Sept. ì?, i946. 2,407,911 `4 L. TONKS ETAL. WAVE PROPAGATI ON Filed April 16, 1942 2 vSheets-Sheet l Fig. | MED/UM / MED/UM 2 /FEFLEG‘TED WAVE Fig. 2. ÍNGIDÁ'NT WAVE p/mscrLY Eff-L £0750/ / CUM/’ONENTS PRoPAßAr/ON caNSTAA/r :be /MffoA/vcf = za ng. 3. lnventors: Lewi To?ks, LeRoy Apker, by .7% Their` Attorney. Sept° 17p E946. 2,407,91l L. TONKS ET AL WAVE’ PHOPAGATION lFiled April 16, 1942 2 Sheets-Sheet 2 ‘ Fig. 4. 43 60 H39. Fig. | l . fa 70 Fig. l0. F193. l2. W Inventors : y LA /T oA/¿t ¿www œ|w QW@ .w TA wm, L@rse, Patented Sept. 17, 1946 2,407,911 UNITED STATES PATENT.OFFICE 2,407,911 WAVE PROPAGATION Lewi Tonks and Le Roy Anker, Schenectady, N. Y., assîgnors to General Electric Company, a corporation of New York Application April 16, 1942, Serial No. 439,243 7 Claims. (Cl. 178-44) 1 2 This invention relates to the propagation and described in the following for each distinctive control of electromagnetic waves in the range of wave-lengths below one meter, such waves being designated for convenience as centimeter waves. It is well known that the passage of electro case By the use of a reflection-controlling system which embodies several (i. e. two or more) sepa rate transition elements it is found that many magnetic waves from a first propagating region into a second propagating region of different of the limitations inherent in previously used impedance transforming methods are avoided. electrical characteristics is ordinarily attended That is to say, the relatively greater numberiof independently variable factors leads to greater by the reiiection of a portion of the incident en ergy. Such reiiection occurs, for example, when 10 freedom in the design of the individual compo nents and to greater flexibility in the matter of a wave is caused to pass from a section of trans adjusting them. These considerations will be mission line having one characteristic imped come more fully apparent as the details of the in ance to a section of line having a diiferent ‘char acteristic impedance, It occurs in another case when a wave passes from one dielectric medium into a second medium of diiîerent dielectric vention are described; ' . ` The features of the invention especially de sired to be protected herein are pointed out in properties. the appended claims. The invention itself, to gether with its further objects and advantages, It is desirable in many cases to control the amount of wave reflection occurring at appara may best be understood by reference to the fol tus transition points, and certain devices, some 20 lowing description taken in connection with the drawings, in which Figs. 1 to 3 are schematic il times referred to as impedance transformers, lustrations useful in explaining the invention; have been devised for this purpose. However, Fig. 4 is a graphical representation of certain impedance transforming devices heretofore data of significance in interpreting the inven available have been usable only in special situa tions and with somewhat inconvenient limita 25 tion; Fig. 5 illustrates a first exemplary applica tion of the invention; Fig. 5a is a section on line tions. It is an object of the present invention to a-a of Fig. 5; and Figs. 6 to 12 show various provide reflection controlling agencies which are alternative applications. applicable in a very wide variety of cases and which are highly iiexible in the matters of de sign and mode of use. „ 30 _ Single surface refiection In explaining the invention it will be conven It is a more particular object of the invention ient first to refer to a relatively simple case and to provide means usable in connection with the then to extend the theory to include more gen propagation of centimeter waves, as above de eral and complex cases. With this in mind, the fined, for preventing or eliminating and control ling reflection of such waves. As will be more 35 line :ru of Fig. 1 may be considered as defining the boundary between a first dielectric region or fully explained in the following, special diñ’icul medium of propagation constant h1 and a second ties are encountered in this range of wave lengths dielectric region or medium of propagation con because of the need for taking into accurate ac stant h2. It is desired to consider the action of count certain factors which may be ignored at an electromagnetic wave which impinges on :ro longer Wave lengths. from the left, the direction of propagation of the In general, the invention involves the use of a wave being indicated by the arrow A. plurality of transition elements which by virtue It is useful to note preliminarily that under of their dimensions, spacings and other proper appropriate conditions electromagnetic Waves ties are able to efîect the reilectionless transmis may exist in numerous forms. For example, in sion of electromagnetic waves from one propa considering free space propagation, plane trans gating region to another. In one embodiment verse waves are ordinarily assumed. On the the transition elements employed take the form other hand, in a wave guide, such as a rod of di of two or more dielectric slabs or plates of appro electric or the space enclosed by a hollow Con priate configuration and arrangement. In an 50 ductor, confined ultra-high frequency waves may other they comprise discrete impedance-Varying sections spatially and dimensionally correlated be developed and propagated which have ñeld components not only at right angles to the di to assure attainment of the desired results, The rection of propagation but also in the direction considerations which determine the proper form of propagation, One such wave, which may be‘ and relationship of the means employed will be 55 produced, for example, in a hollow 'cylindrical 2,407,911 4 0 mensions is more complex, being defined as fol conductor, is the so-called Ho wave which has lows in the case of I-I waves traversing a rectan gular wave guide having a dimension œ which is magnetic components parallel to and transverse to the direction of propagation and an azimuth ally directed electric component in a plane trans verse to the direction of propagation. Another type, frequently called the En wave, has lines of electric force parallel and transverse to the di perpendicular to the transverse electric field and a dimension y which is parallel to the transverse electric ñeld. (l rection of propagation and_has lines of magnetic (25) force azimuthal with respect to the axis of prop agation. In general, however, any electromag l() netic wave may be considered as fully specified for most purposes when its classification is given, and when the magnitude of one of its field com where c, fi, and 7c have the meanings assigned above; a is one-half the operating wave length, and an is the smallest value which x may assume and still permit Vpropagation of waves of this wave length'. (For a circular guide 11:11?, and the ratio ponents is stated, the remaining components be ing then readily determinable from relatively simple relationships. .1i/:c becomes unity). ' With these considerations in mind, let the Wave For E waves indicated by a directed arrow A in Fig. 1 be char acterized by the transverse component, __T 20 ZE: C/.L of the electric field associated with it. Here t represents time, œ is distance from an arbitrary origin to the left of ro, and h1 is the propagation constant of the medium ‘1. If the medium is non dissipative, h1 is ya pure imaginary; otherwise >it is complex. In order to satisfy the boundary conditions at the surface :L'o in Fig. 1 we must have in addition to the incident wave a reflected wave «ke-1 G10 ’y l# œ (2C) a'o »Where x now represents the wave guide dimen sion perpendicular to the transverse magnetic iield, y is the dimension parallel to this ñeld and the other quantities have the same meanings as above.> In general, a definite relationship exists be tween the impedance, Z, of a propagating system and the propagation -constant h of the same sys tem. For plane waves in free space and H waves in guides h2 is the propagation constant of the medium to the right of :120. The coeiìîcients r and b` are determined by matching the electric and mag netic fields at :1:0 according to a wellunderstood For E waves in guides Z~h. procedure. These coeñicients are real ‘in the case We notice from vcomparison of Equations 1 and of Fig. 1 if the dielectrics are non-dissipative, but 2 that b=1+r. Although the amplitude of the in general they are complex. They give both the 40 transmitted wave is greater than that of the amplitude and the phase of `the reflected and incident wave if Z2 is greater than Z1, the energy transmitted waves at :no referred to the incident transferred by it is necessarily less. The greater wave at the same boundary. amplitude is consistent with the consideration For the case of Fig. 1, r and h are found to be that in different media the power density is pro portional not only to the square of electric am plitude but also the reciprocal of the impedance. The reñection and transmission coeflicients are not the same for waves incident from the right as they .are for those incident from the left. If 50 primed symbols refer to the `former case, we find The quantity Z in ythe foregoing equations is >that defined »as the ratio of the transverse .electric component of the propagated wave to the trans (3) verse magnetic component for the particular propagating region under consideration and cor responds to the “characteristic impedance” of the propagating system as that term is custom (4) arily employed. Reflection and tránsmission at a slab (See Electromagnetic Theory We may examine the case of two boundaries by J. A. Stratton, iirsll ed. pp. 282-284). As thus by considering the arrangement of Fig. 2, in defined, Z is dependent both upon the intrinsic 60 which the space to the left of m0 is occupied by dielectric properties of the propagating medium and the boundary conditions of the propagating system. For example, in the case of a Coaxial conductor transmission line (where the useful waves are of plane transverse character) (2a) where c is the velocity of light, ii is the perme ability of the medium between the conductors, lc is the dielectric constant of the medium, and ro and r1 are, respectively, the radii of the outer and inner conductors. On the other hand, in a `wave 'guide comprising a single hollow conductor th'e relationship between impedance and guide di medium 1, the space between 3:0 and x1 is occu pied by a refractive dielectric a, and the space to the right of x1 is occupied by a medium 2 (which may be the same as or different from medium 1). Considering the wave situation at the left of xo, we may attack the problem by summing the multiple reflections that occur at the various surfaces as indicated in Fig. 2. In the following, the characters 1' and T’ represent reñection co emcients in the forward and reverse directions respectively, b and b’ represent corresponding transmission coefficients, and the various sub scripts identify the surfaces to which these co e?l'lcients- are referred. 2,407,91 1 5 The complete reñected wave, hand memfber of Equation 7 is set equal to zero Arx0eíwt+h1(a:-zg) as follows: (10) If all the dielectrîcs involved are non-dissipative, so that 0 becomes real, this condition can be satis is determined by the reflection coeñicient fro where A10 = T10 is +the bzorzlb’zoe amplitude _ 2m +ofbzorîlTlxob'roe-uß the incident wave, fled if |r¢0!=lre1|. (lrœol and [fall represent the respective absolute values of reo and nl.) When re0=-mp Equation 10 is satisfied pro Amo is the amplitude of the reflected wave, and 10 vided I0|=-n1r, and when re0=re1, then The ñrst term of the right hand member of Equation 5 is the component which is reflected directly from the surface nto. The second term is the component which traverses the surface rco, is reflected at the surface :1:1 and again traverses :vo out into medium l. Having passed through a double thickness of the dielectric a assumed to suffices. (Here n is an integer or zero.) 1 As we have seen in connection with the deriva tion of Equation 7a, re0=-1^r1 represents the case of a plate o-f non-dissipative dielectric separating identical media. Reference to Equation 7 and to the considerations stated in the preceding par be contained between the surfaces xo and cci, it suffers the phase lag 20. The subsequent terms 20 agraph shows that such a plate gives zero reflec tion (i. e. R1~(1'e0-l-1'e1e-2f°)=0) when the plate account for the further multiple reflections. The is any integral number of half wave lengths thick resulting infinite series is directly summable to (i. e. when |6|=n1r) . From a practical standpoint give brama-21'“ <6) R1 - Tzu +__1__ Txlrfzofm Using Equations 3 and 4 in connection with Equation 6, we i'lnd that R it is important to note further that where non dissipative media are concerned, the condition of zero reflection automatically implies a condition of complete transmission (i. e. in accordance with energy conservation requirements). This is a consideration the value of which will become 30 more apparent in the following. Consideration of Equation 1 will show that for (7) rx0=rz1, v(the second of the two cases proposed __ T10-traf” P_Ws in the next to last paragraph) the media on op For the transmitted wave Atzleíwl-hah-:D a similar calculation gives the transmission coef ficient posite sides of the refractive plate must be of different impedance and the plate must have an impedance which is the geometrical mean of the impedances of the media which it separates. Assuming this condition and assuming the fur ther condition that the plate is an odd multiple of Atz bz bT e-f@ Amo l r :013,16 1 = *l = î¥-îß (8) 40 a quarter of the operating wavelength (in the re fractive plate) in thickness (i. e. and using Equations 3 and 4, we have T1: bxubzle-í'7 43 where n is an odd integer, including unity) we see from (10) that the plate in question may be An important case is that in which media 1 and 2 are identical. Then r (Equation 1) =Re0=--nl and 1.... -21'9 RFHîÃî-za (7") Also, bx0=1+r and bzlr-l-r, so that (1-r2) 6*"1'" T1=m , used to introduce a wave without reflection (i. e. with complete transmission) from the first of the separated media into the second. This result 50 holds stricth7 only for non-dissipative dielectrics but is easily corrected to take into account ap preciable dissipation in one or more of the media, and the resulting correction is small. A match ing plate may thus be used to introduce a wave without reflection into a dissipative medium where it may be totally absorbed. The maximum reflection obtainable from a non-dissipative plate separating identical media occurs when Equations 6 to 9a give the amplitudes and phases of the waves reilected and transmitted by 60 the plate or slab of dielectric contained between the surfaces :v1 and :170. These amplitudes and phases are specified at the surface :12o for the re flected wave and at the surface :ci for the transmit ted wave and are referred to the incident wave at the ñrst surface. The coefficients of Equations 5 to 9a are in general complex for both dissipative and non-dissipative dielectrics. They completely describe the effect of the dielectric medium be tween xo and x1 on the incident wave, and there is no need for referring to any process inside this medium once we have them. #meng in Equation 7a. Then, by Equation 1 (11) where 1’ is the reflection coefficient at the incident surface. From comparison with Equation l it is seen that such a plate’s reflection is equivalent to the reflection from a single surface where the im For a practical application of the results ob pedance ratio is equal to the square of that for tained in the foregoing, we may ñrst consider the plate. Values of reflection between zero and the situation in which the numerator of the right 75 R1 max may be obtained by using a slab thickness 2,407,911. 7 between the value indicated by 0:1111» and the value indicated by 8 will be seen that both these quantities are domi nant factors in determining the total reflection from a multislab system. In other words, in any propagating system in which the operating wave length is not extremely large in comparison with the dimensions of the structural elements in volved, reflection cannot be eliminated, as has ‘ Two 0r more4 slabs For the case to which the present invention been previously suggested by various writers, sole especially pertains, namely, in which two or more ly by a quarter wave spacing of refractive ele refractive elements are involved, a system such 10 ments. as that illustrated in Fig. 3 may be considered. Except for the factor eîi’f, Equation 19 is for In this figure the refractive regions a and b are mally the same as that for a single plate (see understood to -be included between two pairs of Equation 7a). By setting the numerator of its separate reference surfaces xo, :1:1 and x2, xs. right-hand member equal to Zero (i. e., the con We shall assume that the refractive regions a and dition for zero reflection) we find that zero re b are completely specified by known coefñcients iiection is obtained when ra, r’a, ba, b’a, applying to a as a -whole and rb, T'b, etc. applying to b. These coefficients are an alogous to the reñection and transmission c0 where n is an integer and where, necessarily, eilîcients for the surfaces of a single slab as pre l h2 ](x2--œi) is greater than zero. 20 viously derived (e. g. in Equations 7a and 9a). Fig. 4 is a plot of the phase angle, ip, which Following an analytical procedure similar to that used above, we ñnd that the overall reflec tion and transmission coefficients for the system which includes the two refractive regions a and b are formally of the character indicated by VEqua tions 6 and 9, being specified as follows: determines the spacing h2(œ2-:1:1) in degrees of phase, as a function of the phase thickness, 9, of the plates. The impedance ratio 25 î=2 is taken as a parameter. While it is not immediately evident from Equa tion 19, it can be shown from that equation that R2 is maximum when e*2m=-1. This is an equality which is satisfied when 35 These formulas apply to dissipative as well as to non-dissipative dielectrics and in general are In the event of the fulfillment of this condition complex for both cases. 40 Since we have the reñection and transmission (21) coefficients for single slabs (Equations ’7 and 9), we may use them in Equations 12 and 14 to in vestigate the useful properties of pairs of slabs. In this connection consider two identical non dissipative plates immersed in a non-dissipative medium of different impedance in an arrange ment generally similar to that of Fig, 3. Under these circumstances the R1 and T1 of Equations 7a, and 9a are respectively the n, ra', Tb and the ba. and ba’ of Equations 12 and 14. If they are expressed in polar form R1=1R1|ef¢ (15) T1=lT1[ei(¢+"/2) (15a) and This is equal to the reflection from a single sur face having an impedance ratio equal to the fourth power of that for the slabs, as can be seen by substituting from Equation 11 and corn paring it with Equation 1. At the same time it appears that it is equivalent to the reflection from a single slab having an impedance ratio equal to the square of that for the two slabs. Amounts of reflection intermediate between the minimum value of zero and the maximum value denoted by Equation 21 can obviously be obtained by choosing spacings between the points deñned by Equation 20 and Equation 20a. This is an important feature of multislab combina tions when used for neutralizing reflection from a reflecting boundary outside the combination __t _1 l-rz since it means that the reflection obtainable with IÍ’- an m2 Cot Ü 60 such combinations is to a large extent independ» (Equations 15 and 15a are obtainable by expand ent of the characteristics of the individual slabs. ing the right-hand members of Equations '7a and If the two refractive regions are not identical 9a into their real and imaginary components and slabs, there is, in general, no separation giving then evaluating the angular arguments of the zero reflection. However, in the special case inv where resulting expressions.) Substitution from into Equations 12 and 14 yields 15 65 which l Ta [=| rb l, we ñnd that no reflection occurs when (19) where R2 is the over-all reflection of the two-slab system and (19a) Ihzl ($2 _1121) = (22) In justifying Equation 22 we may ñrst observe» that a condition to be fulfilled if there is to beI cancellation of the portion of the incident wave which tends to be reñected from the first reflect ing slab (Fig. 3) is that the various wave com Since (œ2-x1) represents the slab spacing and since Blf depends directly upon slab thickness, it 75 ponents which pass through the first slabI and, 2,407,911 . 10 9: after single or multiple reflection from the sec ond slab, effect repenetration into medium I mustbe in opposite phase with respect to the pri marily reflected wave. To show that Equation 22 represents the condition-for a proper phase relationship of the internally reflected wave com ponents, consider an incident wave of phase zero at :to (Fig. 3) . The phase of the primary reñec I2 is shown at I3. It is reasonable to assume that a material of _fairly low impedance may prove suitable for the slabs II and I2 and since quartz is such a material, it will be worth while to investigate the possibility of using this sub stance. If this is at all possible, it can be done when [rb] (i. e., the reñection coeflicient of slab l2) is a minimum. That this Yoccurs when tion from the ñrst slab referred to the plane 0:0 is tba by Equation 15. The phase of the primary 10 transmitted wave at :L'i is can be seen from Equation '7, the equation for reñection from a single slab, in which now both by Equation 15a. At :v2 the phase has been ad vanced by | h2 {(:cz-xl) . The portion of the wave which is reflected from the slab b is retarded by :pb and this wave is again advanced in phase dur ing its passage from r2 to x1 by an amount equal to [hz Mrz-x1). Combining all these phase dif ferences we get no and nl are negative because the impedances of the various successive media are progressively less in the direction of propagation. The follow ing data will be used: A Hm wave having a free space wave length of 10 cm. propagated in a 7.62 cm. (3") rectangular guide having a limiting wave length of 15.24 cm. for the relative phase of the internally reñected wave at mi. A part of this wave is retransmitted through the dielectric region a into medium I, and a still further portion is again reflected at .r1 and> suffers further internal reflections be tween the boundaries mi and m2. Y ' Dielectric constant of quartz È 3.6 Dielectric constant of water È 70 From these data and by means of known rela tionships (see definitive Equation 2b) We are able to compute various impedances that we need: Considering only the portion of the wave which is transmit 30 ted through the dielectric a into medium I at the ñrst opportunity for such transmission, it is Where subscript 1- refers to the air-ñlled portion apparent that this portion will suffer a retarda of the wave guide, subscripts a' and b to the slabs tion of phase during such transmission of II and I2 respectively, and subscript 3 to the water-filled section I3; where »y and a: are re spectively the minor and major dimensions of the wave guide, and where the factor Zo is the im (i. e., according to Equation 15a). The total pedance encountered by a plane wave in lfree phase lag of this part of the wave which is avail space. (_The ratio 'yl/m cancels out in the com 40 able for interference with the primary reflected putation of reflection and transmission coeiîi wave is therefore the algebraic sum of the indi cients ’and therefore does not require to be nu vidual phase diiîerences: merically specified.) ' ` " The reflection coefficients for the various slab surfaces are found by using Equation 1: For this interfering wave to be wholly out of phase with the directly reflected wave which, as From (7) , we have seen, has the relative phase angle gba, it is clear that the phase diñ'erence between the in 50 = -l-.321 (23) terfering wave parts must be some odd number of 1r radians. Mathematically expressed, this Now the maximum reflection obtainable from means that a quartz plate in airis, from (11) This reduces directly to Equation 22. This equa tion shows, among other things, that reflection cancellation depends upon the maintenance of a proper spacing between the reñecting agencies by which the cancellation is to be produced. This relationship is true moreover, for all points in medium I since the phase of the two reflected Since' this is greater in absolute value than rb, thematching is possible. To make Ira l=| rbl it is only necessary to use a thinner front plate than is indicated by (24). From (7a), wel: Waves varies equally and in the same sense. Equation 22 can be applied to the problem of introducing a wave from air into water (neglect ing for the moment the slight effect of attenua tion on the water reflected wave) by using a re fractive slab for a and a. refractive slab backed by water for b. This arrangement is illustrated in Fig. 5 which shows a wave guide in the form of a hollow conductor ID along which electro magnetic waves are assumed to be propagated. The relative position of the refractive slabs is in where r=rœ0=-.393, the reflection at one sur face, and where that value of 0 is to be found for which Ira l=.321. One ñnds that 21.6° is approximately correct and this is the phase thick ness 0 >of the ñrst plate. Its actual thickness (anexo) is determined from the original defini tion of@ as being equal tov [ hal (r1-uso). Having adjusted the amplitudes of the reñec tion coeñicients properly, we still have to ñx the phases by choosing the correct separation of the dicated at II and I2 and water backing the slab 75 plates. This is given by Equation 22. 2,407,9»1 i i1 In using Equation 22 it should first be recalled that (x3-m2) was arbitrarily so chosen that 12 location of the plate 32 requires a preliminary determi-nation by measurement or computation, of the reflection cceflicient of the surface of di electric 3 |. With this quantity known, the thick ness of the plate required to give an equal co efficient can then be» computed. Finally, the spac ing of the plate with respect to the dielectric 3| which» is necessary to assure-mutually anni hilative interference of the »two reflected wave components may be determined by a procedure like that used in justifying Equation 22. 'I‘he spacing chosen should, of course, be such that at a plane located in advance of both the plate 32 and the dielectric 3| with reference to the is a matter of convenience only. Some other direction of wave propagation, a phase displace value might equally well have been taken in which ment of mr radians exists between reflections case the further treatment' of the problem would attributable to the plate and those attributable have been complicated to the extent of having to the dielectric, 71. being an odd integer. to deal with a finite value of rbb throughout.) A- singl’e plate such as the plate 32 may alter Using the impedance ratio Z1/Za=2.'24, Fig. 4 gives yba=-118°. (Fig. 4 shows the variation of 20 natively «be used to annul reflections due to re flective discontinuities other than a discontinuity 1]/ with 0 for different values of the impedance attributable toV a change in the propagating di ratio Zl/Za. For cases where 0 is below. 90° use is electric. Examples of other discontinuities are made of the upper abscissa scale and the right those produced (l) by a change in dimensions of hand ordinate scale. For cases where 9 is be a wave guide, or (2) by a change in direction of tween 90° and 180° the lower left-hand scales are a waveguide, or (3) fby the junction of a wave used.) It follows that [h1 l (m2-:131) =121°, from which the plate spacing (m2-ain) is, of course, directly determinable. If the maximum reflection from the plate || had not been greater in absolute value 'than the minimum reflection from plate I2, it would not have been possible to eliminate reflections with two plates of quartz only, although the desired guideY with a devicehaving an effective charac teristic impedance different from that of the wave guide. Fig. 8’ represents a construction in„which a wave guide, indicated at 35, is to be employed to conduct waves from. a high frequency source within which such waves are generated. The source, which is indicated in part only, comprises result could have been obtained by using a ma terial having an impedance closer to that of a metallic enclosure 35 within which are con higher impedance ratio. wave guide 35, a glass plug 39 is sealed into the entrance to the wave guide for the purpose of tained electrode structures 31 such as the elec trodes of a split anode magnetron. The entrance water. However, by adding a third plate, identi of the wave guide 35 is- assumed to be arranged cal to || and positioned ahead of ||, and by in such relation to ,the electrodes 31 as to assure applying the general formulas to the resultant three-plate system, it is easy to show that the 40 that high frequency wave energy will be propa gated along the guide. range of impedance over which zero reilection In order to preserve the vacuum tightness of may be obtained is greatly'exten'ded, for, the first the container 36 in spite of the insertion of the two plates then behave like a` single plate with a This arrangement is illustrated in Fig. 6 which indicates a wave guide 2D (either of cylindrical or rectangular form) con taining a series of three mutually spaced dielec forming a vacuum-tight closure. In accordance withI the considerations previously given herein, it willfbe understood that the plug 3€) constitutes tric slabs 2|, 22, and 23, the plate 23 being backed at least a partial barrier to the passage of waves by water, as indicated at 24. A special advan tage of the three-plate arrangement is that not 50 and may lead to objectionable reflection of such waves. The geometry of the system in question only the impedance but also. the thickness of the makes it inexpedient to eliminate such reflection individual plates may be chosen within much by means of slabs located in the guide within wider limits than is possible where only two plates the container 36. However, an equivalent effect are employed. Y can «be obtained by means of a pair of dielectric This three-plate matching `apparatus has an slabs 4| and 42 arranged Within the guide at analogue in which single surfaces replace plates. a point outside the container 35. A wave may zbe introduced without reflection into In order to determine the proper arrangement a body of dielectric if` at the proper distance in of the slabs.4| and 42, it is necessary first to de front of the dielectric we place a refractive plate of the correct thickness. This is indicated in 60 termine the over-all reflection coenicient of the Fig. 7 in which is shown a hollow wave guide 30 4terminating in a dielectric section 3| and having within its interior a dielectric plate 32. Since the condition to be satisfied for zero reflection plug 39, referred, for example, to the left-hand surface of the plug. Thereafter Íby use of Equa tions 19- and 19a a spacing of the slabs 4| and 42 may be determined which will give an equivalent is merely that they over-all reflection coefficient 65 reñection coefficient referred to the left-hand sur of the plate shall equal in magnitude that-of the face of the slab 4|. This spacing will, of course, single surface of dielectric 3|, the only restric be a, function of the thickness and dielectric tion on the impedance ratio of the platev (with properties of the respective plugs. Once the respect to the medium in which it is immersed) is that it be greater than the square- root of that. 70 proper location of the plugs 4| and 42 with respect to one another is fixed, the distance between the for the dielectric surface (see Equation 14) . left-hand surface. of the plug 39 and the cor Within these limits a plate of any impedancev may responding surface of the slab 4| required to as be used provided its thickness and location are sure destructive interference of the waves respec properly chosen. Determination of the proper dimensions and. 75 tivelyreflected from the two reflecting` units may 2,407,911 14v 13? be computed by an analysis similar to Lthat in volved in the derivation of vEquation l22. Fig. 9 represents the application of the inven similar to those used in connection with the con structions of Figs. 5 to 10, one may determine the dimensions and spacing of the sleeves S3 and tion to the case of a wave guide 43 _which is ter 64 >which are required to cancel the reiiection minally connected to a smaller wave guide 44. 5 occurring at the extremity of the transmission line (i. e., at'its junction with the antenna BI’). Due to the difference-in dimensions of the.Y two Wave guide sections, they will under ordinary cir A further .modification of this same principle cumstances have different characteristic imped is shown in Fig. 12 in which annular sleeves 13 ances and wave reflection will occur at their junc and 14, functionally similar tothe sleeves B3 and tion. `To annul this reflection there are provided 64 of Fig. 11, are secured to the inner surface two identical dielectric slabs 45 and 45 which are of a tubular conductor 'lll which forms the outer respectively spaced from one anotherA and from member of a coaxial'conductor transmission line. the entrance extremity of the waveguide 44.> By appropriate choice of the dimensions and In designing an arrangement such as that of spacings of the members 'i3 and 14, terminal re Fig. 9, the composition of the plates t5 and 46 ilections due to the junction of the transmission may be chosen rather arbitrarily with a View to line with an antenna 'H' may be neutralized. employing materials which are structurally suit Reflection-preventing sleeves of the character able. Moreover, the thickness of theplates is illustrated in Figs. 11 and 12 may also be used in arbitrary within relatively wide limits. With the connection with single pipe wave guides. How impedance and the thickness of the plates given, 20 ever, in the latter application it is considered that it is possible to vary the spacing of the plates dielectric slabs have an advantage over transition With reference to one another in accordance with Equation 19 to produce a reflection coefficientl for the combination which equals in absolute magni tude thecomputed or observed reilection coeffi cient of the boundary between the wave guide sections 43 and 4i. Thereafter, the spacing of the left-hand surface of the plate ¿5 with respect to the entrance extremity of the guide section de elements of other forms in that they have no tendency to introduce new types of waves (i. e., waves of a form diiferent from the form of the incident wave) . In summary, it may be said that in a large class of cases unwanted reflection from a reflec~ tion-producing discontinuity may be cancelled or annulled by providing in connection with the (i. e., the reflecting boundary) must be adjusted 30 discontinuity a neutralizing system having a re to assure (2n-1)”- phase displacement between iîection coefficient equal to that of the disconti nuity and having a spacing with respect to the the reflected waves Whose destructive interference 'discontinuity such that at planes in advance of is desired. ` In the wave guide construction of Fig. 9, the all the reflecting agencies a phase displacement reflective slabs or plates may alternatively be located in the smaller wave guide section d4.' ñections attributable to the discontinuity and re A still further application of a multiple plate of approximately mr radians exists between re flections attributable to the neutralizing system, n being an odd integer. It should be noted, how combination as a reflection reducing agency is ever, that the question of whether the provision illustrated in Fig. 10. In this case there is shown a coaxial conductor transmission line having an 4.0 of equal reflection coeûlcients represents a proper . condition for complete neutralization depends to outer conductor 5i! and an inner conductor 5I. some extent upon the nature of the reflecting The inner conductor terminates in an unshielded agencies involved. More specifically, it is a con portion 5|’ which may be assumed to constitute dition which is applicable in an arrangement in a radiating antenna or to connect with an an which the neutralizing system is ahead of the tenna or other utilization device. It is obvious discontinuity desired to be neutralized,.provided that the effective impedance of the unshielded a-phase displacement of 90° exists between wave section 5I’ will be different from theimpedance components reñected by the system and wave of the transmission line combination, so that components transmitted by the system. In other wave reflection at their junction may be antici pated. To avoid this, there are provided a pair 50 words, the relationship assumed in Equations l5 and 15a must be valid. Where the discontinuity of dielectric plates or disks 53, 511 which are fitted is ahead of the neutralizing means (as in Fig. 8), into the conductor 59 and which have dimensions then the discontinuity (and not necessarily the and spacings calculated in accordance with the neutralizing means) must comply with the afore principles previously given herein to neutralize reflection from the transmission line termination. 55. mentioned relationship. ‘ In connection with a coaxial transmission line v A phase displacement of 90° between reñected system, the dielectric plates 53 and 54 of Fig. 10 may be replaced by equivalent transition ele and transmitted components represents an as sumption which is justified in the event there ments of a different structural character.` This iiection-producing agency in question comprises possibility is illustrated in one embodiment in Fig. 60 a single, substantially non~dissipative, dielectric 11 which-shows a coaxial transmission line hav slab or a plurality of identical such slabs. ing conductors 60 and 6l, the inner conductor not justified where the reflection-reducing system It is is made up of a number of dissimilar slabs or terminating in an antenna section t l ’. Attached where it is made up of structural discontinuities to the conductor 6l within the confines of the conductor B0 are a, pair of annular conductive 65 such as those illustrated in Figs. 11 and 12. Ac cordingly, in connection with reflection-reducing (e. g., metal) sleeves 63, E4 which are of similar agencies of the latter class, it will be found that dimensions and which are mutually spaced. for -complete neutralization rto be obtained the It is apparent that each of the sleeves 63 and reflection coefficient of the neutralizing means 64 introduces into the transmission line system a short section (corresponding to the length of 70 must ordinarily be somewhat different from the ` reflection coeflicient of the discontinuity which the sleeve in question) having an impedance give-s rise »to fthe reiiections desired to be an which is different from that of the transmission line proper. In this respect then, each of the sleeves is equivalent to one of the dielectric plates nulled. This qualification also applies in cases' where the reflection-reducing means introduces a 53,' 54 .of Fig. 9. _Moreover, by, considerations 7.5.' material .amount of dissipation.V _ ì 2,407,911 While the. inventionhasbeen described by ref erence to particular applications and specific em bodiments, it will be understood that numerous modifications may be made by those .slcilled' inthe art without departing from the invention. We, therefore, aim inthe appended claims to` cover all such equivalent variations of.' structure or use as, come within the true spirit and scope of the; foregoing disclosure. . What we claim as new and-desire to secure by Letters Patent of the United States is.: ' 164 tinuity with reference to the direction of Wave propagation and eachhaving a thickness which is amaterialV fraction ofl the wave length ofV the waves'to be propagatedY whereby the overall re ñection from said combination is defined. by a re flection coefficient in which both the spacing and thickness of the plates enter as dominant factors, the spacing of said plates with respect to one another Abeing adjusted- to produce a reflection coeihcient for the combination equal to that of the said discontinuity, and the spacing of said 1. An electromagnetic system. for propagating plates with respect to the discontinuity being centimeter waves comprising a wave-propagating structure having a discontinuity at which reflec tion tends to occur, and means in proximity to said discontinuity and in the path of wave propa such that at any plane in said structure located in` advance of the said plates a phase displace ment of approximately mr radians exists between. reflections attributable to the discontinuity and reñections attributable to the said plates, n being gation for annulling the said reflection, said an odd integer. 4. In combination, a source of centimeter short section of wave-propagating structure and 20 waves, a wave guide connecting with said source for propagating waves derived from the source, having a thickness in the direction of wave prop and means for annulling the reflection of waves agation which is a material fraction of the Wave at the junction between said source and said wave length of the waves to be> propagated whereby,l guide, said last-named means comprising a ccm the overall reflection from said combination is defined by a reflection coefllcientin which both 25 bination of spaced dielectric plates which are lo means comprising the combination of a plurality of spaced elements each constituting in itselfV a cated within said wave guide in proximity to the spacing and thickness of the elements enter the said junction and which are of a thickness as dominant factors, the spacing of said elements corresponding to a material fraction of the wave with respect to one anotherl being so adjusted length of the waves derived from said source that at any plane in said structure located in advance of the said elements and the vsaid dis' 30 whereby the overall reflection from said combina tion is defined by a reflection coeñlcient in which continuity with reference to the direction of wave both the spacing and thickness of the plates propagation the rellection attributable to the ele enter as dominant factors, the spacing of said ments is equal to that attributable .to the said plates with respect to one another being so ad discontinuity, and the spacing of said elements with respect to the discontinuity being such that 35 justed that at a plane between the said source and the said junction the reflection attributable at the said plane a phase displacement of ap to the plates is equal to that attributable to the proximately mr radians exists between reflections junction, and the spacing of said plates with re attributable to :the discontinuity and reflections spect to the junction being such that at the said attributable to the elements, n being an odd in teger. 40 plane a phase displacement of approximately ne radians exists between reflections attributable to 2. An electromagnetic system for propagating centimeter waves comprising a wave-propagating structure having a discontinuity at which reflec tion tends to occur, and means in proximity to the said discontinuity and in the path of wave propagation for annulling the said reflection, said. the junction and reflections attributable to the plates, n being an odd integer. 5. In combination, a hollow conductive wave guide defining a first propagating region, means adjoining said wave guide and defining a second propagating region of different characteristic im pedance than the ñrst, and a plurality of iden of spaced dielectric plates each having a thick-` tical dielectric plates successively arranged in ad ness which is a material fraction of the wave length of the waves to be propagated whereby 50 vance of the junction of said iirst and second regions for facilitating the reilectionless transfer the overall reflection from said combination is means comprising the combination of a plurality deñned by a reflection coefficient in which both of wave energy between the regions, the dimen said reflection, said means comprising the com bination of a plurality ofV identical dielectric and in the path of the propagated waves for as sisting the non-reflective transfer of wave energy sions and spacing of said plates with respect to the spacing and thickness of the plates has domi one another being such that the overall reflec nant factors, the spacing of said plates with re tion coeillcient resulting from their combination spect to one another ‘being- so adjusted that at is equal to the reflection coefficient of the said any plane in said structure located in advance of junction, and the spacing between the junction the said plates and the said discontinuity with and the plates being such that with respect to reference to the direction of wave propagation waves which pass through the various plates, are the reflection attributable to .the plates is equal reflected at the said junction and retraverse the to> that attributable to the said discontinuity, and the spacing of said plates-with respect to the» 60 plates, the phase shift attributable to said spacing plus the phase shift attributable to the plates discontinuity .being such that at the said plane a themselves differs by approximately mr radians phase displacement of approximately mr radians from the phase shift of waves reflected directly exists between reflections attributable to the dis from the first of said plates, n being an odd continuity and reflections attributable to» the integer. plates, n being: an odd integer. 6. In an electromagnetic system which is 3. An electromagnetic system for propagating adapted to propagate centimeter waves and which centimeter `waves comprising a wave-propagat comprises two adjacent propagating regionsV of ing structure having a discontinuity at which reflection tends to occur in an amount deter 70 different characteristic impedance; an arrange ment which includes at least two spaced elements mined by a reilection coeñicient assignable to in proximity to the junction of the said regions the discontinuity, and means for> annulling the plates located in advance of the said discon» 75 from one region to the other, each of said ele 2,407,911 ments constituting a short section of Wave-prop agating structure and being of a thickness which is a material fraction of the Wave length of the waves desired to be propagated by the system whereby the overall rei‘iection from said arrange ment is defined by a reiiection coefficient in which both the spacing and thickness of the elements enter as dominant factors, the spacing of said elements with respect to one another being so ad justed that at a plane locate-:l in advance of the said elements and the said junction with refer ence to the direction of Wave propagation the re iîection attributable to the elements is equal to that attributable to the junction, and the spacing of said elements with respect to said junction be ing adjusted to secure phase opposition between Said reiìections to obtain destructive interference thereof. 7. In an electromagnetic system, an elongated hollow Wave conñning structure denning a first Wave-propagating region, and means for facili tating the transfer of Wave energy from said region. to a second region of different eiîective impedance, said means comprising a plurality of 18 localized constrictions provided within said struc ture at mutually displaced points near its junc tion with said second region, the extension of said constrictions in the direction of wave propa gation comprising a material fraction of the wave length of the Waves desired to be propagated whereby the overall reflection of the 'various con strictions is donned by a reilecticn coenicient in which both the spacing and extension of the con strictions enter as dominant factors, the spacing of said constrictions with respect to one another being so adjusted that at a plane located in ad vance of the said constrictions and the said junc tion with reference to the direction of propaga, tion the reflection attributable to the construc tions is equal to that attributable to the junction, and the spacing of the constrictions with respect to the junction being such that at the said plane a phase displacement of approximately 1in- radi ans exists between reflections attributable to the junction and reflections attributable to the con strictions, n being an odd integer. LEWI TONKS. LE ROY APKER.

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