'hile the higher frequency an 1s s o 1c y represented at' l, as bein appsligd between conductor No. 2 and con uctor No. 3. p Treating the two transmission systems as y inde ndent systems and employing Formula the attenuation for .the inner circuit is represented by the group of curves designated a. and the attenuation for the outer circuit is indicated by the curve designated ab. These curves are plotted on the assumption that b., the radius of the inner surface of shell No. 3, is twice bg, the radius ofthe inner surface of shell No. 2. Assuming the copper skin to be 0.01 inch in thickness, when f= In the group of curves designated a. inFig. 3, the strai ht line curve represents the attenuation or the case when the inner and intermediate conductors comprise two copper cylinders with thick walls. The solid line curve 21 represents-the case where the conductors No. 1 and No. 2 are thin-walled copper shells, while the dotted line curve 21 represente' the case for a system in which lconductors No. 1 and No. 2 arelead conductors 'with co r skins on their contiguous surfaces e proximity of curves 21 and '21l` when n 0.51r indicates that the current in that region is almost entirely confined to the copper so thatthe presence of the lead' makes practically no difference and the convergence of .the two curves with the straight line at about 1.3 yindicates skin conduction. f The plotted) a stra' ht curve indicating at at the high rel l a clesinvolved the transmission over conab actors No. 2 and No. 3 is-entirely confined to the two circuits thus formed (the .tenuation' curves are the copper skin. Obvious] therefore, some other material of low con uctivity might be substituted for the lead between the two copper skins of conductor No. 2,- or the entire conductor might be solid copper. In the latter case it would, however, be necessary to use selective apparatus at the terminal to separate the two frequency ranges involved;

The curves' 20, 21 and 21 are not plotted in Fig. 3 for values of n lower than .5-1r. The curve 20, however, continues as a straight line at the lower frequencies justas did the curve 10 kof Fig. 1. The character of' curves 2,1 and 21 for values of nlower than .51: may be obtained from curves 1-1 and 11 of Fig. 2 by multiplying the ordinates lotted inthe latter ligure by 2. This is for t e reason that in the case of the conducting' s stem plotted in Fig. 3 it was-assumed that t e inner diameter b, of conductor No. 34 was the same as the inner diameter vb `of the outer` conductor of Fig. 2, while in Fig. `3 we are further assuming b3/b2=2. p

Returning again to Fig. 3, it will be noted that a., as lndicated by curve 21, increases relatively from 4 at n=.51r.` to 8 at n=1.3vr, thev latter corresponding to a frequency of about 2.5 1O5 cycles per'second. Now, if this latter frequency were impressed between the two outer conductors instead of between the two inner conductors u, the attenuation would be reduced by the factorbz/b, which, in the case assumed in the drawing, is 1/2.

Consequently, if all frequencies from 2.5 X 10i lw to 10Q/are impressed on the outer circuit, the attenuation a infthis band will also increase in relative value a proximately from 4 to 8. On the other han if the outer circuit comprising conductors No. 2 and No. 3 had been used for the whole frequency range, the increase in attenuation would befrom about 2 to 8.

The ranve of variation in attenuation may be reducedo by increasing the number of intermediate conductors. The number is,of course', limited by the overall size of the system, andthe absolute value of the attenuation will naturally increase as the ratio of the diameters of the outer and innermost 1.15

circuits increases. y

In the fore oing discussion of Fig. 3, it has been assume tems (conductor No. 1 with conductor No. 2 as a return and conductor No. 2 vwith conductor No. 3 as a return) may, without subthat the two conducting sysstantal error, be treated as two independent conducting systems. Consequently, the curves a. and a., 4in Fig. 3 were plotted b y using Formula (III). How` littleerror 1s involved in this assum tion will be clear' from a consideration o Fig. 4.- Here ati lotted or a system 1nvolving `conductors o. 1, No... 2 and No. 3, .each comprising a thin-walled copper shell.

The radii for the ,several shells were v'so' Curve 41 other,

chosen that the value of the ratio p for minimum attenuation is obtained. In other words, bs/az and Z22/a1 are both made equal to 3.59. As it happens these particular valuesarenotwellchosenfromlthestand int of equalization of attenuation, and etter equalization would have been obtained if the radius of conductor No. 2 had been made larger. However, this does not affect the point which is now being made, namely, that no substantial error is involved in the assumption that the three-conductor ,system may be treated as two two-conductor systems. y

By the use of Eqluation (IVa in a manner analogous to t at alread escribed in connection with Equation (I the full line curve 31 is obtained. This curve represents the attenuation when the s stem is employed with conductors No. 2 andyNo. 3 in parallel as a return forconductor No. 1. The dotted line curve 31 of Fig. 4 is plotted in accordance with Formula (II) for the case where conductor No. 2 acts as a return for conductor No. 1. The close approximation of the two curves is evident from the drawing.

In a similar manner the curve 41 of Fig. 4 is plotted from Equation (IVb) and represent-s the attenuation when the i conductors is used with conductors No. 2 in c. 1 and ,parallel as the return for No. 3.

No. 2 plotted from`Formula (II). As before, the two 'curves closely Va proximate each and in both cases when n is in the neighborhood of vr or larger, the two sets of curves become vpractically identical. It is, therefore, evident that Ywe are justified in treating any twoadjacent conductors, when used as a transmission system, as though the third conductor were not present.

As previously stated, by making the radius of conductor No. 2 larger than was' chosen for thenparticular curves lotted in Fig. 4 the attenuation a.' would e lower and the attenuation ab would be higher, so that a fair degree of equalization of attenuation would be obtained by transmitting the lower band of frequencies over one air of conductors and the higher band of) frequencies over the other pair, as described 1nk connection with Fig. 3.

It'will be obvious that the general prin- "ciples herein disclosed may be embodied in many other organizations widely different from those illustrated without departing from the irit of the invention as' defined in the fol owing claims.

` Whatis claimed is:

1. In a conducting system for the communication of intelligence, a pair of conductors in the form of concentrically arranged cylinf drical shells of conducting material the thicknessl of the AWalls being^proport1onedl stem of Y represents the attentuation for conductor No. 3 as a return for conductor'v quency with res t to a reassi ed f uency, so that a bapld of frelquenciegsilfrcnliegero up lto said preassi ed fr uency will be'transmltted -with'su stantiilly uniform attenuation and negligible phase distortion.

2. In a conducting system for the communication of intelligence, a pair of conductors in the form of concentrically arranged cylindrical shells of conducting material, the thickness of the walls being proportioned with respect to a preassigned frequency substantially in accor ance with the relation where f is the preassigned frequency and d is the thickness of the wall in centimeters, whereby all frequencies from zero up to f will be transmitted with substantiallyfuniform attenuation and negligible phase distortion.

3. Ina conducting system for the communication of intelligence, a pair of conductors in the form of concentrically arranged c lindrical shells of conducting material, the thickness of the walls being proportioned with respect to a preassigned frequency substantially in accordance with the relation 4. In a conducting system for the communication of (intelligence, a pair of conductors in the form of concentrically arranged cylinders, the outer cylindercomprising a skin .of highl conductive material on the lnner sur ace of a sheath of less conductive material, .the thickness of said skin being proportioned with respect to a preassigned frequency, so that a band offreuencies from zero up to said reassigned re ue'ncy will be transmitted with substafnf tial y uniform attenuation and negligible phase distortion.

5. In' a conducting system for the communication of intelligence, a pair of conductors in the' form o f concentrically-arranged cylvinders, the outer c linderfcoml risin a skin y P g of highly conductivematerial on the inner surface of .a sheath of less conductive material, the thickness of said skin being proportioned with respect '.to a preassigned fra substantially in accordance withthe relation 1 Fm where f isthe 'preassigned frequency and 'J Alszo is'the thickness of the wall in centimeter-sy whereby all frequencies from zero `up to f lwill be transmitted with, substantialll unistorportioned with res ect to a preassigned fre-` quency substantial y in accordance with the relation 1 z f'w where f is the preassigned frequency and d is the thickness, of the Wall in centimeters, wherebyk all frequencies from zero ui) to f/4 will b e transmitted with substantia y uniform attenuation and the increasein attenuation of frequencies from f/4 to f will be less than fifty per cent.v

7. In a conducting system for the commu-y nication of intelligence, at least three cylindrical conductors concentrically arranged,

the inner and intermediate conductorsA being' connected to form one transmission circuit,

and the intermediate and third conductors .forming another and independent transmission circuit.

- ductors 8. In a conducting system for the communication of intelligence, at least three cylindrical conductors concentrically arranged, the inner and intermediate conductors being connected to transmit one range of frequencies, and the intermediate and third con-l n.ductors being connected to transmit another range of frequencies.

9. In a conducting system for the communication of intelligence, at least three cylindrical conductors concentrically arranged, the inner and intermediate conductors being v connected to transmit a lower of frequencies and the intermediate and 'rd conbeing connected totransmit a higher range of frequencies.

In testimony whereof, we'have ed our names to this specification-this 1 day of May, 1929.

JOHNR. CARSON. SALLIE P. MEAD.

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