U.S. patent number 3,662,393 [Application Number 05/012,970] was granted by the patent office on 1972-05-09 for multimode horn antenna.
This patent grant is currently assigned to Emerson Electric Co.. Invention is credited to Seymour B. Cohn.
United States Patent |
3,662,393 |
Cohn |
May 9, 1972 |
MULTIMODE HORN ANTENNA
Abstract
A conical or pyramidal horn-radiator having small flare angle
changes within the horn at cross-section dimensions much larger
than the input waveguide, to excite higher order modes which
control the E-plane aperture distribution and produce a tapered
aperture field in the E-plane. Equal E- and H-plane beamwidths are
thereby obtained. The horn has particular use as a feed for a
parabolic reflector, such as a Cassegrain antenna. The flare angle
changes are used for pattern improvement in a first frequency band,
and separate means are provided for pattern improvement in a second
band.
Inventors: |
Cohn; Seymour B. (Tarzana,
CA) |
Assignee: |
Emerson Electric Co. (St.
Louis, MO)
|
Family
ID: |
21757626 |
Appl.
No.: |
05/012,970 |
Filed: |
February 20, 1970 |
Current U.S.
Class: |
343/786 |
Current CPC
Class: |
H01Q
13/025 (20130101) |
Current International
Class: |
H01Q
13/02 (20060101); H01Q 13/00 (20060101); H01q
013/00 () |
Field of
Search: |
;343/772,783,786 |
References Cited
[Referenced By]
U.S. Patent Documents
Primary Examiner: Lieberman; Eli
Claims
Having thus described the invention, what is claimed and desired to
be secured by Letters Patent is:
1. Means for transmitting or receiving a beam of electromagnetic
wave energy comprising:
an input transmission line having an output end, said transmission
line comprising at least one waveguide proportioned to propagate
electromagnetic wave energy in at least a first frequency band in a
dominant mode, and
a horn of regular cross-section, said horn comprising:
a first flared section having a positive flare angle and having an
input end and an output end, said input end of said first flared
section communicating with said output end of said input
transmission line, said output end of said first flared section
having a large cross-sectional dimension at least three times the
cross-sectional dimension of the output end of the waveguide;
an output flared section having a positive flare angle and having
an input end and an output end, said output end of said output
flared section comprising an aperture opening into free space;
and
connecting means for connecting said output end of said first
flared section with said input end of said output flared section,
said connecting means forming a plurality of small angle changes
within said horn including at least a first flare angle change with
said first flared section and an output flare angle change with
said output flared section,
said flare angle changes being proportioned to convert a desired
portion of electromagnetic wave energy transmitted from said input
transmission line through said horn in said first frequency band,
from said dominant mode to at least one higher mode, and
said sections and said connecting means being proportioned such
that in transmitting from said input transmission line through said
horn in said first frequency band, said higher mode wave energy
produced at said flare angle changes causes the horn to suppress
sidelobes and to produce approximately equal E- and H-plane
beamwidths.
2. The means of claim 1 wherein said input transmission line is a
waveguide of the same regular cross-section as said horn.
3. The means of claim 1 wherein said horn is square in
cross-section, said dominant mode is TE.sub.10, and said one higher
mode comprises TE/TM.sub.12.
4. The means of claim 1 wherein said connecting means comprises a
second flared section connected to said first flared section and a
third section connected to said second flared section, the flare
angle of said second flared section being approximately half the
sum of the flare angle of said first flared section and the flare
angle of the third section, said second flared section being so
proportioned that the flare angle change between said second flared
section and said third section cancels substantially all of a mode,
different from said dominant mode and said one higher mode,
produced at the flare angle change between said first flared
section and said second flared section.
5. The means of claim 3 wherein said portion of TE/TM.sub.12 mode
produced at said flare angle changes yields a ratio of TE/TM.sub.12
to TE.sub.10 of between about 0.65 and about 0.84.
6. Means for transmitting and receiving electromagnetic wave energy
comprising:
a waveguide part of uniform, regular cross-section, said waveguide
part being proportioned to support a first mode in a transmit
frequency band and in a receive frequency band, and to support a
second, higher, mode in one only of said frequency bands,
a horn part of the same regular cross-section as said waveguide
part connected to said waveguide part,
means in said waveguide part for converting a desired portion of
said first mode of said one of said frequency bands to said higher
mode, said means in said waveguide part having substantially no
effect on the other of said frequency bands, and
means in said horn part for converting a desired portion of said
first mode of the other of said frequency bands to a second,
higher, mode, said means in said horn part comprising a plurality
of small flare angle changes at large cross-sectional dimensions of
said horn part at least three times the cross-sectional dimension
of the waveguide part.
7. Antenna means for transmitting and receiving electromagnetic
wave energy comprising:
an input transmission line part having an output end, said
transmission line comprising at least one waveguide proportioned to
propagate electromagnetic wave energy in a dominant mode in at
least a transmit frequency band and in a receive frequency band,
and
a horn part connected to said waveguide part at one end and having
an aperture at its other end,
first means in said horn part for converting a desired portion of
said first mode of one of said frequency bands to a second, higher,
mode, said first means comprising at least one small flare angle
change at a large cross-sectional dimension of said horn part at
least three times the cross-sectional dimension of the output end
of the waveguide, said horn part being proportioned to produce a
desired phase relationship between said first and second modes at
said aperture, and
second means at the output end of the transmission line part for
converting a portion of said first mode of the other of said
frequency bands to said higher mode, said second means being
located at a cross-sectional dimension of said antenna means
substantially smaller than said first means and having
substantially no effect on said one frequency band.
8. Means for transmitting or receiving a beam of electromagnetic
wave energy comprising:
an input transmission line comprising at least one waveguide
proportioned to propagate electromagnetic wave energy in at least a
first frequency band in a dominant mode,
a horn part connected to said transmission line, said horn part
having at least four axial flare sections of different flaring
angles, one of said flare sections converting a desired portion of
said dominant mode to a higher order mode and comprising a small
flare angle change in said horn at a large cross-sectional
dimension of said horn part at least three times the
cross-sectional dimension of the input waveguide, said horn part
being proportioned to produce a desired phase relationship between
said dominant mode and said higher order mode induced by said flare
angle change.
9. The means of claim 8 wherein said small flare angle change
induces said first-mentioned higher order mode and a second higher
order mode, and including means, comprising at least a second small
flare angle change, proportioned and spaced from said
first-mentioned small flare angle change to cancel said second
higher order mode.
10. Means for transmitting or receiving a beam of electromagnetic
wave energy comprising:
an input transmission line having an output end, said transmission
line being proportioned to propagate electromagnetic wave energy in
at least a first frequency band in a dominant mode, and
a horn of regular cross-section, said horn comprising a first
section; a second, flared, section connected to said first section
to form a first flare angle change at a first cross-sectional
dimension of said horn; and a third section connected to said
second section to form a second flare angle change at a second
cross-sectional dimension of said horn, the product of said first
flare angle change times said first cross-sectional dimension being
approximately equal to the product of the second flare angle change
times said second cross-sectional dimension, said first flare
change inducing a first higher order mode and a second higher order
mode in said first frequency band, said second section being so
proportioned that said second flare angle change cancels
substantially all of the second higher order mode in said first
frequency band.
Description
BACKGROUND OF THE INVENTION
This invention relates to an improved horn design and a method for
improving the E-plane aperture distribution of a pyramidal or
conical horn (i.e. a horn having, respectively, a square or a
circular cross-section throughout its length). For convenience, a
horn of either of these configurations will be referred to herein
as a horn of regular cross-section. It has particular, but not
exclusive, use as a feed horn for a parabolic reflector.
It has long been sought, in the use of both pyramidal and conical
feed horns for radiating electromagnetic energy from a waveguide
into free space, to produce beams having low sidelobes and equal E-
and H-plane beamwidths. A number of proposals have been made for
producing these desirable characteristics in a horn, many of which
have been rather successful. All of these approaches, however, have
had certain drawbacks, such as limitation to narrow bandwidths,
high dissipation or reflection losses, low power capabilities,
limitation to particular polarizations, cost of fabrication, or
complexity.
One of the objects of this invention is to provide a horn and a
method for reducing the sidelobes and equalizing the E- and H-plane
beamwidths of a transmitted beam.
Another object is to produce such a horn which is of regular
cross-section, thereby permitting circular or any linear
polarization.
Still another object is to provide such a horn which has a simple,
clean construction providing economical fabrication, high power
capabilities, minimal dissipation loss, and low VSWR.
Other objects will become apparent to those skilled in the art in
the light of the following description and accompanying
drawings.
SUMMARY OF THE INVENTION
In accordance with this invention, generally stated, a horn and
method are provided for producing a desired tapered aperture field
in the E-plane in a horn of regular cross-section, by inducing
higher order modes in the horn by means of small changes of flare
angle at one or more points within the horn. The changes of flare
angle are at large cross-sectional dimensions of the horn. The term
"small" as applied to the flare angle changes is used herein to
indicate a change of a few degrees, up to approximately 15.degree..
The change may be either positive or negative, as will be explained
more fully hereinafter. The term "large" as applied to the
dimensions at which the changes occur indicates a width of at least
three or four times that of the smallest waveguide, of the same
regular cross-section as the horn, which will support a dominant
mode of a frequency band to be affected by the horn. Otherwise
stated, although widths larger than the free space wavelengths are
required to propagate TE.sub.12 or TM.sub.11 modes respectively in
square or circular cross-sections, the means known heretofore have
involved the use of rather severe discontinuities, such as steps or
large flare angle changes, for inducing higher order modes at
dimensions of less than 1.5 wavelengths. The discontinuities of
this invention are at dimensions which are substantially greater
than 1.5 wavelengths. Flare angle changes at smaller dimensions may
also be utilized, but the major part of the higher order mode
energy is induced by the flare angle changes at large
cross-sectional dimensions.
For convenience, the operation of the horn of this invention is
described in terms of transmitting wave energy from a transmission
line feeding the throat of the horn, through the horn and out of
the horn's aperture. It will be understood, however, that the
operation of the horn may be, and generally will be, reciprocal.
Therefore, in a frequency band for which the flare changes are
designed to be effective, the horn will provide the same advantages
in either a transmit or receive function. In fact, as will be
described more fully hereinafter, in the preferred embodiment the
flared sections are proportioned to have a minimal cumulative
effect on wave energy in a transmit band, and are effective only on
wave energy in a lower frequency receive band. Separate means are
provided in the throat of the horn for stimulating higher order
modes in the transmit band.
In a preferred form of the invention, the horn is a feed horn for a
Cassegrain type antenna, fed at its throat through a waveguide of
the same regular cross-section as the horn. Also in the preferred
embodiment, two approximately equal flare angle changes are
provided in at least one part of the horn, and the length of the
section between the changes is proportioned to cancel yet higher
modes than the dominant mode supported by the waveguide or a first
higher order mode induced by the flare angle changes. Also in the
preferred embodiment, the regular cross-section of the horn is
square, the dominant mode in the waveguide is TE.sub.10, and the
first higher order mode induced by the flare angle changes is
TE/TM.sub.12. The term TE/TM.sub.12 denotes a linear superposition
of TE.sub.12 and TM.sub.12 mode amplitudes in such amplitude
relationship that cross-polarized E-field components are
cancelled.
For small flare angle changes, the effect of multiple changes is
additive. Therefore, multiple flare angle changes may be utilized
to produce sufficient amplitude of the higher order mode for
equalizing the E- and H-plane beamwidths, for example.
BRIEF DESCRIPTION OF THE DRAWINGS
In the drawings,
FIG. 1 is a view in side elevation of one illustrative embodiment
of antenna of this invention;
FIG. 2 is a diagrammatic detail in section showing theoretical
phase front relationships at a flare angle change (involving a
decrease in flare angle) of a horn part of an antenna of this
invention;
FIG. 3 is a diagrammatic sectional view corresponding to FIG. 2,
showing theoretical phase front relationships at an increasing
flare angle change;
FIG. 4 is a detail illustrating one aspect of the present
invention;
FIG. 5 is a detail in section of a waveguide part of the antenna
shown in FIG. 1;
FIG. 6 is a diagrammatic representation of the antenna of FIG. 1 as
a cascaded directional coupler; and
FIGS. 7a-7c show a set of graphs showing receive band E- and
H-plane aperture distribution.
DESCRIPTION OF THE PREFERRED EMBODIMENT
Referring now to the drawings, and particularly to FIG. 1,
reference numeral 1 indicates one illustrative embodiment of means
of this invention for transmitting or receiving a beam of
electromagnetic wave energy, i.e. an antenna. The antenna 1
includes an input transmission line part 3 in the form of a
waveguide 31 and a horn part 5. The waveguide 31 is square in
cross-section and is proportioned to support electromagnetic wave
propagation in the TE.sub.10 mode in both a 3.7 to 4.2 GHz receive
band and a 5.925 to 6.425 GHz transmit band. These frequencies
correspond to wavelengths on the order of 3 and 2 inches
respectively. Means 35 are provided in the waveguide for inducing
higher order modes in the transmit band. The waveguide 31 is
proportioned to support a dominant mode in both the receive and
transmit band, but to support the higher mode induced by the means
35 only in the higher frequency transmit band.
The horn part 5 is pyramidal, that is it is square in cross-section
throughout its length. The horn part 5 consists of a series of
sections 51, 53, 55, 57 and 59, joined to each other in end to end
relationship to form flare angle changes 61, 63, 65 and 67
respectively. The input end of the first section 51 is joined to
the output end of the waveguide part 3 to form a flare angle change
33. The output end of the waveguide and of each section matches the
input dimension of the next successive section, so that the flare
angle changes form discontinuities, but not steps, in the horn
part. Each section has a flare angle .theta. which may be defined
as the angle formed by the sides of the section with a central axis
of symmetry of the antenna. The first flared section 51 has an
input dimension a.sub.1 and a positive flare angle .theta..sub.1,
the second flared section 53 has an input dimension a.sub.2 and a
flare angle .theta..sub.2, less than .theta..sub.1 ; the third
section 55 is straight, and has a cross-sectional dimension a.sub.3
and a flare angle .theta..sub.3 equaling zero; the third flared
section 57 has an input dimension a.sub.4 equal to a.sub.3 and a
positive flare angle .theta..sub.4 ; and the output flared section
59 has an input dimension a.sub.5 and a positive flare angle
.theta..sub.5 greater than .theta..sub.4. The output flared section
59 has an output dimension, i.e. an antenna aperture 52 dimension,
of a.sub.6. The sections between the first flared section 51 and
the output flared section 59 may be considered as connecting means
for these two flared sections.
The antenna 1 forms a part of an antenna system, which includes
signal generating and receiving means, not shown. The antenna of
FIG. 1 is particularly adapted for use in a Cassegrain antenna with
a 97 foot diameter parabolic reflector for communication satellite
systems. Cassegrain antenna systems are well known and are not here
illustrated. Such a system also requires a transmit-receive
junction, circular polarizer and difference-pattern couplers, all
of which may be of standard construction and are not shown.
The details of the structure of the antenna 1 may best be
understood after a brief discussion of an approximate analysis of
the principles used in designing such a device.
The use of flare angle changes to induce higher modes for aperture
pattern improvement has been described heretofore, but application
of this technique has been limited both by lack of understanding of
the principles involved and by a belief that changes should be at
the smallest possible dimensions, to suppress higher order modes.
As a result, the design of such devices has been confined to
rudimentary and inflexible designs useful only in narrow bandwidths
and for limited purposes. They have therefore been impractical for
most uses, especially uses requiring both transmit and receive
functions to be performed by the same horn.
The following analysis of the effects of flare angle changes and
section lengths on relative phase amplitudes, relative phase angles
and aperture distribution involves a number of approximations, but
is accurate enough to provide formulas adequate for design
purposes.
In FIG. 2 a section 71 of flare angle .theta..sub.a is joined to a
section 73 of flare angle .theta..sub.b = 0. Phase fronts d and e
apply to the two horn sections 71 and 73 respectively and intersect
at the flare angle discontinuity point 75 at cross-sectional
diameter a. The maximum separation between these phase fronts
is
.DELTA.z = R - L = a/2 [csc.theta..sub.a - cot.theta..sub.a ] = a/2
tan .theta..sub.a
If .theta..sub.a is less than about 0.4 radians (23.degree.),
.DELTA.z may be approximated by
Similarly, if .theta..sub.a and .theta..sub.b both differ from
zero, as shown in FIG. 3, the phase front separation is
.DELTA.z = (a/4) (.theta..sub.a - .theta..sub.b) (3)
The TE.sub.10 mode phase difference corresponding to
.DELTA.z is .phi..sub.m = 2 .pi..DELTA.z/.lambda..sub.g, or
where .lambda..sub.g is guide wavelength of the TE.sub.10 horn mode
and a is the E-plane height at the flare change point 75. For
.theta..sub.a and .theta..sub.b small, and an H-plane width greater
than about two wavelengths, .lambda..sub.g is approximately equal
to .lambda..
Assume for now that the horn is sectoral with E-plane flare and
constant H-plane width. Then with a small flare angle change, an
incident TE.sub.10 wave arriving from the left yields predominately
TE.sub.10 on the right plus small amplitudes of TE/TM.sub.12,
TE/TM.sub.14, etc. Reflected waves in the various modes are
relatively much smaller and will be ignored. In FIG. 2 the y axis
lies in a phase front of the .theta..sub.b = 0 horn section 73.
This case is sufficiently general for analysis, since equation 4
shows that .theta..sub.a - .theta..sub.b defines the phase front
discontinuity, rather than .theta..sub.a and .theta..sub.b
individually. The phase difference .phi. as a function of y is a
circular arc.
As a first order approximation subject to .theta..sub.a being
small, the sum of the TE.sub.10 and higher order waves to the right
of the discontinuity will match the incident TE.sub.10 wave in both
amplitude and phase. For .theta..sub.a small, incident E.sub.y is
constant from y = -a/2 to a/2, and E.sub.z may be neglected.
Therefore, the sum of the waves on the right should match the
.phi.(y) and E.sub.y (y) functions:
where A.sub.2n represents complex amplitudes of the TE.sub.10,
TE/TM.sub.12, TE/TM.sub.14, etc., modes. To a first order with
A.sub.2, A.sub.4, . . . <<A.sub.0 equation 5 can be satisfied
by
Thus, the TE/TM.sub.12, TE/TM.sub.14, . . . components are
imaginary and are in phase quadrature with respect to the
transmitted TE.sub.10 component.
Equation (6) is a Fourier series in the period y = -a/2 to a/2. To
simplify the result, let .phi.(y) be approximated by a half sine
wave. Then the Fourier coefficients yield the following
TE/TM.sub.1,2n mode amplitudes for the TE.sub.10 mode: ##SPC1##
These amplitudes apply in the region just to the right of the
discontinuity.
If a pyramidal rather than sectoral horn in considered, the phase
fronts will be spherical; hence TE.sub.30, TE.sub.50, TE/TM.sub.32,
etc., modes will be needed to satisfy E.sub.y (x) = sin (.pi.x/a)
and .phi. = .phi.(x). However, the half-sine-wave variation of
E.sub.y (x) results in extremely rapid convergence of the Fourier
expansion for [ sin (.pi.x/a)] . e.sup.j .sup.(x), and modes of
higher order than unity in the H-plane may be neglected in
practical design.
The formula for the amplitude A.sub.2 of the TE/TM.sub.12 mode as
given by equation 7 may be used to design the flare angle change
that yields a desired ratio of TE/TM.sub.12 amplitude to TE.sub.10
amplitude. Note that the phase angle of A.sub.2 lags A.sub.0 by
90.degree. when .theta..sub.a - .theta..sub.b <0. Therefore, if
the length of horn between the flare change and the aperture has
90.degree. differential phase shift between the TE.sub.10 and
TE/TM.sub.12 modes, these modes will be in phase at the center of
the aperture. Similarly, when .theta..sub.a - .theta..sub.b >0,
270.degree. differential phase shift is required. Thus, the
decrease in flare angle in FIG. 2 should be followed by 270.degree.
differential phase shift, and the increase in flare angle in FIG. 3
by 90.degree..
The phase shift .phi..sub.n of the TE.sub.1n and TM.sub.1n modes in
a square pyramidal horn is given in radians by ##SPC2##
where a.sub.1 is the aperture height and width at the left; a.sub.2
is the same at the right, and .theta. is the flare angle. This
formula is an approximation valid for small and moderate flare
angles. The axial length is
L = (a.sub.2 - a.sub.1 /2) cot .theta. .
When .theta. = 0 and a.sub.1 = a.sub.2, .phi..sub.n is simply
Equation 8 or 10 with n set equal to 0 and 2 is used to calculate
the differential phase shift .phi..sub.0 - .phi..sub.2 for the
TE.sub.10 and TE/TM.sub.12 modes.
The parameters a.sub.1, a.sub.2, .theta. and L should be adjusted
by successive trials to provide the desired A.sub.2 values, with
required 90.degree. or 270.degree. differential phase shifts and
reasonable dimensions. If sufficient A.sub.2 cannot be produced by
a single flare change, two flare changes may be used. Small A.sub.2
values are directly additive to first order at the aperture.
Frequency sensitivity is greater, however, than in the case of a
single flare change at 90.degree. differential phase spacing from
the aperture.
Equation 7 shows that the amplitudes A.sub.2, A.sub.4, . . . are a
rapidly decreasing progression. Therefore, the presence in the
aperture of components of order greater than A.sub.2 will affect
the radiation pattern only in a minor way. However, these mode
amplitudes may be cancelled by the technique shown in FIG. 4 where
the flare angle change .theta..sub.a - .theta..sub.b is taken in
two steps .theta..sub.a - .theta..sub.e and .theta..sub.e -
.theta..sub.b separated by an intermediate section 77 of axial
length M. The length M is chosen so that the differential phase
shift .theta..sub.0 - .theta..sub.4 between the TE.sub.10 and the
TE/TM.sub.14 modes is 180.degree.. To make the TE/TM.sub.14
amplitudes generated at each step equal, the sizes of the steps
.theta..sub.a - .theta..sub.e and .theta..sub.e - .theta..sub.b are
chosen in such a way that the product of the flare angle change
.theta..sub.a - .theta..sub.e times the cross-sectional dimension
a.sub.a at the first step is approximately equal to the product of
.theta..sub.a - .theta..sub.e times a.sub.b at the second step.
Because the dimension a is frequently about the same for each step,
the angle changes are generally about equal. Then the small
TE/TM.sub.14 component excited at the first discontinuity will be
canceled by that at the second.
In view of the foregoing theoretical considerations, the antenna of
FIG. 1 may be considered in more detail. The general approach in
designing this antenna was to provide two major flare angle changes
connected by an adjustable straight section to provide additive
conversion of TE.sub.10 mode to TE/TM.sub.12 mode. Each major flare
change was then divided into two approximately equal flare changes
for higher mode cancellation. The exact proportions were then
adjusted to provide optimum expected performance, and a final
design was built and tested.
The flare angle .theta..sub.1 of the first flared section 51 is
chosen to produce a desired amplitude of TE/TM.sub.12 mode at a
reasonable cross-section a.sub.3. The dimension a.sub.3 should be
several times the width of the input waveguide 31, and may be on
the order of two-thirds of the desired output aperture. The
provision of the straight section 55 allows adjustment of the
overall length of the horn, for experimental pattern improvement,
and provides a substantial length for the TE/TM.sub.12 modes to
phase properly with the TE.sub.10 mode. The two flare angle changes
between the section 55 and 59 provide additional TE/TM.sub.12
amplitude. The flare angle of the output flared section 59 is
determined by the difference between the dimension a.sub.3 and the
desired aperture dimension a.sub.2, and by the length/flare angle
combination which will provide approximately 90.degree.
differential phase shift with these parameters.
The flare angle change between the first flared section 51 and the
straight connecting section 55 is divided into two approximately
equal flare angle changes at 61 and 63 by an intermediate section
53. Likewise, the flare angle change between the connecting section
55 and the output flared section 59 is divided into two
approximately equal flare angle changes at 65 and 67 by an
intermediate flared section 57. As has been discussed, the
intermediate sections 53 and 57 are proportioned to cause a
180.degree. differential phase shift in their length between
TE.sub.10 mode and TE/TM.sub.14 modes at center bandwidth.
To a first approximation, the design criteria require a distance
producing a 270.degree. differential phase shift (between TE.sub.10
and TE/TM.sub.12) between the center of section 53 and the aperture
52, and 90.degree. between the center of section 57 and the
aperture 52. The amplitudes of the TE/TM.sub.12 mode excited at
each of these flare angle changes may be added, and the desired
cumulative amplitude relative to that of the TE.sub.10 mode
selected. A ratio of TE/TM.sub.12 to TE.sub.10 of 0.66 at the
aperture would yield equal E- and H-plane beamwidths at the 10 db
points. A ratio of 0.84 would yield best suppression of sidelobes.
The illustrative embodiment was designed by application of the
foregoing theory to provide a ratio near the first of these values,
to produce equal beamwidths. The lengths were computed to give a
good approximation to a plane phase front in the aperture and to
suppress TE/TM.sub.14 components.
Three factors need to be taken into account other than those
already mentioned in designing a horn such as the illustrative
embodiment shown in FIG. 1.
In calculating amplitudes of induced higher order modes,
consideration must be given to the fact that the use of successive
approximately half angle changes in the flare angle to cancel
higher order modes causes some relative phase shift between the
portion of the TE/TM.sub.12 mode energy converted at the first
flare angle change and that produced at the second flare angle
change. In the illustrative embodiment, the length of intermediate
flared section typically yields a relative phase shift between the
TE.sub.10 mode and the TE/TM.sub.12 mode of about 42.degree.; hence
the total amplitude of the two equal TE/TM.sub.12 modes is reduced
by the factor cos (42.degree./2) = 0.934 at each end of the
straight section 55 as compared with a single flare change at each
end of this section.
The second factor is that the flare angle of the output flared
section 59 produces a phase front curvature at the aperture. The
phase curvature error is equivalent to a flare angle change from
the output section flare angle to an imaginary .theta. = 0 section
at the aperture. The TE/TM.sub.12 component produced by the flare
angle change is in phase quadrature with the incident TE.sub.10
component. The simplest way of correcting this effect and achieving
an approximately planar phase front is by making the length of the
straight section 55 such that the TE/TM.sub.12 wave arriving at the
aperture has a component equal in amplitude and 180.degree. out of
phase with the component produced at the aperture.
The third factor is that consideration must be made of not only the
decrease in TE.sub.10 mode at each successive flare angle change,
but also the effect of the presence of other components,
particularly TE/TM.sub.12, in the incident wave. A far better
quantitative analysis of the relative mode amplitudes, hence of
aperture patterns, of a multiflare horn may be accomplished by
treating the flare angle changes as equivalent to cascaded
directional couplers as shown in FIG. 6. Although this technique
was not used in the design of the illustrative embodiment of FIG.
1, it yields predicted values closely conforming to experimentally
determined values for this embodiment. The formulas for directional
couplers may be applied directly, with the ratio of input amplitude
of one mode to output amplitude of a second =j (2/3) .sup..
a/.lambda. .sup. . (.theta..sub.a - .theta..sub.b) radians, and
with .phi..sub.n taken from equations (8) or (10). It has been
found that much more accurate results are obtained if the aperture
52 is treated as a flare angle change from the output section 59 to
an imaginary section having a flare angle = 0.degree..
The inducement of higher modes in the transmit (5.925 to 6.425 GHz)
band may be accomplished by any of a number of well-known
expedients, such as a discontinuity 35 positioned in the throat of
the device (i.e. in the area of the junction of the waveguide 31
with the horn 5), inside the waveguide 31 a short distance. The
cut-off frequency of the TE/TM.sub.12 mode in the waveguide is 5.32
GHz. Hence the discontinuity 35 and the first flare angle change 61
have no effect in the receive band, and may be independently
optimized for best amplitude and relative phasing in the transmit
band. Final experimental patterns in the transmit band are similar
to those in FIG. 7b. As expected, the discontinuity 35 did not
change the receive band patterns. In the transmit band, the flare
angle changes of the illustrative embodiment of horn produce a set
of TE/TM.sub.12 components whose phasor sum computes to almost
zero. This condition is confirmed experimentally by an E-plane
pattern without discontinuity 35 very nearly that of a pure
TE.sub.10 distribution in beamwidth and sidelobes. In any design,
the effect of the small flare angle changes on a higher frequency
band should be calculated before the parameters of the separate
means for generating higher modes in that frequency band are
calculated for that design.
By way of illustration, the dimensions of the antenna shown in FIG.
1 may be as shown in the following table:
WIDTH (INCHES) a.sub.1 2.80 a.sub.2 12.20 a.sub.3 14.00 a.sub.4
14.00 a.sub.5 15.38 a.sub.6 22.1 LENGTH (INCHES) 51 31.8 53 13.25
55 50.18 57 16.96 59 42.5 FLARE ANGLE (DEGREES) .theta..sub.1 8.40
.theta..sub.2 3.90 .theta..sub.3 0 .theta..sub.4 2.34 .theta..sub.5
4.54
the antenna of FIG. 1 was built and tested. Experimental adjustment
of less than 10 percent in the length of straight section 55 was
required to produce the best compromise patterns across the entire
3.7 - 4.2 GHz bandwidth. The E- and H-plane patterns obtained are
shown for 3.7, 3.95 and 4.2 GHz respectively in FIGS. 7a, 7b and
7c. As shown in FIG. 7, E- and H-plane patterns across the receive
band show that the design achieves its intended objectives: the E-
and H-plane beamwidths are closely equal, the H-plane patterns are
scarcely affected by flare changes, and both the E- and H-plane
sidelobes are highly suppressed. In comparison, the theoretical
beamwidths of the H-plane and E-plane pattern of an aperture
containing a pure, plane TE.sub.10 field are in the ratio of
1.35:1, while the theoretical sidelobe levels are 23 and 13 db,
respectively. The maximum input VSWR measured 1.02 or less in both
the receive band and the transmit band.
Although a particular embodiment of the invention has been
described, it will be understood that numerous variations, within
the scope of the appended claims, will be apparent to those skilled
in the art in the light of the foregoing description. For example,
cancelling of higher order modes may be accomplished by
combinations of flare angle changes other than two sequential
approximately equal changes spaced at 180.degree. differential
phase shift. Negative, as well as positive, flare angles may be
provided in the horn. The modes utilized may be other than those
described. The means for inducing a higher order mode in the higher
frequency band may comprise one or more flare changes between the
waveguide and the first flared section, at a cross-sectional
dimension smaller than the large dimensions at which the major part
of the higher order modes are induced in the lower frequency band.
These variations are merely illustrative.
* * * * *