Multimode horn antenna

[57] 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.

Claims, 9 Drawing Figures

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PATENTEDmay 91972

3,662,393

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PATENTEDMAY 91972

3,662,393

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PATENTED hay 919zz 3,662,393

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PIQ. 7CL

Seymour b. Coum

3,662,393

MULTIMODE HORN ANTENNA

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°. 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 TE₁₂ or TM_n 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_I0, and the first higher order mode induced by the flare angle changes is TE/TM_I2. The term TE/TM₁₂ denotes a linear superposition of TE₁₂ and TM₁₂ 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 in vention;

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. Ία-Ic show a set of graphs showing receive band Eand 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 TE₁₀ 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 Θ

3,662,393 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 ai and a positive flare angle the second flared section 53 has an input dimension a_t and a flare angle β₂, less than 0_t; the third section 55 is straight, and has a cross-sectional dimension a₃ and a flare angle 0₃ equaling zero; the third flared section 57 has an input dimension a₄ equal to a₃ and a positive flare angle 0₄, and the output flared section 59 has an input dimension a₃ and a positive flare angle 0₃ greater than 0_t. The output flared section 59 has an output dimension, i.e. an antenna aperture 52 dimension, of a,. 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.

that 0_a — 0_b defines the phase front discontinuity, rather than 0_a and 0_b individually. The phase difference φ as a function of y is a circular arc.

As a first order approximation subject to 0„ being small, the 5 sum of the TE₁₀ and higher order waves to the right of the discontinuity will match the incident TE,₀ wave in both amplitude and phase. For 0_a small, incident |E„ | is constant from y = —a/2 to a/2, and E_t may be neglected. Therefore, the sum of the waves on the right should match the φ(γ) and |E„(y)| 10 functions:

Τ? A_2a cos ^^=6^(^^1+^(//) n=0 “ (5) where A_2n represents complex amplitudes of the TE₁₀, TE/TM₁₂, TE/TM_u, etc., modes. To a first order with A₂, A₄,.. . &lt;&lt;A₀ equation 5 can be satisfied by ²⁰ A₀=l . 2irny . , , &gt; 4, cos —— n=l “ (6)

The details of the structure of the antenna 1 may best be un- 25 derstood 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 30 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 pur- 35 poses. 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 40 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 0_a is joined to a section 73 of flare angle 0_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

Az = Λ — £ = a/2 [csc0„ — cot0_o] = a/2 tan 0_a/2(1)

If 0_a is less than about 0.4 radians (23°), Az may be approximatedby

A«=-jⁱ&gt; (0_a in radians)..

⁴(2)

Similarly, if 0_a and 0_b both differ from zero, as shown in FIG. $$ 3, the phase front separation is

Δζ = (α/4) (0„-0₆)(3)

The TE₁₀ mode phase difference corresponding to

Az is φ„ = 2 πΔζ/λ_β, or ^0m=2^(4) where λ, is guide wavelength of the TE_I0 horn mode and a is the E-plane height at the flare change point 75. For 0_a and 0_b 65 small, and an H-plane width greater than about two wavelengths, K_b is approximately equal to λ.

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 TE₁₀ wave arriving from the left yields 70 predominately TE_I0 on the right plus small amplitudes of TE/TM₁₂, TE/TM_m, 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 0_b = 0 horn section 73. This case is sufficiently general for analysis, since equation 4 shows 75

Thus, the TE/TM₁₂, TE/TMi₄, . .. components are imaginary and are in phase quadrature with respect to the transmitted TEjo component.

Equation (6) is a Fourier series in the period y = —a/2 to a/2. To simplify the result, let φ(γ) be approximated by a half sine wave. Then the Fourier coefficients yield the following TE/TM_1&gt;2„ mode amplitudes for the TE₁₀ mode:

A₀=i;

A₂=j ^2α(θ“~^θ^ (by Equation (4)); Ο7Γ ΟΛ

A&lt;= —= +₂;

d ^Ae=35 _-3(-l)n ^Λ2η~ (2n)‘-l ^Λ (7)

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_M, TE_M, ΤΕ/ΤΜ», etc., modes will be needed to satisfy E_y(x) = sin (πχ/α) and φ = φ(χ). However, the half-sine-wave variation of E_y(x) results in extremely rapid convergence of the Fourier expansion for [ sin (πχ/α)]. Η^(τ&gt;, and modes of higher order than unity in the H-plane may be neglected in practical design.

The formula for the amplitude A_t of the TE/TM₁₂ mode as given by equation 7 may be used to design the flare angle change that yields a desired ratio of TE/TMj₂ amplitude to ' TE₁₀ amplitude. Note that the phase angle of A₂ lags A_b by 90° when 0_a — 0_b&lt;O. Therefore, if the length of horn between the flare change and the aperture has 90° differential phase shift between the TE₁₀ and TE/TM₁₂ modes, these modes will be in phase at the center of the aperture. Similarly, when 0„ — 0_b&gt;O, 270° differential phase shift is required. Thus, the decrease in flare angle in FIG. 2 should be followed by 270° differential phase shift, and the increase in flare angle in FIG. 3 by 90°.

The phase shift φ_η of the TE_ln and TM,„ modes in a square pyramidal horn is given in radians by ν^ΐ-(1+η2)(έ)²

-^l-(l+n²)(^.)²₊|Vl+^[_Sin-i (^Vl+«²) ^Sin-1 (έ^νϊΤ^)]} (8)

3,662,393 where a₁ is the aperture height and width at the left; a₂ is the same at the right, and Θ is the flare angle. This formula is an approximation valid for small and moderate flare angles. The axial length is £ = (¾ — Ci/2) cot 0 . (9)

When 0 = 0 and a_t = ,¾. φ„ is simply

Equation 8 or 10 with n set equal to 0 and 2 is used to calculate the differential phase shift φ₀— φ₂ for the TE₁₀ and TE/TM₁₂ modes.

The parameters a_t, a₂, Θ and £ should be adjusted by successive trials to provide the desired T₂ values, with required 90° or 270° differential phase shifts and reasonable dimensions. If sufficient A₂ cannot be produced by a single flare change, two flare changes may be used. Small zl₂ 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° differential phase spacing from the aperture.

Equation 7 shows that the amplitudes A₂, A_it . . . are a rapidly decreasing progression. Therefore, the presence in the aperture of components of order greater than A₂ 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 θ_α — 0_b is taken in two steps θ_α — 0_r and 0_r — 6_b separated by an intermediate section 77 of axial length M. The length M is chosen so that the differential phase shift θ_α — θ₄ between the TE_I0 and the TE/TM₁₄ modes is 180°. To make the TE/TM₁₄ amplitudes generated at each step equal, the sizes of the steps θ_α — 0_e and — 0_b are chosen in such a way that the product of the flare angle change 0_a — 0_etimes the cross-sectional dimension a_a at the first step is approximately equal to the product of 0_a — 0_e times a_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_m 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 TE₁₀ mode to TE/TM₁₂mode. 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 0_X of the first flared section 51 is chosen to produce a desired amplitude of TE/TM₁₂ mode at a reasonable cross-section a₃. The dimension a₃ 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_I2 modes to phase properly with the TE₁₀ mode. The two flare angle changes between the section 55 and 59 provide additional TE/TM₁₂ amplitude. The flare angle of the output flared section 59 is determined by the difference between the dimension a₃ and the desired aperture dimension a₂, and by the length/flare angle combination which will provide approximately 90° 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° differential phase shift in their length between TE_I0 mode and TE/TM_H modes at center bandwidth.

To a first approximation, the design criteria require a distance producing a 270° differential phase shift (between TE₁₀ and TE/TM₁₂) between the center of section 53 and the aperture 52, and 90° between the center of section 57 and the aperture 52. The amplitudes of the TE/TM_I2 mode excited at each of these flare angle changes may be added, and the desired cumulative amplitude relative to that of the TE₁₀ mode selected. A ratio of TE/TM₁₂ to TE₁₀ 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_m 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/TM₁₂ 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 TE₁₀ mode and the TE/TM₁₂ mode of about 42°; hence the total amplitude of the two equal TE/TM₁₂modes is reduced by the factor cos (42°/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 0 = 0 section at the aperture. The TE/TM₁₂ component produced by the flare angle change is in phase quadrature with the incident TEjo 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/TM₁₂wave arriving at the aperture has a component equal in amplitude and 180° 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_l0 mode at each successive flare angle change, but also the effect of the presence of other components, particularly TE/TM₁₂, 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) · a/K (θ_α — 6_b) radians, and with φ_ηtaken 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°.

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/TM₁₂ 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

3,662,393 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 5 the illustrative embodiment of horn produce a set of TE/TM₁₂components 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 TE₁₀ distribution in beamwidth and sidelobes. In any design, the effect 10 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 ¹⁵in FIG. 1 may be as shown in the following table:

WIDTH (INCHES)

<td> di</td><td> 2.80</td>

<td> a_t</td><td> 12.20</td>

<td> a₃</td><td> 14.00</td>

<td> a₄</td><td> 14.00</td>

<td> at</td><td> 15.38</td>

<td> a₄</td><td> 22.1</td>

<td> LENGTH (INCHES)</td><td></td>

<td> 51</td><td> 31.8</td>

<td> 53</td><td> 13.25</td>

<td> 55</td><td> 50.18</td>

<td> 57</td><td> 16.96</td>

<td> 59</td><td> 42.5</td>

<td colspan="2"> FLARE ANGLE (DEGREES)</td>

<td> e,</td><td> 8.40</td>

<td></td><td> 3.90</td>

<td> β,</td><td> 0</td>

<td></td><td> 2.34</td>

<td></td><td> 4.54</td>

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 Hplane patterns obtained are shown for 3.7, 3.95 and 4.2 GHz respectively in FIGS. 7α, 7b and 7c. As shown in FIG. 7, E- and Η-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 TE₁₀ 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° 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.