# Патент USA US2115826

код для вставкиMay 3, 1'938. E. |_. NORTON ET Al. 2,115,826 IMPEDANCE TRÁNSFORMERFiled Sept. 30, 1936 2 Sheets-Sheet 1 ATTORA/Eff Patented May 3, 1938 v UNITED STATES PATENT OFFICE 2,115,826 IMPEDANCE TRANSFORMER Edward L. Norton, Summit, N. J., and Ronald F. yWick, St. George, N. Y., assignors to Bell Tele phone Laboratories, Incorporated, New York, N. Y., a. corporation of New York Application September 30, 1936, Serial No. 103,316 ' 1s claims. (o1. 17a-44) 'I'his invention relates to impedance transform- rents induced in it by the coil. While this effect ers for coupling lines or electrical devices of un- could be eliminated or reduced to a small value equal impedance and has for an object to provide an impedance transformer which will be substan5 tially independent of the frequency over a Wide range of high frequencies. In the preferred embodiment the coupling de- by slitting the sheath, it is desirable because it permits a much greater rate of change in e than would otherwise obtain, and also because it acts 5 as an electromagnetic shield for the coil. The tapering effect can be controlled by varying the vice takes the form of a tapered transmission line comprising a long cylindrical coil of a large lo number of turns surrounded by a concentric metallic sheath of circular cross-section in which the sheath or the coil is tapered in radius. The diameter- of sheath or of coil or both, or by vary ing the number of turns per unit length of the coil. This latter could be accomplished by vary- 10 ing the pitch of the winding or by using a multi layer winding and varying the number of layers. dimensions of the coil and sheath and the rate of taper have values dependent upon certain fac16 tors such as the ratio of the two impedances to In the embodiments hereinafter described, single layer coils of constant pitch have been used, with either the coil diameter uniform and sheath di- l5 be connected by the device and the minimum frequency to be transmitted as will be explained hereinafter. In employing such> a properly de- ameter variable, or vice versa. When a tapered line is so constructed that its impedance varies from some value, 21, at one end to a different signed device as ahigh frequency transformer between a low impedance line and a high impedance value, 22, at the other, it behaves like a trans former at suiiiciently high frequencies. It is this line one terminal of the low impedance line is property with which We» are here concerned. connected to the low impedance end of the coil, Nl 0 Referring to the drawings, one terminal of the high impedance line is conFig. i represents a longitudinal section and Fig. nected to the high impedance end of the coil, » 2 a cross-section of an impedance transformer in o5 and the other two terminals of the two lines are which the coil is of constant radius and the sur- 2, connected to opposite ends of the surrounding metallic sheath. The parameters of such a tapered line may be readily computed in order that its rounding sheath is tapered; Fig. 3 represents the manner of connecting the impedance transformer of Fig. l in a transmis impedance at each end will be substantially equal sion circuit; 30 to the impedance of the line connected thereto. The device constructed in this manner will act efficiently as a step-up transformer over a wide range of frequencies and the device is of particular interest in the frequency range above one Figs. 4 and 5 represent another type of im- 30 pedance transformer in which the coll is of ta pered diameter and the surrounding sheath is of constant radius; Fig. 6 is an enlarged longitudinal section of the 35 million cycles per second. tapered line of Fig. 4; _ A uniform transmission line is characterized by an impedance, f- 35 Fig. '7 represents the frequency transmission characteristic of the tapered line of Fig. l; /f 1=\ ë ¿o Fig. 8 represents the contour of the tapered coil line of Fig. 4; and Fig. 9 represents the contour of the tapered 40 and a, velocity constant, 1 a :w/_L-ö 45 where L and C are the inductance and capacity per unit length of the line. It is possible so to construct aline thatLand C vary along its length, giving thus a tapered line. A flexible and practical arrangement consists of a solenoid enclosed 50 in a conducting sheath. The ratio of sheath diame-ter to coil diameter at any point then deter- mines C, while L is determined by this ratio, the number of turns per unit length, and the diameter of the coil, at that point. The sheath af5 fects the inductance, of course, because of cur- Sheath line 0f Fig, 1_ v In determining the parameters of such tapered line used as an impedance transformer advantage is taken of the observation that when the dif ferential equations are expressed in terms of the 45 time required fOr a Wave t0 Travel along the line, instead of in terms of the distance, the ve locity function drops out. That is, the electrical characteristics of a tapered line depend solely on the Way in which the impedance varies with the 50 time of transmission. Thus all the electrical characteristics obtainable with tapered lines can be studied by considering different functions for this one parameter. A particular function for the impedance having been chosen, the actual 55 2 2,115,826 shape of the line, for any desired type of con struction can be found by direct means. We begin the mathematical discussion by writ ing down the fundamental differential equation for a non-dissipative transmission line with a sinusoidal applied voltage of frequency (d is the value of the line impedance at the low im pedance end, say the left-hand end. The phys ical significance of t1 is explained as follows: Sup pose the line were extended to the left until a point was reached where the line impedance was zero. Then t1 is the time required for a wave, started at this end of the line, to reach that part of the line where 2:::1 (the actual extremity of the physical line). Another type of characteristic is the exponen tial: 10 x(t)=z1e"‘ (5) in which the rate of taper is determined by a. 'I'his is a limiting case of (4) obtained by allow ing m and t1 to approach infinity in such a way that i==current at same point L=inductance per unit length at this point C=capacity per unit length at this point 20 10 f1 remains constant, j:«/îî When the function (4) is used for zu), Equa tion (3) becomes Expressed in terms of the impedance, .=\/ë C 25 and the velocity, 25 1 8:: A «l C these equations are: d'v 30 z “ai-wal d _ 1 "ai Jwza" (l) Then Equation (6) becomes d‘W (2) 35 The time required for a wave to travel to this point from the end where X=0 is clW -1 2 ßLîsï-i-ad--l-[?-(E-r) :IW/:0 (7) S This is Bessel’s equation and the general solution for the current in a tapered line having the type 35 of taper given by Equation (4) is thus X f= 0 «Qi 8 where 40 from which 40 @11m-Hol and lf2-¿ammi 2 2 si _i dX-_a Since are Bessel functions of ñrst and second kind, re d spectively, and of order df d _ 1 d äîf=üaît-îdt m-l Equations (1) and (2) can be written l 2 and argument w(t+t1). Aand B are constants which are to be determined by the boundary conditions. The voltage can be found from the 50 current by Equation (2') . When a tapered line is used as a transformer 'I'he velocity, a, has canceled out, showing that the electrical characteristics of the line depend only on the impedance 2 regarded as a function of the time t. Diiîerentiating Equation (2') once with respect to t and using (1') and (2') to eliminate o and the values of the line impedance z, at the ends oi' the line are made equal to the terminal imped ances at the respective ends. The measure of the electrical performance we take to be the “insertion gain ofthe line between the terminal resistances”, which we deñne as Insertion gaìnE 20 log). ä-,db 60 we get df2+zdfdf+w F0 (3) In order to study the various possible electrical characteristics it is now necessary to assume a particular functional form for ad). One of the simplest is 'I‘he rate of taper is fixed by the pure number m. This function leads to solutions of (3) which, for general values of m, contain Bessel functions. 60 >where I2 is the current in the receiving resistance when an E. M. F. is applied to the other end of the line through the terminal resistance appro priate to that end, and I2' is the current which would iiow in the receiving resistance if the ta pered line were removed and the input connected directly to the receiving termination. The boundary conditions are: At the low impedance end, 70 t=0 and E=z|i(0)-{-v(0); at the high impedance end, (9) V(fz)_ t = t3, say, and i( t2) ,-z, When m is an even integer, the solutions are in 75 terms of sines and cosines. In Equation (4), 21 E is the generator E. M. F.; tz is the time re 75 2,115,826 quired for a wave to travel the length oi' the line; i(0), 11(0) are the current'l and voltage at the low impedance end of the line; i(tz), v(tz) are the current and voltage at the high impedance end; and 21, z2 are the values of the terminal imped ances. The constant t2 is determined in terms of zi, zz, t1, and m by Equation (4) : In the ilrst two cases when à f1 is fixed the insertion gain may be plotted as a function of mtl. The ratio - .a t’i is found from the impedance ratio by Equation (4): 10 wier-1l -t-z=í7--1, for linear line, Z1 Equations (9) thus permit the determination of 16 the constants A and B, and ñnally the insertion gain. Z The insertion gain will now be given for different rates of taper of the impedance by ñrst, making m=1 (so-called linear line) ; second, making m=2 (so-called conical line); and third, making m as well as t1 approach inñnity in such a Way that 2 fl sertion gain may be plotted as a function oi' ` z_w a The parameter atz is determined from the im pedance ratio by Equation (5) : dl 25 ‘E 2\/í’ 30 . In the exponential case, when at: is fixed the in 25 remains constant (so-called exponential line). ' For the linear line (m=1) : Insertion gain=20 log", . ;2l for conical line. l The quantity t1, in the case of linear and conical lines, or a, in the case oi’. exponential lines, is 30 IV _- 20 lOgm L 85 wtl'l' D00 N 1 in which (10) fx determined in any speciñc case by the lowest 40 40 45 The J- and Y-functions are Bessel functions of the ñrst and second kind, respectively, and vsatis iy the same recurrence formulae. ` For the conical line (m=2) : 14,--’1 Insertion gain=20 logm--É zz Zi frequency it is desired to transmit. The “cut-oft` frequency” of a tapered line is not, in general, 50 sharply defined. Consequently, one should plot the insertion gain for the impedance ratio de sired before deciding upon the value of t1 ( or a). The above discussion was concerned with the study of possible electrical characteristics of ‘ tapered lines without regard to the mechanical cos 2 graff-«2 -wtl sin 2 t1 60 For the exponential line (m and t1= œ y2=a> l‘1 Insertion gain=20 loglu fl (u) construction. We shall now show how to deter mine the shape, size, and number of turns of wire for two particular kinds of mechanical construc 65 tion, first, where a tapered sheath and a constant radius coil are employed and, second, where a tapered coil and a constant radius sheath are employed. 70 I-Development of equations for transformer , 70 with. tapered sheath First, let the tapered line be made up of a long cylindrical coil of circular cross-section having a constant radius ro and N turns per unit length, 75 2,115,826 4 surrounded by a shield with a variable radius r. Now g The inductance per unit length is: dy is found from (19): dx 1 l-e-U-i-ye‘” This is substituted into (23), Ygiving the differ ential equation 10 where c=3><101° centimeters per second, the velocity of light. The factor 2 15 in the inductance formula takes account of the "short-circuiting” effect of the sheath which per mits taper in the inductance. The impedance and velocity are given by X= (24) 20 The appearance of a function of t in the inte grand may be confusing, since integration is to be performed with respect to y. 'I'he way this is to be handled will be made clear in the speciñc cases now to be discussed. 25 Let the function f(t) be that determined by Equation (4): f(f)=(1 + 2)" 30 30 Differentiating : and let the subscripts 1, 2 reier to the low and high impedance ends of the tapered line, respec tively. Then 2 -9 z=c E: #yO-ew) (18) But what) lll-l 35 l and from (19) or 1+i-7mm" f(f)= „_-yë el?) 1_ ,qw/¿(1151). y1(1 -- e’f’i) 40 (19) (20) We want a relation between X, the axial distance, and y. By deñnition of t, ' _gg y(1-e“”) î tl 1(lg-_e-Ul) The possibility of expressing f’(t) explicitly in terms of f(t) was necessary to the solution of the present problem, the determination of a usable relation between X and y to arrive at the shape of 50 _din dX '_ a and from (20) ï =~----1d y avv m Hence we have m-l y a=8n 11;; 40 .Y1 1_8 (21) the tapered sheath. Finally, substituting this expression for f'(t) into (24) we get the desired equation 55 Suppose We consider a perfectly general variation of z with respect to t and write it (25) z=z1f(t) Later, the speciñc forms of f(t) given by Equa tions (4) and (5) will be taken up. Diiîerentiat ing (22) we have dz__ , 'd-t-Ilf (t) Where This integral of Equation (25) can be expressed in series form, the ñrst few terms of which will be given for certain values of m. These give suflìcient accuracy for practical design purposes. If greater accuracy is desired, more terms must be computed. But it should be noted that when ever a series is diillcult to compute one can al f'm-f f'ïf ways resort to graphical integration. For the linear line (m=1, (25) becomes But 70 75 «Langres dt dydXdt and using (21) we get 70 (26) 75 «wat TIT-1 :a Mg M2,7. 1 t* (1_0-"luf," For the exponential line 15 and nnauy 13 ` 2Xm Sat1 20 20 l1 or expressed in the series form 25 au _210gyl (36) __96 -l-“V + . . . II-Development of equations ,for transformer with tapered coil Equations (25), (26), (27.) and (28) refer to which corresponds to Equation (25). 25 The equations corresponding to (26), (27) and (28) are then: For the linear line: 30 the case of a line with uniform coil and tapered 30 sheath as in Fig. 1. The corresponding equations for a line with tapered coil and uniform sheath as in Fig. 4 are derived in a similar fashion. 35 Let r :radius of coil Tozradius of sheath N=number turns per unit length r1=radius of coil at low impedance end r2=radius of coil at high impedance end 35 40 y=2 10g ç fram which Si) _ _K__gê z__ 2 _l a .__ --llosyx 960' y1) 960'“ _ y1) - -- In ¿A III-Calculations for specific case involving ta pered coil z=z1 ( (34) 1 (3 5) It will now be shown how the design is to be carried out for the case where the coil is tapered 60 and the sheath has a constant radius for which the equations are given in Section II. We shall assume a given problem in which the lowest fre quency fc which the tapered line is required to pass is 5.2 X106 cycles per second, that the im pedance a1 at the small end of the tapered line should be 70 ohms and the impedance z2 at the large end of the tapered line should be '700 ohms. One must first decide upon the desired taper oi the sheath whether it should be linear, conical or 70 exponential. From the standpoint of electrical characteristics the exponential taper is prefer able and will be chosen for the following discus sion. Certain preliminary steps are involved before 6 2,115,826 one can directly ñnd the parameters of the ta pered line for the given values of zi, zz and fc. Assuming we desire the exponential type of taper we must ñrst find the value of ata, in order that this value may be used in Equation (12) for the insertion gain of the device. From Equation (5) 700 at: =10g É1 =10g 10 (40) the impedance of the tapered line will not vary monotonically from one end to the other. Fur thermore if we took 59== 2.06 l' the shape of the coil form would have an iniìnite slope at the high impedance end which would be undesirable in practice. Therefore we have the requirement that It is now necessary to consider the insertion fo gain characteristic of the exponential tapered line and for this purpose a curve should be plotted with various assigned values of must be less than 2.06 and since 15 15 _ as abscissae, and as ordinates the resulting in sertion gains as given by Equation (12). For our assumed problem, the resulting curve will take the form shown in Fig. 7. It will now be neces sary to choose some “cut«olï” point for TT beyond which the insertion gain is at a satisfac tory high level, and assume that We choose this cut-off point as the point A on the curve of Fig. 7 for which the insertion gain is 4.5 decibels. It 30 will be noted that for the point A the value of is 2.43 for our speciiìc example. Designate this value of Q .Y2-2 10E r2 T this means that y2 should be less than 1.44 in the case of the tapered coil-uniform sheath line. At the same time it must be noted that the smaller 20 y2 is chosen the smaller will be y1 and if y1 is made very small the separation between the sheath and the coil at the low impedance end will also be very small. A study of these factors indicates that y2==1 is a reasonable value. 25 Assuming this value of 112:1, we now solve for the values of y1 and ao. The value of y1 is to be obtained from Equation (34) letting 2:22 and ¿1:11a in that equation from which 30 This is a transcendental equation in y1 and its exact solution cannot be obtained algebraically. Although a graphical solution is generally advis 35 able, we can use the first few terms in the power series for an approximate formula for y1 in terms of y2 and El providing Z2 40 Up to the present point the calculations apply to either a tapered sheath or a tapered coil. Ii.' we wish a tapered coil and uniform sheath we El 45 have by deñnition from Equation (30) the follow ing expressions for y1 (the value of y at the low impedance end of the line) and 'J2 (the value of y at the high impedance end .of 50 the line): 50 the radical 1/yze_"”(1-e-U2) 55 Where To is the radius of the sheath, r1 theA radius of the small end of the coil and r2 the radius of the large end of the coil. As an expression in volving N, the number of turns per centimeter of is equal to 0.483. Thus, from the above equation 1li-10.050 Nòw from Equation (33) mung 2:22 and 11:11: 60 the winding surrounded by the sheath, we also have by definition from Equation (29) , 60 9X 1020>( 10ng X 0.483 One is free to specify any one of the quanti 85 ties y1, y2 or au, after which the others may be 65 uniquely determined. But it is preferable to as sign a deñnite value to yz for it can be shown from Equation (31) that the largest value which can be used for l' is 2.06 and that for a larger value of 75 70 We can now choose N and ro in any way as long as their product equals '7.71. If, for exam ple, we make ro=1 inch, then N becomes 7.71 turns per inch, a reasonable value. 75 'aliases Y rv.-'cazenlmmm> fer meme we involving ta 'or x where y=m and hence rmmnquauon (so) ` pered sheath after_aiviainqhothmiedery ’l‘helengthLofthe-taperedcoilisthatvalue It 'wm now be shown how the design‘is to be 4 carried out for the case where the sheath is ta-- pered and the coil is >of constant radius, the a. Í ` `y ' 2sy v . 1 L-F-:Dog¿jmoe-ym-mw-m]- p > . ' es.: cm.=25.7 inches The value oi' X corresponding to each value of y chosen between w=0.050 and m=1 can be com puted in the same way. l'br example, ten values ci' y intermediate thesetwo values may be chosen. The shape oi'- the form which supports the ta pered coil may be found by plotting ' lo' ' III that 21 the low impedance» is 70 ohms, zz the high impedance is 700 ohms, and the cut-oil' frequency fs is 5.2x10‘ cycles per second. The 10 notations employed are similar to those -em ployed for the tapered coil except that in the present case r is the variable radius o! the sheath and n is the radius of the coil. ~ The expression for the value oi' the insertion 15 gain for the tapered sheath device is the same as that used for the tapered coil, namely, Equation (12), so that the curve oi insertion gain plotted _ against elk the value ot equations for which are given in Section I. ` We shall assume as in the other example in Section ’ 20 l’ will be that of Fig. 7 and we will utilize the same fo cut-oi! point where being »computed for each chosen value of y by v the Formula (30) ' ' 25 @was - a from which a=26.9X10° as in previous example. Again let yz=1 as in previous case, although it 30 may be pointed out that the restriction that 1l: for the tapered coil line should be less than 2.06 does not apply to the tapered sheath construc tion. We have by deiìnitlon from Equation (17) For these assigned values of y between y1=0.050 and m=1 we can ilnd not only the ratio ' 35 a» f but also .the distance that ratio holds from the small impedance end ot the line by means of Equation (39) and hence can plot fo ' t against L as has been done for our example in Fig. 81'` f-'I'he` curve of Fig. 8, therefore. sives the coil shape for our' speciñc example. - ' ' 'I'he radii of the two ends‘of the 'coil canfrbe where ri is the radius of small impedance end of sheath; ra is radius of large impedance end of sheath; ro is radius of coil; and N is the number 45 of turnsoi' coil per unit length. Equation` (i9) gives an expression for m in terms ofk the knownquantities ya, zi and zz or readily determined since rq=1 inch and since rr ' is the value oi' r where `11=y1=0.050 and rz is the value of r where y=yn= 1. That is 50 and as in the case of the tapered coil we will use the nrst i'ew terms of the power series of e and obtain an approximate solution for y1, 55 namely `ell-0.606 inch e 2 e î That is, for our typical example the tapered i coil ywill be 25.7 inches long, will have a radius of 0.975 inch at its low impedance end, will have a radius of 0.606 inch at‘its high impedance end and will have the Vcontour prescribed by the curve of Fig. 8. This coil will, of course, be sur although a graphical solution of Equation (19) 60 may be employed if desired. 65 we obtain from the above formula rounded by a sheath of‘constant radius of 1 inch. I'I'his construction, it will be recalled, is for cou 70 pling a line of 70 ohm impedance to a line of 700 ohm -impedance with a lower cut-ofi frequency of 52x10“ cyclesper second, and as previously stated thel amount of vinsertion gain in decibels ,. realized by the employment of this device is 75 shown by' Fig. 7. n Now for 112:1 and 111:0.081 Also from Equation (18) we obtain 70 from which a0= 1.023 X 10“ 76 9,115,926 inch. Surrounding the winding Il is a circum~ ferentially complete cylindrical sheath I3 of conducting material such as copper, the shape of the sheath being in conformity with the curve of Fig. 9 previously described. The sheath Il may be suitably supported about the coil II by r0N'=4.68. means of spaced washers I4 of insulating ma terial. This tapered line oi Fig. 1 is shown in cross-section in Fig. 2. ` If we take ro (the radius of the coil) as equal It has been assumed that the low impedance to 1 inch then N=4.68, that is, the coil will have - end of the tapered line is to be connected to a 4.68 turns per inch. line having an impedance of 70 ohms for the ire For the length of the coil we have from Equa quency range to be transmitted while the high tion (28) (where L is the value of X where 1l=ilz> impedance end is to be connected to a line hav after dividing both sides of the equation by ing an impedance of 700 ohms. The manner of connection is shown in Fig. 3 where line I5 hav gg ing an impedance of 70 ohms has one terminal B0 connected to the terminal I6 of coil II and has 20 and by substituting the known values. L=95.5 cm.=37.6 inches. The shape of the sheath is computed by solv 25 ing Equation (28) for X for several values of y between 111:0.081 and :12:1 and then calculat ing the ratio . its other terminal connected to the surrounding sheath I 3, while line I8 having an impedance of 20 700 ohms has one terminal connected to ter minal I1 of coil Il and has its other terminal connected to sheath I3. 'I'he insertion gain achieved by the use of this impedance trans former for the transmission of current from the 25 frequency source I9 to line I8 is slightly more than 4.5 decibels as shown by Fig. 7 and this substantially constant insertion gain applies for a frequency range of ten to one or greater. 30 for each of these values of y by the Formula (17) l.' e2 Finally a curve is plotted of 35 _1S L ` Versus 40 to obtain the shape of the sheath and such a curve is shown in Fig. 10. If we wish the values of r1, the radius of the sheath at the low impedance end, and n, the 45 radius of the sheath at the high impedance end, we have from Equation (17), knowing that ro=1 inch, ¿L 0.081 2=e 2 =1.041 inches 50 and EL ' .1. n=e2=e2=1.649 inches Therefore, when employing a tapered sheath construction for coupling a 70 ohm impedance 55 line to a 700 ohm impedanceline and with a y The other type /of tapered line which has been 30 computed has a tapered coil with a surrounding sheath of constant radius as described in Sec tions II and III. Such a tapered line is shown in Fig. 4 where the winding 20 is wound on a tapered cylindrical form 2| of insulating ma 35 terial tapered in accordance with the curve of Fig. 8 for the example specifically calculated in order to give the proper taper to the winding. 'I'he winding as shown more clearly in Fig. 6 may comprise ribbon shaped wire fitting into a 40 helical groove in the external surface of the cyl inder Z'I. Surrounding the winding 20 is a con centric sheath 23 of conducting material such as copper suitably supported by one or more in termediate insulating washers 24. The core 2l 45 at the high impedance end of the winding may have a collar 25 which supports the sheath at that end while at the low impedance end oi’ the transformer the sheath 23 may be in contact with core 2I at a point beyond the termina 50 tion of the winding 20. The tapered line of Fig. 4 may be employed in the transmission circuit of Fig. 3 in the same manner as the tapered line of Fig. 1, the low impedance end oi' winding 20 being connected to line I5 and the high imped 55 lower cut-off frequency of 5.2><10s cycles per - ance end of winding 20 being connected to line I8. Although certain specific embodiments of this second, the coil will have a radius of 1 inch. will be 37.6 inches long, will have 4.68 turns invention have been described for illustrative ' per in'ch and this coil will be surrounded by a purposes it is to be understood that the inven sheath having the shape shown by the curve of tion is not hunted thereto as other embodiments 60 Fig. l() with a radius of 1.041 inches at the low can be readily realized commensurate with the >in_ipedance end and a radius of 1.649 inches at scope of the appended claims. What is claimed is: v . the high- impedance end. (We will now refer more in detail to the tapered l. In- combination, two circuits each having a 65 line constructions shown in the drawings. fixed, predetermined impedance, and means con 65 In Fig. 1 the impedance transformer is of necting said circuits in energy transfer relation the tapered sheath type the parameters of which comprising an impedance transformer, said im are given generally in Section I above, and for pedance transformer comprising two elements. a speciñc example in Section IV above. The first. a long cylindrical coil and. second. a con 70 coil I I is of constant radius being wound on a centric metallic sheath surrounding said coil, at 70 suitable cylinder I2 of insulating material. As least one of said elements being tapered in ra explained under Section IV for use between im dius'over substantially its entire length. the in pedances of 70 and 700 ohms and with a lower put and output impedances of said transformer cut-oil frequency of 5.2)(106 the coil Il would be 37.6 inches long with a constant radius of one being equal to the respective impedances of said two circuits. 75 2,115,826 2. In combination, two circuits each having a fixed, predetermined impedance, and means con necting said circuits in energy transfer relation comprising an impedance transformer, said im pedance transformer comprising two elements, ñrst, a long cylindrical coil, and second, a con centric metallic sheath surrounding said coil, one oi' said elements being tapered in radius over substantially its entire length, the other of said elements being of substantially constant radius over its entire length, the input and output im pedances of said transformer being equal to the respective impedances of said two circuits. 3. In combination, two circuits each having a 15 fixed, predetermined impedance, and means con necting said circuits in energy transferl relation comprising an impedance transformer, said im pedance transformer comprising a long single layer solenoidal winding of substantially constant 20 radius throughout its length and a metallic sheath of substantially circular cross-section sur rounding said winding, said sheath being tapered in radius over substantially its entire length, the input and output impedances of said transformer 25 being equal to the respective impedances of said two circuits. 4. In combination, two circuits each having a fixed, predetermined impedance, and means con necting said circuits in energy transfer relation 30 comprising an impedance transformer, said im pedance transformer comprising a long single -layer solenoidal winding and a metallic sheath of substantially circular cross-section surrounding 9 having such parameters that the impedance of said device tapers approximately exponentially as the time of wave transmission along its length whereby its terminals present impedances having values which are substantially equal to the im pedances to be faced. 8. A radio frequency impedance matching de 5 vice in accordance with claim 7 in which said winding is tapered in radius along its length and said sheath is of substantially constant radius. 9. A radio frequency impedance matching de vice in accordance with claim 7 in which said sheath is tapered substantially continuously alongV its length and said winding is of substan tially constant radius. _ 15 10. In combination, a pair of radio frequency electrical circuits having different impedances, an impedance matching device whose terminals are adapted to connect together said pair of cir cuits, each set of terminals of said device pre 20 senting an impedance substantially equal to the impedance of the electric circuit which it faces, said device comprising a long cylindrical coil and a concentric conducting sheath surrounding said coil, one set of terminals of said device compris~ 25 ing one end of said Winding and the adjacent end of said sheath, the other set of terminals of said device comprising the other end of said winding and the adjacent end of said sheath, said device having an impedance which tapers continuously along its length substantially in accordance with Equation (4). 11. An impedance transformer comprising a long cylindrical shaped winding and a concentric metallic tapered sheath surrounding said winding said winding, said sheath being of substantially 35 constant radius throughout its length, the radius of said winding being tapered over substantially in which the parameters of the transformer are its entire length, the input and output imped»` substantially deñned by the formula ances of said transformer being equal to the re spective impedances of said two circuits. 5. An impedance transformer comprising a long cylindrical coil and aconcentric metallic sheath surrounding said coil, said coil being ta pered in radius over substantially its entire length, said sheath being of substantially con stant radius, the ratio of sheath radius to coil radius at the high impedance end of said trans former being less than 2.06. U 1 .Y l +eV-1 m-ldy wlan-(5%)?? tryo-WNW where X=axial length of winding 45 4 6. A radio frequency impedance matching de vice Whose terminals are adapted to face different impedances comprising two elements, ñrst, a ro=radius of winding solenoidal winding, and second, a conducting sheath enclosing said winding, one set of termi y-2 log t--c N=number of turns of winding per unit length r nals for said device comprising one end of said winding and the adjacent end of said sheath, the other set of terminals for said device comprising the other end of said Winding and the adjacent end of said sheath, said elements having such parameters that the impedance of said device ta pers substantially -exponentially as the time of Wave transmission along its length, whereby its r=radius of sheath at any point along its length r1=radius of sheath at low impedance end t1 is the value obtained from the expression t2 terminals present impedances having values which are substantially equal to the impedances to be faced. ’7. A radio frequency impedance matching de 65 vice whose terminals are adapted to face different impedances comprising two elements, first, a long cylindrical shaped winding, and second, a conducting sheath enclosing said winding, the radius of at least one of said elements varying 70 substantially continuously along its length, one set of terminals for said device comprising one end of said winding and the adjacent end of said sheath, the other set of terminals for said device comprising the other end of said winding and the adjacent end of said sheath, said elements l [film-1 zl tz--time required for a wave to travel the length of the winding z1=impedance at low impedance end z2=impedance at high impedance end m=a constant preferably one of the following values: 1, 2, infinity e=base of natural logarithms 70 12. An impedance transformer comprising a long cylindrical shaped winding whose radius is tapered along its axis and a concentric metallic sheath surrounding said winding in which the 76 audace 10 parameters of the transformer are substantially defined by the formula 1 X: t an l i y l +----y ev»- l m-idy 10 matching device interconnecting them for the transfer of radio frequency waves occupying a wide range of radio frequencies such that the . highest frequency of said range is at least several times the lowest frequency, said device compris ing a long cylindrical coil and a concentric me tallic sheath surrounding said coil, at least one of said elements being tapered in radius over sub stantially its entire length in such manner that the impedance varies with the time of transmis 10 sion of said waves in accordance with Equa tion (4). N=number of turns of coil per unit length 15 t1=value of expression t) 1*- *__*-21 for the transfer of radio frequency waves com prising a long cylindrical coil and a concentric er -1 11 conducting sheath surrounding said coil, the im pedance of said line varying gradually along said t t2=time required for a wave to travel the length of the winding z2=impedance at high impedance end z1=impedance at low impedance end rozradîus of sheath y=2 log L; 30 ' 14. In combination, two electrical circuits hav ing different impedances and an impedance matching transmission line interconnecting them " line with the time of transmission in such man 20 ner that the insertion gain is substantially uni- , form over a frequency band the highest frequency of which is at least several times the lowest. 15. A combination in accordance with claim 14 in which said sheath is of substantially constant radius throughout its length and the ratio of sheath radius to coil radius at the high impedance end is less than 2.06. 16. A combination in accordance with claim 14 r=radîus of winding at any point along its axis ` in which. said line is tapered in impedance in ac m=a constant preferably one of the following cordance with Equation (4), where m lies be tween 2 and infinity. values: 1, 2, infinity e=base of natural logarithms EDWARD L. NORTON. 13. In combination, two electrical circuits hav RONALD F'. WICK. ing different impedances and an impedance 30

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