US1606817A - Electrical network - Google Patents

Description

Nov. 16 1926. 1,606,817

G. H. STEVENSON ELECTRICAL; NETWORK Filed Dec. '7, 1925 @f E, W2, C O B D Impedance NE@ O o ATTenuaTon fados Frequncg I Ve/2f.

@e/ye /7 Sfax/mm -y Alfy Patented Nov. 116, 1926.

i UNITED STATES PATENT ori-"lcs,

GEOBG'EH. STEVENSO, 0F SOND BEACH, CONNECTICUT, ASSIGNOR TO BELL TELE- PHONE LABORATORIES; INCORPORATED, OF NEWYYORK, N. Y., A CORPORATIGN 0F NEW YORK.

ELECTRICAL NETWORK.

Application led December This invention relates to electrical networks, and more particularly to transmis' sion equalizingvnetworks of the type known as constant resistance networks.

Various forms of constant resistance equalizing networks are described in the copending applications of O. J. Zobel, Se-

rial No. 7 22,506, 'filed June 26, 1924, in which the general properties of the type, and its application to the equalization of the attenu-y ation in transmission systems are also discussed.

The presentA invention is an improved form of network, the object ot the improvement being the reduction'of the number of elements required for the construction of a network of symmetrical structure and characteristics, to provide a, specified attenuation correction.

A characteristic feature of constant resistance equalizing networks is the use ot a pair of two-terminal impedance networks, including reactance elements, in which the coefficients of the impedance elements and the interconnections between the elements, are related in an inverse manner, so that the product of the two impedances is a constant quantity, having the electrical dimensions of a resistance squared. Two im` pedances so related are termed inverse networks of constant resistance product, or more simply, inverse networks.

In the constant resistance equalizing net- -works of the types heretofore known it has been necessary to use two pairs of inverse networks to secure symmetry with respect to the structural form.y and the electrical prope'rties. ln accordance with the present invention symmetry, both in form and in transmision characteristics, is obtained withv a single pair of inverse networks.

rlhe nature of the invention will be more 'fully understoodby referring to the following detailed description and to the drawing, forming a part thereof, in which*- Fig. 1 shows in-schematic, the most gen- 7. 1925. Serial No. 73,578.

eral form of the improved network of the network constructed in accordance with the invention; and l Figs. 4 and 5 are illustrative of the prop- Verties of the specific form shown in Fig. 3. rial No. 580,769, iled August 9, 1922, and Se- As shown in Fig. 1, the network in its most general form comprises a pair of equal resistances connected in series in one side of a transmission line, and a pair of inverse networks, one of which Z1, is bridged across the outer terminals of the two resistances, and the other of which, Z2, is connected in shunt between the junction point of the two resistances and the other side of the line. The line terminals are designated A, B, C and D. A A

The relationships between the impedance Z1, Z2, and R. necessary to impart the consta-nt resistance characteristic. to the network may be -found by examining the formulze for the image impedances of the network, which in accordance with known principles, may be derived from the open circuit and short circuit impedances measured at each pair of the network terminals. For a comprehensive account of the image parameters of a network and of their relation to the transmission characteristics, refpendances respectively equal to the image impedances for the corresponding terminals there are no wave reflections at theaterminaljunction points. Under this condition the output current is determined solely by the magnitude of the image impedances and the attenuation factor of the network.

Generally the image impedance has a frequency characteristic suc that it cannot be simulated by anysimp e combination of physical elements, but inthe networks of the present invention the image impedances are constant resistances and may be very 'readily simulated. 'It follows, then, that'if in which XEL and Y.L are respectivel the open circuit and the short circuit impe ances .of the network measured at terminals A B,

and in which W is theimage impedance. On account of the symmetry of thel structure the image impedances at both pairs of terminals are equal.

In terms of Z1, Z2, andl R the impedances Xa and Ya are given by the equations Jia- 1) (R +225 1T; (3)

which it follows that y Now, impedances Z1 and Z2 are inversely related, and if their magnitudes be so chosen that their constant'value'" product is equal to R2, it will be found that' equation 4 reduces w-..R. f (5) The rules for designing a pair of impedance networks, so that they may be inversely related to each other by the constant factor R2, will be elucidated by a consideration of the networks shown in Figs. 2 and 3. In the network of Fig. 2 the impedance Z1 comprises an inductance L1 and a capacity C1, in terms of which the impedance is eX- pressed by Now, since it is stipulated that ZlZFW (7) Rt in which.Y. is the admittance corresponding.

2 the value of Y, m'ay at once be written The form of equation 5 indicates that the admittance comprises two parallel paths, the component admittances being simply additive. Further, the first term on the right hand side has the electrical dimen-v sions and the characteristic frequency. variation of the admittance of a capacity, while the second term, in like manner, corresponds to an inductance. -It is therefore possible to express the value of Y2 in the form in which C2 and L2: C1R2.

In this case the inverse impedance, Z2, of Z,L

consists of an inductance connected in parallel with a capacity, the Value of the inductancebeing inverselyrelated tothe Value of the capacity in impedance Z1L by the fao tor R2, and the capacity being correspondingly related to the inductance L1. For the more complicated network shown in Fig. 3, the admittance Y1 of impedance Z1 is eX- pressed by the formula t 1 (1o) :1.6901 By equation 7 the value of impedance Z2 for the inverse relationship is which is identified with the value when Y R2R1 u =IR2. (13) evidently lequation 12 corresponds to the im- 'pedance of a network comprising a resistance, an inductance, and an anti-resonant inductance-capacity pair, all connected in series, as shown in the figure.

Out of these two examples, the following rules, which are general in their application, may be stated: Additive impedances in the one network are replaced by additive admittances in the inverse network, and vice-verysa; vinductive elements vin the one network llu are replaced by capacitive elements in the inverse network, and vice versa; and resistauces are replaced by resistances, the roducts of the impedances of each pair 0 corresponding elements being equal to R2.

The propagation constant, denoted by P, of the network of Fig. 1 may be found in terms of the impedance coefficients of the elements from the following equation Y; Tanh P=\/;

which holds for any symmetrical network. Substituting in this equation the values ot X. and Ya given by equations 2 and 3, and utilizing the inverse relationship Z1 and Z2 to simplify the expression, the value of Tanh P is found to be The propagation constant P is a complex quantity having real and imaginary components defined by Pzal-jv the real component a being the attenua-tion factor, and the imaginary component ,B being the phase constant of the network. To determine the values of a and an explicit formula foi` P may first be obtained from equation 15, using the relationship 1 -I- tanh P 1 tanh P the value of P so found being Z1 r=10ge 1+g 17)Y if the total resistance and the total reactance of Z1 be denoted by S1 and X1 respectively, the value of P becomes between two lsections of a transmission line or system, the unpedance of each of which is resistive and equal to R, there will be no` refiection edects at the junction points, and the change produced in the received current will be controlled entirely by the propagation constant P of the network. In this case the ratio of the absolute value of the received current, ILOI, before the ynetwork is inserted; to the modified value, ILI, due

to the insertion ofthe network is given by the equation Ilo a S1 2 X1 2 L -e -\/(1+R -l-(R) (20) 1 If the two terminating impedances are not resistive and equal to R the relationship between the received currents in the two cases will be less simple than that given by equations 20 on account of reiection effects.. It is generally possible, however, to find a point 1n any transmission system at which the impedance on both sides, or at least on one side, of the section is substantially a constant resistance. ln the latter case the reflection effects are unchanged by the insertion of the network, and the ratio of the two currents is again in accordance with equation 20.

The design problem is that of finding a network structure which will have a specified attenuation characteristic. As a rule an exact solution cannot be found, but by successive trials it is generally possible to select a network which will provide the requisite attenuation through a substantial frequency range with as great accuracy as may be desired.

Equations 20 may be transformedto #STX-#Mm (21) which gives the absolute value of the impedance Z1, in terms of the constant resistance R and the specified attenuation factor a. The quantity on the right hand side of equation 21 may be computed for several frequencies from the specified attenuation characteristic, and a curve, showing the computed values plotted against frequency,

IDO

is also the curve showing thev required frel quency variation of impedance Z1.

rlhe selection of the proper network is facilitated by a familiarity with the characteristics of two-terminal impedance netl works. The general characteristics of such` networks, when' composed entirely of reactive elements, are described by R. M. Foster llO' in the Bell System Technical Journal, Vol.

III, No. 2, April, 1924, in an article entitled A reactance theorem. The dominating characteristics of reactive networks is the alternate recurrence of resonance and autiresonance frequencies, and the uniformly positive rate of increase of reactance with frequency.

The network corresponding to Z1 in Fig.

3 is of the above mentioned type, but having a resistance R1 added in parallel to the reactive elements. The effect of the added resistance is illustrated in vFigure 4 which shows the frequency variation of the two components S1 and X1 of the impedance.

At the frequencies of anti-resonance, or the frequencies for which the impedance of Vso is con ned to the limits and the variation between these values becomes more 'and more nearly linear vas the value of R1 diminishes. The presence of the shunt resistance R1 has therefore theF eiect of limiting the attenuation range of the network and of reducing the amount of curvature in the attenuation characteristics in the range between the points of maximumattenuation and of minimum attenuation.A

A portion of the attenuation lcharacteristic ofl the network of Fig. 3 is shown in Fig. 5 in which curve 1 shows the variation of the attenuation factor a with respect to frequency. For the purpose of a qualitative comparison the variation of a for the case in which R1 is infinite is shown by curve 2. Networks of the t pe shown in Fig. 3 have been Jfound useful or compensating the attenuation of uniform transmission lines at high frequencies, the attenuation in such lines being a substantially linear function of the frequency.

Thepinvention is not useful in this field alone, however, but nds application widely wherever it is desired to modifythe transmission characteristics of wave systems or ap aratus in general.

n the appended claims, by which the scope of the invention is pointed out, the term inverse network is used to define a network which is so related to a given network, in its structure and in the composition of the elements, that, for the impedance of each element, and each group of elements, in the given network, it presents a corresponding admittance, the ratio of the impedance in the one case to the corresponding admittance in the other being a constant quantity.

A pair of inverse networks defines two networks one of which is inversely related to the other, whereby the impedance of the one bears a constant ratio to the admittance of the other, or the product of the two impedances is a constant quantity.

What is Iclaimed is:

l. A wave transmission network having a pair of input terminals and a pair of output terminals said network comprising an electrical path between each input terminal and a corresponding output terminal, a pair of equal resistances connected in series in one -of saidpaths, a eneral impedance Z1 connected in paralle with said resistances between the outer terminals thereof and a second general impedance Zz connected between the junction pointof said resistances and a point lin the other of said paths, the impedances Z1 and Z2 having a product that is a constant quantity at all frequencies.

2. A wave transmission network having a pair of input terminals and a pair of output terminals said network comprising an electrical path between each. input terminal and a corresponding output terminal, one of said paths including a pair of equal resistances of4 resistance R connected in series and a eneral impedance Z1 in parallel therewit and a second general impedance Z2 included in a shunt path between the junction point of said resistances and a point in the other of said paths, the impedances Z1 and Z2 having a constant product equal to R2.

3. A wave transmission network having a `pair of input terminals and a lpair of output terminals, said network comprising electrical paths between each input terminal and a respectively associated output terminal a pair of equal resistances of resistance lt included in series in one of said paths, an impedance network including reactive elements connected in vparallel with said resistances between the outer terminals thereof, and a network, inversely related to said impedance network by the constant impedance product equal to R2, connected in a shunt pathbetween the junction point of said resistances and a point in the other of said paths. A

4. A wave transmission network having a pair of input terminals and a pair of output terminals, said network comprising an electrical path between each input terminal and a respectively associated output terminal, a pair of equal resistances of resistance R included in series in one of said lll minals thereof, the other of said networks being connected between the-junction point of said resistances and a point in the other of said electrical paths, and the first mentioned network having an impedance Z1 designed in accordance with the formula in which P is a preassigned propagation constant. I

5. A wave transmission network having a pair of input terminals and a pair of output terminals, said network comprising an electrical path between' each input ter.- minal and a respectively associated output terminal, a pair of equal resistances of resistance R included in series in one of said paths, a general impedance Zlconnected in parallel with said resista-Dees, a second irnpedance Z2 inversely related to Z1 by the constant factor R2, included in a path between the junction front of said resistances and the other of said paths, and said network being designed to have a preassigned attenuation, denoted by a, by proportioning the impedance Z1 in .accordance with the formula @harceler in which Sl and X1 are respectively the GEORGE H. STEVENSON.

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