Abstract:
A constant gain sector beam array is obtained by applying equal amplitude, equal phase excitations to a sector array characterized by a curved array geometry. In a simple form, the curve is the arc of a portion of a circle. The radiation pattern can be further enhanced by using a more complex curvature geometry, and by minor adjustments to the amplitudes in the slots. Other forms of shaped beams, such as a cosecant squared antenna pattern, may be obtained by appropriately shaping the curvature geometry.

Description:
BACKGROUND OF THE INVENTION 
     The present invention relates to array antennas, and more particularly to an array employing equal amplitude and phase excitations of the radiating elements. 
     It is well known that array antennas of closely spaced radiating elements will produce a constant gain sector beam on a polar radiation pattern plot, or a flat topped beam on a rectangular radiation pattern plot. In the conventional design, all of the radiators lie in a plane which is essentially perpendicular to the direction of the flat topped beam. The radiating elements must be excited according to values of the function (sin(x))/x where x is in radians. That function changes its magnitude values rapidly, and also undergoes abrupt phase changes of 3.1416 radians. Because of mutual coupling between radiating elements, it is difficult to obtain an array whose elements conform to the desired (sin(x))/x function, especially when the desired sector beam is to cover a large angular region. 
     Sector beams are used, for example, to give uniform power density over the 3° to 4° sectoral extent of a nation as seen from a geostationary satellite. In terrestrial communication and broadcasting systems it is often desired to uniformly illuminate just one community which may be entirely within a, say, 80° sector as seen from the system&#39;s site. Complex power dividers and various lengths of transmission line have been used in the past to achieve the needed sin(x)/x excitations. But, mutual coupling between elements of the array forces a number of trial and error iterations before the desired pattern is obtained. Using the principle of this invention, easy-to-design uniform power dividers and equal length transmission lines to the radiating elements lower the design and fabrication costs. Shaped beams other than constant gain sector beams can be obtained by locating the radiating elements along paths other than the arc of a circle. Where the sector is to be a large angle, such as 120° or more, antennas embodying the invention will work, whereas the conventional sin(x)/x synthesis from a planar aperture will not. 
     SUMMARY OF THE INVENTION 
     The purpose of this invention is to eliminate the struggle to fit the radiating element excitation magnitudes and phase to the sin(x)/x demands and other problematic excitation functions used to attain shaped beams. Instead, easier-to-achieve equal amplitude, equal phase excitations are used. In accordance within the invention, the array is curved in order to obtain the case of a sector beam. In its simplest embodiment, the curve is in the form of an arc of a circle. The radiation pattern shape can be further enhanced by using curves which are more complex than simply the arc of a circle, or by minor adjustments to the field amplitudes at the radiators. In the latter instance, simple changes from the equal amplitude case while maintaining equal phase can enhance pattern shape in some instances. 
    
    
     BRIEF DESCRIPTION OF THE DRAWING 
     These and other features and advantages of the present invention will become more apparent from the following detailed description of an exemplary embodiment thereof, as illustrated in the accompanying drawings, in which: 
     FIG. 1 is a simplified schematic diagram illustrative of the geometry of a conventional sector beam antenna. 
     FIG. 2 is a diagram of the radiation pattern of the conventional array of FIG. 1. 
     FIG. 3 is a simplified schematic diagram of a sector beam antenna embodying the invention. 
     FIG. 4 is a diagram of the radiation pattern of the novel array configuration of FIG. 3. 
     FIG. 5 is a simplified schematic diagram of an antenna array in accordance with the invention which may be used to generate a beam having a cosecant squared shape. 
     FIGS. 6, 7 and 8 illustrate antenna arrays in accordance with the invention which may be used to produce beams of more complex shapes. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT 
     The invention will be described by first noting the geometry of the conventional approach, as well as the resulting radiation pattern. The same will then be done for a design based on this invention. FIG. 1 illustrates the geometry of a conventionally designed sector beam antenna, where all of the radiators lie in a plane which is essentially perpendicular to the direction of the flat-topped beam. Table I sets forth a table of the excitation coefficients for the antenna of FIG. 1. FIG. 2 illustrates the resulting radiation pattern for the sector beam antenna of FIG. 1 excited in accordance with Table I. 
     
                       TABLE I______________________________________Array Element #         Voltage Amplitude                       Phase______________________________________1 and 20      0.06          0 radians2 and 19      0.06          03 and 18      0.08          π4 and 17      0.07          π5 and 16      0.10          06 and 15      0.11          07 and 14      0.14          π8 and 13      0.20          π9 and 12      0.34          010 and 11     1.00          0______________________________________ 
    
     FIG. 3 illustrates an antenna designed according to this invention. In this exemplary embodiment, the antenna 50 comprises a waveguide which defines a circular arc of radius R. The radiating elements R 1  -R 20  of antenna 20 comprise radiating slots formed in the convex side of the curved waveguide. It will be apparent that the physical antenna of FIG. 3 is similar to that of FIG. 1, except for the curvature of the element 52. However, whereas the radiating elements of conventional antenna of FIG. 1 must be excited by the (sin x)/x distribution to achieve a constant gain sector antenna, the radiating elements of antenna 50 of FIG. 3 are excited by in-phase and equal amplitude signals provided by spacing the slot radiators one-half waveguide wavelength apart and using alternating offsets or inclinations slot radiators in a manner well known to those familiar with slotted waveguide arrays. 
     Table II sets forth the excitation coefficients for the antenna of FIG. 3. FIG. 4 illustrates the resulting radiation pattern for the sector beam antenna of FIG. 3, excited in accordance with Table II. 
     
                       TABLE II______________________________________Array Element Voltage Amplitude                       Phase______________________________________All           1.0           0 radians______________________________________ 
    
     Instead of slot radiators spaced along a single waveguide, a central power divider and the use of equal-path-length lines feeding of the antenna elements allows broadband operation, since the radiating elements remain in-phase regardless of the frequency. This type of antenna feed circuit is typically referred to as a corporate feed. 
     Sector beams of narrow widths, or of extremely wide widths are achieved with equal ease, using this invention. Analysis has shown that there is a radius of curvature and a number of radiators which will achieve any desired sector width. A computer program has been developed to plot the sector beam radiation pattern obtained by a circularly curved antenna embodying the present invention. The program is listed in Table III. The program receives as user input the total angle over which constant gain is desired, the arc length between radiating elements, the design frequency, the circle radius and the angle over which the computer radiation pattern is to be plotted. The program outputs a plot of the resulting radiation. The program can be used to design a curved antenna having a desired radiation pattern, since it predicts the pattern of antenna with defined parameters. By plotting the patterns of various antennas having different parameters, one can determine the parameters of an antenna having a desired radiation pattern. 
     
                       TABLE III______________________________________10   REM:    THIS IS A &#34;BASIC&#34; LANGUAGE PROGRAM100  REM:    THIS PROGRAM COMPUTES THE        PATTERN OF SECTOR BEAM PRODUCED110  REM:    BY AN ARRAY OF POINT SOURCES        AROUND A PORTION OF A CYLINDER120  REM:    OF RADIOUS &#34;0&#34;. THE POINT SOURCES        ARE EQUALLY SPACED AND LIE130  REM:    IN A PLANE PERPENDICULAR TO THE        CYLINDER AXIS, AND THE PATTERN140  REM:    COMPUTED BY THIS PROGRAM IS THE        PATTERN IN THAT PLANE150  REM:    THIS PROGRAM IS ALSO APPLICABLE        POINT SOURCES ARE EXPANDED TO160  REM:    BE LINE SOURCES PARALLEL TO THE        CYLINDER AXIS AND PASSING170  REM:    THE POINT SOURCE LOCATIONS180  REM:    THE VARIABLE USED ARE AS FOLLOWS190  REM:    A1=TOTAL ANGLE OVER WHICH THE        PATTERN WILL BE PLOTTED200  REM:    S1=TOTAL ANGLE OF THE DESIRED        CONSTANT GAIN SECTOR210  REM:    D=ARC LENGTH BETWEEN POINT        SOURCES, IN FREE SPACE        WAVELENGTHS220  REM:    0=CYLINDER RADIUS IN INCHES230  REM:    F=MICROWAVE FREQUENCY IN GHZ240  REM:    W=FREE SPACE WAVELENGTH AT F        GHZ, IN INCHES250  REM:260  REM:    C=CONVERSION FACTOR, DEGREES        TO RADIANS270  REM:    A=A1 EXPRESSED IN RADIANS280  REM:    T=ANGULAR SPACING BETWEEN POINT        SOURCES, IN RADIANS290  REM:    S=NUMBER OF POINT SOURCE SPACING        ANGLES WITHIN A1300  REM:    Q1=HALF THE NUMBER OF POINT        SOURCES EMPLOYED304  DIM     P(3421,4)310  C=57.29578320  A1=5330  S1=4340  D=.7071350  O=393360  F=12.45370  W=11.80285/F380  E=D*W400  A=A1/C410  T=E/O420  S=A/T430  S2=INT(S1/(C*T))+1440  IF S2/2&gt;INT(S2/2) THEN 450 ELSE 460450  S2=S2-1460  Q1=S2/2470  Q2=INT(1.570798/T+.5)480  LPRINT &#34;SLOT SPACINT=&#34;360*D&#34;DEGREES INFREE SPACE.&#34;485  REM:    PROGRAM LINES 490 TO 630 ARE USED TO        SET UP THE PLOTTING485  REM:    PROGRAM TO PLOT THE OUTPUT OF        THIS COMPUTATION. WITH487  REM:    VARIOUS MACHINES THESE LINES MUST        FIT YOUR PLOTTER490  FILE #1=&#34;TAPE2&#34;500  RESTORE #1510  FILE #2=&#34;FPLIST&#34;520  RESTORE #2530  PRINT #2, &#34; $FPLIST PATF=1,&#34;540  PRINT #2,&#34; NORFF=0,&#34;550  PRINT #2,&#34; VLEN=9, VMAXL=2&#34;560  PRINT #2,&#34; VMINL=-28,VDIVL=9,&#34;570  PRINT #2,&#34; HLEN=6.5,HDIVL=7,&#34;580  PRINT #2,&#34; HMINL=&#34;=A1/2&#34;,HMAXL=&#34;A1/2&#34;,&#34;590  PRINT #2,&#34; SC(1,1)=.2,1,.12,2,2,2&#34;600  PRINT #2,&#34; SA(1)=&#39;&#34;2*q1&#34;SLOTS&#34;D&#34;WVLNGTHSPCD ON&#34;O&#34;IN. RADIUS&#39;,&#34;610  PRINT #2,&#34; SC(1,2Z0.2,.7,.12,2,2,2,&#34;620  PRINT #2,&#34; SA((12)=&#39;=&#34;O/W&#34;WVLNGTH RADIUS.SOURCES COVER&#34; (2*Q1-1)*T*C&#34;DEG.&#39;,&#34;630  PRlNT #2,&#34; $,&#34;650  G=.532345*F660  U=INT(S/2)670  IF U/2&gt;INT(U/2) THEN 680 ELSE 690680  U=U-1682  REM:    LINES 690 THROUGH 730 ESTABLISH THE        PATH LENGTH FROM EACH684  REM:    ELEMENT TO A PLANE PERPENDICULAR        TO THE RADIUS OF THE CIRCLE686  REM:    OF RADIUS O. THESE LINES WOULD        HAVE TO BE DIFFERENT IF A SHAPE688  REM:    OTHER THAN A CIRCLE IS USED TO        ACHIEVE SOME OTHER PATTERN THAN689  REM:    A SECTOR BEAM690  FOR B=0 TO 4700  FOR N=1 TO 2*Q2710  P(N,B)=-(1-COS(1.57096-T*(N-1.1+.2*B)))*O*G720  NEXT N730  NEXT B740  IF Q2-Q1&lt;0 THEN 760750  GO TO 770760  Q1=Q2762  REM:    LINES 770 THROUGH 810 HAVE THE SOLE        FUNCTION OF DETERMINING THE784  REM:    CONSTANT BY WHICH TO NORMALIZE        THE PEAK OF THE PATTERN TO A766  REM:    VALUE OF OR NEAR ZERO dB.770  FOR N=Q2-Q1 TO Q2+Q1-1780  R=R+COS(P(N,1))790  I=I+SIN(P(N,1))800  NEXT N810  M=R 2+I 2820  R=0830  I=0832  REM:    LINES 850 THROUGH 970 PERFORM THE        THEORETICAL RADIATION PATTERN834  REM:    CALCULATION OVER THE ANGULAR        REGION -A1/2 TOA1/2 DEGREES850  FOR H=-U+1 TO U860  FOR B=0 TO 4870  FOR N=1 TO 2*Q1880  Y=H-N+Q1+Q2+1890  R=R+COS(P(Y,B)900  I=I+SIN(P(Y,B))910  NEXT N920  C1=R 2+I 2930  C2=4.343*LOG(C1/M)950  A2=(H-.7+.2*B)*T*C955  REM:    LINE 970 PUTS THE DATA INTO A        PLOTTING FILE FOR THE PARTICULAR956  REM:    PLOTTING PROGRAM, &#34;FASTPLOT&#34;,        BEING USED. OTHER USER WOULD HAVE957  REM:    TO USE A FORM OF LINE 970 TO SUIT        THE PLOT PROGRAM THEY WISH.970  PRINT #1 USING &#34;#####.##&#34;,0;A2;C2980  I=0990  R=01000 NEXT B1010 NEXT H1020 END______________________________________ 
    
     For achieving other beam shapes, such as the widely used cosecant squared antenna beam shape for mapping radar systems, a different computer program would have to be used. The position line of the radiating elements can become a combination of concave and convex curvatures of differing radii. 
     FIG. 5 illustrates in simplified form an antenna embodying the invention wherein the curvature of the antenna structure 102 defining the radiating elements R 1  -R n  is not a simple arc of a circle. Once again, the antenna feed circuit 104 feeds the respective radiating elements with equal amplitude, equal phase electromagnetic energy in accordance with the invention. The structure 102, which may comprise a waveguide in which radiating slots are formed, defines a straight section 106, a first curved section 108 of radius R c , a second curved section 110 of radius R b , and a third curved section 112 of radius R a , where R a  is less than R b , which is in turn less than R c . Such a complex shape of the antenna structure 102 can be used to generate a shaped beam such as a cosecant squared beam shape. 
     FIG. 6 shows a more complexly shaped antenna 120 comprising antenna structure 122 and antenna feed circuit 124. The feed circuit 124 feeds each radiating element R 1  -R n  with equal amplitude, equal phase electromagnetic energy. In this embodiment, the structure 122 defines a shape having adjacent convex and concave surfaces. Thus, the structure 122 includes a first section 126 having a convex curvature of radius R c , an intermediate curved section 128 having a radius R b , and a third curved section 130 of radius R a , where R a  and R c  are of opposite sense (convex/concave) and the intermediate curvature R b  is a transition between the two curved sections 126 and 130. The antenna 120 can be used to generate more complex beam shapes. 
     FIG. 7 shows an antenna array 140 which is shaped as a sector of a cylinder, with a linear arrangement of the elements in one direction and a simple curved shape in the orthogonal direction. This antenna structure can be used to generate a shaped beam in one plane and a pencil beam in the orthogonal plane. The array 140 includes an antenna structure 142 which defines the curvature of the antenna, and carries or defines the respective rows of adjacent radiating elements R 1  -R n . All the radiating elements are fed by the antenna feed circuit 144 with equal amplitude, equal phase electromagnetic energy. The structure 142 is characterized by a curvature of radius R in one sense, and is linear along an orthogonal sense. 
     FIG. 8 shows an antenna array 160 which includes a structure 162 carrying or defining an array of radiating elements R 1  -R n  in respective adjacent rows, and an antenna feed circuit 162. The feed circuit 162 provides all the radiating elements of the array 160 with equal amplitude, equal phase electromagnetic energy. The structure 162 is characterized by a complex curvature such as defined by a surface sector of an ellipse. Thus, the structure 162 defines a surface having a radius of R h  in a horizontal plane, and a radius of R v  in a vertical plane. The antenna 160 can be used to provide a shaped beam oriented in a vertical plane, and also in a horizontal plane, wherein the shaping in the respective planes can be alike or different, dependent on R a  and R b . 
     It is understood that the above-described embodiments are merely illustrative of the possible specific embodiments which may represent principles of the present invention. Other arrangements may readily be devised in accordance with these principles by those skilled in the art without departing from the scope and spirit of the invention. For example, the radiating elements could be groundplane-backed electric dipoles, helix radiators or polyrod radiators, etc., located along the needed curved path.