US2914741A - Waveguide bend - Google Patents

Waveguide bend Download PDF

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Publication number
US2914741A
US2914741A US681027A US68102757A US2914741A US 2914741 A US2914741 A US 2914741A US 681027 A US681027 A US 681027A US 68102757 A US68102757 A US 68102757A US 2914741 A US2914741 A US 2914741A
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United States
Prior art keywords
waveguide
curvature
bend
section
mode
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Expired - Lifetime
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US681027A
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English (en)
Inventor
Unger Hans-Georg
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AT&T Corp
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Bell Telephone Laboratories Inc
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Priority to DENDAT1071168D priority Critical patent/DE1071168B/de
Application filed by Bell Telephone Laboratories Inc filed Critical Bell Telephone Laboratories Inc
Priority to US681027A priority patent/US2914741A/en
Priority to GB27042/58A priority patent/GB845492A/en
Priority to FR1209693D priority patent/FR1209693A/fr
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Publication of US2914741A publication Critical patent/US2914741A/en
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    • HELECTRICITY
    • H01ELECTRIC ELEMENTS
    • H01PWAVEGUIDES; RESONATORS, LINES, OR OTHER DEVICES OF THE WAVEGUIDE TYPE
    • H01P1/00Auxiliary devices
    • H01P1/02Bends; Corners; Twists

Definitions

  • This invention relates ,to guided electromagnetic wave transmission and, more particularly, to. waveguide configurations for transmitting the TE circular electric wave mode through curved waveguide sections.
  • the term bend will be considered generic to all-waveguide configurations which deviate smoothly froin'axial linearity.
  • ErAs is: now wellappreciated in, the wave transmission art, the propagation of microwave energy in the form of TE -waves, in circular waveguides is especially suited to long distance transmission since the attenuation characconversion losses sulfered by wave energyin the circular,
  • a more specific. object is to bend an elastic waveguide section into a configuration, having a tapered curvature through the application of an external force at the enter of the section directed radially opposite to the external forces applied at the section extremities.
  • a waveguidebend in accordance with the invention has a radius of curvature associated therewith at a point just beyond the junction considerably greater than that which would normally re suit, from the stresses and 7 strains associated with an ordinary bent membero;
  • Such a novel waveguide bend is designated atapered curvaturenormal mode bend.
  • any 31 deviation from straightness of thelongitudinal axisof the waveguide may excite waves of other modes and thus produce serious losses. These lossesare due-mainly to the fact thagwaveguide curvature induces acoupling between the desiredjTEi and other wave transmission modes.
  • a tapered curvature normal mode bend is fabricated by bending a waveguide section while under the influence of at least one external force directed radially outward at. the point of maximum curvature. Physically, this indicates that a bend in accordance with .theinvention is formed by bending a waveguide section around at leastonefixed point.
  • a waveguide section is physically shaped to possess a curvature whichtconforms with the graphical representation of theFourier transform of a Tscheby scheif polynomial of infinite degree.
  • Such a configuraf tion represents an optimum tapered curvature normal mode waveguide bend from an electrical transmission viewpoint.
  • I n r p In accordance with a second principal embodiment of the invention, a waveguide section is physically shaped to possess a tapered curvature characteristic which gradu ally.increases fromgero over a first portion of its length and .al tape redcurvature characteristic which gradually decreases tQI ZGIOQVQS' a second-portion of its length. These portions may be directly connecte'lor they may be connected by a third portion having constant curvature.
  • Fig. 1 is a perspective view of a simplified waveguide
  • Fig. 2 illustrates a pair of angularly related straight waveguides connected by several types of waveguide bends;
  • Fig. 3 is a graphical representation of the length of a prior art waveguide bend
  • FIG. 4' is a graphical representation of the length versus curvature characteristic of one waveguide embodiment of the invention
  • Fig. 5 is a waveguide bend having the curvature characteristic 'of Fig. 4;
  • Figs. 6A and 6B are graphs illustrating the length versus curvature characteristic of additional waveguide embodiments of the invention.
  • Fig. 7 illustrates a method of fabricating a curved waveguide section having the curvature characteristic of Fig.-6B.
  • Fig. 1 illustrates a simplified microwave installation comprising microwave. source'10 supplying energy in the form of TE waves to a microwave utilizing means 11 through a continuous circular waveguiding passage.
  • Utilizing means 1-1 maybe .a microwave amplifier, a receiver, or an antenna, for example.
  • the circular waveguiding passage comprises angularly related straight sections 12, 13 which are joined by smoothly curved section 14, the paJticuIar design of which will be explained in detail in a later portion of this specification.
  • a of the circular pipe guide selected for the propagation of these waves must be greater than the critical or cut-off radius 01 for the TE mode.
  • a is equal to 0.611 where n is the wavelength in free space of the lowest frequency wave in the transmission band.
  • a is 'made greater than a and may vary in different systems from' 1.51 to 151
  • this mode conversion may be reduced by modifying section 14 in such a way as to remove the propagation constant equality between the TE and TM wave modes.
  • mode conversion to TM wave energy is not completely eliminated by such modification.
  • mode conversion to modes other than TM persists.
  • a suitable inner radius for the waveguide structures to be described herein may be 7. 7a or 4.7M.
  • TE wave propagation'through curved seetion14 is most'easily explained in terms of normal modes; thatis, those waves for' a particular waveguiding structure which propagate with- Normal modes represent solutions of the wave' equations inthe particular waveguiding structure being investigated.
  • the normal mode of interest is the TEm mode;
  • normal modes of a curved waveguide section are not so simple as those of a straight section. They may, however, be expressed as'a sum of the straight guide normal modes.
  • the normal mode in the curved guide which is of'interest is that one which, when represented as a sum of straight guide modes, has the greatest part of its power in the TE mode portion of the sum.
  • the curved guide normal mode of interest is very similar to the T E mode of the straight guide.
  • the total power inmodes other than the TE mode in section 13 thus represents mode conversion loss introduced by curved section 14.
  • such a waveguide transition can be realized by tapering the curvature of the curved waveguide section from zero at its junction with the straight waveguide.
  • the curvature of bend 14 is tapered over its length from zero to a finite value and then back to zero, the normal TE' mode incident from straight section 12 will be gradually transformed into the particular normal mode of bend 14 which is most similar in field configuration to the circular electric wave.
  • there is only one normal mode consistent with the value of curvature presented by the bend to the propagating wave energy as well as being similar in field configuration to the TE mode.
  • By gradually tapering the curvature of the bend the propagating wave energy is retained in the desired normal wave mode throughout the bend.
  • Such a bend is the tapered curvature normal 'mode bend.
  • the waveguide sections under consideration in this specification have physical dimensions large enough to permitmore than one wave mode to propagate therein.
  • the two or more wave modes which may propagate together have differing phase constants. This is true even for the TE -TM phase constants in the modified bend section 14 from which their inherent degeneracy has been removed. Since the phase constant of the TM as well as those of other modes capable of propagating in the circular waveguide are different from that of the TE there will be a periodic phasal reinforcement or'addition and a periodic phasal destruction or subtraction between the TE and each of the unwanted higherorder modes.
  • each mode pair comprising the TE and oneof the unwanted higher order modes is a periodic distancebetween consecutive points of equal amplitude and phase. This distance is called the beat wave length, A f or'that particular mode pair.
  • length z should be of the order of or longer than the longest heat wave length associated with the structure. That is, since It can be seen that, for plain circular waveguide bends; that is, those in which the degeneracy between the TE and 'TM phase constant has not been removed, the normal mode. taper would have to be infinite in length.
  • V ,Fig. .2 illustrates in comparative relationship, the physical shape of an embodiment of the present invention together with physical shapes of the general types of P9ibl P r Wa eguide bends.
  • Sections 20, 21 are illustrated as being angularly related by 9.0 degrees'but the invention may 7 be utilizedto connect waveguide sections of any angular relationship.
  • a curved section of constant bending radius was thought to be. the ideal waveguide bend configuration for joining seg-- December 18, 1956, to S. E. Miller, bends'of constant" curvature, or constant bending radius, are utilized
  • Such a bend is illustrated in 24 of circle 29 which has a radiusR I
  • Curved segments 25, 26 represent physicalshapesl'of curyed waveguide sections for Whichthe linear dimension of the.wave path is too short and too long, respectively, to form the constant curvature bend represented by arc;;24. Segment presents a curvature discontinuity at junctions 22,:23. even more severe than'that ofarc 24. .Both arc 24 and segment, 25 have a radius of, curvature associated therewith at a location just beyond their junction points with the straight sections considerably less than doesthe tapered curvature normal mode bend in accordance;with the present invention.
  • Curvedlsegment 26 presents," in addition to acurvature discontinuity at junctions 22, 23, a curvature characteristic which reversessense twice overits longitudinal extent. That is, as'curved segment 26,.is' traversed be-.
  • Fig. 2as arc directed with respect flte .thel icurvaturel atjits are; of
  • Fig.- c'urved fsegrnent 27 represents thephysical shape of a tapered curvature normal mode bend in accordance with the invention. From.Fig. 2, it may be I seen qthat, given a pair of; angularly related straight waveguide sections, the length of a'ta'pered curvature bendor transition section joining them'is greater than the length of a bend of constant curvature. However, the tapered curvature transition is not one into which a waveguidesection will deform under the influence of the normalstresses and strains associatedi'with the application of bending moments "at the extremities of the sections. In order.
  • f i i s Fig. "3 illustrates. the lengthlversus curvature 'charac teristic of a circular arc of constant bending radius such as for example, arc24o fFig 2. At points 22, 23, representing junctions 22, 23 of Fig.2, the curvature suffers an abrupt discontinuity. It is this type of dis continuity and its-associatedmode conversion effects which the present invention eliminates.
  • such a-form comprises rectangular sheet or slab 40 whichhas template 41,,and clampingsupports 42 disposed on its surface.
  • Template 41. is designedto have, a; physical shape corresponding to the particular; bend. shape desired.
  • template 4L isshaped to possess the curvature characteristic of Fig. 4.
  • Waveguidesection 43 is placed over template 41 and physically deformed to conform to the shape thereof.
  • 'a wayeguide section described by the curvature characteristic represented thereon comprises two distinct regions.
  • the first of these regions, represented by segment 50 is described by'a curvature which-tapers linearly from zero to a finite yalue k
  • the second region, represented by segment 51 is the reverse of segment '50 and is describedfby a curvature which tapers linearly from value [c to zero, (The total .length of the curved section com- -prising. curvature segments 50, 51 is defined as l and each of the regions of tapered curvature has a length Z
  • Fig. 6B a waveguide section described'by' the curvature characteristic represented thereon'cornprises three distinct regions.
  • the first of these regions, represented by segment 52 is described by a curvature which tapers linearly from zero to a finite value 19,.
  • the second region, represented by segment 53 is described by a constant curvature k over its length;
  • The-thirdregion represented by segment 54, is the re- Y T$haracteristic of segment '52 and is described by aicurvature which tapers linearly from value k to'zero.
  • the total length of the curved section is again defined as-l andeach of the regions of tapered curvature has a length. 1 v
  • an optimum total length I may be derived. The derivation of such an optimum relationship will be presented in a later portion of this specification;
  • waveguide section "60" comprises a conductively bounded hollow round pipefrom which the T E 'TM phase constant degeneracy has been removed. This pipe is bent around circular form 61 in a manner not exceeding the elastic deformation limits of the physical waveguide.
  • Form 61 is illustrated as being circular.
  • form 61 provides the outwardly directed force noted above which imparts the tapered curvature characteristic to section -60.
  • ThllS,fIOI1l the left end of-section 60 to the point of contact 64 between guide 60 and form 61, a distance 31, the pipe curvature increases linearly fromzero (descriptive of straight waveguide) to the constant value-associated with form 61 over its area'of contact with-section 60.
  • the curvature of waveguide 60 has a con stant valueover this interval. From point of contact 65 to-the right end ofsec tion 60, again a distance 2 the curvature decreases linearly from the constant value as-' sociated withform '60 to zero.
  • the constant curvature of form 61 is defined as k and the point of contact between form 61 and section 60 along the length l of said section is defined as Z the curvature k at any point along the lineartaperis V I shown for Fig. 6B. .That is, in Fig. 7, the region of contact of guide 60 and form 61 is reducedsubstantially to zero. of "the distributed force provided byf orm 61. tice this could be accomplished by bending a waveguide section over a fixed pin having a radius negligiblewith respect to the'length of the waveguide bend. Bending would be accomplishedthrough the application of forces, identical to forces 62, 63 of Fig. 7, at the extremities of the waveguide section to be bent.
  • a curve described by the curvature expressed in (3) is known as Cornus spiral.
  • the length of the tapered curvature sections in a waveguide embodiment of the invention must be of the order of or greater than the largest beat wave length associated with the curved waveguide section.
  • the bending form When a constraining form is used and the elastic limit of the waveguide is exceeded, the bending form may be removed after bending is completed. However, there will be a certain fspringback factor associated with the metal pipe and this must be taken into account when the layout of the constraints is planned.
  • the total bend loss A in a normal mode bend can be expressed as 1 p 1-4u A c1z+C1 W (6) in which C C and C are quantities depending on total bending angle, physical waveguide parameters and frequency; and
  • Equations 7 indicate that all con-- pled modes should be taken into account.
  • I optimum geometry is where w is positiveiroot the calculated y. If y l, the optimum geometry is The normal mode bend is inherently a broad band device. Some terms contributing to total bend loss decrease with frequency while others increase. The over-alll frequency dependence, other than the oscillations of the mode conversion portion of the total loss as caused by spurious mode'ph'asing, is vof the same order as is the frequency dependence of the loss in the straight waveguide.
  • a tapered curvature normal mode waveguide bend having first and second terminal ends for transmitting the circular electric wave mode between angularly re-- lated waveguide paths, said bend comprising a sectiom of bounded waveguide which is curved with a constant sense as the bend is traversed and in which the TE and. TM wave modes have difierent propagation constants, the tapered curvature portions of said section each having a length greater than the longest beat wavelength: associated with said section and each tapering between zero curvature at said terminal ends and a given curva' 2.
  • a transmission system having first and second terminal ends for electromagnetic wave energy in the circular electric wave mode, a source of said wave energy connected to said first terminal end, utilizing means for said energy connected 'to said second terminal end, and at least one curved section of nondegenerate circular waveguide between said source and said utilizing means, said section having at least one region of curvature taper: ing smoothly in one sense from zero over a length greater than the longest beat wavelength, associated with said section.
  • a transmission system for electromagnetic wave energy in the circular electric wave mode comprising first and second angularly related straight waveguide sections joined ,by a smoothly curved waveguide section which is curved in one sense between said straight sections, said curved section having a radius of curvature at a locationjust beyond the junction with said first straight section considerably greater than that associated with a circular arc mutually tangent to said straight sections, said curved section having a radius of curvature at the center thereof considerably less than that associated with said arc, said curved section having a radius of curvature at a location just before the junction with said second straight section considerably greater than that associated with said arc, said curved section having a length between said junction and said center greater than the longest beat wavelength associated with said section.

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US681027A 1957-08-29 1957-08-29 Waveguide bend Expired - Lifetime US2914741A (en)

Priority Applications (4)

Application Number Priority Date Filing Date Title
DENDAT1071168D DE1071168B (hu) 1957-08-29
US681027A US2914741A (en) 1957-08-29 1957-08-29 Waveguide bend
GB27042/58A GB845492A (en) 1957-08-29 1958-08-22 Improvements in or relating to electromagnetic waveguide transmission systems
FR1209693D FR1209693A (fr) 1957-08-29 1958-08-28 Guide d'ondes coudé

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US681027A US2914741A (en) 1957-08-29 1957-08-29 Waveguide bend

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