US1254475A - Signaling-circuit. - Google Patents

Description

G.A.CAMPBELL SIGNALING CIHCUIL APPLICATION FILED MAR. I5. 1911.

LQMA Patented Jan. 22,1918.

INVENTOR unten smarrita GORGE A. CAMPBELL, OF UPPER MONTCLAR, NEW JERSEY, ASSSllG-d T tlfillttllthiixl TELEPHONE AND TELEGRAPH CMPANY, A CDRERATIOSWE" NEW lrtl' SIGNALING-CIRCUIT.

Specification of Letters Patent.

' ;l. .t l "t i w, Patented an., ist, nella,

Original application le September 9, 1916, Serial No. 119,282. Divided and this application filed. March To all whom `it may concern:

Be it known that l, GEORGE A. CAMPBELL,

vresiding at Upper Montclair, in the county- I termed, inaccordance with common usage, a

substation, and more particularly in the combination of a substation and a telephone line. lts object is to provide a signaling circuit arrangement which in cooperative combination with a similar and equal communicating arrangement or station shall deliver 4the maximum amount of energy to the receiving apparatus of said communicating station or arrangement. A further object is to provide an arrangement such that the receiving apparatus is protected from interference by the transmission energy originatin'g at the same station. ln other words its object is to provide signaling means characterized by the maximum possible ratio of received 'and transmitted energy and iturther characterized by the absence of side tone.

A The object of the invention is attained, in its specific aspect, by providinga substation consisting of transmitter, receiver, auxiliary resis ance', and a transformer having a. plu ral' y of windings which, in combination withI a, telephone line, shall satisfy the tollowing fundamental requirement: Given two identical substations designed for invariable two-wa y--communicatipn, and connected by al line of given impedance and length, the amount of energy absorbed by the receiver at the receiving station sliali be the maximum part of the ,total telephonie energy developed by the 'transmitter at the transmitting station consistent with invariable two-way communication, and, as hereinafter explained, consistent with a desirable amount of discrimination against disturbing line noise. This Jlfundamental ren serial iro. leases.

quirement maybe stated in terms of the following subordinate requirements which are necessary for its satisfaction: (l) The transmitter and receiver Shall be conjugate,

that s there shall be negligible side tone inv the receiver in consequence of the actuation of the transmitter by sound waves.; (2) the line and auxiliary resistance shall be con jugate in order that none of the energy ab sorbe'd by the substation from the line shall be wasted in said auxiliary resistance; (d) for a given4 line having a definite impedance the telephonie energy delivered. by the transm mitter shall be a maximum; (d) the amount of energy delivered by the line to the sub station shall be a maximum, in other Words the impedance of the substation as seen from the line shall be equal to the impedance or the line; (5) at a small sacrifice of eiiiciency it shall be possible to discriminate effectively i against disturbing line noise as distinguished from the telephonie signals from the communicating station.

A substation satisfying the above-meii tioned requirements is ideal in that its overall efficiency from transmitter of one substation to receiver of the communicating substation is a theoretical maximum which cannot be exceeded loy any invariable substations whether satisfying the requirement of transmitter and receiver conjugacy or not. 'it further ideal in the sense that a minimum number of elements is employed since at least one auxiliary element is necessary to secure reedomrom side tonen lt might be interred that the addition of an auxiliary resistance element, necessary as it is to secure 'freedom 'from side tone, would at the same time nec-es .ily reduce the ei ticiency et the' substation since is un-= avoidably wasted in said auxiliary resist. ance. rThat this is not the case and that the lil@ other across the line. l'n suoli an arrangement the over-all efficiency is a maximum when the resistance of the receiver is equal to that oi the transmitter. lVhen this condition is satisfied obviously fifty per cent. oiE

the energy delivered by the line to the substation is wasted in the transmitter and titty per cent. orf the energy delivered by the transmitter is Wasted in the receiver. Further if) such an arrangement labors under the disadvantage of full side tone. ln the sub-l station of my invention fifty per cent. of the energy deliveredby the line to the substation is wasted in the transmitter but none in the auxiliary resistance il' said auxiliary resistance and said line are conjugate; hence the etliciency ci' receiving is as great as 'that of the simple series,- substation. l/Vhen trans mitting no energy is wasted in the receiver but titty per cent. ot the energy delivered by the transmitter is wasted in the auxiliary resistance. The transmitting eliiciency is their tore also a, theoretical mi simum and neither transmitting nor receiving elliciency is reduced by the addition ot the auxiliary resistance which is necessary to secure treedom from side tone. The foregoing consideration will serve to explain the desirability of having the line and auxiliary resistanee conjugate as well as the transmitter and receiver.

ln my present invention l provide a substation comprising transmitter, receiver, auxiliary resistance and transformer, and

so proportion said component elements and so relate them to a telephone line and to each other that, in combination with said telephone line, said substation satisfies all et the foregoing requirements.

4@ l have discovered that the above-menH tioned requirements may be satislied by a large number of arrangements employing the minimum number of elements and all equally etlicient and without side tone.

i5 -While theoretically all these arrangements are equally good, practical considerations malte certain arrangements preferable.

rllhisl application is a division ot applica tion Serial Number 119,282, tiled September 9, SlG. The invention is best understood by reference to the accompanying drawings in which:

Figure l is a diagram illustrating one form of substation embodying the invention of this application.

1Figs. 2 and 3 are diagrams illustrating the current flow in the substation oi' Fig. l dur ing transmission and reception respectively.

Fig. l is a schematic diagram of' the substation illustrated in Figs. 1,2 and 3.

In order to illustrate the scope of my invention and elucidate the principles on which all specific embodiments rest, a general theoretical discumion will new be given which applies to all substations satisfying- 'the requirements heretofore stated in this specification. ln this discussion and the equations and formulae included in this specification the subscripts 1,2, 3 and a will refer to transw mitter, receiver., auxiliary resistance and line respectively. Thus L, l2, I3, l, will denote the currents flowing in transmitter, receiver, auxiliary resistance and line respectively, while ll, will denote the resistance ot the transmitter, l, the resistance ot the receiver, etc. 1

'Consider' a substation consisting of transmitter, receiver', auxiliary resistance and appropriate transformer windings, connectedto a line ot given impedance. In practice the line connects two similar and equal substations between which communication is established. It is a well known principle that it 'a terminal impedance is connected to a source ol electromotive force through a line ot impedance where is the resistance and it, the reactance component oli' the impedance, 'the terminal impedance must be lltf-z'llt, for maximum absorption of energy. ln particular it the lineimpedance has no reactance component. the impedance ot the terminal arrangement as seen trom the line should be equal to the resistance component of the impedance oir' the lino. The condition, then, that the substation shall have maximum energy absorption from the line is that its impedance, as seen from the line, shall be equal to the line impedance. The signilicance of the foregoing statement may be explained by reference to Fig. l as follows; Let the substation be disconnected from the line and let the impedance of the substation be meas urcd across terminals Ll and 5. Then the impedance so measured shall be equal to the impedance ot the line. lith the line terminated at each end by a substation satisfying this condition, the line may bereplaced, as regards transmission from either substation, by an impedance element of resistance equal to the impcdanceotL the line. Any react-,ance eli'ect, which is in practice small, may be eliminated by neutralizing reactance and, therefore, need not be considered. rThe condition, then, that the substation have maximum energy absorption trom the line is that its impedance as seen from the line be a pure resistance of value equal to the impedance ol the line. This condition is evidently equivalent to the following requirement; let an electromotive torce be impressed on the substation terminals through a resistance equal to the impedance of the line; then. the energy consumed in the silbstation Ashall be equal to the energy consumed in said resistance.

matarte Further, line and auxiliary resistance are conjugate by requirement (2), as herembefore stated, or in other words, the auxiliary resistance is connected to points of equal potential with respect to an electrolnotive force applied to the line terminals. Moreover, the impedance of the substations as seen from the line should be equal to that of the line. Let, 'then an electromotive force E4 be impresseddshrough a resistance R4 on a substatiorifw,1 ,feti transmitter and receiver resistances areVR1 and R2 respectively, and the resultant currents in line, transmitter and receiver be I4, I1 and I2 respectively. Then, the impedance across the substation terminals'must be R4 as seen from the line and the total resistance in series with E4 is 2R44, and since the current in the line is I4,

el may be formulated by the following equation E 2 ai; (l)

This equation states that the energy consumption in the resistance R4 is equal to that in the substation, and'that the substation is equivalent. as seen from the line, to a resistance of value R4. 4

Similarly, if transmitter and receiver are conjugate the condition that the transmitter shall have its maximum output to line and auxiliary resistance may be formulated as follows: Let an electromotive force E, in the transmitter produce currents Il, 'T4 and T., in

vtransmitter, line and auxiliary resistance.

Then, for maximum output, it follows that:

`Equation (2) is the analogue of equation (D'Qand may be interpreted as follows by reference to l: Lot the transmitter be disconnected from terminals 1 and 6 and let the impedance be measured across said terminal. Then if equation (2) is satisfied the impedance so measured is equal to the impedance of the transmitter itself. In other words, the impedance of the combination, as seen from the transmitter is equal to that of the transmitter itself.

-s hereinafter shown for the particular( embodiments of my invention, equation (2) follows as a consequence of the conditions of double conjugacy and equation (l). There fore the foregoing four requirements impose but three restrictions on the substation.

To complete the general discussion it remains to consider the energy division between receiver and transmitter when receiving, and between line and auxiliary resistance when transmitting. Let W0 be the total amount of telephonie energy developed by the transmitter at the transmitting substation; then, by equation (2), l/Qlfl/'O is the amount of energy delivered to line and aux iliary resistance. Let the amount of energy taken by the auxiliary resistance be m times that taken by the line, then the amount of energy taken by the line is Y l l/zwom so that the transmitting efficiency is measured by Of the total energy delivered to the receiving substation, let the transmitter absorb jl/ times that absorbed by receiver; then the receiving efficiency is measured by The over-all efficiency from transmitter of one station to receiver of communicating station is clearly proportional to the product of the transmission efficiency and receiving efiiciency; therefore the over-all efficiency is -by formulae and (4f): y

ln order to demonstrate the above state ment, namely that .fag/:1, designate the elements or branches T, R,-X and L by l, 2, 3 and 4, respectively, and let 1 and 2 be con jugate and also 3 and l be conjugate. iurther it Will be assumed for an electromotive force in branch 4:, equation (l) is satisfied r while for an electromotive force in branch. (1.),'equation (2) is satisfied. Let 55,', de-

,note the current produced in. branch or eleicc ment 1 by a unit electromotive force in branch 1, S12 the current produced in branch 2 by a unit electromotive force in branch 1, etc. Then by the conjugacy of branches 1 and 2 and branches 3 and 4, it follows that Sizzsaizo Also by equation (1) l l Y SMR# SARZ l SuZRi Tft; (l l and by equation (2) 3112K! SiazRs 'l SirzR-i i (2,)

New in accordance with the notation adopted in this specification, the energy consumed in branch 3 ig a: times that consumed in branch 4 when an electroinotive force acts in branch 1; therefore Also the energy consumed in branch 1 is y times that consumed in branch 2 when an electroinotive force acts in branch Zl; whence From (c) and (0l) it follows at once that afg/:1.

bviously the expression given by lormula is a maximum when g/:L This means that for a given amount of telephonie energy developed inbthe transmitter at the transmitting substation a maximum amount is usefully delivered to the receiver at the receiving substation connected by the line, when g/:L Since the maximum amount 0l' energy in the receiver is the prime desideratum of telephony, it would appear that the substation should'be designed to make /zl. Another consideration, i however, modifies this conclusion somewhat, namely, the effect of line noise. Since the line noise originates in the line the amount delivered to the receiver is proportional to 1 1 -l-y (see equation 4) while the amount oit energy testina/5 delivered from the transmitter of the coinmunicating station is proportional to (see equation 5). The ratio oif the latter to the former is and this increases as y increases beyond unity. Tt will be clear, then, that if 'y is made greater than unity the substation discriminates against linev noise as coinpared with the signals it is desired to receive. The amount ot discrimination de sired depends ot' course on the amount of line noise present. `li`or conditions occurring in practice I have found by experiment that a desirable value for 1,1/ is lWith Lthis value of y the over-all eiiicieiicy is reduced 2.8% below the maximum for y/l, while the receiving elliciency alone is reduced 16.6%. 1t is thus seen that a goed degree ot discrimination against line noise is obtained with a small loss in over-all etlicieiicy.

The above consideration as to over-all elliciency and discrimination against line noise may be formulated as for an electromotive force inserted in the line. ln this equation y is to have a value lying between 1 and 1.5 preferably.

Proceeding now to a description or' the specific circuits, in liig. 1 a telephone line L is shown as connected to a substation coinprising a transmitter T, a receiver 1t, an auxiliary resistance X, and a transformer having four windings NU N2, N3 `and N4. Said windings are on the same magnetic circuit and the transformer is preferably respectively, are connected together by con` duetor 12 while terminals 13 and 14 of wind ings N2 and N are connected together by conductor 15. Conductors 12 and 15 are connected by condenser 16. The function of condenser 1G is to conline the direct-current battery supply current, transmitted to the substation over line 1, to the transmitter and to exclude it from the receiver and auxiliary resistance. Said condenser should therefore be of reiatively large capacity so as to have negligible impedance at telephonie tren quency. that impedance it presents at telephonie frequencies is largely neutralized by theunavoidable magnetic leakage or the transformer so that the eiiect of said conn denser will be ignored as regards the true telephonie currents as distinguished from the direct battery supply current.

Referring to liig. 2 which. is a diagram illustrating the operation of transmitting in which condenser 1G is omitted for simplicity, arrows indicate the relative direction of telephonic current ilowy through the various branches and circuits. The direct battery supply current is notindicated, said current merely serving to energize the transmitter so that actuations of said transmitter cause it to function is a source of telephonie energy. In said figure elements in which there is no riow of current corresponding to actuation of the transmitter are indicated in dotted lines. Referring to Fig. 2, the operation of transmitting will now he described. Actuation of the 'transmitter T sets up a Vtlow of alternating current i-n said transf mitter. The current flowing in the transmitter, denoted hy l1, divides at terminal ll, a part l, flowing out over the line, said current being the usefully transmitted current, while a part l, flows through the auX- iliary resistance and is wasted therein. Since when the substation is proportioned in accordance with the rulesof design hereinafter set forth, the substation is free from side tone, no telephonie current flows in receiver R 4during transmission, and said element is indicated therefore in dotted lines. This 'condition is only attained when the relative number of turns of windings N1, N2, N3 and lil, are properly proportioned with refered/ce to the impedances of line L and auxiliary resistance X. l/Vhen they are so properly proportioned the induced Voltage in 'winding N2 just balances the potential dirference between terminals 7 and i3 and no current flows in said branch.

The proportioning or' the component elements substation of l in order to satisfy r {i1-'rement that the transmitter i iY all he conjugate, will now he deduced.

ln tie derivation of the succeeding niule certain simplifying assumptions will be made. it ill he assumed that vthe resistances of the transformer windings and the reactance of the condenser" are negligihly small, that there is no magnetic leakage loetween the transformer windings and that the self-inductances of said windings are Very large compared with the impedances of any ot' the other component elements of the substation and the line inipedance.4 En

perience has shown that these simplifying assumptions are :gustn'ied and that the assumed conditions may he closely realized in.

all, :udg-Mnl@ Consequently, as regards transmission (nf-THS) a: (ne-"7711)4 Now letting V denote the potential (liderence between terminals 11 and t5, it is clear that the same potential dili'e'rence exists between terminals l0 and 5, 13 and 7, and

lll and 8. The voltages induced in the four coils are clearly proportional to the relative number of turns of the coils; thus if K de notes the voltage induced per turn the Voltages induced in coils N1, N2, N3 and N, are clearly Kal, Kw2, Kn, and Km respectively. lt will then be evident that, since the voltage impressed between two terminals is equal to the impedance drop between said terminals,

Eliminating V whence Aso Equation (8) expresses the relations which must obtain ani-ong the component elements vin order that no current shall flow through the receiver in consequence of the actuation of the transmitter.

Referring' now to Fig. 3 which is a diagram illustrating the operation of reception of signals over line L 'from a distant sta tion, current L flowing over line L enters the substation through Winding' N4. current divides at. terminal il, a part l1, flowing through transmitter T, and 'the remainder l2 fiowing through receiver ll.. lit. is the latter current which constitutes the usefully received Current. lo current llows in auxiliary resistance X when the, eomponent elements are properly proportioned ashereinaifter set forth. This is due to the fact that the voltage induced in Winding N3 just lialanees the voltage impressed between terminals 5 and 10.

The proper prnmortioning` for conjugaejy' of line and auxiliary resistance will now be deduced. Referring to Fig. 3 andenriiloying the same notation as that used in deriving equation (8), it will vhe Clear that Lzl-l-QZ and that when the niagnetizing current is negligible,

lt therefore follows that, as regards reception,

Further it V denotes the potential diferenee between terminals 10 andL 5 and l tne induced voltage drops per turn of each iena-eral thang-riga Eliminating lili t by equation (9) it follows .H1 ('T (La) This is the formulation of the relations Whieh must obtain among; the component elements 1n order that line and auxiliary resistance shall sonstige This The conditions necessary to the satisfaction of the remainingjT fundamental require ments of the ideal substation, will now be formulated for the substation of Fig. l. Considering requirement (4i) which is iormulated in equation (l), it is evident that this requirement may loe Written. as:

i 2 i'. 2 Kahlil.) Walt) whence by equation (9) ein 2 @fat R4-R1 W2Mni +R2 nfnzj (il) Considering next requirement (il) as formulated by equation (2) and eliminating the currents therefrom by aid of equau Equations 8, 10, il, 12 and 13 formulate all the conditions necessary'to the satisfaction of the fundamental substation requirements. it remains to put these equations in more Convenient 'form 'for use design formulae. ln particular it is desirable to express the constants of the substation in terms of R1, lt,i and 1/ since these quantities lgenerally speciied in practice. The combination of equations (10) and (11) givesby the elimination of E2.,

The saaie result follows vfrom the elimination ot from equations (8) and (l2).

Equations (l0), (13) and reduce to lin 'these ias-'t twoequations the right hand 1 l saolutiraa. with narrative signs. lf the iii RA 2 iat inode of Winding corresponding to the'| lll) naaaava 5 15 are expressed in the following design formulae: l

The type of substation disclosed above and illustrated in lthe accompanying drawing is but one of a large number employing only one transformer and one auxiliary resistance and all of these are ideal in the sense that they satisfy the fundamental requirements for an ideal substation, as stated heretofore in this specification. It will be understood therefore, that my invention is not limited to the specific embodiments herein illustrated, but is broadly directed to providing a substation comprising a single transformer and only one auxiliary element, Which is so proportioned With reference to the line With which it is to be cooperatively combined, that it is ideally efficient and substantially without side tone. Furthermore, 1 do not desirel to limit the design of thesubstations herein disclosed and illustrated to the accompanying design formulae. These formulae are derived on the assumption that ideal transformers are employed and that the component elements have no reactance, assumptions which are only approximately justitieel in practice. When particularly high precision is desired I may, therefore, proportion the substation more precisely by taking into account the fact that the transformer impedances are finite, and that the line and the various substation elements may have in general some reactance. The accompanying formulzc, however, give quite satisfactory results, and the methods by which they are derived will enable one skilled in the art, to compute more precisely the substation constants when desired.

1t will be understood 4that in the appended claims, lWhere certain elements are said to be conjugate, or certain impedance relations are said to exist, since in practice these conditions can, in general, only be approximated, these expressions will be satised by structures substantially conforming thereto, especially ivhere some compromise with regard to the rigid requirements is necessary in order to discriminate against line noise. llt Will be further understood that While 1 have specifically illustrated and described my invention as embodied in a telephone substation it is capable of many and varied embodiments which render it applicable in other kinds of signaling and consequently my invention is not to be limited to the particular form and use herein disclosed.

What is claimed is:

1. The combination of a substation and a telephone line, said substation comprising a transmitter, a receiver and an auxiliary resistance, a terminal common to said line and three substation elements, a for coil transformer, each coil being individua ly in A series with one of said four elements and a telephone line, said substation comprising a' transmitter, a receiver and an auxiliary resistance, a terminal common to said line and A three substation elements, a four coil trans.- former, each coil being individually in series with one of said four elements and a terminal common to said four coils, the compo nent elements of said substation being so proportioned that said line and auxiliary resistance are conjugate.

4. The combination of a substation and a telephone-line, said substation comprising a. transmitter, a receiver and an auxiliary resistance, a terminal common to said line and three substation elements, a four coil transformer, each coil being individually in series with one of said four elements and a terminal common tosaid four coils, the component elements of said substation being so proportioned that the impedance of the substation, as seen from the line equal to that of the line.

5. The combination of a substation and a telephone line, said substation comprising a transmitter, a receiver and an auxiliary resistance, a terminal common to said line and three substation elements, a four coil transformer, each coil being individually in series with one orsaid four elements and a terminal common to said four coils, the component elements of said substation being so proportioned that the impedance of the combination consisting,- o'l line, receiver and auxiliary resistance, as seen from the transmitter, is equal to that of the transmitter.

6. The combination of a substation and a telephone line, said substation comprising a transmitter, a receiver and an auxiliary resistance, aterniinal common to said line and three substation elements, a tour coil transformer, each coil being individually in series with one oli said four elements and a terminal common to said four coils, the com ponent elements of said substation being so proportioned that said transmitter and receiver are conjugate, said line and auxiliary resistance are conjugate, the impedance of the substation, as from the line is equal to that of 'the line, the impedance of the combination consisting of line, receiver and auxiliary resistance, as seen from the transmitter, is equal to that of the transmitter.

'7. ln a two-Way signaling' system, an induction coil having' four windings, a circuit for the transmission and reception ot signals including' one windingl of: said induction coil, a transniittinpcircuit proper comprising a transmitting apparatus and a second winding of said induction coil, a

, receiving circuit proper comprising a receiving apparatus and a tliird Winding of said induction coil, and a balancing circuit including the fourth finding of said induction coil, all ci' said circuits having a common terminal, and said elements being so proportioned and related that the iin pedanee ot the combination comprising said iii-st nan'ied circuit, said receivingr circuit proper, said balancing circuit and said transformer, as seen from said transniitting.;n circuit proijier, is equal to the impedance of said transinitting circuit piopcr.

aliing system, an inr windings, a cirssion and reception or" oneY wli'iding said in- ,i i'tt' circuit proper a iran, nitting' apparatus and winding said induction coil, a uit y )er comprising," a re and a. tliird Winding of a lmlancinfi` circuit 'ling of said inducts having;q a coinbeing s0 id receiving eeivinif: ap

'.7 `.`-/'..4..,., 'l sain inductmn con, includine` tbe fourth tion coil, allot A circuit and said transmitting circuit proper are conjugate.

9. In a twoway signaling system, an induction coil having .tour windings, a circuit for' the transmission and reception of signals including' one Winding of said inductiony coil, a transmitting circuit proper comprising transmitting apparatus and a second winding of said induction coil, a receu/ing clrcuit proper comprising a receiving apparatus and a third Winding of said induction coil, and a balancing circuit including the :tour-th Winding ot' said induction coil, all of said circuits having a common terminal, and said elements being so proportioned and related that said balancing circuit and said first named circuit are con jugate.

l0. In a two-Way signaling system, an induction coil having four windings, cir- 8 ril cuit for the transmission and reception of i signals including one winding et said indue tion coil, a transmitting circuit proper coinprising a transmitting' apparatus and a second Winding of said induction. coil, a receiving circuit proper comprising a receiving apparatus and a third Winding of said induction coil, and a balancing` circuit inn duction'coil. having tour Windinc's, a circuit lfor the 'transmission and .reception of signals including one Winding, oi" said induction coil, a transmitting1r circuit proper comprising a transmitting apparatus and a second Winding of said induction coil, a re-1 ceiving circuit proper comprising a receiving apparatus and a third Winding of said induction coil, and a lmlancinp,- circuit including the ourtli Winding; of tion coil, all of said circuits liriiving a corn@ mon terminal, and said elc'ents being' proportioned and related tb. id trav ting' circuit and said receiving," circui conjugate; said llrst named circuit and lialar-icingcircuit are conjugate; tlfie impedance oil' tlie combination, comprisinpr i tiret named circuit, said recei'ifing ciMd proper, said balancing circuit and se transformer, as seen Jfrom said transmitting circuit is equal to the impedance of sait transniittin,gcircuit; and the impedance i fir a Said induc- Ddr@ u the combination, comprising said transmitname to this specification in thc presence of ting circuit proper, said receiving circuit two subscribing Witnesses, this 10th day of proper, said balancing .circuit and said March 1917.

transformer, as seen from said first named GEORGE A. CAMPBELL.

5 circuit is equal to the impedance of said Witnesses:

first named circuit. KENNETH L. WILKINSON,

1n testlmony whereof, I have signed my ALFRED KAUFMANN.

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