US2407911A - Wave propagation - Google Patents

Description

Sept. i946.

L. TONKS ETAL.

WAVE PROPAGATI ON Filed April 16, 1942 Fig.

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L. TONKS ET AL WAVE PHOPAGATION lFiled April 16, 1942 2 Sheets-Sheet 2 Fig. 4.

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Inventors www se, r wm, L@ oA/t T A |w .w QW@ LAL/T Patented Sept. 17, 1946 WAVE PROPAGATION Lewi Tonks and Le Roy Anker, Schenectady, N. Y., assgnors to General Electric Company, a corporation of New York Application April 16, 1942, Serial No. 439,243

7 Claims. 1

This invention relates to the propagation and 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 electromagnetic waves from a first propagating region into a second propagating region of different electrical characteristics is ordinarily attended by the reiiection of a portion of the incident energy. Such reiiection occurs, for example, when a wave is caused to pass from a section of transmission line having one characteristic impedance to a section of line having a diiferent characteristic impedance, It occurs in another case when a wave passes from one dielectric medium into a second medium of diierent dielectric properties.

It is desirable in many cases to control the amount of wave reflection occurring at apparatus transition points, and certain devices, sometimes referred to as impedance transformers, have been devised for this purpose. However, impedance transforming devices heretofore available have been usable only in special situations and with somewhat inconvenient limitations. It is an object of the present invention to provide reflection controlling agencies which are applicable in a very wide variety of cases and which are highly iiexible in the matters of design and mode of use.

It is a more particular object of the invention to provide means usable in connection with the propagation of centimeter waves, as above defined, for preventing or eliminating and controlling reflection of such waves. As will be more fully explained in the following, special diiculties are encountered in this range of wave lengths because of the need for taking into accurate account certain factors which may be ignored at longer Wave lengths.

In general, the invention involves the use of a plurality of transition elements which by virtue of their dimensions, spacings and other properties are able to efect the reilectionless transmission of electromagnetic waves from one propagating region to another. In one embodiment the transition elements employed take the form of two or more dielectric slabs or plates of appropriate configuration and arrangement. In another they comprise discrete impedance-Varying sections spatially and dimensionally correlated to assure attainment of the desired results, The considerations which determine the proper form and relationship of the means employed will be described in the following for each distinctive case By the use of a reflection-controlling system which embodies several (i. e. two or more) separate transition elements it is found that many of the limitations inherent in previously used impedance transforming methods are avoided. That is to say, the relatively greater numberiof independently variable factors leads to greater freedom in the design of the individual components and to greater flexibility in the matter of adjusting them. These considerations will become more fully apparent as the details of the invention are described;

The features of the invention especially desired to be protected herein are pointed out in the appended claims. The invention itself, together with its further objects and advantages, may best be understood by reference to the following description taken in connection with the drawings, in which Figs. 1 to 3 are schematic illustrations useful in explaining the invention; Fig. 4 is a graphical representation of certain data of significance in interpreting the invention; Fig. 5 illustrates a first exemplary application of the invention; Fig. 5a is a section on line a-a of Fig. 5; and Figs. 6 to 12 show various alternative applications.

Single surface refiection In explaining the invention it will be convenient first to refer to a relatively simple case and then to extend the theory to include more general and complex cases. With this in mind, the line :ru of Fig. 1 may be considered as defining the boundary between a first dielectric region or medium of propagation constant h1 and a second dielectric region or medium of propagation constant h2. It is desired to consider the action of an electromagnetic wave which impinges on :ro from the left, the direction of propagation of the wave being indicated by the arrow A.

It is useful to note preliminarily that under appropriate conditions electromagnetic Waves may exist in numerous forms. For example, in considering free space propagation, plane transverse waves are ordinarily assumed. On the other hand, in a wave guide, such as a rod of dielectric or the space enclosed by a hollow Conductor, confined ultra-high frequency waves may be developed and propagated which have eld components not only at right angles to the direction of propagation but also in the direction of propagation, One such wave, which may be produced, for example, in a hollow 'cylindrical conductor, is the so-called Ho wave which has magnetic components parallel to and transverse to the direction of propagation and an azimuthally directed electric component in a plane transverse to the direction of propagation. Another type, frequently called the En wave, has lines of electric force parallel and transverse to the direction of propagation and has lines of magnetic force azimuthal with respect to the axis of propagation. In general, however, any electromagnetic wave may be considered as fully specified for most purposes when its classification is given, and when the magnitude of one of its field components is stated, the remaining components being then readily determinable from relatively simple relationships.

' With these considerations in mind, let the Wave indicated by a directed arrow A in Fig. 1 be characterized by the transverse component,

of the electric field associated with it. Here t represents time, 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 nondissipative, 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 h2 is the propagation constant of the medium to the right of :120. The coeicients r and b` are determined by matching the electric and magnetic fields at :1:0 according to a wellunderstood procedure. These coeicients are real in the case of Fig. 1 if the dielectrics are non-dissipative, but in general they are complex. They give both the amplitude and the phase of `the reflected and transmitted waves at :no referred to the incident wave at the same boundary.

For the case of Fig. 1, r and h are found to be The quantity Z in ythe foregoing equations is defined as the ratio of the transverse .electric component of the propagated wave to the transverse magnetic component for the particular propagating region under consideration and corresponds to the characteristic impedance of the propagating system as that term is customarily employed. (See Electromagnetic Theory by J. A. Stratton, iirsll ed. pp. 282-284). As thus defined, Z is dependent both upon the intrinsic 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) where c is the velocity of light, ii is the permeability 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- 4 mensions is more complex, being defined as follows in the case of I-I waves traversing a rectangular wave guide having a dimension which is perpendicular to the transverse electric field and a dimension y which is parallel to the transverse electric eld.

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 .1i/:c becomes unity).

T ke-1 G10 y l# For E waves ZE: C/.L

For E waves in guides Z-h.

We notice from vcomparison of Equations 1 and 2 that b=1+r. Although the amplitude of the transmitted wave is greater than that of the incident wave if Z2 is greater than Z1, the energy transferred by it is necessarily less. The greater amplitude is consistent with the consideration that in different media the power density is proportional not only to the square of electric amplitude but also the reciprocal of the impedance.

The reection and transmission coeflicients are not the same for waves incident from the right as they .are for those incident from the left. If primed symbols refer to the `former case, we find that Reflection and trnsmission at a slab We may examine the case of two boundaries by considering the arrangement of Fig. 2, in which the space to the left of m0 is occupied by medium 1, the space between 3:0 and x1 is occupied 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 reection coemcients in the forward and reverse directions respectively, b and b represent corresponding transmission coefficients, and the various subscripts identify the surfaces to which these coel'lcients are referred.

The complete reected wave,

Arxewt+h1(a:zg) is determined by the reflection coeicient fro Using Equations 3 and 4 in connection with Equation 6, we i'lnd that T10-traf P Ws For the transmitted wave Atzlewl-hah-:D

a similar calculation gives the transmission coefficient Atz bz bT e-f@ 1 *l (8) Amo l r :013,16

and using Equations 3 and 4, we have bxubzle-'7 An important case is that in which media 1 and 2 are identical. Then r (Equation 1) =Re0=nl and 1.... -21'9 RFH-za (7") Also, bx0=1+r and bzlr-l-r, so that (1-r2) 6*"1'" T1=m Equations 6 to 9a give the amplitudes and phases of the waves reilected and transmitted by 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 reflected wave and at the surface :ci for the transmitted wave and are referred to the incident wave at the rst surface. The coefficients of Equations to 9a are in general complex for both dissipative and non-dissipative dielectrics. They completely describe the effect of the dielectric medium between xo and x1 on the incident wave, and there is no need for referring to any process inside this medium once we have them.

For a practical application of the results obtained in the foregoing, we may rst consider the situation in which the numerator of the right hand memfber of Equation 7 is set equal to zero as follows:

If all the dielectrcs involved are non-dissipative, so that 0 becomes real, this condition can be satisfled if |r0!=lre1|. (lrol and [fall represent the respective absolute values of reo and nl.)

When re0=mp Equation 10 is satisfied provided I0|=-n1r, and when re0=re1, then suffices. (Here n is an integer or zero.) 1

As we have seen in connection with the derivation of Equation 7a, re0=1^r1 represents the case of a plate of non-dissipative dielectric separating identical media. Reference to Equation 7 and to the considerations stated in the preceding paragraph shows that such a plate gives zero reflection (i. e. R1-(1'e0-l-1'e1e2f)=0) when the plate is any integral number of half wave lengths thick (i. e. when |6|=n1r) From a practical standpoint it is important to note further that where nondissipative 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 more apparent in the following.

Consideration of Equation 1 will show that for rx0=rz1, v(the second of the two cases proposed in the next to last paragraph) the media on opposite 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 further condition that the plate is an odd multiple of a quarter of the operating wavelength (in the refractive plate) in thickness (i. e.

where n is an odd integer, including unity) we see from (10) that the plate in question may be used to introduce a wave without reflection (i. e. with complete transmission) from the first of the separated media into the second. This result holds stricth7 only for non-dissipative dielectrics but is easily corrected to take into account appreciable dissipation in one or more of the media, and the resulting correction is small. A matching 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 #meng Then, by Equation 1 in Equation 7a.

between the value indicated by :1111 and the value indicated by Two 0r more4 slabs For the case to which the present invention especially pertains, namely, in which two or more refractive elements are involved, a system such as that illustrated in Fig. 3 may be considered. In this figure the refractive regions a and b are understood to -be included between two pairs of separate reference surfaces xo, :1:1 and x2, xs. We shall assume that the refractive regions a and b are completely specified by known coefcients ra, ra, ba, ba, applying to a as a -whole and rb, T'b, etc. applying to b. These coefficients are analogous to the reection and transmission c0- eilcients for the surfaces of a single slab as previously derived (e. g. in Equations 7a and 9a).

Following an analytical procedure similar to that used above, we nd that the overall reflection and transmission coefficients for the system which includes the two refractive regions a and b are formally of the character indicated by VEquations 6 and 9, being specified as follows:

These formulas apply to dissipative as well as to non-dissipative dielectrics and in general are complex for both cases.

Since we have the reection and transmission coefficients for single slabs (Equations 7 and 9), we may use them in Equations 12 and 14 to investigate the useful properties of pairs of slabs. In this connection consider two identical nondissipative plates immersed in a non-dissipative medium of different impedance in an arrangement 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 (Equations 15 and 15a are obtainable by expanding the right-hand members of Equations '7a and 9a into their real and imaginary components and then evaluating the angular arguments of the resulting expressions.) Substitution from 15 into Equations 12 and 14 yields where R2 is the over-all reflection of the two-slab system and Since (2-x1) represents the slab spacing and since Blf depends directly upon slab thickness, it

will be seen that both these quantities are dominant 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 involved, reflection cannot be eliminated, as has been previously suggested by various writers, solely by a quarter wave spacing of refractive elements.

Except for the factor eif, Equation 19 is formally the same as that for a single plate (see Equation 7a). By setting the numerator of its right-hand member equal to Zero (i. e., the condition for zero reflection) we find that zero reiiection is obtained when where n is an integer and where, necessarily, l h2 ](x2-i) is greater than zero.

Fig. 4 is a plot of the phase angle, ip, which determines the spacing h2(2-:1:1) in degrees of phase, as a function of the phase thickness, 9, of the plates. The impedance ratio is taken as a parameter.

While it is not immediately evident from Equation 19, it can be shown from that equation that R2 is maximum when e*2m=-1. This is an equality which is satisfied when In the event of the fulfillment of this condition This is equal to the reflection from a single surface having an impedance ratio equal to the fourth power of that for the slabs, as can be seen by substituting from Equation 11 and cornparing 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 dened by Equation 20 and Equation 20a. This is an important feature of multislab combinations when used for neutralizing reflection from a reflecting boundary outside the combination since it means that the reflection obtainable with such combinations is to a large extent independ ent of the characteristics of the individual slabs.

If the two refractive regions are not identical slabs, there is, in general, no separation giving zero reflection. However, in the special case inv which l Ta rb l, we nd that no reflection occurs when Ihzl ($2 1121) (22) In justifying Equation 22 we may rst observe that a condition to be fulfilled if there is to beI cancellation of the portion of the incident wave which tends to be reected from the first reflecting slab (Fig. 3) is that the various wave components which pass through the first slabI and,

. 9: after single or multiple reflection from the second slab, effect repenetration into medium I mustbe in opposite phase with respect to the primarily reflected wave. To show that Equation 22 represents the condition-for a proper phase relationship of the internally reflected wave components, consider an incident wave of phase zero at :to (Fig. 3) The phase of the primary reection from the rst slab referred to the plane :0 is tba by Equation 15. The phase of the primary transmitted wave at :L'i is by Equation 15a. At :v2 the phase has been advanced 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 during its passage from r2 to x1 by an amount equal to [hz Mrz-x1). Combining all these phase differences we get for the relative phase of the internally reected 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 between the boundaries mi and m2. Considering only the portion of the wave which is transmitted through the dielectric a into medium I at the rst opportunity for such transmission, it is apparent that this portion will suffer a retardation of phase during such transmission of (i. e., according to Equation 15a). The total phase lag of this part of the wave which is available for interference with the primary reflected wave is therefore the algebraic sum of the individual phase diierences:

For this interfering wave to be wholly out of phase with the directly reflected wave which, as we have seen, has the relative phase angle gba, it is clear that the phase di'erence between the interfering wave parts must be some odd number of 1r radians. Mathematically expressed, this means that This reduces directly to Equation 22. This equation shows, among other things, that reflection cancellation depends upon the maintenance of a proper spacing between the reecting 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 Waves varies equally and in the same sense.

Equation 22 can be applied to the problem of introducing a wave from air into water (neglecting for the moment the slight effect of attenuation on the water reflected wave) by using a refractive slab for a and a. refractive slab backed by water for b. This arrangement is illustrated in Fig. which shows a wave guide in the form of a hollow conductor ID along which electromagnetic waves are assumed to be propagated. The relative position of the refractive slabs is indicated at II and I2 and water backing the slab 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 substance. If this is at all possible, it can be done when [rb] (i. e., the reection coeflicient of slab l2) is a minimum. That this Yoccurs when can be seen from Equation '7, the equation for reection from a single slab, in which now both no and nl are negative because the impedances of the various successive media are progressively less in the direction of propagation. The following 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. Y

Dielectric constant of quartz 3.6

Dielectric constant of water From these data and by means of known relationships (see definitive Equation 2b) We are able to compute various impedances that we need:

Where subscript 1 refers to the air-lled portion of the wave guide, subscripts a' and b to the slabs II and I2 respectively, and subscript 3 to the water-filled section I3; where y and a: are respectively the minor and major dimensions of the wave guide, and where the factor Zo is the impedance encountered by a plane wave in lfree space. The ratio 'yl/m cancels out in the computation of reflection and transmission coeiicients and therefore does not require to be numerically specified.)

The reflection coefficients for the various slab surfaces are found by using Equation 1:

From (7) Now the maximum reflection obtainable from a quartz plate in airis, from (11) 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:

i 1 In using Equation 22 it should first be recalled that (x3-m2) was arbitrarily so chosen that is a matter of convenience only. Some other value might equally well have been taken in which case the further treatment' of the problem would have been complicated to the extent of having to deal with a finite value of rbb throughout.)

Using the impedance ratio Z1/Za=2.'24, Fig. 4 gives yba=118. (Fig. 4 shows the variation of 1]/ with 0 for different values of the impedance ratio Zl/Za. For cases where is below. 90 use is made of the upper abscissa scale and the righthand ordinate scale. For cases where 9 is between 90 and 180 the lower left-hand scales are 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 result could have been obtained by using a material having an impedance closer to that of water. However, by adding a third plate, identical to and positioned ahead of and by applying the general formulas to the resultant three-plate system, it is easy to show that the range of impedance over which zero reilection may be obtained is greatly'exten'ded, for, the first two plates then behave like a` single plate with a higher impedance ratio. This arrangement is illustrated in Fig. 6 which indicates a wave guide 2D (either of cylindrical or rectangular form) containing a series of three mutually spaced dielectric slabs 2|, 22, and 23, the plate 23 being backed by water, as indicated at 24. A special advantage of the three-plate arrangement is that not only the impedance but also. the thickness of the individual plates may be chosen within much wider limits than is possible where only two plates are employed. Y

This three-plate matching `apparatus has an analogue in which single surfaces replace plates. A wave may zbe introduced without reflection into a body of dielectric if` at the proper distance in front of the dielectric we place a refractive plate of the correct thickness. This is indicated in 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 is merely that they over-all reflection coefficient of the plate shall equal in magnitude that-of the single surface of dielectric 3|, the only restriction on the impedance ratio of the platev (with respect to the medium in which it is immersed) is that it be greater than the squareroot of that. for the dielectric surface (see Equation 14) Within these limits a plate of any impedancev may be used provided its thickness and location are properly chosen.

Determination of the proper dimensions and.

location of the plate 32 requires a preliminary determi-nation by measurement or computation, of the reflection cceflicient of the surface of dielectric 3 W ith this quantity known, the thickness of the plate required to give an equal coefficient can then be computed. Finally, the spacing of the plate with respect to the dielectric 3| which is necessary to assure-mutually annihilative interference of the two reflected wave components may be determined by a procedure like that used in justifying Equation 22. 'Ihe 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 direction of wave propagation, a phase displacement of mr radians exists between reflections attributable to the plate and those attributable to the dielectric, 71. being an odd integer.

A- single plate such as the plate 32 may alternatively be used to annul reflections due to reflective discontinuities other than a discontinuity attributable toV a change in the propagating dielectric. Examples of other discontinuities are those produced (l) by a change in dimensions of a wave guide, or (2) by a change in direction of a waveguide, or (3) fby the junction of a wave guideY with a devicehaving an effective characteristic impedance different from that of the wave guide.

Fig. 8 represents a construction inwhich 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 a metallic enclosure 35 within which are contained electrode structures 31 such as the electrodes of a split anode magnetron. The entrance of the wave guide 35 isassumed to be arranged in such relation to ,the electrodes 31 as to assure that high frequency wave energy will be propagated along the guide.

In order to preserve the vacuum tightness of the container 36 in spite of the insertion of the wave guide 35, a glass plug 39 is sealed into the entrance to the wave guide for the purpose of forming a vacuum-tight closure. In accordance withI the considerations previously given herein, it willfbe understood that the plug 3) constitutes at least a partial barrier to the passage of waves and may lead to objectionable reflection of such waves. The geometry of the system in question makes it inexpedient to eliminate such reflection by means of slabs located in the guide within the container 36. However, an equivalent effect can be obtained by means of a pair of dielectric slabs 4| and 42 arranged Within the guide at a point outside the container 35.

In order to determine the proper arrangement of the slabs.4| and 42, it is necessary first to determine the over-all reflection coenicient of the plug 39, referred, for example, to the left-hand surface of the plug. Thereafter by use of Equations 19- and 19a a spacing of the slabs 4| and 42 may be determined which will give an equivalent reection coefficient referred to the left-hand surface of the slab 4|. This spacing will, of course, be a, function of the thickness and dielectric properties of the respective plugs. Once the proper location of the plugs 4| and 42 with respect to one another is fixed, the distance between the left-hand surface. of the plug 39 and the corresponding surface of the slab 4| required to assure destructive interference of the waves respectivelyreflected from the two reflecting` units may 13? be computed by an analysis similar to Lthat involved in the derivation of vEquation l22.

Fig. 9 represents the application of the invention to the case of a wave guide 43 which is terminally connected to a smaller wave guide 44. Due to the difference-in dimensions of the.Y two Wave guide sections, they will under ordinary circumstances have different characteristic impedances and wave reflection will occur at their junction. `To annul this reflection there are provided two identical dielectric slabs 45 and 45 which are respectively spaced from one anotherA and from the entrance extremity of the waveguide 44.

In designing an arrangement such as that of Fig. 9, the composition of the plates t5 and 46 may be chosen rather arbitrarily with a View to employing materials which are structurally suitable. Moreover, the thickness of theplates is arbitrary within relatively wide limits. With the impedance and the thickness of the plates given, it is possible to vary the spacing of the plates With reference to one another in accordance with Equation 19 to produce a reflection coefficientl for the combination which equals in absolute magnitude thecomputed or observed reilection coefficient 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 (i. e., the reflecting boundary) must be adjusted to assure (2n-1)- phase displacement between the reflected waves Whose destructive interference is desired.

` In the wave guide construction of Fig. 9, the reflective slabs or plates may alternatively be located in the smaller wave guide section d4.'

A still further application of a multiple plate combination as a reflection reducing agency is illustrated in Fig. 10. In this case there is shown a coaxial conductor transmission line having an outer conductor 5i! and an inner conductor 5I. The inner conductor terminates in an unshielded portion 5| which may be assumed to constitute a radiating antenna or to connect with an antenna or other utilization device. It is obvious that the effective impedance of the unshielded section 5I will be different from theimpedance of the transmission line combination, so that wave reflection at their junction may be anticipated. To avoid this, there are provided a pair of dielectric plates or disks 53, 511 which are fitted into the conductor 59 and which have dimensions and spacings calculated in accordance with the principles previously given herein to neutralize reflection from the transmission line termination. In connection with a coaxial transmission line system, the dielectric plates 53 and 54 of Fig. 10 may be replaced by equivalent transition elements of a different structural character.` This possibility is illustrated in one embodiment in Fig. 11 which-shows a coaxial transmission line having conductors 60 and 6l, the inner conductor terminating in an antenna section t l Attached to the conductor 6l within the confines of the conductor B are a, pair of annular conductive (e. g., metal) sleeves 63, E4 which are of similar dimensions and which are mutually spaced.

It is apparent that each of the sleeves 63 and 64 introduces into the transmission line system a short section (corresponding to the length of the sleeve in question) having an impedance 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 53,' 54 .of Fig. 9. Moreover, by, considerations 14v similar to those used in connection with the constructions of Figs. 5 to 10, one may determine the dimensions and spacing of the sleeves S3 and 64 which are required to cancel the reiiection occurring at the extremity of the transmission line (i. e., at'its junction with the antenna BI).

A further .modification of this same principle is shown in Fig. 12 in which annular sleeves 13 and 14, functionally similar tothe sleeves B3 and 64 of Fig. 11, are secured to the inner surface of a tubular conductor 'lll which forms the outer member of a coaxial'conductor transmission line. By appropriate choice of the dimensions and spacings of the members 'i3 and 14, terminal reilections due to the junction of the transmission line with an antenna 'H' may be neutralized.

Reflection-preventing sleeves of the character illustrated in Figs. 11 and 12 may also be used in connection with single pipe wave guides. However, in the latter application it is considered that dielectric slabs have an advantage over transition 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 reflection-producing discontinuity may be cancelled or annulled by providing in connection with the discontinuity a neutralizing system having a reiection coefficient equal to that of the discontinuity and having a spacing with respect to the 'discontinuity such that at planes in advance of all the reflecting agencies a phase displacement of approximately mr radians exists between reections attributable to the discontinuity and reflections attributable to the neutralizing system, n being an odd integer. It should be noted, however, that the question of whether the provision of equal reflection coelcients represents a proper condition for complete neutralization depends to some extent upon the nature of the reflecting agencies involved. More specifically, it is a condition which is applicable in an arrangement in which the neutralizing system is ahead of the discontinuity desired to be neutralized,.provided a-phase displacement of exists between wave components reected by the system and wave components transmitted by the system. In other words, the relationship assumed in Equations l5 and 15a must be valid. Where the discontinuity is ahead of the neutralizing means (as in Fig. 8), then the discontinuity (and not necessarily the neutralizing means) must comply with the aforementioned relationship.

v A phase displacement of 90 between reected and transmitted components represents an assumption which is justified in the event thereiiection-producing agency in question comprises a single, substantially non-dissipative, dielectric slab or a plurality of identical such slabs. It is not justified where the reflection-reducing system is made up of a number of dissimilar slabs or where it is made up of structural discontinuities such as those illustrated in Figs. 11 and 12. Accordingly, in connection with reflection-reducing agencies of the latter class, it will be found that for complete neutralization rto be obtained the reflection coefficient of the neutralizing means must ordinarily be somewhat different from the reflection coeflicient of the discontinuity which give-s rise to fthe reiiections desired to be annulled. This qualification also applies in cases' While the. inventionhasbeen described by reference to particular applications and specific embodiments, 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.:

1. An electromagnetic system. for propagating centimeter waves comprising a wave-propagating structure having a discontinuity at which reflection tends to occur, and means in proximity to said discontinuity and in the path of wave propagation for annulling the said reflection, said means comprising the combination of a plurality of spaced elements each constituting in itselfV a short section of wave-propagating structure and having a thickness in the direction of wave propagation which is a material fraction of the Wave length of the waves to be propagated whereby,l the overall reflection from said combination is defined by a reflection coefllcientin which both the spacing and thickness of the elements enter as dominant factors, the spacing of said elements with respect to one anotherl being so adjusted that at any plane in said structure located in advance of the said elements and the vsaid dis'- continuity with reference to the direction of wave propagation the rellection attributable to the elements is equal to that attributable .to the said discontinuity, and the spacing of said elements with respect to the discontinuity being such that at the said plane a phase displacement of approximately mr radians exists between reflections attributable to :the discontinuity and reflections attributable to the elements, n being an odd integer.

2. An electromagnetic system for propagating centimeter waves comprising a wave-propagating structure having a discontinuity at which reflection tends to occur, and means in proximity to the said discontinuity and in the path of wave means comprising the combination of a plurality of spaced dielectric plates each having a thick-` ness which is a material fraction of the wave length of the waves to be propagated whereby the overall reflection from said combination is dened by a reflection coefficient in which both the spacing and thickness of the plates has dominant factors, the spacing of said plates with respect to one another being so adjusted that at any plane in said structure located in advance of the said plates and the said discontinuity with reference to the direction of wave propagation the reflection attributable to .the plates is equal to that attributable to the said discontinuity, and the spacing of said plates-with respect to the discontinuity .being such that at the said plane a phase displacement of approximately mr radians exists between reflections attributable to the discontinuity and reflections attributable to the plates, n being: an odd integer.

3. An electromagnetic system for propagating centimeter `waves comprising a wave-propagating structure having a discontinuity at which reflection tends to occur in an amount determined by a reilection coeicient assignable to the discontinuity, and means for annulling the said reflection, said means comprising the combination of a plurality ofV identical dielectric plates located in advance of the said discon 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 reection from said combination is defined. by a reflection 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 plates with respect to the discontinuity being such that at any plane in said structure located in` advance of the said plates a phase displacement of approximately mr radians exists between. reflections attributable to the discontinuity and reections attributable to the said plates, n being an odd integer.

4. In combination, a source of centimeter waves, a wave guide connecting with said source for propagating waves derived from the source, and means for annulling the reflection of waves at the junction between said source and said wave guide, said last-named means comprising a ccmbination of spaced dielectric plates which are located within said wave guide in proximity to the said junction and which are of a thickness corresponding to a material fraction of the wave length of the waves derived from said source whereby the overall reflection from said combination is defined by a reflection coelcient in which both the spacing and thickness of the plates enter as dominant factors, the spacing of said plates with respect to one another being so adjusted that at a plane between the said source and the said junction the reflection attributable to the plates is equal to that attributable to the junction, and the spacing of said plates with respect to the junction being such that at the said plane a phase displacement of approximately ne radians exists between reflections attributable to 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 impedance than the rst, and a plurality of identical dielectric plates successively arranged in advance of the junction of said iirst and second regions for facilitating the reilectionless transfer of wave energy between the regions, the dimensions and spacing of said plates with respect to one another being such that the overall reflection coeillcient resulting from their combination is equal to the reflection coefficient of the said junction, and the spacing between the junction and the plates being such that with respect to waves which pass through the various plates, are reflected at the said junction and retraverse the plates, the phase shift attributable to said spacing plus the phase shift attributable to the plates themselves differs by approximately mr radians from the phase shift of waves reflected directly from the first of said plates, n being an odd integer.

6. In an electromagnetic system which is adapted to propagate centimeter waves and which comprises two adjacent propagating regionsV of different characteristic impedance; an arrangement which includes at least two spaced elements in proximity to the junction of the said regions and in the path of the propagated waves for assisting the non-reflective transfer of wave energy from one region to the other, each of said elements constituting a short section of Wave-propagating 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 reiiection from said arrangement 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 adjusted that at a plane locate-:l in advance of the said elements and the said junction with reference to the direction of Wave propagation the reiection attributable to the elements is equal to that attributable to the junction, and the spacing of said elements with respect to said junction being adjusted to secure phase opposition between Said reiections to obtain destructive interference thereof.

7. In an electromagnetic system, an elongated hollow Wave conning structure denning a first Wave-propagating region, and means for facilitating the transfer of Wave energy from said region. to a second region of different eiective impedance, said means comprising a plurality of 18 localized constrictions provided within said structure at mutually displaced points near its junction with said second region, the extension of said constrictions in the direction of wave propagation comprising a material fraction of the wave length of the Waves desired to be propagated whereby the overall reflection of the 'various constrictions is donned by a reilecticn coenicient in which both the spacing and extension of the constrictions enter as dominant factors, the spacing of said constrictions with respect to one another being so adjusted that at a plane located in advance of the said constrictions and the said junction with reference to the direction of propaga,- tion the reflection attributable to the constructions 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 1inradians exists between reflections attributable to the junction and reflections attributable to the constrictions, n being an odd integer.

LEWI TONKS. LE ROY APKER.

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