US1781396A - Electrical network - Google Patents

Description

Nov. 11, 1930. K. s. JOHNSON ELECTRICAL NETWORK Filed Jan. l5, 2 Sheets-Sheet l A. F/g/ Nov. l1, 1930. K. s. JoHNsoN 1,781,396

ELECTRICAL NETWORK Filed Jan. 15, 1925 2 Sheecs--Sheec 2 l .7 '8 .9 L0 Ratio x 9%) /m/e/y/ar.' /fe/wef/z 5. dab/25M Patented Nov. 11, 1930 narran-STATES Param* oFFlcI;

KENNETH S. JOHNSON, F JERSEY CITY, NEW' JERSEY, ASSIGNOR, BY MESNE ASSIGN- MEN TS, T0 VEST'ERN ELECTRIC COIVIPANY, INCORPORATED, A CORPORATION 0F NEW YORK ELECTRICAL NETWORK `Aplrlicaton filed January l5, 1925. Serial No. 2,482.

ligible resistance takes place with a "velocity that is constant for all wave frequencies. If,

however, the `medium or'the .line comprises a connected system of discrete. massive and elastic elements, the wave velocity is no long erV constant but is dependent upon the wave frequency.

` VWell known examples of media of the lat terA type are coil loaded telephone lines, and wave filters of the type disclosed in U. S.

patent to G.`A. Campbell, No. 1,227,113 issued May 22', 1917. 1 l.

`The propagation velocity of waves along A uniformlines. may, in accordance with well 25 known principles, be reduced by increasing the distributed inductance `and capacity of the line. circuits but their `cost and size render them y A, impracticable. For this reason an artificial line comprising simple inductive and simple capacitive elements has been preferred despite the difficulty of obtaininguniform wave velocity therein. n y By the application of the present invention artificial lines may be constructed in which, so far as applicant is aware, the uniformity of the propagation velocity is much greater' than it has hitherto been possible to obtain.` y, A feature of the lines, or delay circuits, 4Q" constructed in accordance with the invention is the combination of networks which produce velocity irregularities of opposite types whereby the irregularity due to one network is'ncutraliaed by that due to others.

Theriature et' the: invention will be more neous medium or along uniform lines of neg-` Suchlines could be usedas delay fully understood from the detailed description which follows:

Of the accompanying drawings,

Fig. 1 shows in schematic form one unit an artificial line embodying the invention; `Fig. 2 is a group of curves illustrating the operation of the invention;

`Fig. 3 shows, partly diagrammatically and partly schematically, a system in which the invention is usefully applied;

`Figs. 4 and 5 show schematically additional forms of network embodying the inveir tion;

6 shows an equivalent form of par of the network of Fig. 5; and

Fig. 7 shows in graphic"representation certain impedance characteristics relating to the operation of the invention.

The propagation of waves in an electrical line comprising a connected sequence of fourterxninal networks is controlled by factors which broadly fall into two classes. The first class comprises the self-characteristics of the individual sections, or, the properties they possess by virtue of theirown dimensions andconiiguration. The second class comprises those factors which are present only as the result of the interconnection of the sections.

The properties of a line comprising an infinite number of equal `symmetrical networks have been extensively Studied and it is well known that they are dependent only upon the self-properties of the individual networks. For example. if in an infinitely extended line the electromotive force at the terminals of one network of the sequence be denoted hy E then the current IN leaving the Nth succeeding network in the direction of propagation is expressed by the following equation:

in. which .Zi and. P are respestivelythe iterative impedance and the propagation constant of each of the similar networks.

The impedance Zk and theY constant P depend only upon the dimensions and configuration of the networks; they may` berdetermined by simple measurements upon the complete network by itself or they may be computed lfrom the dimensions of the elements forming the structure.

l.In `a finite line comprising terminal impedanc-es and an intervening sequence of dissimilar networks, factors of the second class also enter into the wave propagation. rI "he received current at one'end of the line corresponding to anv electromagnetic force, E, acting at the other end may be expressed by the equation:

In this equation IR is the received current, ZS and ZR are the terminating impedances at the sending and receiving ends respectively, EPis the sum of Vthe propagation constants ofv the individual sections and EL'is thesum the vfactor FEL is reducedl to a negligiblyY small quantity and the factor @FEP becomes thedominating factor in the transmission. v

The propagation constant P of each section being in general a complex quantity, the equation for the received current in this simplified case may be written A E ED 21H .IVR QX/ZRZSQVg in which ED'is the sum of the real components of VEP'and Ey' is the sum'of the imaginary components. This equation states that Ijs is related to a current having the value E IFA/2 (4) diminution constant 2D, and by aphase constantV 2,8, the former being a measure of y the relative magnitude of the currents I0 Inpractice both terminal impedances, ZR and.

ZS, are made non-reactive and the component sections have iterative impedances that are nonreactive throughout the important frequency range. The input current is consequently in phase with the yelectromotive force and the received current IR differs in phase `from the input current or from the input E. -M. F. Vby the angle E.

iterativer in which j denotes the wave frequency.

rIhequantity V given by the equation in which N denotes the number of sections constituting the line,'expresses the average number of sections traversed by a wavein unit time and so corresponds to the'average propagation velocity through the; system. In l an artificial line there is no properspace distribution whereby the velocity may` be-eX-y pressed in the ordinary manner asso many meters per second, but the concept of the velocity as here defined, in terms of the sections as equivalent space units, 1s nevertheless of great utility and convenience. 1 Y

To obtain a constant velocit-y, or af con-V stant propagation time, it-isn'ecessary that f the phase constant Fa shouldincrease in d1- rect proportion to the frequency. In l'other words, the angular components of the propagation constants of the individual networks should add together to` a sum that is directly proportional tothe wave frequency. Y

In this specificationthe term phaseconstant is used to denote the imaginary, or angular, term of the propagation constant of a network;` thevvariation of the phase-constant withrespectto the waveV frequencyis termed the phasefcharacteristicg and the multiplyingfactorby which the phase-constant is related to the frequency is termed the phase-factor. i

`One combination ofnetworks for which this relationship holds over a wide'frequency rangeis shown in Fig.l 1. kIt comprises two sections S1 of a simple low-pass filter of the Campbell type having series inductance and shunt capacity and a thirdisection S2 com-r prising series inductances and diagonally cross v connected shunt capacities. ductance of alfull series branch ofthe lowpass Vlilter sections is'denotedlby L and the shunt capacity bvvvG; 'these values .being indicated inthe figure. These sections are terminated at the middle' of a series branch5,

or as it is generally'ternied at midfseries, the

individual coils having inductances equal to n Y p kThe inductances'of the section lS2 are relatedY to those of the filter section by a numerical factor a and the shunt capacities to The inf total shunt impedance.

mens-ee the filter shuntl capacities by a second factor To distinguish between the two types of network the terni ladderlhas been used to detine a network of the simple series-shunt type, and the term lattice to denne the diagonally cross connected type,`of which the section S2 is an example. The terms are usedin the present specification in the senses indicated.` l

For an analysis of the characteristics of these networks and for the principal for mulae relating to their propagation constants reference is made to an article by G. A. Campbell, The physical theory of the elecw trio wave `filter, printed in the Bell System Technical Journal` volume l. No. 2 November, 1922. e

The propagation constant of each section of either type of network is a function of the ratio of the total series impedance to the ln the mid-series terminated low-pass filter sections of Fig. 1, each `series arm furnishes one half of the full series impedance. In the lattice sec* tion, the full series impedance is divided equally between `the two lines and the total shunt impedance is that of the two diagonal b-rzmches connected in multiple. y

The propagation constant of one sectionof a ladder network is given by the following general formula P 2 taIlll-l" yy-2 s s s l l s in which y? denotes the ratio of the series impedance to the shunt impedance.

For a lattice network. the propagation con-` ,1 stantis expressed by The subscript L being used to distinguish the cov-efficients of the lattice network from 'those of the ladder networkt If the ladder network is composed of reterniifnedby Fermula (7) may be either real or imaginary depending upon the value of .y but it cannot be complex. It will be imagi- 2 e nary for all frequenciesat which gj is nega-` tive and less than unity,` and realV for all other values. Thissignies that the wave propagation through such a network, or through a continued sequence of them constituting awave filter, is characterized? either bya modification ofthe wave intensity withoutchange of phase, thus denng the atten nation range or by a progressive change of phase without attenuation of the wave.

The propagation constant of the lattice section of Fig. 1 is imaginary for all values of the frequency. The section therefore produces only a phase change in the transmitted waves, which are propagated at all frequencies without attenuation. e

The phase characteristics of the component networks of Fig. 1 are shown in Fig. 2 along with the resultant phase characteristic of the combination. The abscissae are proportional to the ratio, denoted by m, of the wave frequency f to the cut-olf frequency fc of the low pass filter sections; the ordinates represent the phase angles in degrees. i

The curve OA represents the phase characteristic of the two ladder sections together and the curve OB the phase characteristic of the lattice network. The ordinates of curve OC are equal to half the sum of the ordinates of the other two curves, or to half the resultant phase angles of the combination. The curves OA and OB are curved in opposite senses and for a range of frequencies extending from zero to about seven-tenths of the cutoff frequency the departure from linearity of the` one curve is ust sufhcient to neutralize the departure of the other curve. Up to this point the curve OC is practically straight, indicating that all waves of lower frequency are propagated through the combined network with a uniform velocity.

The accuracy of the compensation may be examined more fully by determining and` comparing explicit formulae for the phase-` constants of each type of network,`

By well known mathematical processes formulae 7 and 8 may be expanded `into the following infinite series, which apply within the transmission range,

The ratios y and y1, may be expressed in terms of the constants of the structural elements and the wave frequency; for the structures of Fig. lthey are y jam/F and m a /a (10) yL=jgrafik/ELO:3*/631i Further, since the cut-olf frequency of the ladder filter sections 1s defined by varan@ 12) the quantity lThe real parts of P and PL are zero throughfr out the transmission range and the'imaginary parts, or the phase constants and m'are respectively Y -2x+ 3m +20x5+567+ and 13) which by'iEq-ua'tions yexpresses the rela-'- tionshipbetween y and yp, being written as Z for convenience.

- spectively y.

The 'combination' .of two. ladder sections with one lattice section has a resultant phase constant 1=2lt=Y i from which theterm involving m13 disappears` when Z is equal to unity.V

The straightening out of the phase-constant characteristic isdue to the elimination of-this I, one-v ha'lfwsection of the Vladder type..` vAp-l propriatevalues of d may be determined,

which in each case reduce the resultant third power variation to Zero. v For the additional examples cited the proper values of d are rev l.' i i i .and thelatter/value applying tol bothrof they i last two' combinations mentioned above,-

which are essentially similan' The combination of one lattice and one half ladder section corresponds to the partofFig. lfbetween the dottedlines AA. and BB. l.

Combination units of the Vaforementioned types may be joined together to form an artificial line in which the phase constant has the same uniformity as in the individual- V sections and in which the retardation time is proportional to the number of units in the line.- By the use of a suflicient number of' units the retardation time may be adjusted to any value and variable lines may be made'by the addition of switching means for cutting out or inserting the individual units.

To preserve the uniformity of velocity ob- K tained by the combinations it is necessary that the iterative impedances of-the succes-V sive sections should, throughout the range of frequencies to be utilized, be alike as nearly as possible and should be substantially equal to the impedance of the terminal apparatus or of the lines to which theY artivcial line may be connected. v

The iterative impedance, denoted by KL, of a lattice network of the type under consideration is constant and non-reactive at all frequencies. In terms of the co-efficients indicated in Fig. it is The iterative impedance, denoted by K of the mid-seriesvv terminated lfilter sections is Va variable quantity. v At zero frequency'it lhas the value and at higher lfrequencies it diminishes continuously to Zero at theA cut-oli7 frequency.

The variation withfrequency is expressed by the Vequation I fl-:13, (17) and is illustrated kby the curve Grof Fig. 7 inwhich'the ratio Y Y y is plotted as a function of y Y y.

The combination network of Fig. 1 has `a linear phase characteristic through a range of Afrequencies corresponding .to values Yof between Zero' and 0.7. In the foregoing,l

analysis, which indicates that this linearityis principally due to the eliminationy of the third power frequency variation, thev effect of the difference between the .iterative impedances ofthe networks is ignored. Detail calculations show that if the iterative impedance of the lattice networkv is made-equal to the initial iterative impedance of the ladder net-V work, that is, to the impedance-correspond ing to Zero frequency, the disparity ofthe iterative impedances thr'oughout'the range of as from zero to 0.8 does not affect the phase constant more than one partin fivehun-1 dred.

The disparity of the impedances may be made less byproportioning the lattice net# work so thatthe iterative impedance is somef, what Lkless than the initial iterative impedance of the/ladder network. If, forexample, itis made equal to 0.8Aof the initial impedance of.

the Y ladder network the disparityat eighttenths of the cutoff frequency will bereduced by half and the effect upon the phase constant.

will be diminished correspondingly at all frequencies greater than 0.4 of the cut-off frequency.

It was shown in an earlier part of the specification that the elimination of the third power frequency variations fixed the value of the coefficient d and thereby determined by means of Equations (10) the relationship between the impedance ratio y and yL of the component networks. The individual impedances may be variedwithout changing the values of the impedance ratios andmaylbe chosen to give the networks any desired iterative impedance. The selection of a definite value for the iterative impedance determines the proportions of the component networks in relation to each other; the numerical values of the individual inductances and capacities are finally determined bythe specification of the frequency range through which compensation is desired.

As an example, the design of a network of the three section type shown in Fig. 1 may be considered, the conditions being postulated that the network be suited for use in connection `with a transmission line of 600 ohms impedance and that uniform velocity, or uniform delay, be obtained for all frequencies up to 8,000 c. p. s.

The network has a linear phase`-character istie up to 0.7 of the cut-o frequency; it is desirable therefore that the cut-off frequency should eXceed 4,200 c. p. s. As a convenient value 5,000 c. p. s. may be chosen.

Inserting the value of the cut-off frequency in Equation (11) gives LU=.00405 X 10";V (18) The iterative impedance of Athe lattice sec-` tions, being uniform, should be made equal to the line impedance or 600 ohms, and, to minimizel refiection losses most effectually, should be equal to 0.8 of the initial iterative impedance of the ladder section. v

and (16) gives lz-JF 750 ohms `(19) and a-b 0.64 numeric (2 0) The condition that the third power frequency variation be eliminated requires in accordance with Equation 14, that the factor cl `be unity, or, p

` e 1 b The final solution of Equations (18) to "(21) gives thenumerical values of L, C, a, and l), Y as follows:

L= .048 henrys C= .085 microfarads a= b 0.8

The retardation time of one network of this type as obtained from Equations (5) and (14) is tlf-3.82 X 10* seconds.

In Figs. 4 and 5 are shown composite net works which include filter sections other than the simple low pass type hereinbefore considered. In Fig. 4 the ladder section comprises an anti-resonant circuit in the series branch and a simple capacity in the shunt branch, and in Fig. 5 the series branches include inductances mutually coupled together, the sense of the coupling being such that the mutual inductance increases the total inductance of the series branches.

Filter sections of these types are fully considered in a paper by O. J. Zobel, Theory and design of uniform and composite electric wave filters, printed in the Bell System Technical Journal, Vol. II, No. 1, January, 1923. In the paper referred to they are termed M-type wave filters and are divided into two classes, midshunt, and mid-series, which are defined by the properties of their respective iterative impedances. The properties of these filters are related by the formulae given by Zobel to the properties of certain of the Campbell type filters which have the unique property that the product of the series and the shunt branch impedances is constant.

The simple low pass filter sections of Fig. 1 are examples of this type to `which the term constant-lc has been applied by Zobel. The mid-shunt M-type sections are so defined because they have the same mid-shunt iterative impedance as the constant-lc section to which they are related. A corresponding relationship holds in connection with the midseries tft-type sections. y

The ladder type filter section of Fig. 4 of the mid-shunt M-type. It has the same f initial iterative impedance and the same cut Inserting these values in Equations (15)Y off frequency as the simple low pass filter sections of Fig. 1 provided that the co-efiicients of the elements are related to the inductance L and the capacity C of the simple filter by certain numerical factors, the values of which are defined as follows.` The series inductance and the shunt capacity of the lVl-type filter sections are equal to the corresponding co-eicients of the simple filter section multiplied bya factor m which is a simple numeric and which may have any positive valve between zero and unity. The capacity ofthe full series branch is related to the shunt capacity of the simple filter by the factor ists between the propagation constant of an property, and in a mid-series type section itt-type filter section and the' propagation constant of the corresponding constant-7n filter. This expressed by the following equation Y Y y P n .y Pk

tanh-2@=mtanh- (22) in .which Fm and Pk are respectively the propagation constants of them-type. and the corresponding .constant-c sections.

. z The value of the propagation constant of aconstant-c.9 filter Vis-'given by Equation (1?.) by means of which Equation (2 2) may be transformed to l invwhich the subscript Ic denotes that the ratio y refers tothe constant-70,7 filter. rlhis equation gives the propagation constant of any iVl-type filter interni of theco-efficients of the simple Campbell7 or. constant-la type.

hand side of Equation may be expanded into an. infinite series lwhich when. eiipressed by means of Equation (12) in terms of m yinstead of y contains Vonly,iinaginary terms and therefore expressed the'value ofthe phaseconstant The first t ireeterms of the series are ` is evident that this equation may be satisfied by a' multiplicity of values of m and d, and that anV additional condition must be fixed before a single solution can be found.

A useful feature of the lv'ttype filter sections, which has been pointed out by Zobel inthe aforementioned reference, is that one offthe midasection iterative impedances is, y for yvalues of "m, around 0.6, exceptionallyA constant throughout the .transmission range. ln a mid-shunt lvl-type section 1t isv the midseries iterative impedance that possesses this it is the mid-shunt iterative impedance. The curve H of Fig. 7 illustrates the varialn the case of a low pass filter, the right.

tion o f the mid-series iterative impedance ,of Vthe fyi-type section orfnFigt4, whenthe co-eiiicient mhas the value 0.6. Y'Illu-,ordifv nat-es of the lcurve represent the ratios ,of the iterative impedance to its initial value'` andk v'the abscissae are proportional to vthe fre-- quency ratiov At zero frequency the iter? ative impedance has the same value ,asf` that of the simple low passl filter and thisvalue is maintained withl great uniformity up to a value of a equal to 0.85. 1

Fixing the value of mimakes Equation i(25)(,determinate and givesa solution for the factor Z upon which depend the oonstants of the lattice structure., Thechoice ofthe particular value 0.6 enables the ladder section to be designed so thatthere will be practically n0 disparity of. the iterative jiinpedances and 4consequently11o-reflection effects to impair the uniformity .of the wave velocity. i

Under this condition the value off-l for the combination shown in Fig. 4 is found The actual values of the elements may be determined for any particular case in yaccor-dance with the procedure already described.Y

Acomposite network comprising one latticeand one mid-shunt M-type'network may also be designed to have a substantially constant4 velocity characteristic.

is found to be g Y v In Fig. 5 is illustrated a4 third type of coinposite network in which also the `inventive idea ispresent. The section having coupled series arms is equivalent to` the network illustrated in Fig. 6 when the sense of coupling is such that the mutual inductance increases ythe series Varm inductances. Itis la mid-'ser` ries Mftype section'having properties related to those of the simple filter section` with y which it is associated provided that Y p .Y Itis evident that lthe'secondjof these `rela-kv tionships can hold only when m has a value greater'than unity. A.

A comparison of Equations (13) and"(24) shows .that the condition `nesessary 'for'V the eliminationwofv the-third power ,frequency If the'. same j value of m is usedy the value of Z in this case variation of the phase Constantin thiscoinbination is wlw..

GOIN) variation in its phase constant.

from the line as desired.

the real root of which may be found by graphical methods to be The proportions of L1, Ml and C2 follow from Equation (26).

The Inidseries iterative impedance of the M-type section is the same as that of the simple filter section consequently there is no impedance disparity at the junction of the sections.

It should be noted that a single section of the co-upled impedance type may by itself be made to have no third power frequency The necessary condition is that 071:1.225 This value of m corresponds to a coupling factor of 0.2 between the half-series inductances L1.

The application of the invention in connection with a binaural system for determining the bearing of a source of sound waves is shown in Fig. 3(

An arrangement of this sort is described in Patent 1,628,992 to John Mills, dated May 17, 1927.

Use is made of the principle that sound waves arriving at the same instant upon the two ears of an observer appear to come from source located directly before him.

rlwo microphones M1 and M2 spaced apart on a reference base line receive sound waves from the source to be located and translate them into electric waves which are transmitted through independent channels to the receivers l. and T2 of an observers head set. With each channel is associated a number of artificial line units, 2, which by means of switches, 1, may be inserted into or removed The line units, which are indicated diagrammatically, are similar in construction throughout the system and may consist of composite networks of any of the types illustrated in Figs. 1, 4 and 5.

The microphones are supplied with current by the batteries i which are isolated from the other apparatus of the channels by transformer 8. The networks are designed in accordance with the foregoing principles to match the impedance of the receivers 'lll and T2 and the transformers serve the additional purpose of transforming the microphone impedance to the saine value.

Waves arriving from a direction making an angle 6 to the direction normal to the base line arrive at the microphones at different instants separated by a time interval t which has the value The distance between the microphones being denoted by Z and the velocity of the wavesby V. lf the two channels were alike in their electrical lengths the waves would reach the telephone receivers at different instants and would give the observer the impression of a sound coming 'trom a source located to one side of him. By inserting a sufficient number of line sections in one of the channels,

which one depending upon the sense of the apparent. bearing, binaural centering may be obtained in which the sound appears to come from a source squarely in front of the observer. The time t can be estimated by means of Equation from the sum of the phasefactors of the line sect-ions necessary 4to produce the binaural centering and hence by means of Equation (29) the bearing may be obtained.

The constant velocity property of the networks permits a calibration of the system to be made by which the bearing may be determined directly from the number of sections required for binaural centering and which is correct for waves of all important frequencies. A further advantage arising from this property is that all components of a complex tone are equally' delayed and in consequence cannot produce any confusion of the binaural centering such as may occur when the component waves are unequally delayed.

lilthough the utility of the invention has been described in connection with a binaural direction finding system itis to be understood that it is not limited to such systems but only bythe scope of the'appended claims.

l/Vhat is claimed is:

1. A wave retardation circuit comprising a plurality of four-terminal networks in sequence, one of said networks having a phase constant which increases less rapidly than the wave frequency, and the others of said networks consisting of similar ladder-type broad-band wave lter sections adapted to transmit freely` wave frequencies below a critical value, the component elements of said filter sections being so proportioned that the resultant phase constant of the retardation circuit is substantially constant for a wide range of frequencies.

2. A wave retardation network comprising two four-terminal networks connected in sequence, the wave retardation interval of one of said networks diminishing as the wave frequency increases, and the other of said networks consisting of a ladder-type broadband wave filter section adapted to transmit freely waves of frequencies less than a critical value, said filter section being proportioned to have a retardation interval which varies in a complementary manner to that of said rst mentioned networkwhereby the wave retardation interval of said retardation section is made substantially constant for a wide range of frequencies.

ico

3. VA. wave retardation network comprising a lattice type i'our-terlninalV network having simple inductances in the series branches and simple capacities in the shunt branches l thereof, and a ladder type four-terminal network comprisingtwo series inductances and a shunt capacity connected to the junction point thereof, the product of the sum of the inductances and the sum of the capacities of said lattice section being substantially equal to 0.63 times the product of the total inductance and the capacity of said ladder secizo tion.

4f.. A wave retardation network comprising a lattice type four terminal network having simple inductances in the series branches `and simple Capacities in the shunt branches thereof, and a ladder-type four-.terminal network comprising two series inductances and a shunt capacity connected to the junction point thereof, the product of the sum'of the inductances and the sum of the capacities of said lattice section being substantially equal to 0.63 times the product of the total inductance and the capacity of said ladder section, and the iterative impedance of said lattice and said ladder sections being substantially equal for a wide range of frequencies.

5. A wave retardation network comprising a lattice type four-terminal network having simple inductances inthe series branches and simple capacities in the shunt branches thereof, and a ladder-type four-terminal network comprising two series inductances and `a shunt capacity connected to the junction point thereof, andthe ratio of the total inductance to the total capacity in said lattice section being approximately equal toO.8 of

the corresponding ratioin said ladder sec'- tion.

In witness whereof," l hereunto subscribe my naine this 13th day of January A. D.,

KENNETH s. JOHNSON.

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