Self-contained progressive-phase GPS elements and antennas

A self-contained four-dipole element provides a 360 degree phase-progressive-omnidirectional (PPO) circularly polarized antenna pattern. Via a single signal port, a PPO excitation network incorporated into the element excites the four dipoles at phases differing by successive 90 degree increments. The four-dipole element is adapted for efficiently reproducible fabrication using printed circuit techniques. Antennas employing a stack of the elements provide a hemispherical antenna pattern with PPO circular polarization and a sharp cutoff below horizontal. For GPS reception in Differential GPS aircraft landing applications, a 21 element antenna provides multipath suppression and a unitary phase center enabling avoidance of signal phase discrepancies. More or fewer elements may be employed in other applications.

RELATED APPLICATIONS
 (Not Applicable)
 FEDERALLY SPONSORED RESEARCH
 (Not Applicable)
 BACKGROUND OF THE INVENTION
 This invention relates to antennas to receive signals from Global
 Positioning System (GPS) satellites and, more generally, to self-contained
 progressive-phase-omnidirectional elements and antennas utilizing a linear
 vertical array of such elements.
 Antenna systems providing a circular polarization characteristic in all
 directions horizontally and upward from the horizon, with a sharp cut-off
 characteristic below the horizon are described in U.S. Pat. No. 5,534,882,
 issued to A. R. Lopez on Jul. 9, 1996. Antennas having such
 characteristics are particularly suited to reception of signals from GPS
 satellites.
 As described in that patent, application of the GPS for aircraft precision
 approach and landing guidance is subject to various local and other errors
 limiting accuracy. Proposed implementation of Differential GPS (DGPS)
 would provide local corrections to improve accuracy at one or more
 airports in a localized geographical area. A DGPS ground installation
 would provide corrections for errors, such as ionospheric, tropospheric
 and satellite clock and ephemeris errors, effective for local use. The
 ground station would use one or more GPS reception antennas having
 suitable antenna pattern characteristics. Of particular significance is
 the desirability of antennas having the characteristic of a unitary phase
 center of accurately determined position, to permit precision
 determinations of phase of received signals and avoid introduction of
 phase discrepancies. Antenna systems having the desired characteristics
 are described and illustrated in U.S. Pat. No. 5,534,882, which is hereby
 incorporated herein by reference.
 Objects of the present invention are to provide new and improved elements
 and antennas, and elements and antennas having one or more of the
 following characteristics and advantages:
 progressive-phase-omnidirectional elements;
 self-contained elements providing a progressive-phase-omnidirectional
 pattern via a single signal port;
 simplified progressive-phase excitation network includable within a
 self-contained antenna element;
 self-contained four-dipole elements usable in stacked configurations;
 antennas using a stack of identical individually-excited
 progressive-phase-omnidirectional elements;
 antennas including a stack of such elements with excitation of different
 amplitude or phase, or both; and
 antennas utilizing a stack of such elements, including directly excited and
 indirectly excited elements.
 SUMMARY OF THE INVENTION
 In accordance with the invention, a four-dipole element, double tuned for
 reception at two GPS frequencies, incorporates a
 progressive-phase-omnidirectional excitation network. The element includes
 a signal port and first, second, third and fourth dipoles successively
 spaced around a vertical axis and each having two opposed arms. The
 progressive-phase-omnidirectional (PPO) excitation network is coupled
 between the signal port and the four dipoles and includes
 (a) a first quadrature coupler coupled between the first and second dipoles
 to provide first dipole excitation of a first phase and to provide second
 dipole excitation of a quadrature phase,
 (b) a second quadrature coupler coupled between the third and fourth
 dipoles to provide third dipole excitation of a phase differing by 180
 degrees from the first phase and to provide fourth dipole excitation of a
 quadrature phase differing by 180 degrees from the second dipole
 excitation, and
 (c) first and second transmission line sections respectively coupled
 between the signal port and the first and second quadrature couplers; and
 four resonant circuits, one coupled to each dipole to provide double tuning
 for signal reception at two GPS frequencies.
 In the context of each dipole of the above-described four-dipole element
 having a left arm and a right arm when viewed from the vertical axis, the
 element may be configured so that: the first quadrature coupler has a port
 coupled to the left arm of the first dipole and a quadrature port coupled
 to the left arm of the second dipole; and the second quadrature coupler
 has a port coupled to the right arm of the third dipole and a quadrature
 port coupled to the right arm of the fourth dipole.
 Also in accordance with the invention, a GPS antenna with
 progressive-phase-omnidirectional excitation includes a four-dipole first
 element incorporating a PPO excitation network having first and second
 quadrature couplers as described above, and a plurality of four-dipole
 additional elements each substantially the same as the first element. The
 additional elements include upper elements positioned above and lower
 elements positioned below the first element along the vertical axis. The
 antenna also includes a signal distribution network coupled between an
 antenna output port and the signal ports of the first element and a
 plurality of the additional elements. Typically, the signal distribution
 network is arranged to provide excitation signals to the upper elements
 which lags excitation signals provided to the first (middle) element by a
 90 degree phase differential, and excitation signals to the lower elements
 which leads excitation signals provided to the first (middle) element by a
 90 degree phase differential. As a result, PPO excitation of the upper
 elements and lower elements will respectively lag and lead the PPO
 excitation of the first (middle) element by a 90 degree phase
 differential.
 For a better understanding of the invention, together with other and
 further objects, reference is made to the accompanying drawings and the
 scope of the invention will be pointed out in the accompanying claims.

DESCRIPTION OF THE INVENTION
 FIG. 1 shows a four-dipole element 10 in accordance with the invention.
 Element 10 includes first, second, third and fourth dipoles 11, 12, 13,
 14, respectively. Each dipole includes two opposed arms. The ends of the
 arms of dipoles 11 and 13, which would overlap arms of adjacent dipoles in
 this view, have been partially removed for clarity of illustration. In
 actual use, all four dipoles are of substantially identical construction.
 FIG. 1 illustrates an implementation using printed circuit techniques. In
 FIG. 1, conductor configurations are supported on the top surface of an
 insulative layer or substrate 16. The bottom view of FIG. 2, shows the
 bottom surface of a conductive (e.g., copper) layer 18 adhered to
 substrate 16. In this embodiment, individual arms of the dipoles (e.g.,
 arms 12l and 12r of second dipole 12) are separately fabricated and
 soldered or otherwise attached at appropriate positions to the conductive
 layer 18. At particular locations, circuit connections pass through
 openings in conductive layer 18 and substrate 16 to circuit portions
 above. At other locations circuit connections pass through substrate 16
 from above to make conductive contact with layer 18, which represents
 ground potential. Element 10 includes a square central cutout suitable to
 receive a square mast and other cutouts to be described.
 As shown in the FIG. 3 side view of the FIG. 1 four-dipole element, opposed
 arms 12l and 12r of dipole 12 extend respectively upward and downward at
 approximately 45 degrees diagonally to horizontal. Arms 14i and 14r of
 dipole 14, at the back of element 10 in the view of FIG. 3, are also
 visible. The four dipoles 11, 12, 13, 14 of element 10 are successively
 spaced around a vertical axis 40, shown dashed in FIG. 3 and in end view
 in FIGS. 1 and 2. Dipole arms are labeled l and r, representing the left
 arm and right arm when viewed from vertical axis 40 (i.e., viewed from a
 position above the top surface of element 10, looking outward from axis
 40).
 Four-dipole element 10 includes a signal port illustrated as coaxial
 connector 42. Connector 42 is shown with its outer conductor portion
 mounted to conductive layer 18 and its center conductor passing through
 layer 18 to the upper surface of substrate 16.
 Element 10 also includes a progressive-phase-omnidirectional (PPO)
 excitation network coupled between port 42 and dipoles 11, 12, 13, 14. As
 illustrated, the PPO network includes first and second quadrature couplers
 30 and 32, respectively, as shown in FIG. 2 and first and second
 transmission line sections 34 and 36, respectively, as shown in FIG. 1.
 Couplers 30 and 32 in this embodiment are wireline quadrature couplers
 having an external encasement which is soldered or otherwise grounded to
 conductive layer 18. Each wireline device is a 3 dB coupler having four
 signal port conductors: input port "a"; output port "b" providing signals
 of the same phase as input signals; output port "c" providing signals of
 quadrature phase (i.e., 90 degree phase lag relative to input signals);
 and port "d" which is resistively terminated (e.g., 50 ohms to ground).
 While signal input terminology is used for convenience, it will be
 understood that the couplers operate reciprocally for the present signal
 reception application.
 Considering both the bottom view of FIG. 2 and the top view of FIG. 1, it
 will be seen that port a conductor 30a of wireline coupler 30 is coupled
 through layers 18/16 and coupled to signal port 42 via line section 34.
 Port b conductor 30b is coupled through layers 18/16 and coupled to the
 left arm of first dipole 11, via conductor 11a, to provide first dipole
 excitation of a first phase. Conductor 11a and associated shorted stub 11b
 (connected to layer 18 through layer 16) are appropriately dimensioned to
 provide suitable impedance matching to the dipole using known design
 techniques. Similarly, port c conductor 30c is coupled to the left arm of
 second dipole 12 via conductor 12a to provide second dipole excitation of
 a quadrature phase (i.e., differing by 90 degrees). Port d conductor 30d
 passes through layers 18/16 and is terminated by a 50 ohm chip resistor
 30e mounted on the surface of layer 16 and grounded to layer 18.
 Second wireline quadrature coupler 32 is correspondingly coupled to third
 and fourth dipoles 13 and 14, however, in this case couplings are to the
 right arms of dipoles 13 and 14 (rather than to the left arms, as above).
 Thus, port a conductor 32a of coupler 32 is coupled to signal port 42 via
 second transmission line section 36. Port b conductor 32b (zero phase) is
 coupled to the right arm of third dipole 13, via conductor 13a, with the
 phase reversal from opposite-arm excitation (i.e., via right arm v. left
 arm above) resulting in third dipole excitation of a phase opposite (i.e.,
 differing by 180 degrees) to the first phase excitation of first dipole 11
 (e.g., 180 degrees lag). Port c conductor 32c (quadrature phase) is
 coupled to the right arm of fourth dipole 14, via conductor 14a, with the
 quadrature phase and phase reversal from opposite arm excitation resulting
 in fourth dipole excitation of a phase opposite to the second phase
 excitation of second dipole 12 (e.g., 180 degrees lag). Port d conductor
 32d is resistively terminated via chip resistor 32e. Shorted stubs 12b,
 13b, and 14b as shown are provided for dipoles 12, 13 and 14 as discussed
 above with reference to stub 11b.
 During signal reception, this configuration is effective to provide at
 signal port 42 a signal representative of reception via a 360 degree PPO
 azimuth antenna pattern. Thus, the PPO network is effective to provide
 relative signal phasing of zero, -90, -180 and -270 degrees at first,
 second, third and fourth dipoles 11, 12, 13, 14, respectively, with
 received signals combined to provide the PPO signal at port 42. The
 four-dipole element 10 thus operates as a self-contained unit to provide
 this PPO capability.
 For effective GPS operation, the four-dipole element of FIGS. 1-3 is double
 tuned for operation at the two GPS frequencies of 1,572.42 MHZ and 1,227.6
 MHZ. With reference to second dipole 12, double tuning is provided by a
 tuned circuit utilizing the inductance of a stub comprising gap 12c backed
 up by a rectangular opening in conductive layer 18, in combination with
 capacitive stub 12d connected to layer 18 and overlying a portion of
 dipole 12. Provision of this tuned circuit enables the dipole to be double
 tuned using known design techniques, to enable reception at both GPS
 signal frequencies.
 In a presently preferred embodiment, four-dipole element 10 is fabricated
 as a self-contained unit using printed circuit techniques, with the dipole
 arms, wireline quadrature couplers and coaxial connector soldered in
 place. For GPS application, the element 10 has dimensions of approximately
 three and a quarter inches across and an inch and a quarter in height. The
 unit is shown slightly enlarged and some dimensions may be distorted for
 clarity of presentation. The square central opening is dimensioned for
 placement on a square conductive mast 40 of hollow construction (e.g., a
 square aluminum pipe shown sectioned in FIG. 3) with electrical connection
 of ground layer 18 to the mast 40. As will be further described, in a
 preferred antenna configuration 21 elements identical to element 10 are
 positioned on a mast in a vertical stack with approximately one-half
 wavelength element-to-element spacing. In such embodiment, eleven of the
 elements are directly excited via coaxial cables connected to a signal
 distribution network and ten of the elements are indirectly excited by
 radiation coupling. This provides a desired hemispherical antenna pattern
 particularly effective for reception of GPS signals, as will be described.
 Reference is made to FIG. 4a which illustrates a form of antenna system
 described in U.S. Pat. No. 5,534,882 (the '882 patent) issued to one of
 the present inventors. Antennas in accordance with the present invention
 utilize the teaching of the '882 patent in the context of the novel
 self-contained PPO excited elements which have been described above and
 antennas (e.g., the FIG. 7 antenna) to be described below. The FIG. 4a
 antenna system is arranged to provide a first circular polarization
 characteristic (e.g., right circular polarization) horizontally and upward
 from a plane. This characteristic is figuratively illustrated in FIGS. 5a
 and 5b on an ideal basis which, in practice, will be approximated. In FIG.
 5a, a horizontal plane is represented in side view by a dotted line and a
 central vertical axis 8 is shown normal to the plane. The circularly
 polarized antenna pattern is represented by a semicircular solid line 9
 showing an antenna radiation pattern which extends equally at all
 elevations upward to the zenith. The antenna pattern is also shown as
 having a sharp cutoff at the horizontal plane, which provides for enhanced
 multipath signal discrimination. FIG. 5b shows a plan view of the
 omnidirective antenna pattern 9 centered about axis 8 on a portion of the
 horizontal plane, which represents a horizontal stratum for reference
 purposes, and does not represent any physical antenna element or
 reflective surface.
 Referring to the FIG. 4a antenna system, a mast 20 supporting the antenna
 system is shown centered on the vertical axis 8 and normal to the
 horizontal plane. As illustrated, the antenna system includes a plurality
 of element arrays, shown as dipole arrays 1-7, spaced along mast 20.
 Considering element array 1, it consists of four dipoles each supported by
 coupling means illustrated as a base portion (such as shown at 22 with
 respect to dipole lA) extending from mast 20. As shown for dipole 1D, each
 dipole is tilted so that its arm portions are at an angle of approximately
 45 degrees. In FIG. 4a dipole 1D is in the front (permitting its tilted
 orientation to be seen), side dipoles 1A and 1C are seen in side profile
 and rear dipole 1B is shown in simplified form as a tilted line (to
 distinguish it from front dipole 1D). The A, B, C, D dipole labeling is
 typical for each of the other dipole arrays 2-7. The FIG. 4a antenna
 system looks the same when viewed from the front, the back or either side.
 Thus, except for the specific dipole labels as shown, FIG. 4a may be
 considered a front, back or side view. FIG. 4b shows simplified top views
 of dipole arrays 1, 2, and 3 of the FIG. 4a antenna, illustrating the
 symmetrical character of the four dipoles of each array. As shown, the
 four dipoles of each array are equally spaced around the mast 20 at 90
 degree angular increments. The boresight of each dipole is thus aligned at
 an angle differing from the boresight angle of each other dipole in its
 array by an integral multiple of 90 degrees.
 FIG. 6 illustrates portions of four transmission lines A, B, C and D which
 are arranged to serve dipole arrays 1, 2 and 3 of FIG. 4a. As shown in
 FIG. 6 each transmission line is arranged for feeding one predetermined
 dipole of each of the dipole arrays 1, 2 and 3 (and by extension is also
 arranged to feed one dipole in each of arrays 4, 5, 6 and 7). Consider
 transmission line A which, as shown, includes connection points 1A, 2B and
 3D labeled to correspond to the individual dipoles in arrays 1, 2 and 3
 which are fed from these connection points. With reference to FIG. 4a it
 will be seen that in the antenna system as shown, the lettered dipoles of
 arrays 2 and 3 are in vertical alignment with the correspondingly lettered
 dipoles of array 1 (e.g., dipole 2A is directly above, and dipole 3A is
 directly below, dipole lA in FIG. 4a). In FIG. 6 the central portions of
 lines A, B, C and 1 inclined so that, when the FIG. 6 structure is curved
 laterally to form a cylinder, the transmission line A (which may be a
 conductive line on a thin printed circuit substrate) extends both upward
 and laterally. In this way, if the transmission line length is one-half
 wavelength at the signal frequency (180 degrees in phase) between points
 1A and 2B in FIG. 6, a signal at point 2A (vertically above point 1A in
 the cylindrical form) will differ in phase by 90 degrees relative to the
 signal at point 1A, provided lines A, B, C and D are supplied with signals
 differing in phase by successive 90 degree increments. Thus, if the
 transmission line sections coupling the connection points were vertical,
 the half wavelength line lengths between the points would cause 180 degree
 phase differences between dipoles 1A and 2A, which are in vertical
 alignment in the FIG. 4a antennas system. However, since line A, in the
 cylindrical form, progresses laterally one-quarter revolution between
 dipole arrays 1 and 2, the half wavelength line lengths between connection
 points cause only a 90 degree phase difference between dipole 1A and
 dipole 2A, which is directly above dipole 1A.
 The result, as illustrated in FIG. 4b, is that if dipoles 2A, 2D, 2C and 2B
 of array 2 receive reference phase signals effective to cause the four
 dipoles to have relative phasing of zero, 90, 180 and 270 degrees as
 shown, the correspondingly lettered dipoles 1A, 1D, 1C and 1B of array 1
 will have relative phasing of 90, 180, 270 and zero degrees.
 Correspondingly, the dipoles 3A, 3D, 3C and 3B, of array 3 located below
 array 1, will have relative phasing of 180, 270, zero and 90 degrees. In
 FIG. 6 it will be seen that above points 2B, 2C, 2D and 2A, and below
 points 3D, 3A, 3B and 3C, the transmission lines 30, 32, 34 and 36 proceed
 vertically, without any lateral or angular progression. As a result,
 signals at points 4B, 4C, 4D and 4A (not shown in FIG. 6) will have the
 same respective phasing as the signals at points 2B, 2C, 2D and 2A,
 provided that the line lengths separating array 4 from array 2 and array 6
 from array 4 are each equal to one full wavelength at the signal frequency
 (360 degrees in phase). Under similar conditions the signal phasing at
 arrays 5 and 7 will be the same as for array 3. In overview, it will thus
 be seen that each array provides a PPO antenna pattern, however, the
 signal phasing at arrays 2 and 3 have respectively been rotated forward
 (lead) and backward (lag) by 90 degrees relative to the array 1 signal
 phasing. Other portions of a signal distribution arrangement for providing
 signals of appropriate relative phase to the transmission lines A, B, C
 and D are described in the '882 patent.
 As a result of the excitation array 1, with four 45 degree angled dipoles
 positioned symmetrically around mast 20 and supplied with signals as
 described, will be effective to produce a right circular polarized
 radiation pattern around axis 12 which has a 360 degree PPO
 characteristics, as indicated by the relative phasing shown for dipoles
 1A, 1B, 1C and 1D in FIG. 4b. Similarly, signals are coupled to the
 dipoles of the second dipole array of relative phase effective to produce
 a second PPO radiation pattern around axis 12 similar to the first such
 pattern, but which is shifted in azimuth by an angle of 90 degrees (i.e.,
 90 degrees phase lag) and to dipoles 3A, 3B, 3C and 3D to produce a
 similar 360 degree third PPO radiation pattern also shifted in azimuth
 relative to the first such pattern (i.e., 90 degrees phase lead).
 Additional arrays (e.g., some or all of arrays 4, 5, 6 and 7, plus
 additional similar arrays as suitable in particular applications) may be
 included and excited to provide appropriately aligned 360 degree
 circularly polarized PPO radiation patterns. Additional details as to the
 feed configuration, construction and operation of the FIG. 4a antenna
 system are provided in the '882 patent.
 There are thus disclosed in the '882 patent antennas providing a circularly
 polarized hemispherical-type antenna pattern with PPO excitation as
 represented in FIGS. 5a and 5b. The patent utilizes what are therein
 termed element arrays, each including four dipoles, with the element
 arrays positioned along a mast in a vertical configuration. While each
 element array of the patent has similarities to the four-dipole element
 described above pursuant to the present invention (e.g., use of four
 diagonal dipoles positioned around an axis) excitation is implemented in a
 different manner. For each element array of the patent four signal feeds
 are needed, so that as described the four dipoles 1A, 1B, 1C, 1D of
 element array 1 of FIGS. 4a and 4b are respectively fed from points 1A,
 1B, 1C, 1D on the four separate transmission lines of FIG. 6. In contrast,
 for the present invention each four-dipole element of FIG. 1 is fed via a
 single signal port (e.g., port 42 in FIG. 1). The four-dipole element of
 FIG. 1 is thus termed a self-contained unit. Rather than requiring four
 signal feeds, each differing in phase by 90 degrees, to provide a desired
 PPO antenna pattern, self-contained element 10 itself produces the
 relative signal phasing for the four dipoles as necessary to provide the
 PPO antenna pattern.
 The result is that, while an antenna pursuant to the present invention (as
 in FIG. 7, to be described) uses the invention of the '882 patent, a
 four-dipole element as in FIGS. 1-3 is a novel self-contained antenna
 element and may readily be assembled into new and improved forms of GPS
 antennas.
 As illustrated in FIG. 7, one embodiment of a GPS antenna pursuant to the
 invention includes a four-dipole first element 10(1-D) and a plurality of
 additional identical elements, including ten upper elements positioned
 above first element 10(1-D)and ten lower elements positioned below first
 element 10(1-D). The elements are supported along rectangular mast 44 with
 vertical element-to-element spacings of approximately one-half wavelength
 at a frequency in the operating range. In this embodiment, each of the
 elements of the FIG. 7 antenna is identical to element 10 of FIGS. 1-3. In
 FIG. 7, each element is identified with the reference numeral 10,
 indicating correspondence to element 10 of FIGS. 1-3, and a parenthetical
 indicating the individual element number and whether it is directly
 excited by connection to signal combiner 50 (e.g., element 10(4-D) is
 directly excited) or indirectly excited and not connected to signal
 combiner 50 (e.g., element 10(6-I) is indirectly excited). As shown, the
 ten upper elements 10(2-D), 10(4-I), 10(6-D), 10(8-I), 10(10-D), 10(12-I),
 10(14-D), 10(16-I), 10(18-D) and 10(20-I) positioned above first element
 10(1-D) all have individual element numbers which are even and indirectly
 excited elements are in alternating positions with directly excited
 elements. Also, the ten lower elements 10(3-D), 10(5-I), 10(7-D), 10(9-I),
 10(11-D), 10(13-I), 10(15-D), 10(17-I), 10(19-D), and 10(21-I) positioned
 below first element 10(1-D) all have individual element numbers which are
 odd and indirectly excited elements are in alternating positions with
 directly excited elements.
 Although elements are described in terms of being directly or indirectly
 "excited", it will be understood the FIG. 7 antenna is intended for
 reception of GPS satellite signals. As represented in FIG. 7, received
 signals are provided to signal combiner 50 by eleven signal paths 54A-54K
 (e.g., coaxial cables). Each of cables 54A-54K, which are typically of
 equal length, connects to the signal port (e.g., connector 42 of the FIG.
 1 element) of one of the eleven directly excited elements. In this
 embodiment there are no cable connections to the ten indirectly excited
 elements, the signal ports of which may be suitably terminated. To provide
 the desired antenna pattern as discussed above with reference to the FIG.
 4a antenna system, signal combiner 50 is arranged to: provide reference
 phase signals to the first element (element 10(1-D) the center element);
 provide to each of the directly excited upper elements signals which lag
 that reference phase by 90 degrees; and provide to each of the directly
 excited lower elements signals which lead by 90 degrees. As an
 alternative, it will be apparent that the desired PPO excitations which
 lead and lag by 90 degree phase differentials can be provided by
 permanently rotating selected elements by 90 degrees in azimuth and
 coupling of reference or same phase signals to each of the eleven directly
 excited elements. Thus, for this alternative Hiconfiguration all of the
 upper elements above first element 10(1-D) can be placed on the square
 mast 44 in a physical alignment rotated forward (clockwise, looking down
 from above) one quarter turn or 90 degrees, relative to the first element.
 Similarly, all of the lower elements can be placed on the square mast 44
 in a physical alignment rotated backward one quarter turn or 90 degrees,
 relative to the first element 10(1-D).
 Referring again to FIG. 4a, it will be seen that "REL AMP" values are shown
 to the right of arrays 1-7. These values represent the relative amplitude
 (e.g., voltage) of signals provided to dipoles of the respective arrays in
 order to achieve the desired antenna pattern discussed with reference to
 FIGS. 5a and 5b. If only seven of the four-dipole elements of FIG. 7 were
 directly excited, the same relative amplitude of signals could be employed
 for the FIG. 7 antenna. However, with inclusion of eleven directly excited
 four-dipole elements in the FIG. 7 antenna, the following relative voltage
 amplitudes of excitation are employed for this configuration for the
 directly excited elements: