Abstract:
A segmented transmission line used for the transfer of radio frequency energy in which the lengths of the individual segments are individually set to provide an optimally low reflection coefficient over specified frequency ranges.

Description:
FIELD OF THE INVENTION 
       [0001]    The present invention relates to rigid coaxial radio frequency transmission lines particularly those intended for carrying high power television and FM radio signals. Certain aspects of the invention are additionally applicable to non-coaxial waveguides and certain semi-flexible waveguides. 
       BACKGROUND OF THE INVENTION 
       [0002]    For various high power applications, e.g. television transmission or linear accelerators, it is conventional to couple the power source and the power load, e.g. an antenna, using rigid transmission line. Further, in many applications, the power source is located a substantial distance from the load so that the transmission line necessarily comprises multiple sections which most often include a number of elbows to facilitate routing. Traditionally, such multiple sections are essentially all of the same length to simplify design and to afford manufacturing economies. 
         [0003]    To prevent the in-phase addition of periodically occurring reflections, section lengths are selected not to be a multiple of a half wavelength at the designated operating frequency, e.g. at the frequency of the TV channel. Modern trends involve the use of a single transmission line for the power transmission from multiple TV or other power sources operating at different frequencies. In many instances no suitable single length can be found that is not a multiple of a half wavelength at or impractically near one or more of the operating frequencies. 
         [0004]    A number of schemes involving the systematic tapering of individual lengths or of groups of lengths have been proposed as a means of overcoming this problem. Although these schemes eliminate the full addition of periodically occurring reflections, they tend to give a substantially inferior voltage standing wave ratio (VSWR) compared with that available from a constant section length transmission line dedicated to a single signal. These schemes also cannot readily take account of the variation with frequency of the reflection magnitude of transmission line sections, nor can they readily take account of the characteristics of other essential transmission line components such as elbows, transformers, adapters, etc. Further, in providing a low VSWR over a single wide band of frequencies, they compromise the achievement of the lowest VSWR in specific operating channels. 
         [0005]    Among the several objectives of the present invention are: the provision of multi-section transmission line systems having a lower VSWR over bands of frequencies than that achieved by methods heretofore disclosed; the provision of such a transmission line which can be constructed in the form of a rigid or semi-rigid transmission line; the provision of such a transmission line having outer conductors connected together at flange joints; the provision of such a transmission line which is highly reliable and is of relatively simple and inexpensive construction. Other objectives and features will be in part apparent and in point pointed out hereinafter. 
       SUMMARY OF THE INVENTION 
       [0006]    Briefly, the present invention involves a multi-section run of radio-frequency (RF) transmission line having low VSWR characteristics over a band or bands of frequencies F1a to F1b, F2a to F2b, etc. The transmission comprises a sequence of N sections connected by joints which cause impedance discontinuities. In accordance with this invention, the lengths l of the N sections are distributed essentially according to the relationship 
         [0000]    
       
         
           
             
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         [0000]    for n=1 to N, where L is the nominal section length, k is a summation integer whose value ranges from zero to a value m which latter value is greater than 1 but less than or equal to N, and A k  are constants three of which must be non-zero and which are set such that the VSWR of the transmission line best matches a target minimum for each of the frequency bands F1a to F1b, F2a to F2b, etc. The resulting lengths l n  are further adjusted by rounding their values to the nearest multiple of a selected fraction of a wavelength at the highest operating frequency. 
     
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0007]      FIG. 1  is a diagrammatic representation of a transmission line embodying certain aspects of the present invention. 
           [0008]      FIG. 2  is an exploded sectional side view along the line  2 - 2  of  FIG. 1 , of the joint between two sections of the line of  FIG. 1  showing the flange joint which connects the outer conductors and a connector which joins the inner conductors of each coaxial section. 
           [0009]      FIG. 3  is a side sectional view along the line  3 - 3  of  FIG. 1 , of the joint between a section of the line and an elbow  FIG. 1  and showing the flange joint which connects the outer conductors and a connector which joins the inner conductors of each coaxial section. 
           [0010]      FIG. 4  is a graphical representation of the VSWR versus frequency of a transmission line using equal lengths sections in accordance with prior art. 
           [0011]      FIG. 5  is a graphical representation of the VSWR versus frequency of a transmission line using tapered section lengths in accordance with prior art. 
           [0012]      FIG. 6  is graphical representation of the VSWR versus frequency of a transmission line example embodying this invention. 
       
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT 
       [0013]    Referring to  FIG. 1 , the run of transmission line illustrated there comprises a plurality of sections  6 ,  7 ,  8 , 9 ,  48  and  49  and an interposed transmission line elbow  10 , joined by flanged connections  11  and  12 . As is understood, such a multi-section run of coaxial transmission line may be used to connect a television transmitter to an antenna located an appreciable distance away. Such lengths necessarily comprise sections since the length of a transmission line segment that can be shipped is limited, as are the lengths of appropriate tubing available commercially. In the particular embodiment being described by way of example, the outer conductors of the coaxial transmission are six and one eighth inch diameter and the individual lengths are nominally 232 inches long, or thereabout. 
         [0014]    Referring now to  FIG. 2  depicting flanged connection  11 , the outer conductors of adjacent coaxial line sections are designated by reference characters  1  and  2 . A one piece coupling flange  3  is welded to the right hand end of outer conductor  1  while conductor  2  is provided with a two part assembly having an inner ring  4  and an outer rotatable clamping ring  5  which can be bolted to the flange  3  to draw the two sections together into an intimate electrical contact. 
         [0015]    The flange  3  and the ring  5  are cut away, as illustrated, to provide a recess  13 , which can capture and retain an annular support insulator  14  when the outer sections are bolted together. The support insulator  14  serves to locate a coupler assembly  15 , which joins together adjacent inner conductor sections  16  and  17 . The support insulator  14  is received within a groove  18 , in the coupler assembly  15 . Support insulator  14  may, for example, be constructed of poly tetrafluoroethylene (PTFE) and is preferably split so as to allow it to be assembled over the coupler assembly. 
         [0016]    The right-hand side of the coupler assembly  15  includes a connecting portion  26 , which is essentially conventional and is adapted to fixedly attach to the adjacent end of the respective inner conductor  2 . The end of the connecting portion  26  is axially cut at several circumferential locations so as to form radially compliant fingers  19 . These fingers are then resiliently forced outwardly into firm contact with the inner conductor  2  by snap ring springs  20 . An annular plug  21  prevents splitting the fingers apart if there is an initial misalignment during assembly. 
         [0017]    The left-hand side of the coupler assembly  15  also includes a connecting portion  22 , which is adapted to attach to the respective inner conductor  1 . This connecting portion  22  comprises a spacer-guide  33 , a guided right-hand insert  27 , a left-hand insert  28 , a cap screw  31  and washer  32 , a clamp  29 , and also provides a cylindrical bellows  23  which functions as explained hereinafter. Guided right-hand insert  27  is held inside the right-hand extremity of the bellows  23  by the inwards deformation in a uniform manner of the bellows  23  to match the profile of the insert  27 . Similarly, the left-hand insert  28  is held inside the left-hand end of the bellows  23  by the deformation of the left hand extremity of the bellows  23 . The bellows  23  is constrained to compress or extend in an axial direction only by the sliding of the guided right-hand insert  27  on the guide  33 . Constraints are placed on the extent of extension or contraction of bellows  23  by the shoulder  38  on the guide and by the cap screw  31  and washer  32 . The connection of the bellows  23  to the right-hand portion of the coupler assembly  26  is secured by screws  24  and washers  36 . The connection of the bellows to the clamp  29  is secured by screws  25  and washers  36 . 
         [0018]    The right-hand end of inner conductor  16  is inwardly deformed in a uniform manner to match the profile of internally-threaded inner conductor insert  30 . Dimples  37  are formed in the inner conductor  16  to match dimples in inner conductor insert  30  thereby facilitating the retention of inner conductor insert  30  in its correct position during the deformation process. Coupler assembly  15  is secured to inner conductor  16  by the insertion of cap screw  31  into a threaded portion  39  of internally-threaded insert  30 . 
         [0019]    As will be understood the left-hand of the inner conductor section  16  will be fixedly attached with respect to its corresponding outer conductor section by the last connector  15  in the series of coaxial sections in the same manner as the left hand end of the inner conductor section  17 . Thus as differential expansion occurs between the inner and outer conductors, the right hand end of inner conductor  16  will move axially with respect to the coupler member  26 . The bellows  23  freely permits this axial movement while maintaining radial alignment and continuity of the electrical path. The holes  34 ,  35  and  36  function to allow the air pressure inside the inner conductor  16  and the bellows  23  to match that outside these components thus avoiding possible damage through an excessive pressure differential. Such connection configurations have been used heretofore in various connector environments and are conventionally referred to as bullet-bellows assemblies. 
         [0020]    Referring now to  FIG. 3  depicting flanged connection  12 , the outer conductors of adjacent coaxial line sections are designated by reference characters  50  and  51 . A one piece coupling flange  55  is welded to the right hand end of outer conductor  51  while conductor  50  is provided with a two part assembly having an inner ring  59  and an outer rotatable clamping ring  54  which can be bolted to the flange  55  to draw the two sections together into an intimate electrical contact. 
         [0021]    The flange  55  and the ring  59  are cut away, as illustrated, to provide a recess  56 , which can capture and retain an annular support insulator  57  when the outer sections are bolted together. The support insulator  57  serves to locate a coupler assembly  60 , which joins together adjacent inner conductor sections  52  and  53 . The support insulator  57  is received within a groove  58 , in the coupler assembly  60 . Support insulator  57  may, for example, be constructed of poly tetrafluoroethylene (PTFE) and is preferably split so as to allow it to be assembled over the coupler assembly. 
         [0022]    Coupler assembly  60  includes a body  41  which is adapted to fixedly attach to the adjacent end of the respective inner conductors  52  and  53 . Both end portions  61  of the coupler body  41  are axially cut at several circumferential locations so as to form radially compliant fingers  62 . These fingers are then resiliently forced outwardly into firm contact with the inner conductors  52 ,  53  by snap ring springs  43 . An annular plug  42  prevents splitting apart the fingers  62  of the right-hand end of the coupler body  41  if there is an initial misalignment during assembly. 
         [0023]    The left-hand side of the coupler assembly  60  also includes a means of positive retention, of the left-hand inner conductor  52  by coupler assembly  60 , comprising a spacer sleeve  46 , a cap screw  44 , a lock-washer  45 , and an internally-threaded conical plug  47  which conical plug is in intimate peripheral contact with the tips of the fingers  62  of the coupler body  41 . It will be recognized that tightening the aforementioned cap screw  44  will cause the plug  47  to be drawn into the coupler body  41  thereby causing the fingers  62  to deflect radially thus substantially increasing the contact force between said fingers and the internal surface of inner conductor  52  and thereby causing the desired effect of positive retention. Such connection configurations have been used heretofore in various connector environments and are conventionally referred to as bullet assemblies. 
         [0024]    While the flanged connectors  11  and  12  are preferably designed so as to introduce a minimal impedance discontinuity, such flanged joints do necessarily introduce some reflection. In accordance with the present invention the actual length of the individual sections  6 - 9  are varied systematically around a nominal length so as to minimize the accumulation of reflections from the flanged connector discontinuities. In particular, it has been found that a particular regime for length selection provides a highly advantageous low VSWR characteristic over bands of frequencies. 
         [0025]    In the preferred embodiment illustrated, this systematic variation in length is implemented as follows. The individual section lengths are assumed to be in the order of seventeen to twenty feet, which nominal length is designated as L in the formula described hereinafter, and which, in this example, is 232.32 inches. The transmission line is intended to operate over bands of frequencies F1a to F1b, F2a to F2b, etc. In this example these frequencies correspond to the lower and upper frequency limits of UHF TV channels 22, 25, 27, 34, 35, 39, 40, 42. In accordance with this invention, the lengths l of the N sections are distributed essentially according to the relationship 
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         [0000]    for n=1 to N, where L is the nominal section length, k is a summation integer whose value ranges from zero to a value m which latter value is greater than 1 but less than or equal to N, and A k  are constants three of which must be non-zero and which are set such that the VSWR of the transmission line best matches a target minimum for each of the frequency bands F1a to F1b, F2a to F2b, etc. The resulting lengths l n  are further adjusted by rounding their values to the nearest multiple of a selected fraction of a wavelength at the highest operating frequency. This fraction is selected such that its effect on VSWR is negligible, that is, below the level of uncertainty, in the prediction of VSWR, due to the slight random variations in individual flange joint contributions caused by normal manufacturing processes. This rounding has the desirable effect of reducing the number of differing lengths, thus reducing manufacturing and assembly costs. In this example, the value used is 0.05 inches, that is 0.0027 wavelength at 644 MHz, the upper limit of TV channel 42, and this rounding reduces the number of different lengths from 83 to 18. 
         [0026]    As heretofore indicated the value of L has been set to 232.32″. Practitioners of the art will recognize that this value is near-enough the optimum for transmission line of equal length sections carrying the aforementioned channels 22-42. In this example, the total length has been assumed to be 1600 feet. Hence the value of N is 83 to the next whole number. 
         [0027]    Practitioners of the art will recognize that the selection of the constants A k  may be made by any one of the manifold mathematical methods used to find the minimum of a function in an m−1 dimensional space. In this example, the least p th  approximation is used to find extremely near minimax optimum. That is, the function being minimized is 
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         [0000]    where ρ f  is the transmission line reflection coefficient at frequency f, and the exponent p gives emphasis in the summation to the reflection peaks. F may be further modified by placing emphasis on analog rather than digital channels, for example, but has not been done in this example. In the example, it was found that a value of 16 for p produced satisfactory results. In this example, it was also found that a value of 14 for the aforementioned maximum exponent of n, that is m, produced satisfactory results. 
         [0028]    Practitioners of the art will also recognize, that for the small values of the individual reflection coefficients, such as occur in well designed transmission lines, it is sufficiently accurate to obtain ρ f  by simple summation. That is: 
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         [0000]    where: ρ m (f) is the frequency dependent reflection from individual flanged connections  11  and  12 ; α(f,P m ) is the frequency dependent attenuation of the m th  reflection; and D m  is the reflection distance; and those symbols with the subscript e relate correspondingly to the elbow  10 . For simplicity of presentation of the example, it has been assumed that all reflections ρ m (f) are equal, constant with frequency, and have a value of 0.0035, and that the reflection from the elbow ρ e  are essentially zero. 
         [0029]    It will be recognized, by practitioners of the art, that there will be practical circumstances in which certain of the distances to reflections will be fixed by physical constraints, in which circumstances the heretofore described methodology is applied only to those flanges whose locations permit adjustment. Such reflections may include but not be limited to, for example, those of transmission line elbows, reducers, transformers, and gas barriers. 
         [0030]    Referring to  FIG. 4 , the VSWR versus frequency for the eight channels aforementioned is depicted for the transmission line of the said aforementioned example but wherein the sections are of equal length set to 232.32 inches, in accordance with the prior art. Practitioners of the art will recognize that this value for the section length will give a near minimum peak value of VSWR for this set of eight channels. 
         [0031]    Referring to  FIG. 5 , the VSWR versus frequency for the eight channels of the aforementioned example is depicted for the transmission line of the said aforementioned example but wherein the sections are of tapering length, in accordance with prior art, and set to a mean length of 232.32 inches. Practitioners of the art will recognize that this method will give inferior performance over the particular channels of this example, even if the mean length and the degree of taper are adjusted to other values practical values. 
         [0032]    Referring to  FIG. 6 , the VSWR versus frequency for the eight channels of the aforementioned example is depicted for the transmission line of the said aforementioned example wherein the sections have been adjusted in accordance with the methods and formulas of this invention. It may be seen that these methods and formulas produces a significant improvement over the methods and formulas of prior art. 
         [0033]    In view of the forgoing it may be seen that the several advantages of the present invention have been achieved and that other advantageous results have been attained. 
         [0034]    Practitioners of the art will recognize that, as well as being applied to rigid coaxial transmission lines, this invention is equally applicable to other types of transmission line constructed in sections such as, but not limited to, semi-flexible coaxial transmission lines with corrugated conductors, and hollow circular, elliptical, rectangular and rectangular and other waveguides with and without ridges. 
         [0035]    As various changes could be made in the above constructions without departing from the scope of the invention, and that various other formulas could be applied but which could be reduced mathematically and practically to the formulas of this invention, it should be understood that all matters contained in the above description or shown in the accompanying drawings shall be interpreted as illustrative and not in a limiting sense.