US Patent 4,978,934: Semi-flexible double-ridge waveguide

United States Patent [191 [11] [45] Saad [54] SEMI-FLEXIBLE DOUBLE-RIDGE [51] [52] [58] Saad M. Saad, Willowbrook, Ill. Andrew Corportion, Orland Park, Ill. Jun. 12, 1989 Krank et a1. ...................... .. 333/241 3,659,234 4/1972 Schuttloffel et al. . . .. .. . .. .. . ... .. Evered and Company (Metals) Limited, Advertise ment, “Azdar Double Ridged Waveguide”. Primary Examiner—Paul Gensler [57] ABSTRACT A semi-flexible double-ridge waveguide comprises a corrugated tube formed into a special dumbbell-shaped niently optimized to realize improved power-handling U.S. PATENT DOCUMENTS 8/1968 e-Twistable”. cross-section de?ned by parameters which are conve References Cited 3,396,350 Litton Airtron, Advertisement, “Double Ridge Flexibl Attorney, Agent, or Firm-Kareem M. Irfan Int. Cl.5 ....................... .. H01P 3/14;HO1P 3/123 U.S. c1. .............................. .. 333/241; 29/600 Field of Search ...................... .. 333/239, 241, 242 [56] Dec. 18, 1990 guide”. [21] Appl. No.: 365,598 [22] Filed: 4,978,934 ment, “Lets Get Flexible with Continental Flex Wave~ WAVEGUIDE [75] Inventor: [73] Assignee: Patent Number: Date of Patent: 333/241 3,822,411 7/1974 Merle . . . .. 333/241 3,945,552 3/1976 Tobita et a]. ..................... .. 228/ 17.5 OTHER PUBLICATIONS Collado, “An Inside Look at Double-Ridge Guide”, Microwaves & Rf, Jul. 1986, pp. 77-79. Findakly et al., “Attenuation and Cut-off Frequencies of Double-Ridged Waveguides”, The Microwave Journal, pp. 49-50. Raymond Bulley, “Analysis of the Arbitrarily shaped Waveguide by Polynomial Approximation”, IEEE Transactions vol. MTT 18, No. 12, Dec., 1970, pp. 1022-1028. Gabriel Microwave Ltd., Advertisement, “Seamless Flexible & Flexible Twistable Waveguides”. Gabriel Microwave System Ltd., Advertisement, “Ga briel Double Ridge Flexible and Twistable Wave capability as well as improved attenuation and VSWR factors across extended dominant-mode operational bandwidths. The dumbbell-shaped cross-section effi ciently removes the problems typically associated with the use of conventional rigid waveguide, including dif? culty of installation as well as the need for precise align ment of components, by combining ?exibility and ease of manufacture, even for long lengths of waveguide, through use of a continuous, uncomplicated and rela tively inexpensive process. The dumbbell-shaped cross-section is totally devoid of corners and other abrupt protrusions and is de?ned by a geometric equation in which speci?c parameters can be correlatively optiminzed to improve desired electrical properties of the waveguide. The waveguide is ren dered “semi-?exible” by the provision of helical corru gations having a staggered disposition of opposing cor rugation crests and troughs, whereby the breakdown air gap and, consequently, the maximum power rating is increased. guides”. Continental Microwave & Tool Co., Inc., Advertise 11 Claims, 10 Drawing Sheets US. Patent Dec. 18,1990 Sheet 1 of 10 4,978,934 I 5Q 1 PRIOR ART \\ \llr. F1645 PRIOR ART FIC1.Z US. Patent Dec. 18, 1990 Sheet 3 0f 10 4,978,934 (HJNI ) A SZ'O OZ'O Sl'O Ol'O SO'O 00'0 Lllllllllllllllllllllllll ovd _(/h‘Lgmv 8.0 :2:x modcod9.02.0omd£6 Qms/ lllllIlllllllllllllllllll sro om (HON! ) A SO'O OO'O US. Patent Dec. 18, 1990 4,978,934 2 1 40 Sheet 4 0f 10 3.0 F|6.5 20-— nf/zof 1O US. Patent Dec. 18, 1990 Sheet 5 0f 10 4,978,934 (HQNIII $20 020 0-0 Ol'O 900 000 lllllllllllllllllllllllll 0.3450 I l l I l 6 FIG. | 92-0 I I I I I 020 I I I l | I 5Y0 I I I | 0V0 (HON!) A l I Il I | 500 l l l I I| F 00.0 0.30 0.25 0.150.20- 0.10 0.05 0.0 (XlNCH) US. Patent Dec. 18,1990 Sheet 8 0f 10 urmowzh 32mg 4,978,934 W32i] .382”$:1 Illlllllllllllllllllfllrlllllllllllllllllllllllll 235.m39“. US. Patent Dec. 18, 1990 Sheet 9 of 10 4,978,934 US. Patent Dec. 18,1990 Sheet 10 0f 10 4,978,934 52 /5O . if.i 55 57 55 X 57 56 FIG. 11A 1 4,978,934 2 ble and, accordingly, ?exible double-ridge waveguide is commonly available in short lengths only. Although the presence of ridges yields increased SEMI-FLEXIBLE DOUBLE-RIDGE WAVEGUIDE bandwidth, the other electrical characteristics of ridged waveguide are degraded in comparison with rigid non BACKGROUND 'OF THE INVENTION 1. Field of the Invention This invention relates generally to waveguide used for transmission of broadband electromagnetic signals. More particularly, this invention relates to corrugated ridged waveguide of the ?exible kind which can be processed in long lengths by a continuous process and ridged waveguide of comparable length. The attenuation factor is increased and voltage-stand ing-wave-ratios (VSWRs) are degraded to the point where satisfactory performance can be achieved only in very short lengths. Inherent with the use of short lengths are problems associated with the need for cou has improved power-handling capability. pling ?anges and the associated dry air/gas leakage, potential for intermodulation, resultant VSWR degra 2. Description of the Prior Art The use of smooth-walled waveguide is extremely dation, and need for providing mechanical access to the common in microwave transmission systems. Wave coupled lengths for alignment purposes. guide of rectangular cross-section, in particular, is most often employed because it provides satisfactory electri cal performance for a number of waveguide applica tions. Rigid and smooth waveguide, however, is subject Consequently, there exists a need for ?exible wave guide having acceptable electrical characteristics, par ticularly high power-handling capability, suited for use in broadband dominant-mode microwave transmission applications and which can be economically manufac to severe restraints, both economic and utility-based, because the non-?exible nature of such waveguide en tured in long lengths by a continuous process. tails manufacturing in relatively short lengths and re quires use of customized lengths, bends and twist sec tions to suit the equipment layout at each site. In many OBJECTS OF THE INVENTION It is a primary object of this invention to provide a waveguide of the ?exible kind which is capable of dominant-mode operation across extended frequency applications, therefore, waveguide which is rendered ?exible by provision of corrugations is used. Such waveguide is commercially fabricated by ?rst forming a bandwidths with relatively low signal attenuation. smooth-walled tube from a tube of conductive metal It is a related object of this invention to provide a waveguide of the above kind which can be economi cally manufactured in long lengths according to a con tinuous process. Another object of this invention is to provide a ?exi and thereafter corrugating the tube. In applications needing bandwidths greater than can be obtained from rectangular waveguide, some form of ridged waveguide, typically double-ridge waveguide, is used. In such ridged waveguide, ridges realize a pertur ble waveguide of the above type which provides both bation of the cross-section which provides broader relatively high peak~power-handling capability and bandwidth between the cut-off frequency of the domi 35 lower signal attenuation characteristics. nant-mode and the ?rst higher-order mode. However, It is a further object of this invention to provide an there are certain disadvantages inherent with the use of improved ?exible waveguide of the type described double-ridge waveguide. For instance, rectangular dou ble-ridge waveguide, is problematic because the pres above for which desired electrical transmission charac: teristics may conveniently be optimized for different ence of a plurality of corners leads to substantial signal broadband applications. attenuation and the peak-power-handling capability of the waveguide is generally lowered. The sharp corners Other objects and advantages of the invention will be apparent from the following detailed description when taken in conjunction with the accompanying drawings. are also a source of problems in certain manufacturing processes such as electroplating. Double-ridge waveguide of the rigid type is also disadvantageous in that it requires precise alignment 45 SUMMARY OF THE INVENTION Brie?y, in accordance with the present invention, with the system components in order to function effec there is provided a semi-?exible double-ridge wave tively. The lack of ?exibility of rigid waveguide also poses signi?cant dif?culties in handling, storage, and shipping. Rigid waveguide is particularly dif?cult to install and requires accessory coupling components guide comprising a unitary metallic strip formed and even if the system sections to be linked by the wave provide the waveguide with improved signal handling guide are slightly displaced axially. More signi?cantly, characteristics as compared to conventional rigid as it is difficult to economically manufacture rigid double well as ?exible, double-ridge waveguide and yet per mits dominant-mode operation across comparable fre quency bandwidths. The present invention ef?ciently removes the problems associated with dif?culty of in stallation and the bothersome requirement for precise alignment of components that is inherent to conven 60 tional rigid waveguide. As compared to ?exible double ridge waveguide in long lengths through continuous processing techniques. In applications where both ?exibility and broadband operation are essential, such as in many defense-related applications like airborne cabling operations, radar jam ming aboard military aircraft, etc., ?exible double-ridge waveguide, typically of rectangular cross-section, is welded into a tube and subsequently corrugated and formed into a special cross-sectional shape de?ned by controllable parameters which can be optimized to_ used. Flexibility is provided by means of successively formed corrugations of the desired double-ridge cross sectional shape. The manufacturing process involved in fabricating such waveguide is expensive and time con 65 suming because the corrugations are generally non-con tinuous and have to be formed individually. A major disadvantage is that continuous processing is not possi ridge waveguide, the present invention provides the much desired combination of ?exibility, increased power rating, reduced attenuation and ease of manufac ture of long lengths of waveguide by a continuous and relatively uncomplicated and inexpensive process. The semi-?exible double-ridge waveguide of this invention has a special cross-section which is designed to be devoid of corners and conforms substantially to a 3 4,978,934 dumbbell-shaped contour de?ned by a geometric equa tion in which speci?c parameters can be correlatively optimized to substantially enhance desired electrical properties of the waveguide. The semi-?exible wave guide of this type can be optimized to display electrical DESCRIPTION OF THE PREFERRED EMBODIMENT characteristics comparable to or better than those avail able with rigid double-ridge waveguide and retains the characteristics for much longer continuously formed lengths. The specially designed waveguide contour results in increased power-handling capability and im proved attenuation and VSWR factors for comparable 4 FIG. 11B is an illustration of the staggered dispo sition of corrugation crests and troughs, according to a preferred embodiment of this invention. While the invention will be described in connection with certain preferred embodiments, it will be under stood that it is not intended to limit the invention to 0 these particular embodiments. On the contrary, it is intended to cover all alternatives, modi?cations and equivalent arrangements as may be included within the waveguide lengths. The effects of the special waveguide shape are fur spirit and scope of this invention as de?ned by the ap ther enhanced, according to an embodiment of this invention, by the use of non-annular corrugations hav ing a selected pitch which staggers the disposition of corrugation crests and troughs on opposing sides of the FIG. 1A a cross-sectional view of conventional rectan pended claims. Referring now to the drawings, there is shown at gular double-ridge waveguide 10 having a wide dimen sion generally designated as “a” and a narrow dimen waveguide to such an extent as to maximize the distance sion designated as “b”._As is well known, electromag netic energy in the rectangular waveguide travels in the fundamental mode with the ?eld intensity being uni formly distributed about the width of the waveguide, with impedance and power-handling being on the “b” between immediately opposing corrugation troughs, thereby increasing the air gap and, consequently, the power-handling capacity of the waveguide. The combi nation of the special dumbbell-shape having optimizable parameters with the selectively staggered corrugations effectively combines the mechanically advantageous ?exibility provided by standard ?exible double-ridge dimension. 25 waveguide with the superior electrical characteristics of rigid double-ridge waveguide and increased power tending lengthwise along the waveguide. The reduction handling capacity relative to conventional ?exible an nularly corrugated waveguide or rigid double-ridge waveguide. BRIEF DEsCRIPTION OF THE DRAWINGS FIG. 1(a) is a cross-sectional view of conventional double-ridge waveguide having a rectangular cross-sec tion; The double-ridge rectangular waveguide 10 is pro vided with a pair of ridges de?ned by oppositely dis posed substantially rectangular constrictions 12, 14 ex at the center of the “b” dimension decreases the charac 30 teristic impedance and the power-handling capability of the ridge guide but substantially extends the dominant mode operational bandwidth. With such a con?gura tion, the electromagnetic energy is highly concentrated near the center of the cross-section. Double-ridge waveguide of this type is commonly used with broadband transmission equipment and other FIG. 1(b) is a side view of the waveguide shown in FIG. 1 illustrating its smooth-walled nature; applications where extended operational bandwidth and having annular corrugations; tion and lower peak-power-handling capability, due to freedom from moding conditions are mandatory. How ever, rectangular double-ridge waveguide suffers from FIG. 2 is a side view of conventional waveguide having the same cross section shown in FIG. 1 but 40 certain inherent disadvantages, such as higher attenua FIG. 3 is a cross-sectional view of a semi-?exible the presence of the several corners and added surface dumbbell-shaped double-ridge waveguide according to area resulting from the rectangular cross-section and this invention; the opposing constrictions which de?ne the ridges. guide contour in correspondence with variation in the turing process, such as electroplating, problematic. FIG. 4 is a representation of the variation in wave 45 These corners also make certain aspects of the manufac parameter “p”; FIG. 5 is a graphical representation of the bandwidth variation of the waveguide of FIG. 3 relative to the parameter “p”; FIG. 6 is a graphical comparison of the waveguide of the type shown in FIG. 3 to conventional rectangular double-ridge waveguide; As shown in FIG. 1(1)), which is a side view of the ridged waveguide of FIG. 1(a), double-ridge wave guide is typically smooth walled and includes a protec tive jacket 16 over the metallic conductor constituting the guide. A major problem with smooth-walled rectan gular double-ridge waveguide is that the inherent in ?exibility makes routing and installation dif?cult and also renders the use of ?eld-attachable ?anges impracti FIG. 7 is a graphical illustration of the correlation 55 cal due to the necessity for precise alignment between between the cut-off frequency of the ?rst higher-order mode and the parameters “u” and “v”; FIG. 8 is a graphical illustration showing the correla tion between the cut-off frequency of the dominant mode and the parameters “u” and “v”; FIG. 9 is a graphical illustration of the attenuation associated with the semi-?exible waveguide of this in vention; FIG. 10 is a sectional side view of a shaping wheel arrangement used to generate the dumbbell-shaped cross-sectional contour shown in FIG. 3; FIG. 11A is a cross-sectional view of conventional annularly corrugated ridged waveguide; and the components being linked. In applications where ?exibility is essential, double ridge waveguide is rendered ?exible by making the waveguide corrugated along its length while retaining the standard rectangular double-ridge cross-section. As shown in FIG. 2, ?exible ridged waveguide is typically formed of annular corrugations 18 with the direction of corrugation being wholly perpendicular to the axis of the waveguide 10. The corrugations are formed by 65 successively clamping the smooth-walled waveguide at one end and crimping the guide inwardly along its lon gitudinal direction to de?ne the corrugations one at a time. 5 4,978,934 Because the annular corrugations must be individu ally formed, a continuous forming process cannot be 6 will be apparent that a similar variation in shape also applies to the remaining three quadrants. used, thereby making the ?exible waveguide of the type Referring now to FIG. 5, there is shown a graphical illustration of the increase in bandwidth realized by the shown in FIG. 2 difficult and expensive to manufacture and also making formation of long lengths impractical. dumbbell-shaped waveguide of FIGS. 3 and 4. Shown therein is a pair of graphs representing the variation in bandwidth of the waveguide with increasing values of the parameter “p” for different ratios of the length of the major and minor axes “u”, “v”, respectively. In Further, the fully ?exible nature of the waveguide ac cruing from the annular nature of the grooves dramati cally increases the attenuation factor of the waveguide in use. Another problem is that the VSWR remains plotting the curves shown in FIG. 5, the waveguide bandwidth is de?ned as the ratio of the cutoff frequency (F82) of the modi?ed TEZO mode to the cut-off fre quency (F61) of the modified TE10 mode. As evident from the curves, any increase in the value of the param eter “p” brings about an increase in bandwidth de?ned within acceptable limits only for restricted lengths of waveguide. Referring now to FIG. 3, there is shown a cross-sec tional view of an improved semi-?exible double-ridge waveguide according to a preferred embodiment of the present invention. The waveguide 20 is formed of a of any sharp corners and has a dumbbell-like contour by the ratio Fez/F61, with the range of bandwidth being inversely proportional to the selected aspect ratio (v/u) de?ned by the polar equation: for the contour. special cross-sectional shape which is distinctly devoid 20 where “r” is the radical distance between any given point on the contour and the point of origin, and “9” is the angle between the major axis and the radial line along which that point is de?ned on the contour. In equation (1), the constants “a” and “b” are de?ned in terms of the major and minor axes “u”, “v”, respec In order for the desired dumbbell-shaped waveguide contour to be adequately de?ned, equation (1) must be subject to two constraints: (i) the constant “b” must be greater than the constant “a”-otherwise the cross-section will be split into two parts which are symmetric about the y-axis; and (ii) the parameter “p” must have a value greater than two (2) in order to achieve the above-described increase in bandwidth. Provided the above conditions are met, it is possible for the waveguide contour to be optimized conve tively, of the contour as below: 30 niently by considering the change in electrical charac teristics produced by variations in the parameters “11”, “v” and “p” and determining, preferably through some form of computer-based approximately technique, the range of values for these parameters which provides the 35 u a, where “u”, “v”, and p are selectable variables. The dumbbell shape essentially corresponds to that of a rectangular waveguide having oppositely disposed largest possible dominant-mode operational bandwidth and the least amount of signal attenuation. This determi— nation can be supplemented by actually measuring the desired electrical characteristics to determine the opti ridges 22, 24 which are not of the rectangular cross-sec mum value or range of values of the parameters re tional shape shown in FIGS. 1A, 1B and 2 but instead 40 quired to de?ne a waveguide contour which is opti are of a substantially bell-shaped cross-section which mized for the desired bandwidth of dominant-mode extends to generally convex ends 26, 28 of the wave operation, selected attenuation characteristics, etc. guide cross-section de?ned about the major axis. The calculation of the cutoff frequencies of the ?rst In the waveguide cross-section shown in FIG. 3, it should be noted that the polar equation (1) de?nes the contour in such a way that the upturned ends of the two modes, namely the modi?ed TE“) and TEgO modes, for de?ning the operational bandwidth and the accom panying attenuation can be performed conveniently by bell-shaped ridges smoothly merge with the cross-sec tional ends of the waveguide, thereby avoiding the employing one of several computer techniques, such as presence of any corners or abrupt protrusions. The which are known in the industry for analyzing wave contour of FIG. 3 represents the cross-sectional shape of the waveguide 20 according to a preferred embodi guide shapes of arbitrary cross-sections. One exemplary polynomial approximation or ?nite element analysis, technique is described by R. M. Bulley in a paper enti ment where the parameters “u”, “v” and “p” are se tled “Analysis of the arbitrarily shaped waveguide by lected to be 0.702” , 0.128”, and 3.40, respectively, polynomial approximation", as published in IEEE based on a dominant-mode operational bandwidth of Transactions on Microwave Theory and Techniques Vol. 7.5-18.0 GI-lz. 55 MTT-18, pp. 1022-1028, Dec. 1970. A family of curves of the type shown in FIG. 3 can be According to a preferred embodiment of this inven generated by maintaining the parameters “u” and “v” constant, while varying the parameter “p”. Such a fam ily of curves, all having identical major and minor axes, tion, a dumbbell-shaped waveguide was optimized for the 7.5-l8.0 GHz frequency bandwidth commonly used nowadays for defense-related tele-communication pur is shown in FIG. 4, which is an illustration of how a poses. Such an optimized waveguide is illustrated at FIG. 6, which shows a graphical comparison between the dumbbell-shaped contour based on equation (1) for variation in the parameter “p”, while keeping “u” and “v” constant (at 0.702" and O. 128", respectively), affects the cross-sectional shape of the waveguide contour. More speci?cally, increasing values of “p” increase the the case where “p”=3.4 and de?ned for a 7.5—l8.0 GHz dominant-mode bandwidth using the polynomial ap extent to which the waveguide contour strays away 65 proximation technique, and the corresponding ?rst from the minor axis before merging with the cross-sec tional ends. FIG. 4 shows the variation only along the ?rst quadrant of the overall contour cross-section; it quadrant contour (represented by a dashed line) of a conventional double-ridge waveguide having a rectan gular cross-section. 7 4,978,934 8 mercially available rigid and ?exible double-ridge FIG. 7 is a graphical illustration of the correlation between the length of the major and minor axes “u” and waveguide, respectively. “v”, respectively, and the cut-off frequency of the ?rst higher-order mode. As shown therein, the cut~off fre quency F62 gradually decreases with increasing values Referring now to FIG. 10, there is shown a cross-sec tional view of a preferred arrangement for imparting the special dumbbell-shaped contour to form the semi ?exible waveguide of the shape shown in FIG. 3. As shown therein, the cross-section of the waveguide 30 is of “u” when the parameter “v” is maintained constant. Two such correlation graphs are shown for incremental differences in the parameter “u” being equal to 0.0 and 0.04. FIG. 8 is a similar graphical illustration showing the correlation between the dominant mode cut-off fre quency and incremental differences in the length of the de?ned by the oppositely disposed bell-shaped ridge sections 32, 34 and the generally convex end sections 42 and 44 which effectively link the ridges to form the overall dumbbell-shaped contour de?ned by polar equa tion (1) using selected values for parameters “u”, “v” and “p”. As described above, the choice of these param major axis, i.e., the parameter “u”, while maintaining the length of the minor axis, i.e., the parameter “v”, at eters is based upon the desired dominant-mode band width and minimized attenuation, as most advanta a predetermined constant value. Three such correlation curves are shown in FIG. 8 for predetermined constant geously determined by computer-based polynomial values of 0.0, +0.04 and —0.04 of the parameter “v”. It will be obvious from the foregoing that the primary approximation, ?nite element analysis or other like parameters of the polar equation de?ning the dumbbell such techniques to calculation of waveguide parame Once the optimum values of the parameters “u”, “v” and “p” have been determined, the waveguide contour is formed from a continuous length of corrugated circu lar tube by means of a pair of ridge wheels 36, 38 which have driving faces 36A, 36B possessing a shape substan ters, as well as the correlation between the major and tially corresponding, according to a converse relation minor axes and waveguide performance characteristics ship, to the bell-shaped contour of the waveguide ridges 32, 34. The ridge wheels are simultaneously brought into rotating contact on diametrically opposite external technique. shaped contour shown in FIGS. 3 and 4 can be conve _ niently optimized to achieve desired electrical perfor mance characteristics. Relevant details on applying such as dominant-mode bandwidth and attenuation, are well known to those skilled in the art and, accordingly, will not be described in detail herein. For purposes of this description, it suf?ces to state that the parameters “u”, “v” and “p” of the semi-?exi faces of the tubular waveguide as the waveguide is continuously moved across the rotating ridge wheels in a transverse direction. At the same time, a pair of dia ble waveguide de?ned by equation (1) can, according to this invention, be controllably varied to realize signi? metrically opposed support surfaces 40, 41 having con cave faces generally corresponding, according to a converse relationship, to the shape of the convex end sections 42, 44 are brought into supporting contact with cantly improved dominantmode operational frequency bandwidth and reduced attenuation factor compared to that of standard rectangular or circular waveguide. In fact, it has experimentally been con?rmed that such a waveguide can be optimized to provide operational the end sections. The simultaneous positive driving impact of the ridge wheels 36, 38 on diametrically oppo site surfaces of the waveguide forms the two bell dominant-mode bandwidths comparable to or better shaped ridges 32, 34, and the support provided by the than that of standard ridge waveguide while, at the same time, having an attenuation factor signi?cantly lower than that of any commercially available double concave surfaces 40, 41 on the remaining opposite sur ridge waveguide. wheels. Thus, the ridge wheels and the support sur FIG. 9 shows graphical representations of curves based on theoretical and experimental data re?ecting faces of the waveguide prevents any uneven expansion of the waveguide under the driving impact of the ridge 45 faces, in conjunction with each other, generate the overall dumbbell-shaped contour de?ned by the opti the attenuation associated with the semi-?exible wave mized polar equation (1). guide of this invention and the variation in attenuation In order to increase the power handling capability of the waveguide as well as to provide ?exibility, the waveguide of FIG. 3 is rendered semi-?exible by the use of continuously linked corrugations which allow a across the desired frequency bandwidth. The wave guide used for these measurements was optimized for operation across a frequency bandwidth extending be tween 6.0—14.4 6112. In FIG. 9, the curve A represents the theoretically calculated attenuation versus fre quency response for the semi-?exible waveguide, as determined on the basis of polynomial approximation or certain degree of ?exibility without rendering the waveguide completely ?exible like conventional ?exi ble waveguide having discrete annular corrugations. the ranges of 4.0-5.0 5.0 dBs/ 100 ft. and 4.0-6.0 ble double-ridge waveguide. According to a preferred embodiment of this invention, like techniques. The theoretical attenuation remains 55 the waveguide of the desired cross-sectional shape is substantially within the range of 4.0-5.5 dBs/ 100 ft. formed with helical corrugations which provide only a across the frequency band of interest. As compared to restricted amount of ?exibility. In effect, such a wave this, the experimentally measured attenuation, as repre guide is truly “semi-?exible” and has distinct advan sented by curves B and C, remains substantially within tages over both rigid double-ridge waveguide and ?exi~ dBs/ 100 ft., respectively, at the lower and upper ends of the measurement scale. Theoretical calculations based on the waveguide of FIGS. 3 and 9, as optimized for the frequency range of 7.5—l8.0 GI-Iz, con?rmed an attenuation of less than 7 dBs/ 100 ft. which is a signi?cant improvement over the attenuation factors of 10.0-12.0 dBs/ 100 ft. and 20.0—30.0 dBs/ 100 ft. presently associated with com More speci?cally, the semi-?exible waveguide is sig ni?cantly easier to be routed and installed in con?ned areas and ?exible enough to be adapted to minor length adjustments which are essential to accommodate dimen sional tolerances both in the waveguide itself and in the area where the waveguide is to be installed. At the same time, the restricted ?exibility also keeps signal attenua tion down and makes practical the use of waveguide 9 4,978,934 lengths substantially longer than would be possible with completely ?exible waveguide. Flexibility of double-ridge waveguide has conven tionally been achieved by using annular corrugations which are discrete and non-continuous. Such wave guide is typically manufactured by forming a tube from a strip of conductive metal (typically copper or alumi num), welding the tube and shaping it to approximate rectangularity, and forming annular corrugations there 10 wall of the waveguide relative to those on the opposing wall. The result is that, in the waveguide of FIG. 11B, the air gap distance “Y” is de?ned between helical corrugation troughs 65 on the top wall of the wave guide 60 and the corresponding troughs 67 on the bot tom wall and is larger than the distance “X” that would exist if the corrugations were to be annular. This in crease in air gap distance is signi?cant in the case of In order to make the waveguide completely ?exible, the annular corrugations are relatively deep and close double-ridge waveguide of the type shown in FIG. 3 because the constrictions de?ned by the bell-shaped ridges intrinsically reduce the air gap substantially to the point where the air gap becomes comparable to the pitch of the corrugations. Under such conditions, even a small increase in air gap resulting from the expansion of the distance between opposing corrugation troughs spaced. A cross-sectional view of conventional annu and crests can produce a noticeable increase in the max larly corrugated ridged waveguide is illustrated at FIG. imum power rating of the waveguide. upon by clamping the smooth-walled waveguide at one end and successively crimping the waveguide inwardly along its longitudinal direction toward the clamped end to de?ne the corrugations one at a time. 11A. As shown therein, the waveguide 50 has annular It should be noted that FIG. 11B represents the case corrugations 52 spaced apart by a distance “S” (the pitch) and extending to a depth “d” de?ned by the where the relative staggering of opposing corrugations is by the maximum extent possible between the opposite distance between successive crests 54 and troughs 55 of the corrugations. Because the corrugations are annu larly formed, the corrugation crests 54 on one wall of walls of the waveguide. More speci?cally, in FIG. 11B, the staggering is such that the corrugation troughs 65 on the top wall of the waveguide 60 are disposed imme the waveguide are disposed diametrically opposite the . diately opposite the corrugation crests 66 on the bottom corrugation crests 56 on the other wall of the wave 25 wall. However, the breakdown air gap is increased guide and vice versa. The result is that the breakdown even if the corrugations are staggered to a lesser extent air gap, which de?nes the power-handling capability of than that shown in FIG. 11B so that corrugations crests the waveguide and which is a function of the minimum distance between opposing internal surfaces of the waveguide, is restricted for a given internal waveguide diameter. In FIG. 11A, for instance, the annular corru gations are spaced apart by a pitch distance of “S” which is comparable to the corrugation depth “d” and the ratio of corrugation depth to pitch is typically 0.8 or more. The air gap distance, as de?ned by the space on one wall do not directly face the corrugation troughs on the opposite wall, but are merely displaced relative to each other. It will be apparent that any staggering of corrugations relative to the disposition illustrated in FIG. 11A realizes a distance “y” which is greater than the distance “x”, thereby increasing the waveguide air gap and power-handling capability. Thus, the combined use of an decreased ratio of cor between opposing corrugation troughs 55 and 57 is rugation depth to corrugation pitch and the helical designated as “X” in FIG. 11A. Even if the annular corrugations were to be provided in the form of spaced apart groups in order to restrict ?exibility, the break down air gap and, hence, the maximum power rating of staggering of corrugation crests and troughs in a wave guide having the optimizable dumbbell-shaped cross section realizes the much desired combination of ?exi bility and improved electrical characteristics, including In accordance with a feature of this invention, the increased power-handling capability. The helically corrugated waveguide having the power-handling capability of waveguide having the dumbbell-shaped cross-section, according to the present the waveguide remains restricted by the distance “x”. dumbbell-shaped contour of FIG. 3 is increased by invention, is conveniently manufactured in long lengths using continuous non-annular corrugations which are 45 by the use of a continuous process wherein the helically relatively widely spaced compared to the corrugation corrugated waveguide is ?rst formed by the use of depth, as shown in FIG. 11B. It will be apparent that continuous rotating contact between an appropriately the dumbbell-shaped contour generated on the basis of shaped corrugating die or tool and the external surface polar equation 1 is devoid of the sharp edges character of waveguide formed by folding and longitudinally istic of conventional rectangular double-ridge wave 50 welding a strip of metal into a substantially circular guide; the rounded edges (see FIG. 3) avoid the exces tube. The tube is continuously advanced and the corru sive power loss resulting from obstructions presented gating tool is moved wholly transversely in proper by sharp corners in the waveguide cavity. The power synchronism with the advancing motion of the tube. rating of the waveguide is further increased by the use The helically corrugated waveguide is then provided of corrugations which are helically con?gured in such a with the dumbbell-shaped cross-section using the proce way that the corrugation crests and trouqhs on one wall dure described above for using the shaping wheel ar . of the waveguide are staggered relative to those on the rangement of FIG. 10 to impart the shape de?ned by opposite wall. As shown in FIG. 11B, the waveguide 60 equation (1). is formed of helical corrugations 62 which are spaced What is claimed is: apart at a pitch distance “S1”, which is substantially 1. A semi-flexible, double-ridge waveguide having larger than the corrugation depth “d1”. According to a reduced attenuation and increased power-handling ca preferred embodiment, for a waveguide optimized for pability for a given bandwidth, said waveguide com operation within a band width of 7.5—l8.0 GHZ, the prising a continuous length of corrugated tube having a pitch “S1” was selected to be about 0.18” and the depth substantially dumbbell-shaped cross-sectional contour “d1” was selected to be about 0.04” so that the depth-to 65 de?ned about major and minor axes “u” and “v”, re pitch ratio was about 0.22. spectively, by a polar equation relating variables ‘r’ and The helical nature of the corrugations effectively staggers the corrugation crests 64 and troughs 65 on one ‘9’ according to the relationship 4,978,934 11 r21’ — ZarP cos 29 +1:2 =b2, 12 6. The waveguide as set forth in claim 4 further com wherein parameter prising a continuous length of corrugated tube having helical corrugations with a pitch 5 and depth d, said corrugations having crests and troughs disposed in a staggered con?guration such that corrugation crests and troughs on one wall of the waveguide are shifted relative to corresponding corrugation crests and troughs on the opposing wall of the waveguide, thereby increasing the air gap between opposing walls of the and parameter 10 ..b,. : (Mail!) 1 waveguide. 7. The waveguide as set forth in claim 6 wherein the corrugations are characterized by a depth-to-pitch ratio (d/ S) of less than 0.5. 8. A method of increasing the power-handling capa bility of a double-ridge waveguide for a given band width or increasing the Waveguide bandwidth for a said parameter “b” being greater than said parameter “a”; said exponent “p” has a value greater than two; “r” and “9” are variables, “r” being the radial distance between any given point on said contour and the point of origin and “9” being the-angle between the major axis and the radial line along which said given point is given power-handling capacity by shaping the wave guide to have a substantially dumbbell-shaped cross de?ned on said contour, and wherein said corrugated sectional contour de?ned about major and minor axes u tube includes helical corrugations having a pitch “S” and depth - “d”, said corrugations having crests and troughs disposed in a staggered con?guration such that and v, respectively, by the polar equation r2P—2arP cos 29+a2=b2 corrugation crests and troughs on one wall of the wave where r and 9 are variables, r being the radial distance guide are shifted relative to corresponding corrugation between any given point on said contour and the point crests and troughs on the opposing wall of the wave 25 of origin and 9 being the angle between the major axis guide, thereby increasing the air gap between opposing walls of the waveguide. and the radial line along which said given point is de ?ned on said contour, a and b are constants de?ned in terms of said major and minor axes u and v as 2. The waveguide as de?ned in claim 1 wherein the corrugations are characterized by a depth-to-pitch ratio (d/S) of less than 0.5 30 3. The waveguide a de?ned in claim 1 wherein said parameters “u”, “v” and “p” are selected in such a manner as to optimize the bandwidth and attenuation of and the exponent p has a value greater than two, said said waveguide for a given length, and wherein said parameters u, v and p being selected such as to optimize parameter “p” is selected to be within the range of 35 the bandwidth and attenuation of said waveguide for a 2.6-4.0. 4. A double-ridge waveguide having a cross-sectional given length. 9. The method as set forth in claim 8 wherein the exponent p has a value within the range from about 2.6 to about 4.0. 10. The method as set forth in claim 8 wherein the contour de?ned about major and minor axes u and v, respectively, by the polar equation r2P—2arP cos 29+aZ=b2 power-handling capability of said waveguide is further increased by forming said waveguide of a corrugated where r and 9 are variables, r being the radial distance between any given point on said contour and the point of origin and 9 being the angle between the major axis and the radial line along which said given point is de tube having helical corrugations with a pitch S and depth d, said corrugations having crests and troughs 45 ?ned on said contour, a and b are constants de?ned in terms of said major and minor axes u and v as 2D+l 2p+l y disposed in a staggered con?guration such that corruga tion crests and troughs on one wall of the waveguide are shifted relative to corresponding corrugation crests and troughs on the opposing wall of the waveguide, thereby increasing the air gap between opposing walls 50 of the waveguide. 11. The method as set forth in claim 10 wherein the and the exponent p has a value greater than two. corrugations are characterized by a depth-to-pitch ratio (d/S) of less than 0.5. 5. The waveguide of claim 4 wherein the exponent p has a value within the range from about 2.6 to about 4.0. i 55 65 i 1.! i It