US2852753A - High frequency transmission line systems - Google Patents

High frequency transmission line systems Download PDF

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US2852753A
US2852753A US415363A US41536354A US2852753A US 2852753 A US2852753 A US 2852753A US 415363 A US415363 A US 415363A US 41536354 A US41536354 A US 41536354A US 2852753 A US2852753 A US 2852753A
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horn
throat
line
diameter
transmission line
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US415363A
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Gent Alfred Walter
Lawrence Ralph Thomas
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International Standard Electric Corp
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International Standard Electric Corp
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    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01P—WAVEGUIDES; RESONATORS, LINES, OR OTHER DEVICES OF THE WAVEGUIDE TYPE
    • H01P5/00—Coupling devices of the waveguide type
    • H01P5/08—Coupling devices of the waveguide type for linking dissimilar lines or devices
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01P—WAVEGUIDES; RESONATORS, LINES, OR OTHER DEVICES OF THE WAVEGUIDE TYPE
    • H01P3/00—Waveguides; Transmission lines of the waveguide type
    • H01P3/10—Wire waveguides, i.e. with a single solid longitudinal conductor

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  • This-invention relates to high frequency transmission line systems. More particularly, it relates to transmission line systems which include one-or more sections of the type commonly referred to as a G-line i. -e. sections in which the energy is propagated in a surface wave mode guided .by a single conductor which hasa thin dielectric coating (or has been otherwise treated, as for example by cutting a screw threadon the surface ofthe conductor) so as to decrease slightly the phase velocity of waves in the conductor.
  • a horn of circular cross section for coupling a surface wave mode transmission line to a coaxial wave mode transmission line, said horn comprising in series a throat portion and a bell portion merging-smoothly into each other, said throat portion having an axial length of the order of one half of a free space wavelength at the mean operating frequency, the inner diameter of said throat portion varying with the axial distance from the start of said throat portion in accordance with a diameter-distance function such 2,852,753 Patented Sept. 16, 1958 2
  • Figure l is a sectional representation of a quasi-exponential' horn coupling device in accordance with the invention.
  • H Figure-2 is a sectional representation of a quasi-conical horn coupling device in accordance with the invention.
  • the 'G-line conductor' should be an extension of the inner conductor of the coaxial line, preferably without change of-diameter, and that theinn'er surface of the horn should merge smoothly with the inner surface of the coaxial feeder outer conductor.
  • D-' d cosh k ('1') where d is the internal diameter of the coaxial outer conductor, k is a selected constant, and .D is the internal diameter of the horn at a distance x along the horn axis from the start of the throat portion i. e. from the junction of the horn with the :coaxial line. Such'a horn approximatesto the exponential for large'values of x, and
  • FIG. 1 shows a sectional view of a metal horn 1 coupling a coaxial line 2 to a G line conductor indicated at 3 and formed as an extension of the inner conductor 4 of the coaxial line 2.
  • the outer conductor of the coaxial line has internal diameter d.
  • the length of the horn 1 comprises a throat portion extending over the axial length indicated at A, together with a bell portion extending over the axial length indicated at B, the inner surfaces of these two portions merging smoothly into one another, and the inner surface of the throat portion merging into the surface of the coaxial outer conductor 2 in such manner that the first three derivatives of the mathematical function relating the inner diameter D of the horn to the axial distance X from the start of the throat are each equal to zero when x is equal to zero.
  • the length of the throat portion should be of the order of one half a free-space wavelength at the mean operating frequency, while that of the bell portion should be at least one freespace'wavelength.
  • both bell and throat portions follow the same law of growth of diameter, i. e. the bell portion is formed by an extension of the throat to the whole length of the born, the diameter D varying with axial distance x according to the equation.
  • w D ii (cosh Kx+cos K 1'2 (2)
  • K' being selected according to the diameter desired at the mouth of the horn for a given axial length. It has been found in practice that with a total axial length of about 2.5 wavelengths and a final diameter of about 3 wavelengths, a horn shaped in accordance with Equation 2 above gives reflection factors reduced to between 5% and over the waveband 7 cms. to 8 cms., the major part of the residual reflection being attributable to the bell portion rather than to the throat portion of the horn.
  • FIG. 2 there is illustrated a horn coupling arrangement similar to that of Fig. 1 except that the quasi-exponential horn 1 of Fig. 1 has been replaced by a horn 5 the bell portion of which approximates to a frustum ofa cone.
  • both bell and throat portions follow the same law of growth of diameter, the bell portion forming an extension of the throat to the whole axial length of the horn, but this time the diameter D varies with axial distance )4 according to the equation.
  • Equation 2 This equation resembles Equation 2 in that its first three derivatives are each equal to zero when x is zero, but for large values of X it leads to a conical rather than signed in accordance with Equation 3 give even better matching than those designed according to Equation 2, the further improvement being attributed to the performance of the bell portion rather than that of the throat portion.
  • the constant K is determined by the desired final diameter and over-all axial length.
  • the two horns which are illustrated are shaped over the whole of the axial length in'accordance with It has been found that horns detheir respective design equations for the throat portions, it is to be understood that the bell portion may be shaped to some other equation than that governing the throat portion, provided that the two portions merge smoothly into each other i. e. that at least the first derivatives of the functions governing the expansions of the throat and bell portions respectively have like values at the junction of the two portions. It will also be clear that the horns need not be made of metal throughout, so long as the inner surface is electrically conducting. Other modifications will be obvious to thoses killed in the art, and it is to be clearly understood that while the principles of the invention have been described in connection with specific embodiments, such description has been made solely by way of example and not as a limitation on the scope of the invention.
  • ' K a predetermined constant whereby for Zero axial distance the first, second and third derivatives of said function are equal to zero to provide a high order of smooth merging between the coaxial line;

Description

Sept-16, 1958 A. w. GENT ETAL 2,852,753
HIGH FREQUENCY TRANSMISSZ EON LINE SYSTEMS Filed March 10, 1954 Inventors A.W. GENT" R. T. LAWRENC E Attorney HIGH FREQUENCY TRANSMISSION LINE SYSTEMS Alfred Walter 'Gent and Ralph lfhomas Lawrence, London, England, 'assignors. to International Standard Electric Corporation, New York, N. Y.
ApplicationMarch 10, 19 '4,Serial No. 415,363
Chiins priority, application Great Britain March 20, 1953 1 Claim. (Cl. 333-,34)
This-invention relates to high frequency transmission line systems. More particularly, it relates to transmission line systems which include one-or more sections of the type commonly referred to as a G-line i. -e. sections in which the energy is propagated in a surface wave mode guided .by a single conductor which hasa thin dielectric coating (or has been otherwise treated, as for example by cutting a screw threadon the surface ofthe conductor) so as to decrease slightly the phase velocity of waves in the conductor.
In such systems it is necessary to provide coupling means whereby the surface wave mode energy propagated over the G-line can be launched or abstracted. For maximum eifieien'cy it is desirable that the coupling fta'ke's place between the G-line and a coaxial line circuit, since, the field of such a surface wave most nearly approximates to. that of a coaxial line, and it is already .known to use as a coupling. means a horn. having an inner conducting surface and coaxia'lly surrounding the G-line conductor, this horn constituting in efifect a flared extension of the outer conductor of a coaxial line circuit to which the G- line section is to be coupled. In addition .to the use of such couplings at the input and output ends of a G-line section, use may also be made of them at intermediate United States Patent 0 M support points in the case of a long sectionof G-line, where v in order to'reduce'the disturbing effect of the supporting means the G-line is transformed at each support point to. a short length of coaxial line which can readily be supported; forexample by ordinaryinsulator means, withont 'disfurbing the-wave propagation. In a transmission line system includingasection of G-line there may therefore be a large number of coupling horns in series, and itis obviou'sly desi rable that the coupling horns provide good irnpe dance matching; This is particularly desirable when,ias forlexamplein multi-channel systems,the energy to be propagated is distributed over a wide frequency bandlin'which cas e the cumulative eneet of even asmall impedance mismatch at each coupling poi'nt may be very serious.
It'is therefore an object of the present invention to providca horn for coupling a G-line to a coaxial line with a low degree of impedance mismatch over a wide band of frequencies.
According to the present invention there is provided a horn of circular cross section for coupling a surface wave mode transmission line to a coaxial wave mode transmission line, said horn comprising in series a throat portion and a bell portion merging-smoothly into each other, said throat portion having an axial length of the order of one half of a free space wavelength at the mean operating frequency, the inner diameter of said throat portion varying with the axial distance from the start of said throat portion in accordance with a diameter-distance function such 2,852,753 Patented Sept. 16, 1958 2 Figure l is a sectional representation of a quasi-exponential' horn coupling device in accordance with the invention; and
H Figure-2 isa sectional representation of a quasi-conical horn coupling device in accordance with the invention. In the figures, only those parts are shown which are essential to an expanation. of the device, and the same reference numeral is applied to identical parts in both figures. r It is known that in'order to avoidimpedan'ce discontinuities with horn couplin g between a'G-line and a coaxial line, it is desirable that the 'G-line conductor'should be an extension of the inner conductor of the coaxial line, preferably without change of-diameter, and that theinn'er surface of the horn should merge smoothly with the inner surface of the coaxial feeder outer conductor. It might at first sight seem probably that an exponential horn would, by analogy with acoustic horns and with exponentially tapered transmission line tral'i'sforrners, constit'ut'e a suitable coupling device. In point of fa'ct, however, a purelyexponential horn cannot merge smoothlywith the coaxialouter-conductor, since not even the first derivative-of an exponential curve can become, zero at any point-other than at air-infinitely :distant origin, i. --e.' at a point such that the throat -of the-horn would have an infinitesimally sm'alldiameter, whereas the'dnitial diameter of the horn 'throat must in practice be equal to the finite internal-diameter :of the coaxial outer conductor. A first approximation to anexponential horn would be obtained by shaping the horn in such manner as to satisfy the -iequ ation':
D-'=d cosh k ('1') where d is the internal diameter of the coaxial outer conductor, k is a selected constant, and .D is the internal diameter of the horn at a distance x along the horn axis from the start of the throat portion i. e. from the junction of the horn with the :coaxial line. Such'a horn approximatesto the exponential for large'values of x, and
merges fairly smoothly with the coaxial outer conductor, since-the first derivative becomes equal to zero when x is zero. Even so, however, the tapering at the throat is too violent to givesatisfactory freedom from reflections. The throat merges into the coaxial outer conductor, but only by what may be -called-first order merging; the first derivative vanishesat the origin, but not the second. By shaping the {throat of the horn in accordance with a functionwhose first, second, and third derivatives all vanish at the start of the throatthe merging becomes of a high order .i. e. much more smooth, with accompanying .reduction in impedance mismatch. Figures '1 and 2 illustrate two" coupling horns both of which are shaped to give high order merging at'the throat.
Referring now to Figure 1, this shows a sectional view of a metal horn 1 coupling a coaxial line 2 to a G line conductor indicated at 3 and formed as an extension of the inner conductor 4 of the coaxial line 2. The outer conductor of the coaxial line has internal diameter d. The length of the horn 1 comprises a throat portion extending over the axial length indicated at A, together with a bell portion extending over the axial length indicated at B, the inner surfaces of these two portions merging smoothly into one another, and the inner surface of the throat portion merging into the surface of the coaxial outer conductor 2 in such manner that the first three derivatives of the mathematical function relating the inner diameter D of the horn to the axial distance X from the start of the throat are each equal to zero when x is equal to zero. It will be clear that the smooth merging of the throat portion of the horn with the coaxial outer conductor afiects chiefly impedance irregularities arising at the horn junction, while the shaping of the bell portion of the horn governs chiefly irregularities arising at the an exponential horn.
horn mouth. The length of the throat portion should be of the order of one half a free-space wavelength at the mean operating frequency, while that of the bell portion should be at least one freespace'wavelength. Inthe present instanceboth bell and throat portions follow the same law of growth of diameter, i. e. the bell portion is formed by an extension of the throat to the whole length of the born, the diameter D varying with axial distance x according to the equation. l
w D=ii (cosh Kx+cos K 1'2 (2) The shape of a horn constructed to an equation of this type is approximately exponential, the constant K'being selected according to the diameter desired at the mouth of the horn for a given axial length. It has been found in practice that with a total axial length of about 2.5 wavelengths and a final diameter of about 3 wavelengths, a horn shaped in accordance with Equation 2 above gives reflection factors reduced to between 5% and over the waveband 7 cms. to 8 cms., the major part of the residual reflection being attributable to the bell portion rather than to the throat portion of the horn.
- InFig. 2, there is illustrated a horn coupling arrangement similar to that of Fig. 1 except that the quasi-exponential horn 1 of Fig. 1 has been replaced by a horn 5 the bell portion of which approximates to a frustum ofa cone. Here again both bell and throat portions follow the same law of growth of diameter, the bell portion forming an extension of the throat to the whole axial length of the horn, but this time the diameter D varies with axial distance )4 according to the equation.
This equation resembles Equation 2 in that its first three derivatives are each equal to zero when x is zero, but for large values of X it leads to a conical rather than signed in accordance with Equation 3 give even better matching than those designed according to Equation 2, the further improvement being attributed to the performance of the bell portion rather than that of the throat portion. As in the previous case the constant K is determined by the desired final diameter and over-all axial length. The theoretical analysis of horns of generally curved shape, as distinguished from horns whose diameter varies as a linear function of the axial length, presents great difiiculties, and it has so far not been possible to determine the dimensions of an optimum horn. It has however been found that a horn constructed in accordance with Equation 3, and having a total axial length of 25 centimetres and a final diameter of centimetres, gives a reflection factor of less than 1% over a frequency band of at least 600 mc./s. centred on 4000 mc./s. I
While the two horns which are illustrated are shaped over the whole of the axial length in'accordance with It has been found that horns detheir respective design equations for the throat portions, it is to be understood that the bell portion may be shaped to some other equation than that governing the throat portion, provided that the two portions merge smoothly into each other i. e. that at least the first derivatives of the functions governing the expansions of the throat and bell portions respectively have like values at the junction of the two portions. It will also be clear that the horns need not be made of metal throughout, so long as the inner surface is electrically conducting. Other modifications will be obvious to thoses killed in the art, and it is to be clearly understood that while the principles of the invention have been described in connection with specific embodiments, such description has been made solely by way of example and not as a limitation on the scope of the invention.
What we claim is:
A horn of circular cross-section for wide band coupling between a surface wave mode transmission line and 7 other, said throat portion having an axial length of M2,
a coaxial wave mode transmission line, said horn comprising in series a throat portion and a substantially frustro-conical bell section merging smoothly into each where A is the free space wavelength, the frustro-conical section and the throat portion being determined by a diameter-distance function of the form where d =the diameter at the start of said throat portion D=the diameter at an axial distance X from said start,-
and
' K=a predetermined constant whereby for Zero axial distance the first, second and third derivatives of said function are equal to zero to provide a high order of smooth merging between the coaxial line;
and throat portion, respectively.
References Cited in the file of this patent UNITED STATES PATENTS OTHER REFERENCES Microwave Transmission Design Data; pub. No. 23-. Sperry Gyroscope 00., Publications Dept, Great Neck, Long Island, N. Y.; pgs. 34 and 35. (Copy. in Div.
DeVore: abstract of application Serial Number 475,947,
published Oct. 18, 1949, 627 O. G. 873. F
Grieg Mar. 6, 1955 Great Britain Nov. 26, 1952'
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DE968646C (en) 1958-03-13
GB725187A (en) 1955-03-02

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