RADIO FREQUENCY ENERGY ANTENNA

ANTENNE RADIOFREQUENCE

English Abstract

RADIO FREQUENCY ENERGY ANTENNA
Abstract of the Disclosure
A radio frequency energy antenna system for directing a
collimated beam of radio frequency energy in free space over
relatively wide scan angles. The antenna system includes a
plurality of antenna elements disposed along a curved path for
producing a directed, noncollimated beam of radio frequency
energy and a radio frequency lens disposed between the antenna
elements and free space for collimating the radio frequency
energy in the directed, noncollimated beam to produce the col-
limated beam of radio frequency energy in free space. The
arrangement of the antenna elements along a curved path produces
an amplitude distribution across the collimated beam wavefront
which is substantially uniform. A second radio frequency lens
has a plurality of array ports coupled to the plurality of
antenna elements and a plurality of feed ports, each one being
associated with a corresponding collimated beam of radio frequency
energy in free space. With such lens the antenna has a relatively
wide operating bandwidth. The disposition of the antenna elements
along the curved path enables the second lens to be smaller in
size and have a shape wherein the array ports and feed ports face
one another to a greater degree than if the antenna elements were
disposed along a straight line thereby improving the operating
effectiveness of the second lens.

Claims

THE EMBODIMENTS OF THE INVENTION IN WHICH AN EXCLUSIVE
PROPERTY OR PRIVILEGE IS CLAIMED ARE DEFINED AS FOLLOWS:
1. A radio frequency antenna system for producing collimated
beams of radio frequency energy in free space, comprising:
(a) curved array means for providing differently directed,
noncollimated beams of radio frequency energy, each one of such
beams being produced from a common aperture, such aperture
comprising a first probe means disposed along a first nonlinear
path, the direction of the noncollimated beams being produced in
accordance with the distribution of the phase of the radio fre-
quency energy across the first nonlinear path of the common
aperture, each one of such noncollimated beams having a different
phase distribution across the first nonlinear path of the common
aperture; and
(b) radio frequency lens means, disposed between the curved
array means and free space, for collimating the radio frequency
energy in the directed, noncollimated beams to produce correspond-
ing collimated and redirected beams of radio frequency energy in
free space, such radio frequency lens means comprising:
(i) antenna means disposed along a second nonlinear path;
(ii) a second probe means disposed along a third nonlinear
path, such directed noncollimated beams being provided between
the first probe means and the second probe means; and
(iii) means for providing fixed, predetermined electrical
length coupling between the antenna means and the second probe
means.
2. The antenna recited in claim 1 wherein the curved array
means includes a second radio frequency lens means having array
port means coupled to the first probe means and also having a
plurality of feed ports coupled to the array probe means, each
one of such feed ports being associated with a corresponding one
21

of the collimated beams of radio frequency energy in free space,
each one of the plurality of feed ports being coupled to the
array port means.
3. A radio frequency antenna, comprising:
(a) means for providing directed, noncollimated beams of
radio frequency energy, such means including:
(i) a radio frequency lens having a plurality of array
ports and a plurality of feed ports disposed along curved outer
opposing convex shaped peripheral portions of the lens, each one
of such feed ports being associated with a corresponding one of
the directed, noncollimated beams of radio frequency energy; and
(ii) a first plurality of probes disposed along a first
nonlinear path for providing a common aperture for the directed,
noncollimated beams, each one of such first plurality of probes
being coupled to a corresponding one of the array ports, and
(b) radio frequency lens means, disposed between the first
plurality of probes and free space, for collimating and angularly
redirecting the radio frequency energy in the directed, noncol-
limated beams producing corresponding collimated beams of radio
frequency energy in free space, such radio frequency lens means
comprising:
(i) a plurality of antenna elements disposed along a
second nonlinear path;
(ii) a second plurality of probes disposed along a third
nonlinear path, such directed, noncollimated beams being provided
between the first and second pluralities of probes; and
(iii) a plurality of transmission lines, each one thereof
providing a different, fixed, predetermined electrical length
between a corresponding one of the antenna elements and a
corresponding one of the second plurality of probes.
22

4. The radio frequency antenna recited in claim 3 wherein the
second nonlinear path is an arc of radius R1 and the third non-
linear path is disposed along an arc of radius R2 > R1 and
wherein the arc of radius R1 and the arc of radius R2 have a
common origin.
5. The radio frequency antenna recited in claim 4 wherein
the first plurality of probes coupled to the array ports is
disposed along an arc of radius R5, such arc being centered
a distance R4 from the origin of the arc of radius R1, where
R12 + R42 = R52.
6. A radio frequency antenna, comprising:
(a) a first radio frequency lens having an array means
disposed along a peripheral portion of the lens and a plurality
of feed ports disposed along a second, opposing peripheral
portion of the lens, such first and second peripheral portions
being separated by a central portion of the lens, such peripheral
portions being convex outwardly from the central portion of the
lens, each one of such plurality of feed ports being coupled to
such array means through the central portion of the lens, each
one of such feed ports being associated with a corresponding one
of a plurality of beams of radio frequency energy in free space;
(b) probe means diposed along a first nonlinear path to
provide a common aperture for each one of the plurality of beams,
such probe means being coupled to the array means;
(c) a second radio frequency lens, comprising:
(i) a plurality of probe points disposed along a second
nonlinear path; and
(ii) a plurality of antenna points disposed along a third
nonlinear path, the antenna points being coupled to the probe
points through fixed, predetermined electrical lengths.
23

7. The radio frequency antenna recited in claim 6 wherein:
the second nonlinear path is an arc of radius R1; the third
nonlinear path is an arc of radius R2; and the first nonlinear
path is in an arc of radius R5, such arc being centered a
distance R4 from the center of the arc of radius R1, where
R12 + R42 = R52.
8. A radio frequency antenna comprising:
(a) array means, including a plurality of probes, disposed
along a first nonlinear path, such plurality of probes providing
a common aperture, for producing, from such common aperture,
noncollimated beams of radio frequency energy, each one of such
beams having a central ray at a different angle .theta.0 with respect
to a reference axis;
(b) radio frequency lens means, disposed between the
plurality of probes and free space for collimating the non-
collimated beams and angularly redirecting such collimated beams
at correspondingly different angles, such radio frequency lens
means comprising:
(i) probe means disposed along a second nonlinear path,
such noncollimated beams being disposed between the plurality
of probes and the probe means;
(ii) antenna means disposed along a third nonlinear path;
and
(iii) means for providing fixed, predetermined electrical
length coupling between the probe means and the antenna means.
9. The radio frequency antenna recited in claim 8 wherein the
antenna means is disposed along an arc of radius R2 and the probe
means is disposed along an arc of radius R1 where R2 > R1 and
wherein the coupling means provides an electrical length P between
24

points of the probe means and corresponding points of the
antenna means, where:
<IMG>
where .theta.'0 is the angular orientation of the one of the points of
the probe means with respect to the reference axis and K is a
nonunity constant.
10. The radio frequency antenna recited in claim 9 wherein the
plurality of probes is disposed along an arc of radius R5, such
arc being centered at a distance R4 from the center of the arc of
radius R1, where R52 = R12 + R42 .
11. The radio frequency antenna recited in claim 10 where
K > 1.
12. The radio frequency antenna recited in claim 8 wherein the
noncollimated beam producing means includes: a second radio
frequency lens having a plurality of array ports coupled to the
plurality of probes, a plurality of feed ports each one thereof
being coupled to the plurality of array ports, and wherein each
one of the plurality of feed ports is associated with a corres-
ponding one of the collimated beams of radio frequency energy.
13. The radio frequency antenna recited in claim 12 wherein the
antenna means is disposed along an arc of radius R2 and the
probe means is disposed along an arc of radius R1, where R2 > R1,
and wherein the coupling means provides an electrical length P
between points of the probe means and corresponding points of
the antenna means where
<IMG>
where .theta.'0 is the angular orientation of the one of the points

of the probe means with respect to the reference axis, and K is
a nonunity constant.
14. A radio frequency antenna system for producing collimated
beams of radio frequency energy in free space over relatively
wide scan angles, comprising:
(a) parallel plate lens means for providing directed, non-
collimated beams of radio frequency energy from a common aperture,
such aperture comprising a first plurality of probes disposed
along a first nonlinear path, such parallel plate lens means
comprising:
(i) a parallel plate lens having a curved outer peripheral
input portion and an opposing curved outer peripheral output
portion;
(ii) a plurality of transmitter/receiver feed ports coupled
to the curved outer peripheral. input portion of the parallel plate
lens;
(iii) a first plurality of transmission lines coupled to the
curved peripheral output portion of the parallel plate lens, each
one of the first plurality of transmission lines having a pre-
determined electrical length and each one thereof being coupled
to a corresponding one of the first plurality of probes; and
(b) radio frequency lens means, disposed between the
parallel plate lens means and free space, for collimating and
angularly redirecting the radio frequency energy in the directed,
noncollimated beams to produce collimated beams of radio frequency
energy in free space over the relatively large scan angles, such
radio frequency lens means comprising:
(i) a plurality of antenna elements disposed along a
second nonlinear path;
(ii) a second plurality of probes disposed along a third
26

nonlinear path, such directed noncollimated beams being provided
between the first and second pluralities of probes; and
(iii) a second plurality of transmission lines, each one
thereof being coupled to provide a fixed, predetermined electrical
length between a corresponding one of the antenna elements and a
corresponding one of the second plurality of probes.
27

Description

i~3i3s~
Background of the Invention
This invention pertains generally to radio frequency energy
antennas and more particularly to antennas adapted to produce
electromagnetic beams over wide scan angles.
It has been suggested that a so-called "wide angle scanning
array antenna" assembly, as described in U. S. Patent No.
3,755,815, may be used when it is desired to deflect a radar
beam through a deflection angle which may be greater, in any
direction, than the maximum feasible deflection angle of a beam
from a conventional planar phased array. Briefly, such an
antenna assembly consists of a conventional planar phased array
mounted within a structure which acts as a lens. When any por-
tion of such structure is illuminated in a controlled fashion
by a radar beam from the planar phased array, the direction of
such radar 'beam with respect to the boresight line of the planar
phased array is changed in a manner analogous to the way in
which a prism bends visible light. Thus, the deflection angle
of the radar beam propagated in free space may be caused to be
much larger than the greatest deflection angle attainable with
a planar phased array.
Although an assembly made in accordance with the disclosure
of the cited patent is, in theory, suited to the purpose of
deflecting a radar beam through extremely wide deflection angles,
the beam is scanned by controlling the phase provided by each
one of the phase shifters in the planar phased array, and hence
the scan angle is frequency dependent, thereby limiting the
bandwidth of the antenna.

113~35~L
Summary of the Invention
In accordance with the present invention, a radio fre-
quency antenna system is provided for directing a collimated
beam of radio frequency energy in free space, such antenna
system comprising: curved array means, including a plurality of
antenna elements disposed along a nonlinear path, adapted to
direct and provide a noncollimated beam of radio frequency
energy; and, radio frequency lens means, disposed between the
curved array means and free space, adapted to collimate the
radio frequency energy in the directed and noncollimated beam
to produce the collimated beam of radio frequency energy in free
space. With such curved array means, the amplitude distribution
of the collimated beam in free space is significantly more uniform
across the beam compared with that resulting from a planar array
means, thereby improving the perfo-rmance of the antenna system.
In a preferred embodiment of the invention, a second radio
frequency lens means having a plurality of feed ports is
included, each one being associated with a corresponding
collimated beam of radio frequency energy in free space, adapted
for coupling radio frequency energy between each one of the feed
ports and the plurality of antenna elements. With such arrange-
ment, the use of phase shifters in the array means is elimin-
ated, thereby increasing the operating bandwidth of the antenna
system. The disposition of the antenna elements along the curved
path enables the second lens to be smaller in size and have
improved effectiveness.

113135~
In accordance with the present invention, there is provided
a radio frequency antenna system for producing collimated beams of
radio frequency energy in free space, comprising:
(a) curved array means for providing differently directed,
noncollimated beams of radio frequency energy, each one of such
beams being produced from a common aperture, such aperture
comprising a first probe means disposed along a first nonlinear
path, the direction of the noncollimated beams being produced in
accordance with the distribution of the phase of the radio fre-
quency energy across the first nonlinear path of the common
aperture, each one of such noncollimated beams having a different
phase distribution across the first nonlinear path of the common
aperture; and
(b) radio frequency lens means, disposed between the curved
array means and free space, for collimating the radio frequency
energy in the directed, noncollimated beams to produce correspond-
ing collimated and redirected beams of radio frequency energy in
free space, such radio frequency lens means comprising:
(i) antenna means disposed along a second nonlinear path;
(ii) a second probe means disposed along a third nonlinear
path, such directed noncollimated beams being provided between the
first probe means and the second probe means; and
(iii) means for providing fixed, predetermined electrical
length coupling between the antenna means and the second probe
means.
In accordance with the present invention, there is further
provided a radio frequency antenna, comprising:
(a) a first radio frequency lens having an array means
disposed along a peripheral portion of the lens and a plurality
of feed ports disposed along a second, opposing peripheral
portion of the lens, such first and second peripheral portions
- 2a -
'~'`

1131351
being separated by a central portion of the lens, such peripheral
portions being convex outwardly from the central portion of the
lens, each one of such plurality of feed ports being coupled to
such array means through the central portion of the lens, each
one of such feed ports being associated with a corresponding one
of a plurality of beams of radio frequency energy in free space;
(b) probe means disposed along a first nonlinear path to
provide a common aperture for each one of the plurality of beams,
such probe means being coupled to the array means;
(c) a second radio frequency lens, comprising:
(i) a plurality of probe points disposed along a second
nonlinear path; and
(ii) a plurality of antenna points disposed along a third
nonlinear path, the antenna points being coupled to the probe
points through fixed, predetermined electrical lengths.
In accordance with the present invention, there is further
provided a radio frequency antenna comprising:
(a) array means, including a plurality of probes, disposed
along a first nonlinear path, such plurality of probes providing
a common aperture, for producing, from such common aperture,
noncollimated beams of radio frequency energy, each one of such
beams having a central ray at a different angel ~O with respect
to a reference axis;
(b) radio frequency lens means, disposed between the
plurality of probes and free space for collimating the non-
collimated beams and angularly redirecting such collimated beams
at correspondingly different angles, such radio frequency lens
means comprising:
(i) probe means disposed along a second nonlinear path,
such noncollimated beams being disposed between the plurality
of probes and the probe means;
- 2b -

S~l
(ii) antenna means disposed along a third nonlinear path;
and
(iii) means for providing fixed, predetermined electrical
length coupling between the probe means and the anten~ means.
- 2c -

~L~31353~
Brief Description _ f the Drawings
The foregoing features of this invention, as well as the
invention itself, may be more fully understood from the follow-
ing detailed description read together with the accompanying
drawings, in which:
FIG. 1 is a schematic representation of a radio frequency
antenna system according to the invention;
FIG. 2 is a diagram useful in understanding the antenna
system of FIG. l;
10FIG. 3 is a schematic representation of a portion of the
antenna system of FIG. 1 including a ray path diagram for a 90
scan angle;
FIG. 4 is a curve showing the path length differences of
various rays of the portion of the antenna system shown in FIG. 3;
FIG. 5 is a schematic representation of a portion of an
antenna system where antenna elements are disposed along a
straight line and a ray diagram for a 90 scan angle;
FIG. 6 is a curve showing the path length differen.ces of
various rays of the portion of the antenna system shown in FIG. 5;
20FIG. 7 is a diagrammatical sketch of an antenna system
according to the invention;
FIG. 8 is a curve showing the path length error of the
antenna system shown in FIG. 7;
FIG. 9 is a diagrammatical sketch of an antenna system
wherein antenna elements are disposed along a straight line;
FIG. 10 is a curve showing the path length error of the
antenna system shown in FIG. 9;
FIG. 11 is a plan view of an antenna system according to
the invention;
30FIG. 12 is a pictorial view of the antenna system of FIG. 11;
- 3 -

113~35~l
FIG. 13 is a cross-sectional view of a portion of the
antenna sys~em of FIG. 12, such portion being encircled by the
line 13-13 in FIG. 12;
FIG. 14 is a plan view of center conductor circuitry of a
stripline lens parallel plate section used in ths antenna system
of FIG. 13; and
FIGS. 15a, 15b, 15c show antenna patterns of the antenna
system of FIG. 12.
-- 4

~13~3~
Description of the Preferred Embodiments
Referring now to FIG. 1, a radio frequency antenna system 10
is shown to include: a curved arra~ section 11 adap~ed to
direct and provide a non-collimated beam of radio frequency
energy; and, a radio frequency lens 12 disposed between the
curved array section 11 and free spae 13, adapted to col-
limate the energy in the directed and non-collimated beam to
produce a collimated beam of radio frequency energy in free
space. In particular, the radio frequency lens 12 includes a
plurality of antenna elements 14, 16 mounted on the inner and
outer surfaces 18, 20 thereof, respectively, as shown. Each one
o~ pr~cS
of the antenna elements~l4 on the inner surface 18 is connected
through a transmission line 22 to a corresponding one of the
antenna elements 16 on the outer surface 20, as shown. The
length of each one of the transmission lines 22 is selected, in
a manner to be described, to collimate a beam of radio frequency
energy in free space and to increase the deflection angle of
such beam in a manner to be described hereinafter. The spacing
between the individual antenna elements 14 and individual
antenna elements 16 is not critical to the invention so long as
the spacing is such as to avoid grating lobes of the operating
band of frequencies. The ou~er surface 20 of the lens 12 is
disposed about an outer radius R2 from thè center of the lens 12,
and the inner surface 18 of the lens 12 is disposed about an
inner radius Rl from such center, as shown. The center of
lens 12 is at the origin~ O, of an X-Y coordinate system, as
shown. It is now apparent that the lens 12 is here similar to
a known lens such as the one shown in U. S. Patent No. 3,755,815
referred to above.
The curved array sec~ion 11 inclu~ies an arra~ Or
s

s~
p ~ ~L~3s c~
/antenna elements 24 positioned in the near field of the lens 12.
The antenna elements 24 are here regularly spaced along an arc
of a circle having a radius R5 and centered a length R4 from the
center or origin, O, of the semi-circular lens 12, such that
R52 = R12 ~ R42, as shown. The antenna elements 24 of the ~-
c ~rv~d
array means 11 are coupled to array ports 25 of a radio
frequency parallel plate lens 26 through individual transmission
lines 29, here coaxial cables, as shown. The parallel plate
lens 26 has a plurality of feed ports 28 which are coupled to a
conventional radar transmitter/receiver 27. The shape of the
parallel plate lens 26, the length of transmission lines 29,
the position of the antenna elements 24 and length of trans-
mission lines 22 are selected in a manner to be described to
provide a plurality of collimated beams of radio frequency
energy in free-space, each one of such beams being associated
with a corresponding one of the feed ports 28 of the parallel
plate lens 26. The selection of such parameters is described
in connection with the following analysis of the antenna system
10. The analysis is based on geometrical optics, or ray optics.
This approach is valid when, as here, the lens 12 is in the near
field of the curved array section 11.
Referring now also to FIG. 2, the selection of the length
of the transmission lines 22 of lens 12 will be discussed. In
such FIG. 2 an exploded view of two rays 32, 32' is shown
passing through the lens 12, such rays 32, 32' being displaced
a small angle Q~ (FIG 1). The refraction or ray bending caused
by the lens 12 may be determined by comparing the electrical
path length of such rays 32, 32' as they pass through the lens
12 to points D, F along a common planar wavefront, W. For
collimation, the total electrical path length from point A to

1~313S~l
point B to point C to point D of ray 32 must be equal to the
total electrical path length from point E to point F of ray 32'.
That is:
~ = ~ (1~
If the displacement between rays 32, 32' along inner surface 18
is ~Sl and the displacement between such rays 32, 32' along
outer surface 20 is ~S2, and if the electrical lengths of the
transmission line 22 through which such rays 32, 32' pass are
P and P + QP, respectively, then from Eq. ~1) and FIGS. 1 and 2,
10~Sl sin ~ + P + ~S2 sin ~ = P+~P ~2)
where:
= the angle of incidence of ray 32; and
~ is the angle of refraction of ray 32.
Since, from FIG. 1,
~Sl = Rl ~
and QS2 = R2 ~ (3)
where ~9 is small, then from Eqs. ~2) and ~3)
a~ Q9 1 ~a ~0 Rl sin ~ ~ R2 sin ~ (4)
20Considering a "central" Tay (i.e~ ray 34 (PIG. 1) a ray
normal to the lens 12, ~ = O)) from Ea. ~4)
dP¦ = R2 sin ~ = R2 sin ~K~o-ao) (5)
3=~o
where:
K is the angle amplification factor (i.e., the ratio of
the angle of refraction of the central ray 32 to the angle
3O); and
~O is the angle between the central ray 32 and the Y axis,
as shown.
From Eqs. ~4) and ~5)

~131351
p(~O) ; ~ R2 sin (K~o-~o) d~o (6)
= K-l [l-cos (K~o-~o)] (7)
where K is a constant for all angles ~O~
Equation (7) is used to compute the electrical length P of
each one of the transmission lines at each angle oO from the
vertical axis (4) for a predetermined angle amplification ratio
K and outer radius R2.
Having established the electrical lengths of the trans-
misslon lines 22, the phase distribution required across thecurved array of antenn.a..elements. 24 is determined to desi~n
of the curved array section ll, in.particular the position
of the antenna elements 24 and the electrical length of the
transmission lines 29.
From FIG. 1 the arc 27 about which the antenna elements 24
are disposed may be represented by the following equation:
x2 ~ (Y-R4)2 = R52 = R12 ~ R42 (8)
For an exemplary one of the antenna elements 24, here
antenna element 24a, at coordinates Xl, Yl;
Xl = Rl sin ~ - L3 sin (~ 9)
Yl Rl cos ~ - L3 cos (9 - ~) (10)
where (from FIG. 1):
L3 is the electrical length of ray 32 from antenna element
24a to the inner surface 18 of the lens 12; and
a is the angular deviation between:
(a) a normal N from the original, O, of the X-Y
coordinate system to the point of intersection of
ray 32 and inner surface 18; and
(b) the vertical axis, Y.0

~3:~35~
Substituting Eqs. (9) and (10) into Eq. (8) it may be shown that:
L = R cos ~-R cos(~-a) +
3 1 4
.. . .
~[~ cos ~ - R cos (~ )]2+ 2R R cos el (12)
1 4 1 4
(The choice of sign in Eq. (12) is made according to the physical
requirements, that is, positive lengths. The plus sign was used
hereinafter). Further, fTom Eqs. ~4) and ~5)
R sin ~ +R sin ~ = R sin~Ka -~)
1 2 2 o
or
sin ~ = [R /R ] [sin ~K~ -~) - sin ~K9 -~)] ~13)
2 1 o
Therefore, Eq. ~12) may be used to compute L where ~ is
defined by Eq. ~13).
For a predetermined angle amplification ratio K the total
differential pathlength ~L between the central ray 34, i.e. the
ray which passes through X = 0, Y ~ 0, and ray 32 may, from
FIG. 1, be represented as
~L = [L ~9) + P~)] - [L ~a ) + P~ ) + T~)] (14)
3 3 o o
where
T(~) = R [cos ~K~ cos ~K~ -3)] ~15)
2 o o o
FIG. 3 shows a ray diagram for a lens 12 having an inner
radius R of 1.2, an outer radius R of 1.5 and an amplification
factor K of 1.5. Here the ~rved array includes antenna

1~3~3S~
elements 24 disposed along an arc of radius R of 1.7 ~i.e.
R4 = 1.2). A 90 scan is shown, that is 0 = 60 degrees. FIG. 4
shows the differential pathlength ~L as a function of ¦X/R ¦ for
O = 0, + 45, + 60 for the arrangement shown in FIG. 3 where R
o o
is the length of half of the array 24 measured along the X axis,
ere 1.0, as shown in FIG. 1. Note that R , R , R , R are
1 2 4 5
normalized by R .
For comparison, a ray diagram for the lens 12 shown in FIG. 3,
here with a linear array of antenna elements 24 (R = "Flat" or
"linear"), is shown in FIG. 5. A 90 scan is shown, that is,
O = 60 degrees. The differential pathlength ~L for each arrange-
ment as shown in FIG. 5 is shown in FIG. 6 for ~ = 0, + 20,
+ 30, + 40, + 50 and + 60. From FIGS. 3 and 5 it should be
noted that the amplitude distribution across the wavefront is more
uniform for the curved array of antenna elements 24 (FIG. 3) than
for a linear array of antenna elements 24 (FIG. 5). That is, for
the flat or linear array system (FIG. 5) severe amplitude distor-
tion occurs and is visible in the ray density by the "bunching"
of rays of the upper portion of the beam for a 90 scan (0 = 60).
In contrast to this, the curved array in FIG. 3 has very little
amplitude distortion as evidenced by the uniform ray densities
shown in FIG. 3.
Referring-now again to FIG. 1, the disposition of the
antenna elements 24 along the arc of radius R and the lengths of
transmission lines 29 is selected in a manner now to be described
to form a noncollimated beam having an angular direction ~
of the cen~ral ray related to a corresponding one of the feed
ports 28 and having a phase distribution across the curved
array of antenna elements 24 such that the radio frequency lens 12
collimates the radio frequency energy in the directed and non-
collimated beam to produce a collimated beam in free space
- 10 -

~i3i3S~
having an angular deviation K~ . That is, the parallel plate
lens 26, transmission line lengths 29 and disposition of antenna
elements 24 are arranged so that the electrical length from one
of the feedports 28 to all points on the ~avefront of the coTres-
ponding beam in free space is electrically equal. Hence the
antenna system 10 is adapted to produce a plurality of collimated
beams in free space, each one of such beams corresponding to one
of the feed ports 28. (The antenna system 10 may therefore be
considered as being a multibeam antenna system). Here feedports
28a, 28b, 28c direct noncollimated beams having angular deviations
of -60, 0 and +60, respectively. It follows then that the
design of the curved array section 11 is such ~hat the elec~rical
lengths from each one of the feed por~s 28 to the array of antenna
elements 24 are the conjugate of the differential pathlength ~L
shown in FIG. 4 for ~ = 60.
As discussed in an article entitled "Wide-Angle Microwave
Lens for Line Source Applications" by W. Rotman and R. F. Turner
in the November 1963 issue of IEEE Transactions on antennas and
propagation, pgs. 623 to 632, and U. S. Patent No. 3,761,936
entitled "Multi-beam Array Antenna, inventors Donald H. Archer,
Robert J. Prickett and Curtis P. Hartwig, issued September 25,
1973 and assigned to the same assignee as the present invention,
the feed ports 28 may be disposed in an array of arbitrary shape,
but must have a definite length or distance parameter, here X, to
define the position of each antenna element 24 as exemplary
antenna element 24a being shown at length or distance X in FIG. 1.
Further, three focal points are chosen, two at feed ports 28a,
28c, i.e. at focal distances F and angles +~land -~l~ respectively,
and the third at feedport 28b, i.e. at focal length G and
angle ~ = 0.
- 11 -

~13~;~
Considering three arbitrary phase fronts or distribution
across the cur~ed array of a~tenna elements as P ~X),
P (X), P ~X) where P (X) is the phase distribution associated
2 3
with feedport 28a, P (X) is the phase distribution associated
with the feed port 28c and P (X) is the phase distribution
associated with feed port 28b. (It is assumed that the phase
for all distributions at X = 0 is zero, i.e. P (0) = P (0) =
P (0) = 0.) As discussed above, the phase distributions will
then be the conjugate of the differential pathlengths ~L from
the planar wa~efronts of beams at ~O= -60 (scan angle K60),
3 = + 60 (scan angle +K60) and 9 = 0, respectively. For
o o
the analysis below an X, Y' coordinate system is chosen, such
coordinate system being at the center of the arc of the array
ports 25 as shown in FIG. 1.
From FIG. 1 the three pathlength equations may be written
as:
2 2l
v(F cos ~ + Y') + (F sin ~ + X) + W + P (X) = F + W
(16)
~(F cos ~ + Y') + (F sin ~ - X) + W + P (X) = F + W
1 2 2l (17)
I~(G + Y ) + X + W + P (X) = G + W (18)
where W is the electrical length of the central one of the
transmission lines 29; and W is the electrical length of
the transmission line 29 at a distance X from the Y or Y'
~xis.
In solving Equations (16), (17) and (18) W will be assumed
zero for simplification, it belng realized that the addition or
subtraction of equal pathlengths will not change the analytical
design of the curved arra~ sec~ion 11. To further simplily
- 12 -

~L1313~1
the analysis the antenna system 10 is symmetrical about the Y or
Y' axis for both the lens 12 and the parallel plate lens 26.
Equations ~16), (17) and (18) may be rearranged as:
X [Pl(X) P2(X)~ ~(p (X) + P (X) - 2F~ + 2W¦=
4F sin ~ ~ 1 2
= X + X W (19)
0
( ~ p 2~x) p (X) +2G P ~X)
10Y' = - 2(G-F cos ~) l 2 3 3
- FPl(X) - FP2(X)) + 2W (G-F+P (X) + P (X)-2P (X))3
= -(Y + WY ) ~20)
0
Substituting Eqs. (19) and (20) into Equation (18) yields a
quadradric in W:
AW + 2BW + C = 0 (21)
where 2
A = I-X y 2
B = P (X) - G + Y G - X X - Y Y
3 1 . 0 1 0
C = P (X) - 2G P (X) + 2G y - y 2 X 2
3 3 o
That is,
-B + ~
W(X,Y) = .4 (22)
- 13 -

~i3~L35~
where X and Y are found from Eqs. (19) and ~20). The choice of
sign in Eq. 22 is made to assure that the results satisfy the
original pathlength Bquations (16), (17) and (18).
This completes the design of the cl~rved array sec~ion 11.
That is, for three phase distributions P (X), P (X), P (X) the
1 2 3
X,Y position of the antenna elements 24 and the electrical lengths
W of the transmission lines 29 may be calculated for a parallel
plate lens 26 having predetermined focal distances F and G to
provide three "perfect" focal points, i.e. three "perfect"
differential pathlengths at 0 = 0, -60, ~60 to enable colli-
mation by the lens 12 of scan angles of 0, -K60 and +K60,
respectively.
At beam poTts 28 between or intermediate the three "peTfect"
focal points ~i.e. feed ports 28a, 28b, 28c) pathlength errors
will occur. The amount of pathlength error depends on two factors:
~1) the phase distribution P (X) required by the lens 12 at some
intermediate scan angles (i.e. intermediate scan angles -K60,
0, +K60) and (2) the pathlengths provided by the parallel plate
lens 26 for the corresponding intermediate ones of the feed ports
28. The pathlength L' provided by the parallel plate lens 26
from a feed port 28 at an angle y and at a length H to the
antenna elements 24 at distance X may be determined by:
L'(X,y,H) = ~H cos y + Y ) + (H sin y ~ X)2 +W (23)
The total pathlength error of the entire antenna system 10
will therefore be:
E~X,a) = ~L - (L -H) ~24)
- 14 -

11313Sl
FIG. 7 shows an antenna system having the semicircular radio
frequency lens 12 (i.e. R = 1.2, R = 1.5, R = 1.2, K = 1.5)
1 2 4
shown in FIG. 3 with a cuTved array section 11 designe~ to provide
"optimum" performance, "optimum" being loosely defined in terms of
lens size, lens shape, geometry to enable the feed ports 28 and
the array ports 25 to be "facing" and pathlength error for inter-
mediate feed ports 28. For such design G/F-= 1.10, ~1= + 40'
l/F =0.65. FIG. 8 shows the overall path length error E at
intermediate unfocused scan angles over as a function of X/R . As
noted, the peak error spread (maximum negative error to maximum
position error) is in the order of 0.00185R .
For comparison, FIG. 9 shows the "optimum" parallel plate
lens 26 design for a linear array of antenna elements using the
same lens configuration (i.e. R = 1.2, R = 1.5, K = 1.5) as
shown in FIG. 5. Here-G/F = 1.25, ~1= + 25, l/F = .45). It
should first be noted that the size of the parallel plate lens 26
is about 50% larger than the parallel plate lens shown in FIG. 7
using a curved array of antenna elements 24. Further, the shape
of the parallel plate lens in FIG. 9 is relatively inefficient
since it is more circular in shape than the parallel plate lens
shown in FIG. 7, that is, because the extreme portions 27 of the
feed ports 25 are not opposing the arc of array poTts 25 thereby
reducing the effectiveness of the lens 26. Error (E) for this
system is shown in FIG. 10. Note that the error (E) spread is
here 0.015R .
Referring now to FIGS. 11 and 12, an antenna system 10' is
shown to include a parallel plate lens 26 here designed as
described above having a plurality of feed ports 28 along one
portion of its periphery (i.e. portion 48) and a plurality of
array poTts 25 disposed about an opposite portion of the periphery
- 15 -

1~3135~L
~portion 49). The parallel plate lens 26 is coupled to a parallel
plate section 50 through transmission lines 29, as shown. The
transmission lines 29 are here coaxial cables and connect the
array ports 25 of the parallel plate lens 26 to the parallel
plate section 50 using conventional coaxial connectors 51, as
shown. The parallel plate section 50 is used to confine the
radiation between the lens 12 and the parallel plate lens 26 to a
single two-dimensional plane.
The parallel plate section 50 is here of stripline construc-
tion having strip or center conductor circuitry 53 disposed be-
tween a pair of ground planes. The strip or center conductor
circuitry 53 is shown in FIG. 14. Such circuitry 53 is formed on
a suitable dielectric substrate 57 by suitably etching a copper
clad, dielectric substrate 57 using conventional photolithographic
and chemical etching techniques. The coaxial connectors 51 on the
parallel plate section 50 are connected to strip transmission
lines 55 which terminate into antenna elements 24, as shown. The
strip transmission lines 55 are of equal length and are used to
enable sufficient mounting space for the coaxial connectors 51~
As shown in FIG. 14, the antenna elements 24 are disposed along an
arc of radius R where R 2 = R 2 + R 2 and where here R is shown
1 4 4
equal to R . Further, the length of the array of antenna elements
24 is here 2R , as shown. The antenna elements 24 are formed
along a portion of the periphery of a conductive region 59, as
shown. Disposed along an opposite portion of the conductive
region 59 are the antenna elements 14, as shown. Such antenna
elements 14 are coupled to coaxial connectors 61, through strip
transmission lines 63, as shown. The strip transmission lines 63
are of equal length and are used to enable sufficient mounting
mounting space for the coaxial connectors 61.
- 16 -

~L~313S~
The coaxial connectors 61 are connected to transmission
lines 26, as shown. The transmission lines 22 are here coaxial
cables of proper electrical length as discussed in connection
with Equation (7) above~ As shown in FIG. 13, ends of the
coaxial cables 22 provide the antenna elements 16. That is, the
outer conductors of the cables 22 are electrically connected to a
first conductive member 64 and the center conductors 60 of such
cables 22 are connected to a second conductive member 64. The
conductive members 62, 64 form a ribbed, flared radiating struc-
ture for the antenna system. It is noted that the antenna
elements 16 are disposed along an arc of radius R2 as dlscussed
in connection with FIG. 1.
Referring now to FIGS. 15a, 15b, 15c, antenna patterns are
shown for the antenna system shown in FIG. 12 operating at fre-
quencies of 8 GHz, 12 GHz and 15 GHz, respectively, over a + 90
total scan angle, i.e. a from -60 to +60 where K = 1.5;
R /R = 1.2; R /R = 1.2; and R /R = 1.5. The actual value of R
l o 4 o 2 o o
is selected in accordance with the desired beamwidth and operating
band of frequencies. For an operating band in the order of 8 to
15 GHz and a 6 beamwidth a length R of 6.05 inches (in air
dielectric) is typical. It is no~ed that the length R must be
scaled in a well known manner, by the dielectric constant used,
i.e. here by the dielectric constant of substrate 57 ~FIG. 14).
For the lens 26, here F = R /.65; G = l.lOF; and ~1= + 40- Also,
thirty-five array ports 25 and twenty-nine feed ports 28 were used
in the lens 26.
The design of the lens 26 may be determined in accordance
with Equations (19), (20~ and (22) above. Here other positions
for the thirty-five array ports 25 and the length of ~he coaxial
cables 29 are as follows:

Array Ports 25 X ~inches) -Y' (inches) W (inches)
#1, #35 + 6.416 4.051 2.094
#2, #34 + 6.193 3.582 1.837
#3, #33 + 5.939 3.140 1.598
#4, #32 + 5.656 2.727 1.379
#5, #31 + 5.346 2.346 1.178
#6, #30 + 5.015 1.992 0.994
#7, #29 + 4.663 1.669 .829
#8, #28 + 4.292 1.376 .679
#9, #27 + 3.905 1.114 .547
#10, #26 + 3.505 0.880 .431
#]1, #25 + 3.089 0.674 .328
#12, #24 + 2.669 0.496 .240
#13, #23 + 2.235 0.342 .165
#14, #22 + 1.797 0.220 .106
#15, #21 + 1.354 0.125 .061
#16, #20 + 0.912 0.055 ~025
#17, #19 + 0.455 0.013 .006
#18 .0 .0 .0
- 18 -

113i351
Here the positions for the twenty-nine feed ports Z8 are as
follows:
Feed Ports 28 ~ ~degrees)H (inches~
. .
#1, #29 + 40 9.308
#2, #28 + 36.78 9.383
#3, #27 + 33.67 9.478
#4, #26 + 30.64 9.580
#5, #25 + 27.68 9.683
#6, #24 + 24.77 9.782
10#7, #23 + 21.91 9.873
#8, #22 + 19.09 9.957
#9, #21 + 16.30 10.030
#10, #20 + 13.54 10.093
#11, #19 + 10.80 10.145
#12, #19 + 8.09 10.186
#13, #17 + 5.39 10~215
#14, #16 + 2.69 10.233
#15 .0 10.238
It is noted that all dimensions are given for air dielectric and
the actual lens dimensions and cable lengths are reduced by the
refraction index of the material used in accordance with well
known practice.
With regard to the circular lens 12, here sixty-nine antenna
elements 14 ~and sixty-nine antenna elements 16) equally spaced
in angle over 180~ with end elements at 0 and 180, respectively.
Hence, the angular location of the elements, 9 , may be repre-
sented by the following equation:
9 = 90 - 2.6471~n-l)
where n = 1, + 2, + 3... + 35, as shown in FIG. 14 for antenna
- 19 -

~13~3S~
elements 14. The antenna elements 24 are regularly spaced along
an arc having a radius R , as shown in FIG. 14, and such spacing
may be represented by the following equation:
~ = 2.0631 (m-18)
where m = 0, 1, 2...35 and ~m is the angle between the Y axis and
the radius R to the mth antenna element 24, as shown in FIG. 14.
Having described a preferred embodiment of this invention,
it is evident that other embodiments incorporating these concepts
may be used. For example, while a two-dimensional antenna system
has been described to provide a fan-shaped beam, a plurality of
such systems may be stacked to form a planar antenna system to
provide a beam with a planar cross-section. It is felt, there-
fore, that this invention should not be restricted to the dis-
closed embodiments, but rather should be limited only by the
spirit and scope of the appended claims.
- 20 -