U.S. patent number 3,877,031 [Application Number 05/374,830] was granted by the patent office on 1975-04-08 for method and apparatus for suppressing grating lobes in an electronically scanned antenna array.
This patent grant is currently assigned to The Unied States of America as represented by the Secretary of the Air. Invention is credited to Robert J. Mailloux, Allan C. Schell.
United States Patent |
3,877,031 |
Mailloux , et al. |
April 8, 1975 |
METHOD AND APPARATUS FOR SUPPRESSING GRATING LOBES IN AN
ELECTRONICALLY SCANNED ANTENNA ARRAY
Abstract
Grating lobe suppression in an electronically scanned antenna
array is realized by adding odd mode power to the fundamental even
mode power that normally drives each radiating element of the
array. The odd mode power is maintained .+-. 90.degree. out of
phase with the even mode power at each radiating element aperture.
The ratio of even mode power to odd mode power is varied as a
function of main beam displacement from broadside. One class of
circuit for automatically accomplishing the required functions
utilize waveguide power dividers and phase shifters. An alternative
embodiment comprehends the use of passive, reciprocal linear
circuitry to perform the power division. In some circuits the phase
difference between adjacent radiating elements is used to derive
odd and even mode signals.
Inventors: |
Mailloux; Robert J. (Wayland,
MA), Schell; Allan C. (Winchester, MA) |
Assignee: |
The Unied States of America as
represented by the Secretary of the Air (Washington,
DC)
|
Family
ID: |
23478353 |
Appl.
No.: |
05/374,830 |
Filed: |
June 29, 1973 |
Current U.S.
Class: |
343/778;
342/379 |
Current CPC
Class: |
H01Q
25/04 (20130101) |
Current International
Class: |
H01Q
25/04 (20060101); H01Q 25/00 (20060101); H01q
003/26 () |
Field of
Search: |
;343/777,778,854,1LE |
References Cited
[Referenced By]
U.S. Patent Documents
Primary Examiner: Lieberman; Eli
Attorney, Agent or Firm: Herbert, Jr.; Harry A. Matthews,
Jr.; Willard R. Rusz; Joseph E.
Claims
What is claimed is:
1. The method of suppressing grating lobes in an electronically
scanned antenna array comprising the steps of
dividing the fundamental even mode power for each radiating element
of the array into two power sources for each plane of scan
converting the power of one power source for each plane of scan to
odd mode power,
varying the ratio of even mode power to odd mode power as a
function of beam position, and
maintaining a 90.degree. out of phase relationship between even
mode power and odd mode power at each radiating element
aperture.
2. In an antenna system having an array of radiating elements,
circuits for feeding fundamental mode electromagnetic wave power to
each radiating element, and means for electronically scanning the
main beam radiating from the array of radiating elements, the
improvement comprising grating lobe suppression apparatus, said
grating lobe suppression apparatus including
means for dividing the fundamental mode power feed circuit for each
radiating element into two feed channels for each plane of
scan,
means adapted to feed each radiating element through said feed
channels to provide one even mode and one odd mode power source for
each plane of scan,
means associated with each radiating element for varying the ratio
of even mode power to odd mode power as a function of main beam
position, and
means for providing, at each radiating element aperture, a
90.degree. out of phase relationship between odd mode and even mode
power.
3. Grating lobe suppression apparatus as defined in claim 2 wherein
each said means for varying the ratio of even mode power to odd
mode power effects and maintains a null in its associated radiation
element radiation pattern at one principal grating lobe
position.
4. Grating lobe suppression apparatus as defined in claim 3 wherein
said means for providing 90.degree. out of phase relationship
between odd mode and even mode power effects, for each plane of
scan, a +90.degree. out of phase relationship when the main beam is
scanned to one side of broadside and a -90.degree. out of phase
relationship when the main beam is scanned to the opposite side of
broadside.
5. Grating lobe suppression apparatus as defined in claim 4 wherein
said array of radiating elements is a rectangular array of
rectangular horn antennas and said fundamental mode electromagnetic
wave power is LSE.sub.10 mode power.
Description
BACKGROUND OF THE INVENTION
This invention relates to the suppression of grating lobes in
electronically scanned antenna arrays, and more particularly to the
reduction of such effects in limited scan applications using large
array elements and sub-arrays.
There are many applications requiring a high gain antenna with
electronic beam steering over a limited cone of angles near
broadside. These include arrays for communication from synchronous
satellites, for airport precision approach radars, and for
shipboard use. Scanned reflector or lens antenna are most often
proposed or used for these applications because of their high gain,
their simplicity, and especially because they minimize the array
problem. Unfortunately, their scanning capability decreases as the
main reflector gain is increased, and seldom exceeds 15 reflector
beamwidths. Moreover, these structures usually have low aperture
efficiencies and so must be large as compared with an efficiently
illuminated aperture. Finally, they suffer the phase shifter and
scan loss of the phased array and the pattern degradation of the
optical system.
With all of these admitted deficiencies and even in its present
state of development, the scanned reflector and lens systems are
still the only logical choices for most limited cone scanning
systems because the cost, complexity, and weight of a fully steered
phased array with the same gain are unreasonable.
Although until now phased arrays have been used to steer reflection
antennas they have not been used alone for limited scan because of
the large number of elements needed to achieve high gain without
excessive grating loss. There currently exists, therefore, the need
for apparatus that will provide limited angular scanning with a
phased array of a few large elements. The present invention is
directed toward achieving this and other ends.
SUMMARY OF THE INVENTION
Grating lobe suppression is achieved by driving each antenna
element of an electronically scanned array with both even and odd
mode power in each plane of scan. The fundamental even mode power
for each antenna element is divided into two sources for each plane
of scan. The divided sources are coupled to the antenna element in
a manner that provides appropriate even and odd mode power. A .+-.
90.degree. out-of-phase relationship between even and odd mode
power at the antenna element aperture is achieved by either feed
circuit or antenna element design. The ratio of even mode power to
odd mode power is varied as a function of the displacement of the
main antenna beam from broadside. This is accomplished by various
means including a waveguide power divider, phase shifter and
coupling arrangement of the type used in monopulse horn antennas,
and alternatively, a passive, reciprocal, linear circuit that
utilizes the phase difference between adjacent radiating
elements.
It is a principal object of the invention to provide a new and
improved method for reducing grating lobes in an electronically
scanned antenna array.
It is another object of the invention to provide apparatus capable
of providing limited angular scanning with a phased array of a few
large antenna elements.
These, together with other objects, advantages and features of the
invention, will become more readily apparent from the following
detailed description when taken in conjunction with the
accompanying drawings in which like elements are given like
reference numerals throughout.
DESCRIPTION OF THE DRAWINGS
FIG. 1 illustrates a rectangular grid array of rectangular antenna
elements;
FIG. 2 is a curve illustrating element pattern shift due to the
addition of odd mode aperture distribution;
FIG. 3 illustrates a microwave circuit for exciting LSE.sub.10 and
LSE.sub.11 modes at input to a flared horn;
FIG. 4 is a basic power divider;
FIG. 5 is a feed circuit that accomplishes odd mode amplitude
control with a power divider;
FIG. 6 is a feed circuit that accomplishes odd mode amplitude
control using a simplified power divider circuit;
FIG. 7 is a schematic diagram of a circuit for passive odd mode
control;
FIG. 8 is a schematic diagram of an alternative circuit for passive
odd mode control;
FIG. 9 is a schematic diagram of a circuit for deriving odd mode
control signals having good broadside radiation
characteristics;
FIG. 10 illustrates a power divider circuit for scanning in two
planes;
FIG. 11 illustrates a microwave circuit for scanning in two
planes;
FIG. 12 is a circuit for odd mode excitation using waveguide
probes;
FIG. 13 is a circuit for odd mode excitation using a hybrid;
FIG. 14 is a curve illustrating E-plane field patterns for
LSE.sub.10 and LSE.sub.11 waveguide modes;
FIG. 15 is a curve illustrating the H-plane field patterns for
LSE.sub.10 waveguide modes; and
FIG. 16 illustrates H-plane field patterns for LSE.sub.10 plus
LSE.sub.30 waveguide modes combined for broadside grating lobe
suppression and for LSE.sub.20 waveguide modes.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT
Phased arrays cannot in general be constructed with elements longer
than a wavelength in the direction of either plane of scan because
the resulting grating lobes absorb much of the power. Grating lobes
can exist either because of an amplitude or phase taper in each
element aperture which gives the arrays a scalloped aperture field
distribution, or they can come about as the array is scanned
because the single mode apertures can only stepwise approximate the
linear phase taper which should be achieved for proper scanning of
a phased array. Therefore, for elements longer than a wavelength in
the scan plane, even if the power loss at abroadside is tolerable,
the main beam power decreases much too rapidly with scan for most
applications because the grating lobes nearest broadside grow as
they move toward the element pattern maximum.
If the angle of main beam scan is .theta..sub.o, and the spacing
between elements is D (normalized to wavelength), in the
.theta.-plane, then grating lobes appear at the angles
.theta..sub.n associated with
sin .theta..sub.n = sin .theta..sub.o + n/D (1)
for any positive or negative integer values of n which define a
real angle .theta..sub.n. The size of the grating lobes when
.theta..sub.O = 0 (broadside) depends upon the amount of amplitude
and/or phase scalloping in the basic array elements. If there is no
scalloping in one plane, as in the E-plane of an array of thin
walled horn apertures, then the field pattern of an element in the
array (the array element pattern) will have a null at each n/D
point in sin .theta. space excluding n = 0, and all of the grating
lobes will have zero amplitude. This is the optimum pattern
achievable and it is also the narrowest element pattern achievable
without resorting to superdirective apertures. When there is
scalloping, as in the E-plane with the normalized aperture width b
less than the normlized spacing D, or in the H-plane of horn
apertures, the first array element pattern nulls will occur for
.vertline.sin.vertline..theta. > 1/D and therefore will be
beyond the first grating lobes in sin .theta. space. All such
arrays will have non-zero grating lobes at broadside.
The radiation characteristics of a very large array of waveguide
apertures 16 is shown in FIG. 1, and with four incident modes in
each aperture (LSE modes 10, 20, 11, 21) are approximately
characterized by the equation given below (which is given in the
form for an infinitely large array). The equation neglects mutual
coupling and reflections at the element interfaces and is inserted
here to illustrate the grating lobe locations and amplitudes. The
radiated field strength at a point in generalized direction cosine
space is: ##SPC1##
The F.sub.pq (.mu., v) are element patterns for the mode with
subscripts p, q, and the direction cosines .mu. and v are defined
below in general, and for the specific grating lobe positions
.mu..sub.m , v.sub.n for a main beam at .mu..sub.o = sin
.theta..sub.o cos .phi..sub.o, v.sub.o = cos .phi..sub.o sin
.phi..sub.o
.mu. = sin .theta. cos .phi.
v = sin .theta. sin .phi.
The values m amd n are all integers for which the parameter
K.sub.mn = 2 .pi. .sqroot. 1 - .mu..sub.m.sup.2 - v.sub.n.sup.2
(3)
is real, and so the above equation shows the field as made up of a
set of plane waves radiating in the direction of the various
allowed kmn values. The plane wave amplitudes are determined by the
excitation coefficients A pq of the four incident LSE modes and by
their element patterns evaluated at the grating lobe points. Of
particular importance is the fact that these element patterns are
separable in the direction cosine space, that is:
F.sub.pq (.mu., V) = g (p, .mu.) f (q, v)
The lattice spacings are Dx and Dy and the apertures measure a and
b in these same coordinates. All parameters are normalized to
wavelength.
The assumption of four incident modes is necessary because the
basic concept of the invention is to use these higher order modes
to cancel the dominant unwanted grating lobes by placing nulls in
the combined four mode element pattern. Only two incident modes
(LSE10 and 11) are required for scanning in the E-plane (.mu. = 0,
v = sin .theta.), and in principle only two are required for
scanning in the H-plane (LSE10 and 20). In practice some H-plane
pattern shaping is also necessary, as will be described later. The
dominant grating lobes cancelled with this invention are those
nearest broadsides [ (m, n) = (-1, 0), (-1, 01) ] for general scan
angles. Other choices of odd mode amplitude can be made which offer
other advantages, for example, minimizing the total power in the
sum of all grating lobes, but these possibilities follow directly
from the basic concept of using odd modes for cancellation, as
would be obvious to one skilled in the art.
One choice of modal amplitudes is made by designing the array
element for each principle plane of scan. The grating lobe at n =
1, m - 0 with a given v.sub.o and with .mu. = 0 (E-plane scan) can
be eliminated by choosing A.sub.20 and A.sub.21 equal to zero, and
selecting A.sub.11 so that
A.sub.11 = - [A.sub.10 F.sub.10 (.mu..sub.o,
v.sub..sub.-1)]/F.sub.11 (.mu..sub.o, v.sub..sub.-1) (5)
Similarly, the grating lobe of importance (m=-1) for for H-plane
(v.sub.o = O, .mu..sub.o = sin .theta..sub.o) scan is eliminated by
choosing A.sub.11 and A.sub.21 equal to zero, and selecting
A.sub.20 so that: A.sub.20 = [ -A.sub.10 F.sub.10
(.mu..sub..sub.-1, v.sub.o)]/F.sub.20 (.mu..sub..sub.-1, v.sub.o)
(6)
Both of these choices imply that the odd mode amplitudes be .+-.
90.degree. out of phase with the even mode amplitude and that the
A.sub.11 and A.sub.20 amplitudes vary with scan. When scanning in a
skew plane, these two grating lobes must still be cancelled, and
the equations above remain the same. In addition, the grating lobe
at (m- , n) = (-1, -1) must also be cancelled, and because of the
separability condition one can obtain the required A.sub.21 value
from the relation.
A.sub.21 = A.sub.20 A.sub.11 /A.sub.10 (7)
with this choice, the bracketed term of equation (2) is:
A.sub.10 [ f (0, v) + (A.sub.11 /A.sub. 10) f(1, v)] .sup.. [
g(1,.mu. ) + (A.sub.20 /A.sub.10) g (2,.mu.)] = A.sub.10 F (v) G
(.mu.) (8)
This equation shows the separable nature of the combined four mode
element pattern, and indicates the modal choice that can provide
simultaneous cancellation of the three nearest grating lobes.
In the case of E-plane scan with thin walls, E-plane and
intercardinal plane grating lobes are null when an array with b =
D.sub.y is phased at broadside. Only the H-plane grating lobes
remain. As the array is scanned in the E-plane the grating lobes
move out of the element pattern nulls, but if the A.sub.11 mode
amplitude and phase is chosen as noted above, then not only is the
n = -1, m = 0 mode cancelled, but in fact all of the E-plane and
intercardinal plane grating lobes are very substantially reduced.
This is because, to a first approximation, the entire set of
element pattern nulls moves so as to align with the grating lobes
points of the new scan angle.
FIG. 2 shows a comparison of several element patterns, curve 17
illustrating a single LSE.sub.10 mode, and curve 18 illustrating an
element using odd mode LSE.sub.11 signals with an amplitude given
by Equation (7) in addition to the even mode signal. The total
transmitted power is kept constant. With the A.sub.11 mode
amplitude and phase chosen as noted above, not only is the n= -1, m
= 0 mode cancelled, but in fact all of the E-plane grating lobes
are very substantially reduced. This is because, to a first
approximation the entire set of element pattern nulls moves so as
to align with the grating lobe points of the new scan angle. The
main feature of the technique is to laterally displace the entire
element pattern in sin .theta. space.
In the case of the H-plane scan, if the aperture is excited by
waveguide horns with width greater than a wavelength, grating lobes
exist even for the main beam at broadside because the element
pattern nulls occur beyond the grating lobe points. An odd mode
amplitude can still be chosen to cancel the m = -1 lobe even when
the array is at broadside, but it will in general increase the size
of the m = +1 grating lobe.
Therefore, for the H-plane case with scalloped element patterns
(horns) some spatial filter technique may be desirable to suppress
the grating lobes at broadside before applying the oddmode scheme
described herein. Such techniques do exist and are described in the
literature as schemes for increasing horn aperture efficiency and
decreasing beamwidth. Typical of these is the boxhorn in which an
abrupt discontinuity is used to excite the LSE.sub.30 mode with
proper amplitude and phase to significantly increase the H-plane
aperture efficiency.
The salient features of the basic E and H-plane element patterns,
as well as those of the H-plane with broadside grating lobe
suppression are noted below.
Having reference to the E-plane case, the fundamental mode
LSE.sub.10 radiation pattern, shown by curve 21 in FIG. 15, has
zeros at b sin .theta. = .+-.n for n .sup.- 0. It has a maximum at
sin .theta. = 0, and its half power points are approximately 0.89
apart on the b sin .theta. axis.
The grating lobes occur spaced a distance D.sub.y sin .theta. =
.+-.n on the b sin .theta. axis, and so if b = D.sub.y these occur
at the element pattern nulls when sin .theta..sub.o = 0.
The first odd mode (LSE.sub.11) whose radiation pattern is also
shown by curve 22 in FIG. 14, has a null at sin .theta. = 0 and has
zeros at b sin .theta. = .+-.5/2, etc., but not at .+-.1/2.
The first maximum of the LSE.sub.11 mode is at b sin .theta. =
0.75, and the odd mode half beamwidth is approximately 0.33 on the
b sin .theta. axis. Given these facts, one may conclude that the
odd mode radiation can be made to cancel the even mode radiation
from b sin .theta..sub.o = 0 until the n = -1 grating lobe is at
the half power point of the odd mode, that is at
D.sub.y sin .theta..sub..sub.-1 = -0.75 + 0.33 = -0.42.
When b = D.sub.y the main beam is at the angle
b sin .theta..sub.o = 0.58
.about.0.6 (9)
for this case. This formula gives the limit of practical scan
correction using this technique for E-plane scan. FIG. 14 shows a
sketch of the E-plane field distributions f (0,v) and f (1,v) as a
function of b sin .theta. over the region .vertline.b sin .theta.
.vertline..ltoreq.4. The amplitude of the odd mode distribution f
(1,v) is chosen so that the addition of this curve to the F.sub.10
(.theta.) gives a null at b sin .theta. = 0.75, and if b = D.sub.y,
this corresponds to a choice of main beam at sin .theta. = 0.25.
This curve also points out that the grating lobes at sin .theta. =
1.75, -2.75, -3.75, 1.25, 2.25, and 3.25 all tend to cancel. These
curves also reveal that if the main beam is scanned out be b sin
.theta. = 1.5, the odd mode no longer has any influence on each of
the grating lobes since the odd mode zeros are there. There are
also the points where the LSE.sub.10 mode has its maxima, so
although the n = -1 lobe is cancelled, the grating lobes are seen
directly at the maximum sidelobes of the LSE.sub.10 mode. Since the
odd mode power is large for b sin .theta. = 0.5, the n = .+-.1
grating lobe has approximately 3 db less power than the sidelobe at
that point (13 db). Furthermore, this 16 db ratio must be
multiplied by the cosine of the scan ratio to account for the
projection factor of the finite array, and this adds an extra 1 db
suppression of the n = +1 grating lobe for D.sub.y equal to three
or less. Equation (9) therefore provides a practical approximation
of the allowable E-plane scan angle for a given aperture size.
Referring now to the H-plane case .phi.=0, the fundamental mode
LSE.sub.10 radiation pattern, shown by curve 23 in FIG. 15, has
H-plane zeros at a sin .phi. = 1.5,.+-. 2.5,etc.
The grating lobes occur at D.sub.x sin .theta. = .+-.n excluding n
= 0.
The odd mode (LSE.sub.20) nulls shown by curves 24 and 25 in FIG.
16 are at a sin .theta. = .+-.2, .+-.3, . . ., and the first
maximum of the odd mode pattern occurs at approximately a sin
.theta. = .+-.0.77. This is very close to the position of the
E-plane odd mode maximum, and since the H-plane and E-plane odd
mode beamwidths are not very different one can expect that if the
grating lobes which exist for broadside can be tolerated or removed
by pattern shaping, then the formula given for the E-plane limit is
also approximately true in the H-plane,
a sin .theta. = 0.58.
The TE and TM waveguide modes with odd aperture field symmetry in
the E-plane also have cross-polarized radiation fields. Proper
combinations of the TE.sub.11 and TM.sub.11 modes form the linearly
polarized LSE.sub.11 mode, the desired waveguide mode for E-plane
control using this technique. The LSE.sub.20 mode is used for
H-plane control. One circuit for exciting the LSE.sub.11 mode is
shown by waveguide 26 and horn 27 of FIG. 3, an equivalent
magic-tee circuit for H-plane control is also simply implemented.
Power dividers are required with division ratios variable with scan
and which must maintain a .+-. 90.degree. phase difference between
the odd and even modes. One such circuit is shown in FIG. 4 and
comprises input waveguide port 28, 90.degree. hybrid 29, and phase
shifter 30. This well known circuit provides signals at its two
output terminals which are exactly out of phase, and given by
e .sup.j.sup..eta./2 sin .eta./2 and -e.sup.j.sup..eta./2 cos
.eta./2
apart from a constant phase factor, where n is the delay of the
phase shifter shown in the figure. If one of these outputs is used
as the source of odd mode signal and one as the source of even mode
signal, and these are applied to the circuit of FIG. 3, then
varying .eta. will provide the proper odd mode signal for scanning
with a fixed phase relationship between even and odd modes. For
example, if .eta. = 180.degree. is chosen for broadside, all the
power will appear at arm B; choice of .eta. less than 180.degree.
will scan the beam in one direction, and more than 180.degree. will
scan it in the other. In both cases a .+-. 90.degree. phase
difference must appear at the aperture, and this can be adjusted by
proper choice of line lenghts taking into account that the even and
odd modes propagate with difference phase velocities. The phase
shift .eta. is the same for each horn, and this simplifies the
control requirements considerably.
A second circuit for performing the scan function and which can
also be implemented using the power divider circuit of FIG. 4 is
shown in FIG. 5. This circuit includes the elements of FIG. 4 plus
a waveguide power plane converter 31. In this case the outputs at
ports A and B are combined directly at the input of the horn, and
so in the E-plane case, form the excitation of the symmetric
LSE.sub.10 and antisymmetric LSE.sub.11 modes directly with
amplitudes given by (cos .eta./2 + sin n/2) and (cos .eta./2 - sin
.eta./2). The proper selection of .eta. and the proper use of
waveguide and horn propagation characteristics allows the
.+-.90.degree. phase relationship to be maintained throughout the
scan plane. This circuit differs from the one previously discussed
because, though requiring one less hybrid, it does not allow the
odd and even modes to be treated (delayed, advanced in phase or
attenuated) separately, and since they are not separately
accessible it requires a more complicated waveguide design to
achieve the 90.degree. relationship.
The simplest circuit of this type, shown in FIG. 6, is derived by
omitting the second hybrid of FIGS. 4 or 5 and merely using the
phase shift difference to derive even and odd components for
application to the horn as in FIG. 5. Since the two modes propagate
with different phase velocities, it is possible to choose the line
lengths to obtain excitations with e.sup.j.sup..eta./2 sin .eta./2
and e .sup.j.sup..eta. /2 cos .eta./2 dependence upon the inserted
phase shift, as required for circuit behavior. The insertion loss
of the phase shifter n enters into the scan characteristics of each
circuit slightly differently and must be taken into account in the
choice of a final design.
The circuits described above all require phase shifters for power
division. Their main advantage is that they are low loss power
dividers, and their main disadvantage is that one extra phase
shifter is needed for a single plane of scan, three are needed for
a single plane of scan, and three are needed for scan in two
planes. Since all elements require the same power division ratio,
the system control circuitry is substantially simplified, but for
applications requiring a lightweight antenna this increase in the
total number of phase shifters may detract from the attractiveness
of this technique.
Alternatively, power divider circuits based upon the use of
switches and hybrids or directional couplers can also provide
lossless power division, and may in some cases be lighter or more
compact.
A third possibility is the use of passive, reciprocal, linear
circuits to perform the power division. One class of such circuits
uses the phase differenc between adjacent radiators to derive odd
and even mode signals. FIG. 7 comprising the network of pulse
divider 32 and hybrid 33 shows the simplest of these, in which
adjacent signals are split in half, added and subtracted. The sum
and difference signals are:
Sum: e.sup.j.sup..eta. /2 cos .eta./2
Difference: je .sup.j.sup..eta. /2 sin .eta./2 The ratio of the
difference signal to the sum signal changes sign on either side of
broadside as determined by the relative phase difference N at the
input. The ratio is infinity at n = .pi. = (d sin .theta.)2.pi.,
but the null formed by this choice of signal distribution is much
further out in angle than the beam which is being formed. In any
case, even if the odd mode is attenuated, an absolute scanning
maximum is between D sin .theta. = 0.45 and 0.5. Instead of
deriving these signals separately, it is only necessary to combine
the signals e.sup.jn /.sqroot.2 and 1/.sqroot.2 in one oversize
waveguide, (in the manner of FIG. 5), and that the even and odd
modes thus excited will have the same variation within as indicated
above. The circuit described above does not provide a particularly
optimum choice for scanning out ot the D sin .theta. = 0.5 point
because the even mode signal gets small so quickly that the element
pattern null is always at an angle much further out than the array
scan angle. One way around that problem is to derive an odd mode
signal by sampling the incident signals, forming the sum (even) and
difference (odd) parts of these samples, and simply throwing away
the even part. The circuit of FIG. 8 comprises the network of Tee
35, magic Tee 37 and load 36 and shows one means of achieving this
end. If about one half of the power is taken out of the basic
circuit, and combined with the adjacent signal in a difference
hybrid and the result of this combined again with each adjacent
signal in a difference hybrid, the resulting signals will be
proportional to sin.sup.2 .eta./2 and will be at the proper phase
angle for reintroduction into the odd mode arm. If exactly one half
of the power is used, the ratio of odd to even power at D sin
.theta. = 0.5 will be unity, and this is only slightly greater than
that required for this scan position. In addition, the sin.sup.2
.eta./2 behavior near .eta. = 0 makes the scanning more nearly
correct for those angles. This circuit has two disadvantages: (1)
its behavior is an even function of N, and so does not introduce
the required 180.degree. shift when scanning across, broadside; and
(2) more important, approximately one-half of the power is lost at
broadside when scanning out to the D sin .theta..sub.max = 0.5
limit is desired. The first of these is easily remedied by
introducing a 180.degree. switching operation, but the power loss
at broadside can be avoided either by not introducing any off mode
signal until the main beam is scanned a given amount off broadside,
or by re-using the power that would otherwise be lost at broadside.
The first solution is impractical because it allows scan only out
to approximately D sin .theta. = 0.1 (for 20 db grating lobe
suppression) before the odd mode signal is required, and at this
point most of the signal is still lost once it is switched into the
network. The second alternative is shown by the network of Tee 35,
magic Tee 37, loads 36 and short circuits 38 of FIG. 9 and consists
of re-using some of the power at the sum terminals of the magic
tee. At broadside, the line lengths are adjusted to provide an
apparent short circuit at the waveguide-tee and all of the incident
power is properly distributed to the even mode port. At D sin
.theta. = 0.5, the ratio of odd mode to even mode power is two,
corresponding to an element pattern null beyond the 0.5 point.
(this is also the occasion of a 25 percent power reflection in the
main line.) A further increase in sin .theta. decreases the ratio
of odd mode to even mode power until a crossover point is reached
where the element pattern null is exactly where it should be for
the given array pattern. This alternative does not change relative
power ratios, because when these signals are recombined with the
line signal at the hybrid summing network and this network is lossy
whenever the signals are not equal. This loss accounts for one
quarter of the power at D sin .theta. = 0.5. In either case, this
circuit and the one of FIGS. 7 and 8 must be used with a
180.degree. phase reversal to scan to either side of broadside.
FIGS. 7 and 9 are shown using a second magic tee to derive an odd
mode signal at each Nth port with phase progression N.mu./.pi.,
where .eta. = 2.pi.D sin .theta.. This second tee was necessary
because the odd mode output of the first tee was in phase with
N.eta./.pi., and so could not be adjusted to provide a constant
90.degree. phase difference from the even mode signals at phase
N.eta.. Alternatively, this hybrid can be omitted, and the odd mode
signal at N.eta. can be applied directly to the odd mode port. If
this signal is added so that it would be in-phase with the even
mode signal D sin .theta. = 0, then at D sin .theta. = 0.5 this
signal would have the required 90.degree. phase difference from the
even mode. Though the phase difference is not correct for small
angles of scan, the odd mode amplitude is small then, and
reasonable scanning properties can be obtained. The advantage of
this process is the elimination of one hybrid. A 180.degree. switch
is still required to go from a positive to a negative scan
sector.
The waveguide circuits of FIGS. 12 and 13 show schemes for
implementing the sin .eta./2 structure of 7. These are shown in
waveguide and use either probe 40 (FIG. 12) or a magic tee coupler
41 (FIG. 13) to form the proper odd mode signal. The dimension L
provides a 1/4 .lambda. short and S.sub.1 - S.sub.2 = 1/2 .lambda.
so signals will subtract and go to the horn. The geometry shown is
for E-plane scan, but it is obvious that an H-plane version could
also be designed using the folded hydbrid of FIG. 3.
The principle of using an odd mode to cancel at least the first
grating lobe of a phased array scanning in a plane leads to the
requirement of a separable distribution for scanning of either
principal plane.
This distribution can be achieved using a minimum number of power
divider circuits if it is done sequentially as shown in FIG. 10. In
this case, three power dividers are required for each horn element
to scan in two planes. The horn element can be like the one shown
in FIG. 11 with separate input ports 40 for each mode, and in this
case each power divider functions like that of FIG. 4 to completely
serparate the even and odd modes. Alternatively, the horn element
can be like that of the one plane geometry shown in FIG. 5 in which
even and odd modes are combined in the appropriate ratios. In this
second case, great care must be taken to maintain the desired phase
relationships between the modes which all propagate with different
phase velocities in the horns. The odd mode concept for two planes
of scan requires 3N.sup.2 power dividers, where N.sup.2 is the
number of elements in the square array. If phase shifters are used
in the power dividers, then a total of 4N.sup.2 phase shifters are
required to steer the beam and suppress the grating lobes.
The operation of the circuit shown in FIG. 10 is explained as
follows, for the special case of use with the feed of FIG. 11. This
circuit consists of three conventional variable power dividers, the
first one controlled by the inserted phase shift .eta..sub.E for
E-plane/control, and the second two controlled by the identical
inserted phase shifts for H-plane control. The output ports AA, AB
of the first power divider have signals
at A A ; j e j .eta..sub.E /2 sin .eta..sub.E /2
at A B ; j e j .eta. .sub.E /2 cos .eta..sub.E /2 (10)
these are the input signals for the other two power dividers, which
operate in the same manner as the first to give at the output ports
(suppressing the e -j .eta..sub.E /2 e -j .eta..sub.E /2 ):
at C A ; sin .eta..sub.E /2 sin .eta..sub.H /2
at C B ; sin .eta..sub.E /2 cos .eta..sub.H /2
at D A ; cos .eta..sub.E /2 sin .eta..sub.H /2
at D B ; cos .eta..sub.E /2 cos .eta..sub.H /2 (11)
these signals are used to excite the LSE.sub.21, 11, 20 and 10
modes respectively in the throat of the horn using a microwave
circuit like that shown in FIG. 11. The horn structure itself is
designed to provide H-plane control and to collimate the beam in
the E-plane as previously described, and has separable radiation
patterns in the E and H-planes for each of the incident modes. In
direction cosine space these patterns have symmetry as denoted by
the subscripts (e = even) (o = odd)
LSE mode incident Radiation Pattern (.mu., v) 10 f.sub.e (v)
g.sub.e (.mu.) 20 f.sub.e (v) g.sub.o (.mu.) 11 f.sub.o (v) g.sub.e
(.mu.) 21 f.sub.o (v) g.sub.o (.mu.)
Exciting each of these radiation patterns with the output of the
circuit of FIG. 10 (Equation 11) gives the result:
Field (.mu., v) = (cos .eta..sub.E f.sub.e (v) + sin .eta..sub.E
f.sub.o (v). cos .eta..sub.H g.sub.e (.mu.)+ sin .eta..sub.H
g.sub.o (.mu.) = F (v) G (.mu.) (13)
this pattern exhibits the separable distribution as shown in
Equation 8. Since the grating lobe positions .mu..sub.m and v.sub.n
are independent of one another, then one can chose .eta..sub.E to
give nulls at the grating lobe positions in the E-plane (.mu.= 0)
and the separable character of the product above shows that the
circuit of FIG. 10 will position the nulls properly for generalized
scan angles.
If one of the passive linear circuits of FIGS. 7, 8, or 9 is used
to provide odd mode control, then only (N-2) odd mode outputs are
available per column and so the total number of antennas with full
odd mode control is (N-2).sup.2. The antennas at the extreme outer
ring can have no odd mode control, but a fixed level of even modes
power with proper phase can be selected for these outer antennas
and provide good sidelobe and grating lobe characteristics without
loss of gain. The system therefore should control the N.sup.2
array, even though only the central (N-2).sup.2 elements have odd
mode signals.
While it has been shown and described what is considered at present
to be preferred embodiments of the invention, modification thereto
will readily occur to those skilled in the art. In particular,
although horn apertures were used as the waveguide elements, it
should be obvious that the basic techniques of the invention apply
equally well when the array element is itself a sub-array of
dipoles or horn elements. In this case the distributions need not
be trigonometric in nature but may be tailored to provide optimum
coverage. Therefore an odd linear field amplitude distribution or
even one with an inverse taper in the odd mode might well be
preferred for selected scan geometries. It is not therefor desired
that the invention be limited to the specific arrangement shown and
described and it intended to cover in the appended claims all such
modification that fall within the true spirit and scope of the
invention.
* * * * *