US 3572071 A
Abstract available in
Claims available in
Description (OCR text may contain errors)
United States Patent  Inventors Ralph A. Semplak Shrewsbury;
Richard H. Turrin, Colts Neck, N .J 735,334
June 7, 1968 Mar. 23, 1971 Bell Telephone Laboratories, Incorporated Murray Hill, Berkeley Heights, NJ.
[21 Appl. No.  Filed  Patented  Assignee  PARABOLIC REFLECTOR ANTENNAS 1 Claim, 7 Drawing Figs.
 US. Cl. 72/54, 29/421 [5 1] Int. Cl 321d 26/02  Field ofSearch 72/54, 56, 60, 63; 29/421  References Cited UNITED STATES P ATENTS 1,625,914 4/1927 Seibt 72/54 3,136,049 6/1964 Throner, Jr. et al. 72/56 U PPE R v D A PH RAG M K) 3,200,626 8/1965 Callender 72/56 3,220,102 11/1965 Liberman et al 72/60 FOREIGN PATENTS 430,321 9/1933 Great Britain 72/56 39,159 4/1887 Germany 7 2/60 Primary Examiner-Richard .l. Herbst Attorneys-R. J. Guenther and Arthur J. Torsiglieri paraboloidal to a sufficiently high degree of approximation to be useful as a microwave reflector antenna. In addition, refinements in the final shape can he realized by using a plurality of closely spaced blanks in the deformation process;
UPPER RING I2 SPACER RING 32 BOTTOM PRESSURE PLATE Lo-wER A DIAPHRAGM 3| CHAMBER I3 REGULATOR QMKRE VALVE l4 DIAPHRAGM 3I PATENTEUHARZBISYI I 357 1 7 sum 1 or 4 FIG./
PRESSURE FORMED I SURFACE UPPER RING I2 DIAPHRAGM I0 ,H I,
g BOTTOM PRESSURE 1 AV PLATE H I l5 Y GHAMBER I3 I REGULATOR XF VALVE l4 r/c. 2 1 PRESSURE. FORMED DIAPHRAGM I0 ASSEMBLY UPPER RING I2 DIAL INDICATOR 21 OPTICAL BENCH 20 FIG. 4
UPPER 1 L UPPER RING I2 DIAPHRAGM I0 SPACER RING 32 BOTTOM PRESSURE LOWER I PLATE ll CHAMBER l3 0 T MPRESSED v REGULATOR CO A|R VALVE [4 RA. SEMPLAK lNl/ENTORS RH TURR/N A TTORNEV PATENT ED W23 I971 SHEET 2 BF 4 mo o+ qo o+ (53mm) Mom/M30 PATENTED mam sum 3 0r 4 FIG. 5A
RADI-ATION' PATTERN H- PLANE ma wzbjwm FIGSB RADlATlON PATTERN E-PLANE 2 was? PARABOLIC REFLECTOR ANTENNAS This invention relates to a method for making paraboloidal surfaces which has particular application in the fabrication of parabolic reflector antennas.
BACKGROUND OF THE INVENTION Paraboloidal surfaces are useful in .a variety of systems which utilize electromagnetic radiation. For example, such surfaces are useful as parabolic reflector antennas for radio and microwave energy and as parallel beam reflectors in optical systems.
In such systems it is usually important that the surfaces closely approximate that of an ideal paraboloid. For example, surface irregularities and departures from an idealized paraboloid in a parabolic reflectorantenna result in phase errors in the aperturefield which lead to a loss of gain and an increase in sidelobe power levels. In fact, it is generally accepted that for antennas'where the sidelobe power levels are notimportant, a suitable tolerance is of the order of one-sixteenth of a wavelength of the reflected radiation. Thus,-the higher the frequency of the radiation, the greater is the difficulty of malt-- ing a suitable reflector.
Because'presentmethods for producing paraboloidal surfaces are typically dependent upon the smoothness of a mold surface and the skill of a human craftsman, high quality surfaces are both difficult to produce and relatively expensive. Typical among the-numerous techniques presently used are die casting, the assemblingof a plurality of parabolic sectors, spin-casting and spinning." Each of these techniques involves the use of a; mold surface and/or the machining or polishing to final dimensions by a human craftsman. As a result, the surfaces produced by these methods are generally not of sufficiently good quality for use with radiation having wavelengths of a centimeter or.less. For example, the typical tolerance for a 1 meter diameter paraboloid formed by spinning," the most widelyemployed technique, is i 0.8 mm. or 1*: A l 2 at 30 GHz., whichis less than the generally accepted tolerance for that frequency. 3
An experimental technique for forming mathematical surfaces of revolution is describe by S. Timoshenko in Chapters 3 and 13 of Theory of Plates and Shells, 1959. According to this technique, a circular diaphragm with its circumference clamped is subjected to a uniform pressure which is less than that required to exceed the elastic limit of the diaphragm. As a result, the diaphragm is temporarily deformed into a surface of revolution, the general shape of which is determined by the pressure-forming "technique and, to a lesser extent, the homogeniety of the diaphragm material. Since no mold is used, the surface roughness is a function of only the diaphragm material.
This technique, however, is not useful for making per manent paraboloidal surfaces such as.would be required for use as an antenna. Because the elastic limit of the diaphragm material is not exceeded, the deflection obtained exists only while the pressure is maintained; in addition, the deflection produced in the manner is only of the order of magnitude of the diaphragm thickness. Typical practical applications, on the other hand, require permanent deflections which far exceed the thickness of the diaphragm. For example, the focal lengths of reflectors for radio application are dictated in part by the feed requirements and, in general, the maximum deflection required for this application will greatly exceed the thickness of the material.
SUMMARY or THE INVENTION In accordance with the present invention, a paraboloidal surface is formed by applying to a clamped, circular diaphragm a uniform pressure sufficient to substantially exceed the elastic limit of the diaphragm material and, thus, to permanently deform it. Although no analytical predictions regarding the resultant deformed surface are known, it has been discovered empirically. that the surface thus produced is BRIEF DESCRIPTION. OFTHE DRAWING The above and other aspects and-features of the invention will become clearer upon reference to the drawing and to the detailed description thereof which follows:
FIG. 1 is a cross-sectional view of a typical apparatus used to form a paraboloidal surface in accordance with the invention;
FIG. .2 is a cross section of a typical laboratory arrangement used for measuring the surface deviation of a formed surface;
FIGS. 3 and 6 illustrate graphically the amounts by which a number of typical surfaces formed in accordance with the invention differ from an idealized paraboloidal surface;
FIG. 4 is a cross section of an alternative apparatus used to form a paraboloidal surface; and
FIGS. 5A and 5B show radiation patterns of typical parabolic reflector antennas formed in accordance with the invention.
Identical structural features appearing in the FIGS. of the drawing will be given the same identification numerals, and each feature willbe described in detail in connection with the structure of the firstFIG. in which it appears.
DETAILED DESCRIPTION Referring tothe drawings, FIG I is a cross section of one embodiment of apparatus used to form a paraboloidal surface in accordance with the invention. The apparatus comprises a thin, circular diaphragm 10 of malleable material, such as aluminum, clamped between a circular bottom pressure plate 11 and an upper ring 12. Advantageously, the radius of the diaphragm is no larger than the outer radius of the upper ring, and the clamping of the diaphragm circumference is as uniform as possible. Bottom plate 11, in conjunction with diaphragm 10, forms a chamber 13 which is airtight except for anaperture 15 through which a pressurized fluid, such as compressed air, can be introduced intochamber 13. A regulator valve 14 is conveniently placed between a source of such pressurized fluid (not shown) and the chamber. Upper ring 12 is advantageously providedwith a curved inside edge to prevent thering edge from cutting into the diaphragm as it is deformed.
In operation, a paraboloid surface is formed by the steps of immobilizing the circumference of the circular diaphragm while leaving the interior portion free to expand under pressure, applying a sufficient uniform fluid pressure to the clamped diaphragm to permanently deform it, and then reducing the pressure to that of the surrounding atmosphere. The circumference can be conveniently immobilized, for example, by the use of a plurality of C-clamps (not shown) to clamp the diaphragm between upper ring 12 and lower plate II. The clamping should be uniform. The result of nonuniform clamping is circumferential buckling of the diaphragm. Moreover, if the diaphragm is larger than the outer circumference of the upper ring, poor clamping will result in wrinkling of the 7 material outside the clamped region. The uniform fluid pressure is conveniently obtained by filling chamber 13 with compressed air. Valve 14 is used to control the pressure used. The amount of pressure required is dependent upon the thickness and elastic properties of the diaphragm and the amount of the air pressure was released and it was noted that the center of the surface retracted an amount approximately equal to the thickness of the undeformed diaphragm. The material was permanently deformed and the surface, being doubly curved, was stronger than the original flat diaphragm.
Surface deflection was then measured by the mechanical technique illustrated in FIG. 2, employing an optical bench 20 as a diametrical mount, and a micrometer dial indicator 21 as the deflection indicator. The convex side of the antenna was measured by retaining the diaphragm in its clamped form and positioning the ring 12 parallel to the optical bench. With the setup of FIG. 2 accuracies of the order i0.001 inch deflection and :0.005 inch in radial dimension are readily obtainable. Table I below lists measurements made on a 12-inch diameter reflector of 0.012-inch thick half-hard material. The dial indicator deflection readings are shown in the measured column and, for comparison, the calculated column lists the corresponding deflections for a parabola, fitted to the measured data at r= inches; the corresponding focal length is 6.30 inches.
For the case in which a suitable reflector tolerance is stated to 11 so that diaphragm 31 expands. In the process diaphragm 31 expands into diaphragm and permanently deforms it. It has been discovered that upper diaphragm 10 has a more nearly parabolic cross section than is typically obtained using the ap- 5 paratus of FIG. 1. Typical examples of reflectors formed using this apparatus will be described below.
A set of -centimeter-diameter reflectors was made from 0.038 centimeter thick 1 100-0 aluminum using different spacing thicknesses. In each case sufficient air pressure was applied to obtain the desired deflection. The differences between the measured deflections and those of an ideal fitted paraboloid are shown as curves 2, 3, 4 and 5 of FIG. 6. Curve 1 of FIG. 6, included for comparison purposes, illustrates the deviations for a reflector made using a single diaphragm. It will be noted from these curves that the use of a spacer results in a substantial overall improvement. Table II gives the focal lengths and the measured electrical properties of these surfaces used as reflector antennas. These measurements indicate that the surfaces are suitable for use as antennas at frequencies as high as 75 GHz.
TABLE II.-SUMMARY OF MEASURED DATA Two diaphragms with forming Sirgle spacer thickness, mm.
phragm 3. 175 6. 9. 525 12. 7
Measured gain (db) i0. 2 db 36. 7 36. 9 37. 3 37. 2 37. 7 1st side lobe (db), worse plane..- 16.0 17. 0 -18. 5 19.0 -20. 0 Percent efliciency 61.0 53. 5 58. 6 57. 3 64.2 Focal length, cm 13.03 12. 85 12.85 12. 85 12. 52
Spillover --1. 15 1. 10 1. 10 1. 10 1. 05 Aperture blocking 0. 28 0.28 0. 28 -0. 28 0. 28 Aperture Taper 0. 38 0. 38 0. 38 0. 38 0. 38
Total 1.81 1.76 1.76 1.76 1.71
be of order A 16, the measurements tabulated in Table I in- 35 This tflihnicll-le can be extended to the use Ofa larger number,
dicate that the surface is suitable for use at frequencies of the order of 100 GI-Iz. It should be noted also that these measurements are repeatable for other radial directions. Curve 1 of FIG. 3 indicates the departures of this surface from a parabolic surface of the form y =4fx. Where the actual deflection exceeds the calculated deflection, the deviation is positive. Where the actual deflection is less, the deviation is negative.
The principles of the present invention are not limited in their application to small antennas. Additional antennas as large as 30 inches in diameter have been formed using 0.016 inch, type 11000 (annealed) aluminum, and their deviations from a fitted paraboloid are plotted as curves 2 and 3 of FIG. 3. The antenna of curve 2 was formed by increasing the pressure in incremental steps and permitting the surface to rest between each application of increasing air pressure. The antenna of curve 3, on the other hand, was produced by directly applying sufficient pressure to obtain the desired deflection. It will be noted that the deviations of the two surfaces are quite similar.
A more nearly ideal paraboloid can be obtained in a variety of ways. It will be noted from curves 1, 2 and 3 of FIG. 3 that, in all three cases, the measured deflection is less than the calculated deflection over most of the area. Near the center,
n, of spaced diaphragms, where n depends upon the degree of accuracy required for the specific application. In This manner the technique lends itself to forming surfaces that are useful as antenna reflectors at optical frequencies. Moreover, a variety 40 of parameters can be varied in this technique to alter the resulting surface. For example, such parameters as diaphragm thicknesses and diaphragm spacings can be varied. Furthermore, the volume between each pair of diaphragms can be pressure-loaded, as described below, providing still another degree of freedom in the technique.
While only uniform loading of the surface has been considered, more refined control of the resulting deflection can be obtained by using nonuniform fluid pressure loading. For example, the convex surface of the diaphragm can be loaded, for example, by placing a dense liquid, such as mercury, on diaphragm 10 of FIG. 4 within the confines of upper ring 12. Alternatively, the concave surface can be loaded by inverting the structure and disposing diaphragm 10 above a mercury surface so that the center portion of the diaphragm displaces the mercury as it expands FIGS 5 A and 5B illustrate radiation patterns for both the H lane and E pTaE JtypicaI parabolic reflector antenna formed in accordance with the principles of the invention. The patterns were made at a however, the deflection is considerably greater than the ideal frequency of 30 GZ. employing an open-ended circular guide amount. These tendencies can be compensated for in a variety of ways. One type of compensation, for example, is through the use of a diaphragm of variable thickness. In particular, the diaphragm should be circularly symmetric and thicker at the with a 6.5 db. illumination taper as the feed. As shown, each of the patterns is centered about the 0 point and each has immediate sidelobes below-l7 db. Also, the patterns indicate a measured 3 db. beam width of 2.l7 which is in substantial center than at the edges. Alternatively, these tendencies can agreement with the theoretically calculated value. In all cases,
be compensated for by using the apparatus of FIG. 4 to form the surface.
The arrangement of FIG. 4 is similar to that described in connection with FIG. 1 except that two spaced diaphragms are it is to be understood that the above-described embodiments and procedures are only illustrative of the invention. Numerous and varied other arrangements can be devised by those skilled in the art without departing from the spirit and used rather than a single diaphragm. More specifically, a scope ofth invention.
second diaphragm 31 and a second clamping ring 32 are added to the basic apparatus. Ring 32, in this apparatus, also acts as a spacer ring between the two diaphragms.
In operation, a sufficient uniform pressure is applied to the chamber formed by clamped diaphragm 31 and bottom plate We claim: 1. A method of shaping a diaphragm to form a paraboloidal surface comprising the steps of:
spacing apart a plurality of totally overlapping diaphragms such that adjacent diaphragms are free to move relative to each other; immobilizing the circumferences of a tions of all of said diaphragms; and
djacent circular por-