US1815254A - Shunt type impedance equalizer for any smooth line - Google Patents

Description

July 21, 1931.` R. s. How 1,815,254

SHUNV'I` T-Y-PE IMPEDANCE EQUALIZER POR ANY SMOOTH LINE Filed NOV 20, 1929 2 Sheets-Sheet l July 21, 1931. R. s. HOYT 1,815,254

I SHUNT TYPE IMPEDANCE EQUALIZER FOR ANY SMOOTH LINE Filed Nov. 20, 1929 2 Sheets-Sheet 2 I l W Z .Rl Rl -Z' R;

Z5 Z7 l5 55 Z4 65 67 G6 .5"

y /67 {Yy/L9 20 22 INVENTOR E. Jg/mf BY W ATTORNEY Patented July 21, 1931 srArEs PATENT GFFCE RAY S, HOYT, OF RIVER EDGE, NEW JERSEY, ASSIGNOR' TO ANIERICAN TELEPHONE AND TELEGRAPH COMPANY, A CORPORATION OF NEW YORK SHUNT TYPE IMPEDANCE EQUALIZERVFOR ANY SMOOTH 'LINE Application filed November 20,-1929. Serial No. 408,578.

lt is well-known in communication engineering' that the characteristic impedance (iterative impedance) of a smooth line varies considerably with frequency, over the voice liffrequency-range, particularly toward the lower end of this range, though at high frequencies th-e impedance approaches a constant resistance.

The term smooth line here includes, as

lusual, any electrical transmission line whose 15J open-wire lines, non-loaded cables, and uniformly loaded cables (aerial, underground, and submarine). As here used, the term smooth line will be understood to include also any line which is effectively smooth in 20 the sense that over the contem lated frequency-range, its characteristic impedance is approximately the same as though the line parameters were uniformly distributed along the line; thus, for instance, a periodically 3 loaded line is-eectively smooth over the frequency-range in which the distance between loads is small compared with the wave length.

For some purposes the existing rather large departure of the line impedance at the lower frequencies is undesirable, or even very harmful, so that it is desirable to have a compensating network to associate with the initial end of the line in order that the re- 5 sultant impedance shall be approximately a resultant impedance shallbe approximately equalto amere constant resistance over a wide frequencyrange, such as the voicefreq uency-range.

Some of the possible uses of impedance equalizers are as follows:

To enable the impedance of any smooth line, over a wide frequencyerange, to bev simulated or to be balanced by a mere constant resistance.V

To enable two smooth lines, originally having unequal impedances, to balance each other when a Ql-type repeater is worked between them (therequalized lines being rendered equal by the addition of a series resistance to the smaller or by a shunt resistance to the larger, or by the insertion of suitable transformers between the repeater and the equalizedv lines).

To make the power factor of a smooth line, at its terminals, equal toI unity over a wide frequency-range; that is, to eliminate the wattless component of the current entering the system.

To reduce the building-up time of the entering' current, by reducing the transient distortion. (If thennpedance of the system were a pure resistance at all'frequencies,

there would be no transient distortion, and n hence the building-up time would be Zero; thus the current would attain instantly its steady-state value.)

To reduce the discharging time of the system when the source of impressed electromotive force is replaced by an impedance; that is, to reduce the relaxation time of the system. (This reduction can be understood. from the fact that the removal of an electro* motive force is equivalent to the insertion of its negative: the steady-state part of the current produced by this negative e. 1n. f. exactly annuls the current due to the original e. 1n. f.-this current being supposed to have attained its steady-state value-and the transient distortion part produced by the negative c. m. f. is reduced by the presence of the impedance-equalizer, in accordance with the paragraph just preceding.)

Before proceeding further with this speciioation, the attached figures will be summarized: Figures 1 and 2 show generic graphs of the characteristic impedance of smooth lines, over a wide frequency-range (F being proportional to the frequency, f). Fig. 3 represents any two-terminal network, having any impedance, denoted by W; and Fig. l shows this network combined in shunt relation with any smooth line, of characteristic impedance K; in particular, this network, of impedance WV, may be' any one of the shunt-type impedance-eqnalizers of my invention. Fig. 5 shows a generic graph of the requisite value of the equalizer-impedance W in order to attain perfect equalization of the line impedance K, when the line leakance is negligible. Fig. 7 represents semi-generically the shunt-type impedance equalizer of my invention; and Figs. 6, 8, 9, 10, 11, in connect-ion with eXpository matter in the specifi cation, serve to show that the equalizer of Fig. 7 is actually capable of equalizing the line impedance K with a high degree of precision over a wide frequencyrange. Figs. 18, 19, 20, 21 represent four specific forms of .L-element shut-type impedance-equalizers derivable from the semigeneric form of equalizer represented by Fig. 7; thus the equalizers represented by Figs. 18, 19, 20, 21 constitute specific forms of equalizers of my present invention. Figs. 12,

13, 14, 15, 16, 17, in connection with expository matter in the specication, serve to show how the four specific forms of equalizers represented by Figs. 18, 19, 20, 21 are derivable from the semi-generic form represented by Fig. 7. Fig. 22 represents a network equivalent to the network of Fig. 6; each is capable of simulating the line impedance K with high precision over a wide frequency-range; these two figures, 6 and 22, are introduced for eX- pository purposes.

Before setting forth the theory, designmethods, and design-formul of this invention, it will be desirable to review briefly but in a precise manner the nature of the dependence of the characteristic impedance of a smooth line on the frequency. By the characteristic impedance of any transmission line is here meant, as usual, the line impedance when the line is so long that its impedance is sensibly independent of the distant terminating` impedance.

rl"he well-known general formula for the characteristic impedance K of any smooth line is K= miam/(Gertrud (l) R, L, G, C, denoting the line-parameters per tance, leakance, capacity (capacitance) and o denoting 2 times the frequency f; and

The foregoing formula (1) for K has been very thoroughly studi-ed in my paper Impedance of smooth lines and design of simulating networks published in the Bell System rFechnical Journal of April, 1923; also in my U. S. Patent 1,713,603, issued May 21, 1929. As there stated, the effects produced on the impedance K by normal values of the leakance G are slight except at very low frequencies (below the voice range). Hence, for the present expositor-y discussion of the nature of the dependence of the impedance K on the frequency, the leakance may be neglected. This results in a great gain in simplicity of exposition; for, with Gr set equal to zero, Equation (1) can be written Ken/mf@ 2) Where k w// (3) and F =wL/R (4) it is seen that the nature of the dependence of the characteristic impedance of all nonleaky smooth lines on the frequency can be represented by a single graph, namely, a

graph of 1/1 fi/F as a function of F. In Fig. l, which presents such a graph, the upper and lower curves depict respectively the real (Re) part and the negative of the imaginaryrm) part of K/k fri im Hence, in any specific case, these curves, after their ordinates are multiplied by the specific value of 7c, depict respectively the resistance component and the negative of the reactance component of K, as functions of F, as in Fig. 2. The considerable departure of K from its limiting value 7c, particularly at the lower values of F, is clearly and vsimply shown by Fig. 2.

As a generic basis for demonstrating the impedance-equalizing properties possessed by the impedance-equalizers disclosed later here- 1n, and also as a4 generic basis for deriving Z of the System represented-by F ig. l will next be studied.- The formula for Z is, of course,

KW' *W7 6)- Hence, if the desired or prescribed value for Z is denoted by B, then the precision of equalization attained will yevidently be shown by a graph of the ratio Z/B as function of F; and also by a vgraphofthe fractional departure where the two vertical bars enclosing an expression denote that the absolute Value of the expression is to be taken. From (6), and the equation I) from which (Z -B') /B is obtainable by merely subtractingunity, since ization is Il lilm b- (K/c) 7x which thus constitutes the general designformula for expressing the requisite value of V/B in terms of K/c and A, as functionof F.'

In particular, whenZ is prescribed' to be equal to 70, so that 3:70 and =l, andr when the line leakance Gr is negligible so that K/c has the value expressed by' equation then the requisite value Of I/is or, on multiplying numerator and denominator by WW1-#E+ 1), W

For the particular case here contemplated, each. of these equivalent equations, (V11) and (l2), constitutes anexact design-formula for lV/c. Fig. gives a graph of W/c computed therefrom.

If'it were possible/to devise a network whose impedance W would vary with F in exact accordance with Equation that network, when associated with the line as in Fig; 4, would make the resultant impedance Z exactly equal to B at all frequencies. This result can beclosely attained by means of the equalizing networks constituting` my present invention, as will appear in the course of this speciication.

In order to impart a clear understanding of the nature and proportioning of the Various equalizing` networkseof my present invention, I will now outline the steps by which I arrived at them.

Stated Very brieiy, I imagined the line to be replaced by a semi-generic network known to be capable of simulating the line impedance very closely, then I devised a semi-generic impedance-equalizer exactly equalizing the impedance. of this network, and finally I devised various specific forms of this impedance-equalizer. These several steps will next be described more fully.

Fig. 6 represents the semi-generic simulating network by which I imagined the line to be replaced. That this network is capable of simulating the line impedance K over a wide frequency range with a high degree of'precision is known fronixny above-cited article published in the Bell System Technical Journal of April 1923and also from my U. S. Patentl,713,603 issued'May 2l, 1929. For, Fig. 6 is the same as Fig. ,13b of that article and as Fig. 13b of that patent, except for a simplification of the notation, in that S, R1, J of Fig. 6 stand for S, R1, J of the above-cited referencesgthus all of the letters in Figs. 6, 7, e, 9, 10, 11, 14, 15, 1c, 17, 1s, 19, 20, 21 'of the present patent specification are to be regarded, in imagination, as affected with a double prime, or double accent which is actually omitted, merely for sim plicity.

I here call the network of Fig. 6 a semigeneric7 network because parto'l it, namely the J -part, is represented generically rather than specifically; the J -part may take at least two specific forms, as shown later herein. The J-part will be called an excess-simulator, as in my above-cited paper and patent; its impedance is denoted by J R1 and S designate pure resistance elements, and also denote their Values (ohms). Thus, in Fig. 6, the letters J, R1, S play two distinct roles: they designate the parts of the network, and they denote the algebraic values (complex, in general) of the impedances of those parts; this double usage, which has the advantage of brevity, will hardly lead to confusion. The same sort of usage will be employed in connection with all of the other lSG network figures of this specification, except that in specific networks containing capacities and inductances those specific parts will be designated and denoted by capacity symbols and inductance symbols respectively.

The physical significance and functions 0f the R1, J, S parts of the simulating network in Fig. 6 of the present patent application may be briefly outlined as follows: R1 and J are the principal parts, S being a modifying part. Imagining S to be temporarily removed, it may be stated that R1 is a pure resistance element chosen approximately equal to the nominal impedance of the line; thus R1 alone is capable of approximately simulating the line-impedance over the high frequency-range. Now, at all frequencies the line impedance K exceeds the nominal impedance 7a by an amount K-c, called the excess impedance, which, though sensibly Zero at high frequencies, is quite large in the lower part of the voice frequencyrange, as indicated by Fig. :2. Except at extremely low frequencies, the excess impedance of the line is approximately simulated by the impedance J in Fig. 6; the J -part is thus called an excess-simulator. Finally the S-part is a pure resistance serving by its modifying shunting action to improve the simulating properties of the network, particularly at extremely low frequencies.

The physical significance and functions of the R1, J, S parts of Fig. 6 can be stated more precisely, though indirectly, by way of Fig. 22, representing a network to which the network of Fig. 6 is exactly equivalent when these two networks are related in accordance with equations (44), (45), (46) of my abovected article and patent. Thus, on referring to that article and patent, it will be found that R1 is a pure resistance element (called the basic resistance) which is chosen equal to lf-vm and thus simulates closely the line impedance over the high frequency range; J is an impedance simulating closely the excess im- 1oedance K-a of the line except at extremely low frequencies', finally, S is a pure resistance serving by its modifying shunting action to improve the Jpart, particularly at extremely low frequencies.

Fig. 7 represents a semi-generic form of the impedance-equalizers of my invention; the :l-part may take various specific forms (corresponding to the various specific forms of J), as disclosed somewhat later herein.

Fig. 8 represents the network of Fig. 7 combined in shunt with the network of Fig. -which, it will be recalled, simulates the line impedance (with a high degree of precision).

Fig. 9 represents the network of Fig. 8 with S removed, for purposes of exposition. Thus the network` of Fig. 9 consists of the parallel combination of (R1-FJ) and (R1-lul). If the impedance of the network f of Fig. 9 is denoted by X, then X: (R1 l J) (Ri (R1 J) (R1 J) This equation can be written in the form R1 2R12+R1 J+ (14) which yields the important conclusion that X=R1 (15) if Jj `:R12 (16) that is, if

Teef/J (17) afstel/(seele.) (is) Thus, by consideration of Figs. 6, 8, 9, 10, 11, it has been shown that the network of Fig. 7, when bridged across a smooth line of impedance K, will render the resultant impedance Z closely equal to the resistance R0 gf Equation (18), provided merely that the Jpart is proportioned in accordance with Equation (17), which is therefore the designformula for The J-impedance, when proportioned in accordance with Equation (17), will be termed the inverse of the J -impedance with respect to the resistance R1, which will be termed the resistance of inversion. Or, stated symmetrically, the J -impedance and the J-impedance will be termed the inverses of each other with respect to the resistance R1, the resistance of inversion.

Tn order readily to derive specific forms of the J -part corresponding to known specific forms of the J-part, it is desirable to know the general relations which must exist between any two networks in order that their impedances shall be the inverses of each other with respect to a specific resistance. For this purpose consider any two networks, designated as a and Z), each consisting of m 'romane elements. Let Z1, Z2, Zm denote the impedances of the elements of the a-network; and Y1, Y2, Ym the admittancesof the elements of the -network. Finally, let Z, denote the impedance .of the .cz-network, and Yb the admittance of the b-network. Then Z=F(Z1,Z2, Zm) (19) Remi/1.a... Y...)

where Fa and- Fb are functional symbols, in

the usual sense. Now if these two functions are of the same mathematical form, as indicated by the functional equation F.,=F 1,:17, so that Za=F(Z1,Z2, Zm) (21) YU=F(Y1, Y2, YM) (22) or, in words, if the admittance Y1, of the bnetwork is the` same function of its admittance elements Y1, Y2, Ym as the impedance Za of the a-network is of its impedance elements ZMZ, Zm, then the networks a and Z1 will be said to be inverse in form or formally inverse. Further, if the ratio of each impedance element Z1 ofthe wnetwork to the corresponding admittance element Y, of the b-network has anyV value A2 which is the same for all of theelements, in accordance with the equation where A evidently has the dimensions of an impedance, then the two networks, a andv will be the inverses of each other with respect to the impedance A; for, with relation (23) fullled, it is seen that Zh denoting the impedance of the -network. From (23) it is seen that A, the impedance of inversion, has the value show that these-twonetworks-are inverse in form. Also, these two equations show that these two networks will, further, be inverse` with' respect to any resistance A if Zl/Y1=Z2/Y2=Z3/Y3=A2 (29) for' then ZZ1,=Za/YD=A2 (30) ln order to arrive at specific forms of the Jf-part of the impedance-equalizer represented by Fig. 7, it remains to show specific forms of the J-element of Fig. 6. Two precision forms of the J -element are represented by Figs. 14 and 15, which are of the same forinas Figs. 7a* and 7b of my above-cited article and patent. Fig. 16 represents a network which is potentially inverse to the network of Fig. 14 in the sense that the network of Fig. 16 is of suoli nature that it admits of being so proportioned as to be inverse to the network of Fig. 14. Similarly the network of Fig. 17 is potentially in verse to the network of Fig. 15. The resistance-elements in Figs. 1Gand 17 are specified by their conductance values, G3 and G5, in order to preserve the natural symmetry of the inverse relations; similarly in Figs. 18, 1'9, 20. 21. TheV Ls denote inductances.

Figs. 18, 19, 20, 21 represent four specific forms of impedance-equalizers, obtainedA as follows: The equalizer in Fig. 18 is obtained from the semi-generic equalizer in Fig. 7 by substituting `for the generic n:J1-part of Fig. 7 the specilie network of Fig. 16. Simw ilarly Fig. 19 is obtainedi from Fig. 7 by substituting the network of Fig. 17 for the JF* part of Fig. 7. The equalizers represented 'by Figs. 2Ov andr` 21are derivable from that of Fig. 18 by applying transformation A and transformation C, respectively, given in Appendix IH of O. J: Zobels article entitled Theory and design of uniform and composite electric wave-filters publishedl in 'the Bell System Technical Journal of January, 1923; and, incidentally, these same trans formations serve also for verifying that the four equalizers of` Figs. 18, `19, 20, 21 are actually potentially equivalent to each other, in the sense that, when the elements of any one of them are assigned in value, the three other networks admit of being so proportionedV as to have at all frequencies the same im'pedances as the assigned network.

Although the four equalizers of Figs. 18, 19, 20, 21 are potentially equivalent to each other as regards impedance, they may, of course, differ somewhat as regards such features as lfacility of manufacture, cost, and space occupied.

Thefact thatl the equalizer in Fig; 21 consists of two parallel: branches which are of like nature,each co'nsistingof a resistanceinductance series combinatioinsuggests the possibility of attaining still higher precision Yofl equalizationv by constructing the equalizer Y a resistance-capacity series combination (described in my above-cited article and patent specification), and the same fact is known alternatively from my copending patent application Serial No. 408,577 filed in the Patent Oflice November 20, 1929; thus, the equalizer in Fig. 21 is of the same form as though obtained by connecting in parallel two equalizers of the above-mentioned simple form known to be considerably less precise than the equalizer in Fig. 21, particularly at the lower frequencies. Finally, since the equalizer in Fig. 21 is potentially equivalent to each of those in Figs. 20, 19, 18, the further inference may be drawn that an equalizer of the form obtained by connecting any two or more of these four equalizers in parallel would be potentially more precise than any one of them alone.

The requisite proportioning, or desgin, of the impedance-equalizers represented by Figs. 18, 19, 20, 21 will now be treated. Two methods will be presented: An indirect method, and a direct method.

' The indirect method proceeds along the same lines of thought as already employed for expository purposes in the foregoing portion of this patent specification: that is, the indirect method, after its first step, deals not with the given transmission line itself but with a simulating network whose impedance is known to be very closely equal to the impedance of the given line over a sulficiently wide frequency-range. Thus, the first step is to design the simulating network of Fig. 6 in terms of the fundamental parameters of the line; this can be accomplished, for instance, in the manner fully set forth in my above-cited article in the Bell System Technical Journal of April, 1923, and in my U. S. Patent 1,713,603; the J -part of Fig. 6 may take either of the equivalent specific forms represented by Figs. 14 and 15. The nature of the remaining steps in the indirect method of design is clear `from the foregoing portion of the present patent specification.

The direct method of design starts with any chosen one of the equalizers of Figs. 18, 19, 20, 21, each of which is known, from the foregoing portion of this patent specification, to be of such form and kind as potentially to possess equalizing properties; then,

' by means of Equation (10), the direct method imposes the requisite values of the equalizer impedance 1V at any arbitrary (but reasonably chosen) frequencies sufficient in number to determine the fundamental elements constituting the chosen formof equalizer. The direct method will be illustrated by applying it to the design of the equalizer in Fig. 21, whose fundamental elements are the resistances 138:1/08 and R9=1/G9, and the inductances L8 and L9. Since the number of these fundamental elements is 1l, the munber of frequencies at which the impedance W: U+V of the equalizer in Fig. 21 can take on preassigned values is one-half of 4l, namely 2-because, at any one frequency, WV has two components (resistance U and reactance V). The formula for lV: U-l-V of the equalizer in Fig. 21 is, of course,

On clearing Equation (32) of fractions and then equating real parts on the two sides, and likewise equating imaginary parts, we get the following pair of equations to be satislied at any frequency.

Up-wVoi-Ooci-wgzl Vp-iwUawoc-i-Qzo (38) In Equations (37) and (88) the zero terms 0a and O are supplied for formal completeness. F or the purposes of design, the quantities U and V are here toA be regarded as the preassigned requisite values of the equalizer impedance for attaining exact equalization at any specified frequency f=w/27T, these values of U and V being precal-culated by means of Equation (10). The parameters p, a, a, are to be regarded as unknown and to be evaluated. Since these parameters are four in number they cannot be completely evaluated from merely the two equations (37) and (88), but evidently require altogether four equations. By preassigning at any two frequencies, f, and f2, the requisite values of U and V, we obtain from Equations (37) and (38) the following set of four independent simultaneous linear equations in the four unknown parameters p, a, a,

which, of course, sufce for determining p, ir, a, in terms of the preassigned values of o1, U1, V1, og, U2, V2, by the method of determinants or otherwise. Finally, with p, a, a, thus evaluted the values of the fundamental elements RS, LS, R9, L9 constituting the equalizer of Fig. 2l can be found by solving the set of four independent simultaneous Equations (33), (34), (35), (36) for R8, LS, R9, L5, in terms of a, ,8, p, o.

It might perhaps be thought that equalizers of still other forms and kinds could bc obtained by starting with the simulating network represented by Fig. 22 instead of with that represented by Fig. G, the network of Fig. 22 being the same as the network of 13av in my above-cited article in the Bell Sytem Technical Journal of April, 1923 and of my U. S. l/atent 1,713,603. However, as shown in connection with Equations (44), (45), (4G) of the above-cited references, the network of Fig. 22 in the presen-t patent specification is potentially equivalent to the network of Fig. 6; hence, when shunted by the equalizer represented by Fig. 7, the network of Fig. 22 can lead to no shunt-type equalizers other than those obtainable by starting with the simulating network represented by Fig. 6.

It will be obvious that the general principles herein disclosed may be embodied in many other organizations widely different from those illustrated without departing from the spirit of the invention as defined in the following claims.

Thatis claimed is:

l. In a smooth line whose characteristic impedance includes reactance and which may be substantially simulated by a network consisting of two parallel branches, the first branch being a pure resistance and the second branch comprising a series combination of a pure resistance and a compound impedance unit including both resistance and reactance, means to equalize the characteristic impedance of said smooth line over a wide frequency range so that the resultant impedance is substantially aA pure resistance, said means comprising a network shunted across the line, said network being electrically equivalent to a series combination of a resistance equal to the resistance of said second parallel branch and a compound impedance unit which is the inverse with respect to said resistance of the compound impedance unit of said second branch.

2. In a smooth line whose characteristic impedance includes reactance and which may be substantially simulated by a network consisting of two parallel branches, the first branch being a pure resistance and the second branch comprising a pure resistance in series with a constituent network comprising a plurality of component impedance elements so related that the impedance of the constituent network is a definite function of the individual iinpedances of the component impedance elements, meansto equalize the characteristic impedance of said smooth line over a'vwide frequency range so that the resultant 70 impedance is substantially a pure resistance, said meansl comprising a network shunted across said line, said network being electrically equivalent to a series combination of a resistance equal tothe resistance in said second parallel branch and a second constituent network which comprises a plurality of component admittance elements so related that the admittance of said second constituent network will be the saine function of the individual component admittance elements as the function which relates the impedance of -said rst mentioned constituent network to the impedances of the individual elements thereof.

3. In a smooth line whose characteristic impedance includes reactance and which may be substantially simulated by a network consisting of two parallel branches, the first branch being a pure resistance oi value S and the Vsecond branch including a pure resistance of value R1 in series with a compound impedance unit whose value may be expressed by the symbol J where J includes both resistance and reactance components, rmeans to equalize the characteristic impedance of said smooth line over a wide frequency range so that the resultant impedance is substantiallyfa pure resistance, said means comprising a network shunted across the line, said network being electrically equivalentto a series combination of a resistance of value R1 in series with a compound inipedance unit whose value may bc expressed bythe symbol J, where J is equal to R12/J. y

4. :In a smooth line whose characteristic impedance includes reactance, means to equalize the characteristic impedance of said branch'being a pure resistance and the second branch comprising a series combination of a pure resistance and a compound impedance unit including both resistance and reactance, n'ieans to equalize the characteristic impedance of said smooth line over a wide frequencyran'ge so that'the resultant impedance is substantially a pure and constant resistance, said'me'ans comprising anetwork shunted-across vthe line, 'said 'networkbeing electrically equivalent to a series combination lel branches each including'resistance in seof a resistance equal to the resistance of said ries with inductance.

second parallel branch and a compound im- In testimony whereof7 I have signed my pedance unit which is the inverse with rename to this specification this 18th day of branch being a pure resistance and the second branch comprising` a pure resistance in series with a constituent network comprising a plurality of component impedance elements so related that the impedance of the constituent network is a definite function. of the individual impedances of the component impedance elements, means to equalize the characteristic impedance of said smooth line over a wide frequency range so that the resultant impedance is substantially a pure and constant resistance, said means comprising a network shunted across said line, said network being` electrically equivalent to a series combination of a resistance `equal to the resistance in said second parallel branch and a second constituent network which comprises a plurality of component admittance elements so related that the admittance of said second constituent network will be the same function of the individual component admittance elements as the function which relates the impedance of said first mentioned constituent network to the impedances of the individual element thereof.

7. In a smooth line whose characteristic impedance includes reactance and which may be substantially simulated by a network consisting of two parallel branches, the first branch being a pure resistance of value S and the second branch including a pure resistance of value R1 in series with a compound impedance unit whose value may be expressed by the symbol J where J includes both resistance and reactance components, means to equalize the characteristic impedance of said smooth line over a wide frequency range so that the resultant impedance is substantially a pure and constant resista-nce, said means comprising a network shunted across the line, said network being electrically equivalent to a series combination of a resistance of value R1 in series with aV compound impedance said network comprising a plurality of paralj spect to said resistance of the compound im- November, 1929.

RAY S. HOYT.

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