US3130410A - Space coded linear array antenna - Google Patents

Space coded linear array antenna Download PDF

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US3130410A
US3130410A US146906A US14690661A US3130410A US 3130410 A US3130410 A US 3130410A US 146906 A US146906 A US 146906A US 14690661 A US14690661 A US 14690661A US 3130410 A US3130410 A US 3130410A
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array
elements
antenna
chosen
values
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US146906A
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Frank S Gutleber
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TDK Micronas GmbH
International Telephone and Telegraph Corp
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Deutsche ITT Industries GmbH
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Priority to US146906A priority patent/US3130410A/en
Priority to GB39657/62A priority patent/GB1002843A/en
Priority to FR913156A priority patent/FR1346326A/en
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    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01Q—ANTENNAS, i.e. RADIO AERIALS
    • H01Q21/00—Antenna arrays or systems
    • H01Q21/06—Arrays of individually energised antenna units similarly polarised and spaced apart
    • H01Q21/22—Antenna units of the array energised non-uniformly in amplitude or phase, e.g. tapered array or binomial array

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  • This invention relates to antenna systems and more particularly to methods and equipment for obtaining any desired antenna pattern from a linear antenna array.
  • Array antennas of a variety of types are well known in the prior art. These prior art antenna arrays have been of several types. One type has utilized a number of equally spaced antenna elements to build up an array. This type of simple array of equally spaced antenna elements which are provided with equal amplitudes of driving current or voltage produce an antenna pattern whose shape can be controlled to only a Very limited degree. A typical response of such an equally spaced antenna system with equal amplitude driving power at each individual element results in the well known sin x/ x radiation pattern.
  • Schelkunol for example, in United States Patent No. 2,286,839 shows an array antenna utilizing a number of equally spaced individual antenna elements.
  • Schelkunofl ⁇ provides both an individual amplitude control device and an individual phase control device for each of the individual antenna elements that compose his array.
  • the amplitude of the driving current which is applied to each of the antenna elements is different from the amplitude in other antenna elements.
  • the phase of the signal applied to each of the individual antenna elements is in general different from that of other elements in the array.
  • Schelkunoi'f provides a systematic manner of choosing the particular amplitudes and phases supplied to the elements of his array. However, these amplitudes and phases follow a polynomial distribution.
  • a further disadvantage of the prior art systems has resulted from the fact that many of these arrays are built up out of elements spaced in three dimensions from each other. That is,elements are placed at certain points within a given area and also above or below the plane of this area at certain elevations. The difficulty here arises when it is attempted to improve the radiation pattern -of the antenna by utilizing a large number of individual elements.
  • the addition of new elements does not produce any effect which is readily predictable from the type of mathematical analysis provided in the prior art airay systems, and in fact it is often ditlicult to determine where, or in what part of the array, additional elements should be provided.
  • a particular number of individual antenna elements are spaced unequally from each other so as to cause a predetermined effect on the antenna radiation pattern due to each set of elements which make up the array.
  • the individual antenna elements in this array are placed at predetermined unequal distances from each other according to a systematic set of design equations which allow the production of an arbitrary desired antenna pattern utilizing a particular predetermined number of antenna elements.
  • This method allows the particular unequal coded locations of the individual antenna elements of a rst set of elements in the array to be extended to provide the pattern for the entire array.
  • the entire two dimensional array may be driven by supplying equal power at the same relative phase to allof the individual antenna elements.
  • FIGURE l is a diagram illustrating the geometry of an array antenna, as viewed from the top, which lis useful in deriving the equations involved;
  • FIGURE 2a is a schematic diagram of a 16 element array antenna representing a rst embodiment of my sin sin 00- for the antenna of FIGURE 2a;
  • FIGURE 4 is a plot of the radiation intensity field Et of the antenna of FIGURE 2a vs. the physical space angle 6';
  • FIGURE 5a is a schematic diagram of a two-dimensional array antenna which utilizes the antenna design of FIGURE 2a;
  • FIGURE 5b is a block diagram of a portion of the circuit used with the array antenna of FIGURE 5a;
  • FIGURE 6 is a diagram giving the relative spacing in correct proportion of a linear array antenna composed of 32 elements
  • FIGURE 7a is a diagram of the radiation field intensity pattern Et plotted vs. the design parameter K for the antenna of FIGURE 6;
  • FIGURE 7b is a diagram on a smaller scale of the field intensity pattern Eb plotted vs. the physical space angle 0 for the array of FIGURE 6;
  • FIGURE 7c is a composite diagram of the field intensity of the arrays of FIGURES 6 and 2;
  • VFIGURE 8 is a diagram of an array representing a fourth embodiment of my invention and showing another possible coded spacing of an antenna utilizing a l6 element array.
  • FIGURE 9 is a plot of the lield radiation intensity Et produced by ⁇ the antenna of FIGURE 8 vs. the design parameter K;
  • FIGURE l0 is a diagram illustrating the preferred embodiment of my invention, representing an array antenna composed of 64 elements and designed according to my method;
  • FIGURE l1 is a plot of the eld radiation intensity Et produced by the antenna of FIGURE lO vs. the design parameter K;
  • FIGURE Il2 is a plot of the viield radiation intensity Et of the antenna of FIGURE 10 vs. the physical space angle 6.
  • FIGURE 1 the general relationship is shown between the elements of a linear array which are unequally spaced from each other and showing the meaning of the space angle 0.
  • 9 represents the direction of a line v drawn from the array along a particular direction which is of interest at the moment.
  • the angle 0 represents the angle between x, the axis of the antenna, and the line v which may be moved about to examine any particular direction which is of interest.
  • the radiated wave front is perpendicular to the line v as shown.
  • it is ordinarily sufficient to design for values of 0 which run only between 0 and 90 degrees. Because of symmetry, the antenna appears to produce the same pattern whether one stands on one side of the axis x or the other.
  • the second quadrant will produce a pattern which is the same as the pattern in the rst quadrant and is in fact the mirror image of the pattern in the first quadrant. YFor this reason, it is necessary only to work with values of 0 between 0 and 90 degrees for linear array antennas. In the most general case, one would examine 0 for 360 of azimuth, but this is not necessary here.
  • the Viirst two elements of the array are shown separated by a distance d1.
  • the distance d1 sin 0 represents the ditference in distance that two Wave fronts starting from the two elements have traveled along the line v located at the angle 0.
  • Equation 2 Equation 2
  • Equation 2 tI/:the phase of radiation; A equals the wavelength at the particular operating frequency of the antenna; 0 is the physical space angle, as explained above; and d is an elemental uniform distance which represents an equivalent average uniform separation of the antenna elements.
  • Equation 3 the radiation from a linear array antenna may be represented by Equation 3:
  • the position of the iifth element is equal to the position of the rst element N, plus an added increment of distance S1.
  • S1 is so chosen to result in radiations which are completely out of phase from the elements N1 and N5.
  • Equation 6
  • Equation 7 a general term of the series given iu Equation l or Equation 3.
  • the neX-t element is given in terms depending upon the previous element.
  • the quantity 2d sin 6 the quantity 2 occurs because an out-of-phase condition has been chosen.
  • Equation 12 Equation 12
  • Equation 12 thus indicates the basic method for building up the array. Each time it is desired to extend the array by increasing the number of elements, the size of the array will be doubled. lFor each existing element, one more element will be added. Each of the added elements will be the distance 1/2K from its own corresponding previous existing element.
  • the quantity K can still be chosen in such a manner as to facilitate design procedures and to make as' simple Vas possible the computations involved. For this reason, the following steps are taken. Eirst, 60 is dened as the physical space angle where the rst null of the antenna radiation pattern occurs. Now K1 is made equal to 1 at the dirst null when 6 equals 60. By doing this,
  • Equation 1l becomes Equation 13A.
  • Equation 13B Equation 13B
  • Equation 14B can be rewritten by substituting K for sin 6 sin 60 as given by Equation 16:
  • Equation 18 gives the physical coded space relationship.
  • Equation 18 is given in units of wavelengths, that is, depending on .the particular value sin 60 which is chosen, an actual physical array can be built. 60 -it should be remembered, is the angle in space where the rstnull occurs ⁇ for the antenna radiationV pattern. Equations 12, 17 and 18 provide the basis .for computing al1 of the required quantities to buid the array with any arbitrary antenna pattern. To illustrate this, Equation 12 will be rewritten providing an actual index X which indicates how the particular values of K which have been chosen as arbitrary design factors are incorporated to build up the next step of the array.
  • the number of elements in the array must be doubled. This is because each existing element of the previous array must have added to i-t, that is, placed some distance from it which we have denoted by S, another element (whichv N ab will produce at some particular space angle 0, the radiation which is 180 out of phase with the radiation from this corresponding element of the previous array; Thus, the number of elements in the -array must be a power of 2.
  • An array built according to my method therefore may consist of 2 elements, 4 elements, 8 elements, 16 ⁇ elements, 312 elements, 64 elements, and so on, but the number of elements in the array will always be a power of 2. Likewise, for each ladditional power of 2.
  • K In other iwords, in an array which has 16 ⁇ individual antenna elements, four values of K may be chosen arbitrarily. This is because 2 to the 4th power is equal to 16, and the array is in a sense composed of four sets of elements which have been spaced in relationship to each other to produce the result according -to my method.
  • N1 is the iirst element of an existing array.
  • T o increase the size of the array, another element must be added.
  • 1N 2X+1 which is the iirst new element of the next set which is being added to the array.
  • N 2X+1 represents lan element which must be spaced a distance 1/2K(X+1) from N1.
  • Equation l19 shows how to locate the Ifirst additional element when the array is being increased from a given size.
  • Equation 2O shows how to add the second new element of the increased array.
  • Equation 21 shows how to add the last element to increase the array to its iinal size.
  • X is simply an index number which takes on integral values as the size of the array increases. For an array which has two elements, X is equal to tor an array that has four elements, X is equal to l; for an array that has 8 elements, X is equal to 2; for an array that has 16 elements, X is equal to 3; :and so on. Every time the size of the array is doubled, that is, every time X increases one unit, this allows one additional value of K to be arbitrarily chosen.
  • FIGURE 2 there is shown a linear array antenna composed of 16 individual antenna elements numbered 1 through 16. This drawing is in correct relative scale, that is, the correct relative spacing ⁇ of all the elements is actu-ally given in FIGURE 2.
  • a scale is provided in normalized electrical degrees running from 0 degrees, which is the reference value of the tirst element :1, up to 450. The location of the last element 16 is at 435 electrical degrees.
  • the values used for K to create this may are K1 equal to 1, K2 equal to 1%, K3 equal to 2 and K4 equal to 4.
  • a translation device 17 which might be a transmitter or receiver, for example, is shown connected to the 16 elements of the array by feed lines such as 18, ⁇ .18a,l18b,and so on. Equal amounts of power are supplied to each one of the 16 elements in the antenna array; likewise the phase of the signal from the device 17 is exactly the same for each of the 16 elements.
  • Equation 19 the iirst element of the array N1, element l1 of FIGURE 2 is taken as having zero phase, that is, it is the reference element.Y All other elements will be positioned in reference to this first element. Utilizing Equation 19, it is readily perceived where the next element is to be placed. The next element N2 will now provide an array of t-wo elements, this allows exactly one value of Kto be chosen. K has been equal to 1, as indicated before, .to provide a normalized design for convenience. Thus, from Equation 19, it may be seen in Equation 22B, below, that the second element should be placed '180 out of phase with the rst element.
  • Equations 19 and 22A actually give the calculation of the positions in terms of the design parameters K.
  • K in the present instance equals l.
  • Multiplying by 3,60 then converts into electrical degrees, sinceV there are 360 electrical degrees for one wavelength of radiation.
  • this is an arbitrary calculation, and
  • Equation 22A namely 1/2, for example
  • Equation 19 Equation 19
  • the position of the third element of our array can be calculated. It should be remembered 'that each time a power of two is reached in the number of elements in the array, it is necessary to start over and begin adding elements starting from the irst element. In other words, the third element is added to the rst element. The fifth element will be added to the iirst element; likewise, the sixth element will be added to the second element. This is because an array must consist of a number of elements which is a power of two due to the design procedure which is utilized. Thus N3 is equal to 120, since K2 was chosen to be 3/2. .If K2 had been chosen a different value, the position of element N3 would of course be different.
  • Equations 19, 20 and 21 which define the procedure for calculating the additional elements of the array.
  • the fth element is calculated using the third value, K3, for the design parameter K.
  • K3 is equal to 2
  • K4 is equal to 4.
  • K3 is equal to 1
  • K4 is equal to 4.
  • K values may be chosen as integers, fractions, irrational numbers and so on.
  • the dcsignercan review the radiation pattern produced by the number of elements used up to that point and he can pick the additional elements and place them so as to provide an improvement in the radiation pattern and never a degradation.
  • This is a distinct advantage over the prior art design procedures.
  • the addition of Imore elements to the array always improves the radiation pattern and canV never degrade it.
  • array is to be made up of 32 elements. Using the procedures outlined above, the first 16 elements of the array are calculated and their locations noted. Now, one more value for K5 is to be chosen. If the lirst four K values are not changed, the position of the first 16 elements of the array is in no Way affected by the addition of the next 16 elements. Thus the benelicial results obtained from the rst part of the calculations will never be lost or degraded by the addition of additional elements to the array. This is an unusual result and obviously extremely advantageous.
  • FIGURE 6 shows a 32 element array.
  • FIGURE 3 shows the plot of the radiation intensity Et of the antenna of FIGURE 2, plotted versus the design factor K. It should be stressed that this plot is in K and not yet in Suppose that an ⁇ space angle which will illustrate another'important advantage of our method and system. It can indeed be seen that nulls occur in this pattern, that is, zero values of radiation at values or" K equal to 1, 2, 11/2, and 4, as was indicated by our original choice of the values of K1, K2, K3, and K4.
  • one of the advantages of our design procedure is to form the design using plots, such as FIGURE 3, where the abscissa is in units of K. This greatly facilitates the design, and it results in a normalized design which can be adapted for a number of other conditions by certain physical spacing when it is actually constructed.
  • Equation 99 E, is given as a function of K. To form the plot, a value for K is picked, then Equation 99 is calculated and yields a value for Et. Then K is increased a convenient increment and Equation 99 is recalculated forthe new value of K, and so on, for the particular array which has the fixed relative spacing depending upon the design parameters of the constants K1, K2, K3 etc. which have been chosen. This plot of E, versus K is shown for the array of FIGURE 2 in the illustration of FIGURE 3. To evaluate Equation 99, only values of K within a region up to a value of KMAX equal to l/sin 00 need be chosen.
  • FIGURE 5 shows a second embodiment of my invention which illustrates the extreme practical utility of my antenna arrays and the method of building them.
  • the gure shows a similar codedV array, as in FIGURE 2, extended into a two dimensional array. It is a plan view of the array, and the individual antenna elements have been simply shown as dots for convenience. The correct relative proportions are shown and the scale is the same as in FIGURE 2.
  • FIGURE 5 was created from FIGURE 2 with no further computation.
  • the array'antenna of FIG- URE 5 provides an antenna radiation pattern in three dimensions in space, that is, not only does it provide the radiation pattern shown in FIGURE 4 in the plane of the axis of the array of FIGURE 2, but it provides this same pattern in a plane perpendicular to the plane containing the axis of the 16 elements of FIGURE 2.
  • FIGURE 5 An inspection of FIGURE 5 will quickly reveal its pattern.
  • the first row across consisting of 16 individual antenna elements, which might be dipoles, dicones, horns etc. or whatever is convenient, are numbered 1 through 16 and are numbered corresponding to FIGURE 2.
  • the second row of antenna elements, relative to each other is spaced exactly the same way as the first row.
  • element 19 which is the first element of the second row is 45 electrical degrees from element 20 which is the second element of the second row.
  • element 21 is exactly 45 electrical degrees from element 20, just as element 5 is 45 electrical degrees from element 9 in the rst row.
  • the entire second row such as elements, 19, 2t), 21, 22 and so on, is spaced the same distance from the first row as element 9 is spaced from element 1, namely 45 electrical degrees.
  • the rst element of the third row, element 23, is the same distance from element 19 as element 5 is from element 9 in the first row.
  • element 24, which is the iirst element of the fourth row is the same distance from element 2'3, as element 3 is from element 5 in the iirst row.
  • element 25, which is the second element in the fourth row is the same distance from element 24 as element 9 is from element 1 in the iirst row.
  • the pattern is extended in this manner, as shown, as it will be seen that along any line of elements, either horizontal or vertical, the relative spacing is exactly the same as that shown in FIGURE 2 or the rst row in the array of FIGURE 5.
  • the spacing of the array along a single axis in actuality also completely spaces the location of all the elements of a square array consisting of nXn elements, where n is the number of elements in the single axis array.
  • the total number of elements, shown in FIGURE 5 is 16 squared, that is, 256 elements.
  • Y Y Y Y Y Y This property of my antenna arrays, that they may be reproduced in two dimensions to create a three dimensional antenna radiation pattern is obviously of great practical utility and is true of all antenna arrays created according to my method, and Vaccordingly the embodiments of FIGURES 6 and 10 also may be extended in two directions in the same manner.
  • FIGURES 6, 8 and 10 For convenience of illustration, I have only shown the embodiments ofFIGURES 6, 8 and 10 along a single axis. But the embodiments of FIGURES 6, 8 and 10 may likewise be extended into a two dimensional square array in the same manner, and I claim such two dimensional arrays as part of the novelty of my invention.
  • the antenna elements of FIG-Y URE 5 should be supplied with equal amounts of power from a source providing the same phase of signal to each of the elements.
  • the translation device such as 17, has not been shown in FIGURE 5b.
  • FIGURE b merely illustrates what has been mentioned before, that each of the individual antenna elements of my array, such as N1 or N9 or N7 can be individually supplied with a high power transmitting stage for sending purposes for use of the array as a transmitting antenna and with an individual amplier for using the array for receiving purposes.
  • Each of the power transmitting stages, such as 26, 27, 28, and so on, can be exactly identical in design; each transmitting stage, 'such as 26, supplies the same amount of power to its individual antenna element as all the other transmitting stages.
  • these transmitting stages might consist of an individual travelling wave tube, for example, With an associated power supply and frequency control circuits.
  • these individual transmitting stages can each be made to operate at its peak point of design eiciency, and there is no necessity for wasting RF power in power dividing networks for providing unequal amounts of power to the individual elements.
  • each individual antenna element such as N1 may be provided with a high gain, low noise amplifier, such as 29, 30, and 31.
  • a high gain, low noise amplifier such as 29, 30, and 31.
  • Each of these amplifiers is exactly the same as the others and provides an equal amount of gain. This also allows the output from each individual antenna element to be amplified immediately before passing to the connecting lead networks such as 32, where it is connected to the input o'f the rest of the receiver equipment.
  • the ampliier, such as 29, and transmitting stage, such as 26, may be omitted and the array of FIGURE 5 may be supplied with one single transmitting or receiving apparatus, as indicated in FIG- URE 2, by the use of multiple feed lines, such as shown as 18, 18a, 18b, and so on. Whichever is most convenient for a particular application will be used.
  • the individual amplifiers and transmitting stages, such as 26 and 29, can be physically disposed extremely close to the individual antenna elements in the arrays built according to my method.
  • FIGURE 6 shows the correct relative spacing for an array antenna built according to my method and composed of 32 individual antenna elements, spaced according to Table II.
  • the fth value K5 has been chosen as 5A.
  • the quan- 14l tity 1/2K5 is thus equal to 144 electrical degrees and the 16 new values for Code No. 2 may be formed by adding 144 increments to the appropriate terms inl Code No. 1, as has been outlined in the previous development, particularly Equations 19, 20 and 21. Alternatively, the code element positions may be calculated, using Equations 33 through 55.
  • FIGURE 7a shows the rst part of the plot of the radiation intensity Et versus the design parameter K of the antenna of FIGURE 6.
  • FIGURE 7b showsy the same antenna array plotted out to values of KMAX equal to 30.
  • FIGURE 7c will be seen to be an expanded version near the origin of FIGURE 7b.
  • FIGURE 7c also shows Code No. l having 16 elements and Code No. 2 with 32 elements plotted on the same scale for comparison.
  • the antenna radiation pattern has been of the type where it is desired to produce a central lobe which has as high a maximum value relative to the side lobes as possible.
  • the central lobe is intended to be as narrow in angular degrees as possible.
  • the amplitude of the second and third side lobes is intended to be as low as possible, and, in addition, the occurrence of the second and third side lobes is intended to be pushed out as far in angular degrees as possible.
  • FIGURE 7c which is the combined plots of FIGURE 7a and FIGURE 3, the effect of adding 16 additional elements in Code No. 2, to produce an array having 32 elements can be appreciated.
  • the peak of the rst side lobe occurred approximately at a value of K equal to 1.25, as can be seen.
  • K5 was chosen to be equal to 1.25, that is, 5%.
  • a new additional null was chosen to be right in the middle of the first side lobe. In effect this squashed down the rst side lobe.
  • FIGURE 7a Examining FIGURE 7a near the region 00, it can be seen that the rst side lobe, and in fact the second side lobe, have virtually disappeared, their amplitude being so small relative to the main lobe that it is dicult to show it.
  • Code No. 2 has greatly improved the radiation pattern by the addition of more elements in a controlled manner chosen at the designers will.
  • antenna radiation patterns of virtually arbitrary shape can be produced by my method. For example, it may be desired ⁇ to concentrate a side lobe power in some angular region in space that is in a certain range of values for 0. To do this, it is only necessary -to place nulls outside of this region before the beginning of the region and after the end of the region, the resulting power then must appear in the region where nulls were not chosen.
  • nulls were not chosen.
  • FIGURE 2 will show that it is precisely symmetrical about the point located at 217.5". This is exactly the middle of the array, the furthermost element N16 being located at 435 electrical degrees. This physical symmetry is always produced, although the equations given would not indicate it by themselves.
  • FIGURE 10 shows a preferred embodiment of my invention.
  • Table IV gives Code No. 4 which gives the relative physical spacing which was plotted to scale in FIGURE 10.
  • the relative spacing may be arranged arbitrarily in increasing order of distance from the rst element N1. Then the rst half of the set of values may be plotted out, and this will produce the iirst half of the antenna.
  • the second half of the antenna will be exactly similar to this and in fact be the mirror image.
  • FIGURE 8 shows another embodiment of my invention also utilizing'a 16 element array. However, the values of K chosen for this array are different from that shown in Code No. 1.
  • the antenna utilizing Table III with Code No. 3 has been drawn in FIGURE 8 to scale and the resulting radiation pattern as a function of K is shown in FIGURE 9.
  • FIGURE ll The antenna radiation pattern as a function of K has been given in FIGURE llfor the antenna shown in FIG. URE 10 and Table IV, and FIGURE 12 shows the antenna radiation atterri as a function of the physical space angle TABLE III 0 for a vague of sin 00 equal to arc sin M5, namely 9.6.

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v FRAN/vk s. saufen? nigga/M07 /P ATTORNEY April 21, 1964 F. s. GUTLEBER 3,130,410
coDED LINEAR ARRAY ANTENNA Filed oct. 2s, 1961 12 sheets-sheet 11 INVENTOR. FRA/VK 6. GA/TLEHER ATTORNEY April 21 1964 F. s. GUTLEBER 3,130,410
Y s PAcE coman LINEAR ARRAYANTENNA Filed OCT.. 25, 1961 l2 Sheets-Sheet 12 FRANK s. gant-afk ATMRNEY United States Patent Oil ice f 3,130,410 Patented Apr. 2l, 1964 3,130,410 SPACE CODED LINEAR ARRAY ANTENNA Frank S. Gutleber, Wayne Township, Passaic County,
This invention relates to antenna systems and more particularly to methods and equipment for obtaining any desired antenna pattern from a linear antenna array.
Array antennas of a variety of types are well known in the prior art. These prior art antenna arrays have been of several types. One type has utilized a number of equally spaced antenna elements to build up an array. This type of simple array of equally spaced antenna elements which are provided with equal amplitudes of driving current or voltage produce an antenna pattern whose shape can be controlled to only a Very limited degree. A typical response of such an equally spaced antenna system with equal amplitude driving power at each individual element results in the well known sin x/ x radiation pattern. Although such a pattern can produce a narrow central lobe, it suffers from the defect that the irst side lobe is quite high in amplitude compared to the main lobe, and in fact the rst side lobe is down by only 1,4.72 or approximately 13 db. The values of the central or main lobe and the side lobes relative to each other can not be changed no matter how large a number of elements is provided in such an array. The relative values of the side lobes and the central lobe are xed by the geometry of the system. To' improve over such equally spaced linear array antennas, the prior art has resorted to a number of expedents which have been only partly successful. Schelkunol, for example, in United States Patent No. 2,286,839 shows an array antenna utilizing a number of equally spaced individual antenna elements. Schelkunofl` provides both an individual amplitude control device and an individual phase control device for each of the individual antenna elements that compose his array. In general the amplitude of the driving current which is applied to each of the antenna elements is different from the amplitude in other antenna elements. Likewise the phase of the signal applied to each of the individual antenna elements is in general different from that of other elements in the array. Schelkunoi'f provides a systematic manner of choosing the particular amplitudes and phases supplied to the elements of his array. However, these amplitudes and phases follow a polynomial distribution. Although this procedure resulted in a somewhat improved antenna pattern, it has a number of extremely serious drawbacks. The most important of these is the fact that, since diierent amplitudes of signal must be supplied to different individual elements, either transmitting stages of different individual design must be supplied, or else large amounts of available power must be dissipated in power dividing networks etc. to provide the required ratio of feed powers. Also, individual phase control must be supplied to each element. In addition to these practical disadvantages, serious vcomputations problems arise in attempting to design such an antenna array which utilizes individual elements unequally supplied with power at dif ferent phases, because the eiect of an individual antenna element on the array as a whole is by no means readily ascertained from the equations required for the design.
Other prior art systems have attempted to provide antenna arrays which likewise utilize the method of supplying unequal amplitude and phase signals to the individual antenna elements. For example, binomial coeflicients have been utilized to provide the amplitudes supplied to individual elements in the array. Such array antenna sysd tems likewise sufrer from thepractical defects of supply mg unequal power and phase to. the individual elements and from the computational diiiiculties involved which make diilicult or impossible the actual detailed design of a particular desired antenna pattern.
A further disadvantage of the prior art systems has resulted from the fact that many of these arrays are built up out of elements spaced in three dimensions from each other. That is,elements are placed at certain points within a given area and also above or below the plane of this area at certain elevations. The difficulty here arises when it is attempted to improve the radiation pattern -of the antenna by utilizing a large number of individual elements. The addition of new elements does not produce any effect which is readily predictable from the type of mathematical analysis provided in the prior art airay systems, and in fact it is often ditlicult to determine where, or in what part of the array, additional elements should be provided.
Therefore, it is an object of my invention to provide a systematic method for increasing the number of elements in an antenna array to systematically improve the resulting radiation pattern obtainable.
It is another object of my invention to provide a space coded linear array antenna which utilizes individual antenna elements which are fed with equal amounts of power and with equal amounts of driving current which may be supplied at the same phase.
It is a furtherv object of my invention to provide an array antenna system which obtains the maximum benelit possible from a given number of individual elements utilized to build up the array to provide an optimum radiation pattern in space utilizing this given number of elements.
It is a feature of my invention to provide an antenna array composed of a number of individual antenna elements which isan integral power of the base 2. A particular number of individual antenna elements are spaced unequally from each other so as to cause a predetermined effect on the antenna radiation pattern due to each set of elements which make up the array.
It is another feature of my invention to provied` a space coded linear array antenna in which all of the individual antenna elements may be driven with equal amounts of current or voltage and wherein the phase of the signal supplied to all of the individual antenna elements may be the same. The individual antenna elements in this array are placed at predetermined unequal distances from each other according to a systematic set of design equations which allow the production of an arbitrary desired antenna pattern utilizing a particular predetermined number of antenna elements.
It is another feature of the invention to provide a space coded linear array antenna whose design may readily be extended to provide a three dimensional radiation pattern in space with no further additional computation. This method allows the particular unequal coded locations of the individual antenna elements of a rst set of elements in the array to be extended to provide the pattern for the entire array. The entire two dimensional array may be driven by supplying equal power at the same relative phase to allof the individual antenna elements.
The above mentioned and other features and objects of my invention will become more apparent by reference to the following description taken in conjunction with the accompanying drawings in which:
FIGURE l is a diagram illustrating the geometry of an array antenna, as viewed from the top, which lis useful in deriving the equations involved;
FIGURE 2a is a schematic diagram of a 16 element array antenna representing a rst embodiment of my sin sin 00- for the antenna of FIGURE 2a;
FIGURE 4 is a plot of the radiation intensity field Et of the antenna of FIGURE 2a vs. the physical space angle 6';
FIGURE 5a is a schematic diagram of a two-dimensional array antenna which utilizes the antenna design of FIGURE 2a;
FIGURE 5b is a block diagram of a portion of the circuit used with the array antenna of FIGURE 5a;
FIGURE 6 is a diagram giving the relative spacing in correct proportion of a linear array antenna composed of 32 elements;
FIGURE 7a is a diagram of the radiation field intensity pattern Et plotted vs. the design parameter K for the antenna of FIGURE 6;
FIGURE 7b is a diagram on a smaller scale of the field intensity pattern Eb plotted vs. the physical space angle 0 for the array of FIGURE 6;
FIGURE 7c is a composite diagram of the field intensity of the arrays of FIGURES 6 and 2;
VFIGURE 8 is a diagram of an array representing a fourth embodiment of my invention and showing another possible coded spacing of an antenna utilizing a l6 element array.
FIGURE 9 is a plot of the lield radiation intensity Et produced by `the antenna of FIGURE 8 vs. the design parameter K;
FIGURE l0 is a diagram illustrating the preferred embodiment of my invention, representing an array antenna composed of 64 elements and designed according to my method;
FIGURE l1 is a plot of the eld radiation intensity Et produced by the antenna of FIGURE lO vs. the design parameter K;
FIGURE Il2 is a plot of the viield radiation intensity Et of the antenna of FIGURE 10 vs. the physical space angle 6.
Referring now to FIGURE 1, the general relationship is shown between the elements of a linear array which are unequally spaced from each other and showing the meaning of the space angle 0. 9 represents the direction of a line v drawn from the array along a particular direction which is of interest at the moment. The angle 0 represents the angle between x, the axis of the antenna, and the line v which may be moved about to examine any particular direction which is of interest. The radiated wave front is perpendicular to the line v as shown. For a linear array antenna, it is ordinarily sufficient to design for values of 0 which run only between 0 and 90 degrees. Because of symmetry, the antenna appears to produce the same pattern whether one stands on one side of the axis x or the other. Likewise, if the disposition and number of antenna elements is even and their distribution is symmetrical, the second quadrant will produce a pattern which is the same as the pattern in the rst quadrant and is in fact the mirror image of the pattern in the first quadrant. YFor this reason, it is necessary only to work with values of 0 between 0 and 90 degrees for linear array antennas. In the most general case, one would examine 0 for 360 of azimuth, but this is not necessary here. The Viirst two elements of the array are shown separated by a distance d1. The distance d1 sin 0 represents the ditference in distance that two Wave fronts starting from the two elements have traveled along the line v located at the angle 0. The different distances VlO which are traveled by the wavefronts from the individual elements results in ditferences in phases of the radiation from the individual elements at points removed from the antenna, as is well known in the antenna theory. There are a number of ways to characterize an expression for the total radiation due to an array, such as shown in FIGURE l, which has N elements. One representation which is particularly useful for our purposes is given in Equation l.
Where Et equals the intensity of the electric field radiated by the antenna, :1, e is the base of the natural logarithms, all of the amplitude coetiicients A1 through An 1 are either l or 0, and 5b is given by Equation 2.
In Equation 2, tI/:the phase of radiation; A equals the wavelength at the particular operating frequency of the antenna; 0 is the physical space angle, as explained above; and d is an elemental uniform distance which represents an equivalent average uniform separation of the antenna elements.
The actual antenna elements of the array are in general unequally spaced from each other, but the distance d is an equivalent uniform spacing which I use to demonstrate the utility of my method of creating the array. In all the equations e is the base of the natural logarithms. Alternately, the radiation from a linear array antenna may be represented by Equation 3:
(3) Et: 10+ A1eiNn0+ A2eiNz+ Aaemyq; All lestN-w where the terms N represent coded relative spacings of the individual antenna elements, the iirst element being located at the position N, the second element being located at the position N2, and so on. Either approach is equally valid, and it makes no difference which is used in the end result in the array.
To understand the rest of the derivation, it is well to give a general explanation of the technique which will be employed to create the array. Suppose, for example, that there are a given number of elements, say four, in an existing array. For any one of these four elements, another element can be added, that is, a fth element, such that at any given space angle 0, the radiation from the fth element would be exactly out of phase, that is, out of phase, with the radiation from the rst of the four elements. Likewise a second element, that is a sixth element, may be located a certain distance from the second element of the rst four, so as to produce radiation which is exactly out of phase from the radiation produced by the second element of the original array of four elements. In other words, if the position of the first four elements of the existing array were Vgiven as N1, N2, N3, N4 then to extend the array by adding elements which produce zero radiation along a given direction in space, that is, at a given value of 0, elements would be added at distances determined as follows:
Thus, the position of the iifth element, that is, the position N5, is equal to the position of the rst element N, plus an added increment of distance S1. S1 is so chosen to result in radiations which are completely out of phase from the elements N1 and N5.
Likewise to provide a null in the radiation pattern, that is, zero radiation intensity at some value of 0, it is necessary to place an additional element the same incremental distance Sl from each of the original elements in the array. Thus, in Equation 5:
Two more elements N7 and N8 are likewise placed in the same manner from the elements N3 and N4. This tech` nique of building up the array allows a design wherein at certain points in space at certain values of thek angle 6, nulls'are produced in the radiation pattern. It remains however to provide a systematic manner of choosing the incremental distances, such as S1, which must be added to the existing members of the array to produce the next set of members to increase the size of the array.
' .Referring `again either to Equation 1 or Equation 3, we can write Equation 6:
Where ZN=ANeJ`NX,b, a general term of the series given iu Equation l or Equation 3.` For -any particular element -in an existing array, a -second element can be placed a particular distance from this {rst element, such that the radiation is 180 out of phase. This is the meaning of Equation 6. Therefore, lfor the next element, that lis NCLH), the relationship given in Equation 7 prevails:
Thus, the neX-t element is given in terms depending upon the previous element. In the quantity 2d sin 6 the quantity 2 occurs because an out-of-phase condition has been chosen.
:It is now necessary to provide a method of picking S1 (of Equation 4) in terms of some design parameter that will allow a relatively easy manipulation of the design lparameters with a minimum of calculation. At the same time, lit is desirableto pick the design parameter in such a manner that the .total etfect of all of the elements in the array when it is considered -at any particular given value of 6 can be predicted. I now choose anarbitrary design factorv K -in such ya manner. Consider Equation 11.
l Let -d sin 6 Equation 11 is true by deiinition, that is, K was chosen in thismannen From Equation 77 substituted back into Equation 10, Equation 12 Ifollows:
12) Then N X+D=NX+1T lEquation 12 states that to form a new element position CN(X+1), we add the Vquantity 1/ 2K to the previous element position NX. In other words, S1 equals 1/2K1. Equation 12 thus indicates the basic method for building up the array. Each time it is desired to extend the array by increasing the number of elements, the size of the array will be doubled. lFor each existing element, one more element will be added. Each of the added elements will be the distance 1/2K from its own corresponding previous existing element.
-However, the quantity K can still be chosen in such a manner as to facilitate design procedures and to make as' simple Vas possible the computations involved. For this reason, the following steps are taken. Eirst, 60 is dened as the physical space angle where the rst null of the antenna radiation pattern occurs. Now K1 is made equal to 1 at the dirst null when 6 equals 60. By doing this,
the entire design of the array is normalized This will become more apparent as the explanation proceeds. With K equal to 1 and 6 equal to 60, then Equation 1l becomes Equation 13A.
)t 3 (l A) 1 d sin 6 l Equationl3A may n-ow be rewritten as Equation 13B:
(13B) *sin 60 be obtained which show that K equals the ratio of sin 6 divided -by sin 60:
(14A) t sin o (14B) 1p sin 6 d sin 6 A sin 6 (15) K" t sin o., a
sin 6 (16) *sin 60 In other words, K is the ratio of the sine of any particular value of the space angle 6 divided by the sine of the particular space angle where the null of the first lobe occurs, that is, the main lobe of the antenna radiation pattern. Thus Equation 14B can be rewritten by substituting K for sin 6 sin 60 as given by Equation 16:
1{/=(360)K The actual physical position of an element is equal to which, when the above value of yb is substituted, may be written:
sin 6 goNxilf-soNxK-wx sin 00 Now the actual physical coded spacings of the antenna array occur for sin 6:1. In other words at 6 equal to This is because at 6 equal to 90, the array is being examined directly broadside, that is from a side elevational view. Thus Equation 18 gives the physical coded space relationship.
360 Nsin 6 Equation 18 is given in units of wavelengths, that is, depending on .the particular value sin 60 which is chosen, an actual physical array can be built. 60 -it should be remembered, is the angle in space where the rstnull occurs `for the antenna radiationV pattern. Equations 12, 17 and 18 provide the basis .for computing al1 of the required quantities to buid the array with any arbitrary antenna pattern.. To illustrate this, Equation 12 will be rewritten providing an actual index X which indicates how the particular values of K which have been chosen as arbitrary design factors are incorporated to build up the next step of the array.
The basic procedure is this: To forman array of larger size, the number of elements in the array must be doubled. This is because each existing element of the previous array must have added to i-t, that is, placed some distance from it which we have denoted by S, another element (whichv N ab will produce at some particular space angle 0, the radiation which is 180 out of phase with the radiation from this corresponding element of the previous array; Thus, the number of elements in the -array must be a power of 2. An array built according to my method therefore may consist of 2 elements, 4 elements, 8 elements, 16` elements, 312 elements, 64 elements, and so on, but the number of elements in the array will always be a power of 2. Likewise, for each ladditional power of 2. 'which is created when the size of the array is doubled, -another arbitrary value for the design constant K may be chosen. =In other iwords, in an array which has 16` individual antenna elements, four values of K may be chosen arbitrarily. This is because 2 to the 4th power is equal to 16, and the array is in a sense composed of four sets of elements which have been spaced in relationship to each other to produce the result according -to my method.
Equations 19, 20 and 21, written below, symbolize this procedure. -In Equation 19, N1 is the iirst element of an existing array. T o increase the size of the array, another element must be added. This is the term 1N 2X+1) which is the iirst new element of the next set which is being added to the array. This term N 2X+1 represents lan element which must be spaced a distance 1/2K(X+1) from N1.
Stated in another way, Equation l19 shows how to locate the Ifirst additional element when the array is being increased from a given size. Likewise, Equation 2O shows how to add the second new element of the increased array. Equation 21 shows how to add the last element to increase the array to its iinal size.
It should be noted that the subscripts yare powers of 2. X is simply an index number which takes on integral values as the size of the array increases. For an array which has two elements, X is equal to tor an array that has four elements, X is equal to l; for an array that has 8 elements, X is equal to 2; for an array that has 16 elements, X is equal to 3; :and so on. Every time the size of the array is doubled, that is, every time X increases one unit, this allows one additional value of K to be arbitrarily chosen.
Where X=0, 1, 2, 3, etc.
A discussion of the dirst embodiment of our invention shown in FIGURE 2 and some examples will make clear the procedure which can actually be performed extremely rapidly with pencil .and paper in most cases. Referring to FIGURE 2, there is shown a linear array antenna composed of 16 individual antenna elements numbered 1 through 16. This drawing is in correct relative scale, that is, the correct relative spacing `of all the elements is actu-ally given in FIGURE 2. A scale is provided in normalized electrical degrees running from 0 degrees, which is the reference value of the tirst element :1, up to 450. The location of the last element 16 is at 435 electrical degrees. The values used for K to create this may are K1 equal to 1, K2 equal to 1%, K3 equal to 2 and K4 equal to 4. Thus with an array of 16 elements, four values of K may be chosen arbitrarily. A translation device 17, which might be a transmitter or receiver, for example, is shown connected to the 16 elements of the array by feed lines such as 18,\.18a,l18b,and so on. Equal amounts of power are supplied to each one of the 16 elements in the antenna array; likewise the phase of the signal from the device 17 is exactly the same for each of the 16 elements.
I shall now illustrate [with some examples how this array of FIGURE 2 is designed and will show the re- S sultin-g design'curves and the resulting radiation pattern in space. Next to each one of the elements in the array, the identifying position notation such as N1, N2 etc. has been written, so that the elements of the array can be identiiied. p |It should be noted that, although once the array is built, it makes no difference what any particular element is called, in actually designing the array, the numbering of the elements is important until the design has been coma pleted. This is the reason that element N9, for example, is next to element =N1. Likewise the next element proceeding from left to right -is N5 and then N3. 'I'he reason for this will be made clear by the example. In actual physical constructions, since all of the elements are the same, and since each is ifed with the `same amount of power at the same phase, it makes no difference whether or not their notation is preserved.
Code No. 1 is given below:
TABLEHI Code N0. 1 (shown in FIGURES No. 2 and No. 5)
16 element code with forced nulls `chosen at:
K1=\1, K2'=072, K3=2, K4=4 Actually the values listed are N1, .N2 etc. in this table are ipN1, gbNz. In other words, these are normalized electrical degrees and they do not yet represent physical distances, although they tare in the cor-rect relative proportion to each otherto represent physical distances. I have used a shorter notation, such as N1, for the berivity of presentation. These values here are the same as those shown in FIGURES 2 (and 5), as can be veriiied by the reader by simple comparison. 11 lwill show by example how these values for this iirst antenna array were obtained. First, for convenience, the iirst element of the array N1, element l1 of FIGURE 2 is taken as having zero phase, that is, it is the reference element.Y All other elements will be positioned in reference to this first element. Utilizing Equation 19, it is readily perceived where the next element is to be placed. The next element N2 will now provide an array of t-wo elements, this allows exactly one value of Kto be chosen. K has been equal to 1, as indicated before, .to provide a normalized design for convenience. Thus, from Equation 19, it may be seen in Equation 22B, below, that the second element should be placed '180 out of phase with the rst element.
This is actually the basic technique of our invention: to place each successive element out of phase with its corresponding element from the previous array. It should be noted that Equations 19 and 22A actually give the calculation of the positions in terms of the design parameters K. K, in the present instance equals l. Multiplying by 3,60 then converts into electrical degrees, sinceV there are 360 electrical degrees for one wavelength of radiation. However, this is an arbitrary calculation, and
if it is more convenient, the values may be left in the form shown in Equation 22A, namely 1/2, for example,
and the conversion need be done only atv the end. For
the time being, the readers visualization is greatly assisted by converting into electrical degrees.
It should also be remembered that these electrical degrees to be converted into the distances in space depend Obviously on the actual operating frequency chosen for the antenna, since the wavelength changes physically for different frequencies. However, the values given in the Table I also depend upon the particular design parameter 60 which can also be chosen at will, as was indicated in Equation 16. This will also be made clear by the later discussion.
So far the array consists of two elements, namely, N1 and N2. It is now desired to increase the size of this array to four elements. To do this, consider Equation 19. The index X is now equal to l, in other words, a second value K2 for the designed parameter K can be chosen. I have chosen K2 to equal 3/2. Thus from Equation 19, Equation 23 can be written:
The position of the third element of our array can be calculated. It should be remembered 'that each time a power of two is reached in the number of elements in the array, it is necessary to start over and begin adding elements starting from the irst element. In other words, the third element is added to the rst element. The fifth element will be added to the iirst element; likewise, the sixth element will be added to the second element. This is because an array must consist of a number of elements which is a power of two due to the design procedure which is utilized. Thus N3 is equal to 120, since K2 was chosen to be 3/2. .If K2 had been chosen a different value, the position of element N3 would of course be different.
The reader, by examining these equations, will readily perceive that they are simply special cases of Equations 19, 20 and 21 which define the procedure for calculating the additional elements of the array. Thus, when the array reaches 4 elements, the fth element is calculated using the third value, K3, for the design parameter K. Likewise when the array reaches 8 elements, to add the ninth element, the next arbitrary Value K., for the design value K is used. Here K3 is equal to 2 and K4 is equal to 4. The only limitation on the choice of the design values K is that they be numbers greater than one, this is to keep the design normalized with K1 equal to 1. Other than that, K values may be chosen as integers, fractions, irrational numbers and so on.
This also provides an opportune place to point out the distinct advantage of my design procedure. Suppose,
10 l for example, that the design of an array is proceeding and three values of K have been chosen, namely, K1 equal to l, K2 equal to 72, and K3 equal to 4. There are now eight elements in the array, it is desired to add eight more elements and create a 16 element array. An inspection of the plot for the eight elements reveals that it would be desirable to place K4 equal to 2. This is readily done and creates no diiiiculty whatsoever. The 16 element array which results will be exactly the same as that shown in Table I and it makes no difference in what order the particular values of the Ks are chosen. The reader can readily verify this for himself by calculating the elements using the same set of K Values but in a different order.
If the four values for K are chosen as l, 4 and 2 in any order, the numbering of the elements will change in general. However, the relative spacing of the 16 elements will result in an array that is exactly identical to that shown in FIGURE 2 for any ordering of the design Ks. This can be veried by the reader himself in a few moments of calculation. n
Thus, at each step in the array, if the array is increased in size, the dcsignercan review the radiation pattern produced by the number of elements used up to that point and he can pick the additional elements and place them so as to provide an improvement in the radiation pattern and never a degradation. This is a distinct advantage over the prior art design procedures. The addition of Imore elements to the array always improves the radiation pattern and canV never degrade it.
Likewise, there is another feature of great importance in my method of building antennas. array is to be made up of 32 elements. Using the procedures outlined above, the first 16 elements of the array are calculated and their locations noted. Now, one more value for K5 is to be chosen. If the lirst four K values are not changed, the position of the first 16 elements of the array is in no Way affected by the addition of the next 16 elements. Thus the benelicial results obtained from the rst part of the calculations will never be lost or degraded by the addition of additional elements to the array. This is an unusual result and obviously extremely advantageous. Those skilled in the art will appreciate the design and practical advantages of being able to add elements to an array with an assurance that the pattern already obtained can not be degraded, but only improved by the addition of more elements. An example will be given in connection with FIGURE 6 which shows a 32 element array.
I have now explained my design procedure and the process for determining the coded spacings for my antenna elements. For future reference, I now tabulate in algebraic form the general equations for calculating the positions of the elements of an array up to and including 64 elements, that is, 2 tothe power 6, which allows the choice of six values for K, the arbitrary design factor. These equations are simply Equations 19, 20 and 21 written out in algebraic form where each previous element is kept in the algebraic form involving the previous design values chosen for K. These 64 equations are unchanging and they present the general equations for calculating the position of any size array up to'64 elements, that is an array of 2, 4, 8, 16, 32, or 64 elements. The actual positions, of course, depend upon the values chosen for the design parameter K. Although the 64 equations presented here, numbered 33 through 96, appear to be in a rather awkward form, actually there is a practical advantage in presenting these calculations in this manner, rather than using the simpler form of calculation indicated by equations, such as 19. This will be pointed out in particular with reference to FIGURE l0 which shows the left half of a 64 element array.
Returning now to FIGURES 2 and 3, FIGURE 3 shows the plot of the radiation intensity Et of the antenna of FIGURE 2, plotted versus the design factor K. It should be stressed that this plot is in K and not yet in Suppose that an` space angle which will illustrate another'important advantage of our method and system. It can indeed be seen that nulls occur in this pattern, that is, zero values of radiation at values or" K equal to 1, 2, 11/2, and 4, as was indicated by our original choice of the values of K1, K2, K3, and K4. In general, one of the advantages of our design procedure is to form the design using plots, such as FIGURE 3, where the abscissa is in units of K. This greatly facilitates the design, and it results in a normalized design which can be adapted for a number of other conditions by certain physical spacing when it is actually constructed.
It may be noted in FIGURE 3, that the central lobe is extremely sharp and contains a large percentage of the total energy emitted from the array. The total integrated area under the graph represents the total energy emitted by the 16 elements of the antenna of FIGURE 2. Once a particular code has been picked, utilizing given values for K, the radiation pattern can be plotted in terms of K by utilizing Equation 3 which is now rewritten as Equations 98A, 98B and 98C.
all N 2 all N 2 (98C) EF cos Nif) +(Z sin Na) all N where E signifies the summation for all n terms present in the code;
all N 2 all N 2 In Equation 99, E, is given as a function of K. To form the plot, a value for K is picked, then Equation 99 is calculated and yields a value for Et. Then K is increased a convenient increment and Equation 99 is recalculated forthe new value of K, and so on, for the particular array which has the fixed relative spacing depending upon the design parameters of the constants K1, K2, K3 etc. which have been chosen. This plot of E, versus K is shown for the array of FIGURE 2 in the illustration of FIGURE 3. To evaluate Equation 99, only values of K within a region up to a value of KMAX equal to l/sin 00 need be chosen.
In FIGURE 4, the radiation pattern of the antenna of FIGURE 2 has been shown plotted against 0, the physical space angle. To form this plot sin 00 was chosen as equal to 1/6. In other words, @o equals 9.6"' This represents the width of the first lobe, or the main lobe, that is, the point along the 0 axis where the first null occurs, as shown on the diagram. It should be noted that, since sin 0 is equal to K sin 0G, there is no linear correspondence between the values of K and the values of 0, even for a fixed value of 00. This is because 0 and K sin 00 are related by the sum of 0 and not one to one. This causes no computations diiculties, however. It should also be noted that a variation of 0 through 90 physical degrees is sufiicient to specify the full performance of the antenna pattern as was mentioned previously. An examination of FIGURE 3 shows that nulls occur in fact at values of K equal to l, W2, 2 and 4. This is as expected, since these Vpoints were picked to be forced nulls according to the principle of my method of designing array antennas.
FIGURE 5 shows a second embodiment of my invention which illustrates the extreme practical utility of my antenna arrays and the method of building them. The gure shows a similar codedV array, as in FIGURE 2, extended into a two dimensional array. It is a plan view of the array, and the individual antenna elements have been simply shown as dots for convenience. The correct relative proportions are shown and the scale is the same as in FIGURE 2. FIGURE 5 was created from FIGURE 2 with no further computation. The array'antenna of FIG- URE 5 provides an antenna radiation pattern in three dimensions in space, that is, not only does it provide the radiation pattern shown in FIGURE 4 in the plane of the axis of the array of FIGURE 2, but it provides this same pattern in a plane perpendicular to the plane containing the axis of the 16 elements of FIGURE 2.
An inspection of FIGURE 5 will quickly reveal its pattern. The first row across, consisting of 16 individual antenna elements, which might be dipoles, dicones, horns etc. or whatever is convenient, are numbered 1 through 16 and are numbered corresponding to FIGURE 2. It will be seen that the second row of antenna elements, relative to each other, is spaced exactly the same way as the first row. Thus, element 19 which is the first element of the second row is 45 electrical degrees from element 20 which is the second element of the second row. Likewise element 21 is exactly 45 electrical degrees from element 20, just as element 5 is 45 electrical degrees from element 9 in the rst row. However, the entire second row, such as elements, 19, 2t), 21, 22 and so on, is spaced the same distance from the first row as element 9 is spaced from element 1, namely 45 electrical degrees. The rst element of the third row, element 23, is the same distance from element 19 as element 5 is from element 9 in the first row. Likewise element 24, which is the iirst element of the fourth row, is the same distance from element 2'3, as element 3 is from element 5 in the iirst row. Also element 25, which is the second element in the fourth row, is the same distance from element 24 as element 9 is from element 1 in the iirst row. The pattern is extended in this manner, as shown, as it will be seen that along any line of elements, either horizontal or vertical, the relative spacing is exactly the same as that shown in FIGURE 2 or the rst row in the array of FIGURE 5.
Thus, the spacing of the array along a single axis, such as shown in FIGURE 2, in actuality also completely spaces the location of all the elements of a square array consisting of nXn elements, where n is the number of elements in the single axis array. The total number of elements, shown in FIGURE 5 is 16 squared, that is, 256 elements. Y Y Y Y Y This property of my antenna arrays, that they may be reproduced in two dimensions to create a three dimensional antenna radiation pattern is obviously of great practical utility and is true of all antenna arrays created according to my method, and Vaccordingly the embodiments of FIGURES 6 and 10 also may be extended in two directions in the same manner.
For convenience of illustration, I have only shown the embodiments ofFIGURES 6, 8 and 10 along a single axis. But the embodiments of FIGURES 6, 8 and 10 may likewise be extended into a two dimensional square array in the same manner, and I claim such two dimensional arrays as part of the novelty of my invention.
Just as in FIGURE 2, the antenna elements of FIG-Y URE 5 should be supplied with equal amounts of power from a source providing the same phase of signal to each of the elements. ForV convenience, the translation device, such as 17, has not been shown in FIGURE 5b.
For such a relatively large array as is shown in FIG- URE 5, it may be more convenient if a separate power transmitting stage is connected to each of the elements and supplied with a low power level signal from the same local oscillator, for example, as indicated schematically in FIGURE 5b.
FIGURE b merely illustrates what has been mentioned before, that each of the individual antenna elements of my array, such as N1 or N9 or N7 can be individually supplied with a high power transmitting stage for sending purposes for use of the array as a transmitting antenna and with an individual amplier for using the array for receiving purposes. Each of the power transmitting stages, such as 26, 27, 28, and so on, can be exactly identical in design; each transmitting stage, 'such as 26, supplies the same amount of power to its individual antenna element as all the other transmitting stages. Thus, these transmitting stages might consist of an individual travelling wave tube, for example, With an associated power supply and frequency control circuits.
As a result, these individual transmitting stages can each be made to operate at its peak point of design eiciency, and there is no necessity for wasting RF power in power dividing networks for providing unequal amounts of power to the individual elements.
Likewise for receiving purposes, if desired, each individual antenna element such as N1 may be provided with a high gain, low noise amplifier, such as 29, 30, and 31. Each of these amplifiers is exactly the same as the others and provides an equal amount of gain. This also allows the output from each individual antenna element to be amplified immediately before passing to the connecting lead networks such as 32, where it is connected to the input o'f the rest of the receiver equipment.
Obviously, if desired, the ampliier, such as 29, and transmitting stage, such as 26, may be omitted and the array of FIGURE 5 may be supplied with one single transmitting or receiving apparatus, as indicated in FIG- URE 2, by the use of multiple feed lines, such as shown as 18, 18a, 18b, and so on. Whichever is most convenient for a particular application will be used. The individual amplifiers and transmitting stages, such as 26 and 29, can be physically disposed extremely close to the individual antenna elements in the arrays built according to my method.
Refer now to FIGURE 6, which shows the correct relative spacing for an array antenna built according to my method and composed of 32 individual antenna elements, spaced according to Table II.
TABLE II Code N0. 2 (shown in FIGURE 6) 32 element code with forced nulls chosen at:
`when building up Code No. 2 with a 32 element array.
The fth value K5 has been chosen as 5A.. The quan- 14l tity 1/2K5 is thus equal to 144 electrical degrees and the 16 new values for Code No. 2 may be formed by adding 144 increments to the appropriate terms inl Code No. 1, as has been outlined in the previous development, particularly Equations 19, 20 and 21. Alternatively, the code element positions may be calculated, using Equations 33 through 55.
FIGURE 7a shows the rst part of the plot of the radiation intensity Et versus the design parameter K of the antenna of FIGURE 6. FIGURE 7b showsy the same antenna array plotted out to values of KMAX equal to 30. FIGURE 7c will be seen to be an expanded version near the origin of FIGURE 7b. FIGURE 7c also shows Code No. l having 16 elements and Code No. 2 with 32 elements plotted on the same scale for comparison.
It is important to point out at this time a further additional advantage of my method of building antennas. My design, as so far explained, permits a given number of values for the design parameter K to be chosen in an arbitrary manner, depending upon the number of elements in the array. At these chosen values of K, such as K1, K2, K3 and so on, there will be zero radiation in space at the corresponding space angle 0. It can now be stated that in addition there will be a null at every odd integral multiple of the chosen values of K. Thus, if K1 is equal to 1, nulls will also be produced at values of K equal to 3, 5, 7 and so on. Likewise if K2 is chosen to be 5%?, there will be nulls produced at 4.5, 7.5 and so on. Inspection of FIGURE 3 will clearly reveal these nulls which have been circled lightly with dotted lines. This property of the presence of nulls at all odd integral values for all the chosen values of K, in eiect allows double duty to be performed by the chosen values of K.
The values of K which are chosen depend on what type of radiation pattern is to be produced. In the examples given so far, the antenna radiation pattern has been of the type where it is desired to produce a central lobe which has as high a maximum value relative to the side lobes as possible. In addition the central lobe is intended to be as narrow in angular degrees as possible. Further, the amplitude of the second and third side lobes is intended to be as low as possible, and, in addition, the occurrence of the second and third side lobes is intended to be pushed out as far in angular degrees as possible.
By comparing FIGURE 3 with FIGURE 7a, and by referring to FIGURE 7c, which is the combined plots of FIGURE 7a and FIGURE 3, the effect of adding 16 additional elements in Code No. 2, to produce an array having 32 elements can be appreciated. Thus, in FIG- URE 3, the peak of the rst side lobe occurred approximately at a value of K equal to 1.25, as can be seen. Note, that in Code No. 2, FIGURE 7a, K5 was chosen to be equal to 1.25, that is, 5%. Thus, a new additional null was chosen to be right in the middle of the first side lobe. In effect this squashed down the rst side lobe. Examining FIGURE 7a near the region 00, it can be seen that the rst side lobe, and in fact the second side lobe, have virtually disappeared, their amplitude being so small relative to the main lobe that it is dicult to show it.
It can also be seen in FIGURE 7a that an additional null has been produced at K equal to 3.75. This is 3 times 1.25. This additional null at 3.75 had the effect of considerably reducing the magnitude of the fourth side lobe, as can be seen on FIGURE 7c, by comparison of the two curves.
Also note in FIGURE 7c that the sharpness of the main lobe of the 32 element array of Code No. 2 has also been improved.
It can be appreciated that Code No. 2 has greatly improved the radiation pattern by the addition of more elements in a controlled manner chosen at the designers will. Likewise, I wish to point out that antenna radiation patterns of virtually arbitrary shape can be produced by my method. For example, it may be desired `to concentrate a side lobe power in some angular region in space that is in a certain range of values for 0. To do this, it is only necessary -to place nulls outside of this region before the beginning of the region and after the end of the region, the resulting power then must appear in the region where nulls were not chosen. In other words, by being able to choose points in space that have nulls, in effect the maximums of the radiation pattern must exist. in other regions in space, since the total energy supplied to the antenna cannot change, and in effect the designer can locate maximums of radiation by specifying where the minimums occur.
I now wish to point out another feature of my invention vwhich is quite convenient from the viewpoint of physical construction and also as a check of the accuracy of computations. Examination of FIGURE 2 will show that it is precisely symmetrical about the point located at 217.5". This is exactly the middle of the array, the furthermost element N16 being located at 435 electrical degrees. This physical symmetry is always produced, although the equations given would not indicate it by themselves.
This physical symmetry of the codes also indicates that the method of derivation rests on solid physical It will be seen that two. of the K values are the same, namely, l and However, in Code No. 3,'FIGURES 8 and 9, K2 has been chosen as 5A and K4 has been chosen at 11/6. It can be seen from inspection of FIGURE 9 that the first side lobes have immediately been tremendously reduced by this expedient. In Table III presenting Code No. 3, I have simply presented the relative spacing location of the elements in order of increasing value, their computation is exactly the same as that given in Equations 19, 2() and 2l, but the element numbering according to the equations has not been preserved. To distinguish that the elements are arranged simply in order of increasing physical location, I have labeled the locations as P1, P2 and so on, in Table III.
FIGURE 10 shows a preferred embodiment of my invention. Table IV gives Code No. 4 which gives the relative physical spacing which was plotted to scale in FIGURE 10.
TABLE IV foundations, because, as noted, the space angle 0 has only been considered over 90, since the array was stated to be one which will produce symmetrical radiation patterns to begin with. Likewise, in computation, when an array has been completed, if its is plotted out to scale, as shown in FIGURES 3, 5, 8 and 10, and, in fact, the antenna pattern is not symmetrical, then a mistake has been made in the calculations.
This may suggest to the reader a method of saving computations by computing only the equations necessary for one half of the array and then simply duplicating the array about the axis of symmetry. Unfortunately, however,` it is not usually readily apparent which particular elements will lie on one particular side of the array; this is because physically, as the elements are calculated, they are interleaved with the previous existing elements of the previous array and as a result a higher numbered element does not necessarily lie farther from the rst element than a corresponding lower numbered element. Thus, for example, element N9 is actually much nearer 45 to element N1 than element N3 is, and so on.
However, once the array has been calculated completely, the relative spacing may be arranged arbitrarily in increasing order of distance from the rst element N1. Then the rst half of the set of values may be plotted out, and this will produce the iirst half of the antenna. The second half of the antenna will be exactly similar to this and in fact be the mirror image.
FIGURE 8 shows another embodiment of my invention also utilizing'a 16 element array. However, the values of K chosen for this array are different from that shown in Code No. 1. The antenna utilizing Table III with Code No. 3 has been drawn in FIGURE 8 to scale and the resulting radiation pattern as a function of K is shown in FIGURE 9.
The antenna radiation pattern as a function of K has been given in FIGURE llfor the antenna shown in FIG. URE 10 and Table IV, and FIGURE 12 shows the antenna radiation atterri as a function of the physical space angle TABLE III 0 for a vague of sin 00 equal to arc sin M5, namely 9.6.
Code No 3 An inspection of FIGURE i2 wiii immediateiy make 16 element Code with forced nuns chosen at: apparent to those that are skilled in the antenna art that K1=1 [(3:572 65 this antenna radiation pattern is quite unusual. It can be Kzzf/g Kzll5 seen that the main, that is the central lobe, is quite sharp in angular degrees and in fact the width of the main beam P1=0 P9=278-18 at the one half power point is only 5 angular degrees. P2=98-18 P10=3O0 In addition, the rstvtwo side lobes are so low in magni- P3=120 P11=324 70 tude they can hardly be plotted to the same .scale as the P4=144 P12=362-18 main lobe. Further, the rst side lobe which has an l P5: 180 P13=398,18 appreciable amplitude, the third side lobe, haso been physi- P6=218-18 P14=422-18 cally moved out to the region beyond 20 Such an P7=242-18 PM2/444 antenna has an extremely sharp beam which would b e ex- P3=264 75 cellent, for example, for tracking radar service or highly

Claims (1)

1. A LINEAR ARRAY ANTENNA COMPRISING N INDIVIDUAL ELEMENTS, WHERE N IS AN INTEGRAL POWER OF THE BASE 2, AND MEANS FOR SUPPLYING THE SAME AMOUNT OF POWER IN THE SAME SIGNAL PHASE TO EACH OF SAID N INDIVIDUAL ELEMENTS, THE SPACING BETWEEN SAID INDIVIDUAL ELEMENTS BEING DETERMINED BY THE VALUES SELECTED FOR K(X+1), WHERE K IS A DESIGN PARAMETER AND IS THE RATIO OF THE SINE OF ANY PARTICULAR VALUE OF THE SPACE ANGLE 0, FORMED BY THE AXIS OF THE
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Cited By (10)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US3780372A (en) * 1972-01-17 1973-12-18 Univ Kansas Nonuniformly optimally spaced antenna array
US4071848A (en) * 1976-11-26 1978-01-31 Bell Telephone Laboratories, Incorporated Thinned aperiodic antenna arrays with improved peak sidelobe level control
US4431999A (en) * 1978-12-18 1984-02-14 The United States Of America As Represented By The Secretary Of The Army Interference cancelling system using a notch and omnidirectional antenna
US4498083A (en) * 1983-03-30 1985-02-05 The United States Of America As Represented By The Secretary Of The Army Multiple interference null tracking array antenna
US4500883A (en) * 1983-03-07 1985-02-19 The United States Of America As Represented By The Secretary Of The Army Adaptive multiple interference tracking and cancelling antenna
US4580141A (en) * 1983-09-19 1986-04-01 The United States Of America As Represented By The Secretary Of The Army Linear array antenna employing the summation of subarrays
DE3330672A1 (en) * 1982-08-27 1988-01-28 Thomson Csf METHOD FOR IMPULSE COMPRESSION BY SPACE CODING AND APPLICATION OF THE METHOD IN A RADAR DEVICE
US4724441A (en) * 1986-05-23 1988-02-09 Ball Corporation Transmit/receive module for phased array antenna system
US20110298676A1 (en) * 2009-10-22 2011-12-08 Toyota Motor Europe Nv/Sa Antenna having sparsely populated array of elements
CN110967671A (en) * 2018-09-28 2020-04-07 松下知识产权经营株式会社 Radar device, moving object, and stationary object

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Publication number Priority date Publication date Assignee Title
US1908595A (en) * 1925-10-19 1933-05-09 Rca Corp Aerial system for use in wireless telegraphy and telephony
US1922115A (en) * 1930-04-12 1933-08-15 American Telephone & Telegraph Antenna array
US2906363A (en) * 1955-05-06 1959-09-29 Jersey Prod Res Co Multiple transducer array
US3056961A (en) * 1957-08-15 1962-10-02 Post Office Steerable directional random antenna array

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US1908595A (en) * 1925-10-19 1933-05-09 Rca Corp Aerial system for use in wireless telegraphy and telephony
US1922115A (en) * 1930-04-12 1933-08-15 American Telephone & Telegraph Antenna array
US2906363A (en) * 1955-05-06 1959-09-29 Jersey Prod Res Co Multiple transducer array
US3056961A (en) * 1957-08-15 1962-10-02 Post Office Steerable directional random antenna array

Cited By (13)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US3780372A (en) * 1972-01-17 1973-12-18 Univ Kansas Nonuniformly optimally spaced antenna array
US4071848A (en) * 1976-11-26 1978-01-31 Bell Telephone Laboratories, Incorporated Thinned aperiodic antenna arrays with improved peak sidelobe level control
US4431999A (en) * 1978-12-18 1984-02-14 The United States Of America As Represented By The Secretary Of The Army Interference cancelling system using a notch and omnidirectional antenna
DE3330672A1 (en) * 1982-08-27 1988-01-28 Thomson Csf METHOD FOR IMPULSE COMPRESSION BY SPACE CODING AND APPLICATION OF THE METHOD IN A RADAR DEVICE
US4853701A (en) * 1982-08-27 1989-08-01 Thomson-Csf Pulse compression method employing space-coding, and its application to a radar
US4500883A (en) * 1983-03-07 1985-02-19 The United States Of America As Represented By The Secretary Of The Army Adaptive multiple interference tracking and cancelling antenna
US4498083A (en) * 1983-03-30 1985-02-05 The United States Of America As Represented By The Secretary Of The Army Multiple interference null tracking array antenna
US4580141A (en) * 1983-09-19 1986-04-01 The United States Of America As Represented By The Secretary Of The Army Linear array antenna employing the summation of subarrays
US4724441A (en) * 1986-05-23 1988-02-09 Ball Corporation Transmit/receive module for phased array antenna system
US20110298676A1 (en) * 2009-10-22 2011-12-08 Toyota Motor Europe Nv/Sa Antenna having sparsely populated array of elements
US8482476B2 (en) * 2009-10-22 2013-07-09 Toyota Motor Europe Nv/Sa Antenna having sparsely populated array of elements
CN110967671A (en) * 2018-09-28 2020-04-07 松下知识产权经营株式会社 Radar device, moving object, and stationary object
US11448725B2 (en) * 2018-09-28 2022-09-20 Panasonic Intellectual Property Management Co., Ltd. Radar apparatus

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