Multibeam antenna reflector

This invention relates to a reflector for a multibeam antenna which can transmit and receive electromagnetic waves in and from different directions.

BACKGROUND OF THE INVENTION

An example of a multibeam antenna is disclosed in, for example, Japanese unexamined patent publication No. HEI 5-191139 published on Jul. 30, 1993. The antenna disclosed in this publication includes two primary radiators disposed to radiate beams to the same point on an offset paraboloidal reflector of the antenna. In this antenna, an axis passing through the aperture center of the paraboloidal reflector and paralleling the parabola axis of the reflector is defined as a beam axis of the paraboloidal reflector. One of the two primary reflectors is located at the focal point of the reflector, and the other radiator is located on the beam axis. The angle between the line passing through the aperture center and the focal point of the reflector and the parabola axis is defined as a tilt angle. The tilt angle is from 1 to 1.4 times a desired beam width.

A reflector meeting the above-stated condition cannot be a versatile reflector, but it can only reflect a beam in or from a specific direction. Recently, satellite communications and satellite broadcasting are common. Accordingly, parabolic antennas which can be used only single satellites are not desirable in manufacturing cost. In addition, in this type of paraboloidal reflectors, aberration due to displaced feeding is minimized under some specific conditions, which results in a large focal-length-to-aperture ratio, F/D, of the paraboloidal reflector.

Therefore, an object of the present invention is to provide a versatile reflector for a multibeam antenna which has a similar size to an ordinary paraboloidal reflector.

SUMMARY OF THE INVENTION

A multibeam antenna according to the present invention includes a reflector surface expressed by at least first and second corrected surface functions combined or merged together. The first corrected surface function can be defined in a coordinate system having a horizontal axis X

1

, a vertical axis Y

1

and an axis Z

1

perpendicular to the plane defined by the X

1

and Y

1

axes, as follows.

z

1

=[−(x

1

2

+y

1

2

)/4(F

1

+g(x

1

, y

1

))]+F

1

where g(x

1

, y

1

) is expressed by k

1

(y

1

+α)+k

2

(|x

1

|+β), α is a value not smaller than −(of+D) and not greater than (of+D), β is a value not smaller than −D/2 and not greater than D/2, of is the amount of offset of the reflector which is equal to or greater than 0, D is the diameter of a circle resulting from projecting a given area of the first corrected surface function onto the X

1

-Y

1

plane, F

1

is the focal length of the first corrected surface function, and k

1

and k

2

are coefficients.

The second corrected surface function is defined in a coordinate system having a horizontal axis X

2

, a vertical axis Y

2

and an axis Z

2

perpendicular to the plane defined by the X

2

and Y

2

axes, as follows.

z

2

=[−(x

2

2

+y

2

2

)/4(F

2

+g(x

2

,y

2

))]+F

2

where g(x

2

, y

2

) is expressed by k

1

(y

2

+α)+k

2

(|x

2

|+β), α is a value not smaller than −(of+D) and not greater than (of+D), β is a value not smaller than −D/2 and not greater than D/2, of is the amount of offset of the reflector which is equal to or greater than 0, D is the diameter of a circle resulting from projecting a given area of the second corrected surface function onto the X

2

-Y

2

plane, F

2

is the focal length of the second corrected surface function, and k

1

and k

2

are coefficients.

The multibeam antenna reflector is in a combined or merged area expressed by a function formed by weighted-averaging the first and second corrected surface functions with the Z

1

and Z

2

axes disposed in parallel with respective ones of at least two directions from which electromagnetic waves come. The focuses of the first and second corrected surface functions are determined such that the coordinates of the first and second corrected surface functions at the center of the combined area are the same, and that the normals of the first and second corrected surface function at the center of the combined area are in alignment with each other.

It may be that k

2

=0, k

1

<0, and α=−(of+D/2).

It may be that k

1

=0, k

2

>0, and β=0.

It may be that k

1

=0.

It may be that k

1

=k

2

, α=−(of+D/2), and β=0.

It may be that k

1

and k

2

each are equal to or greater than −0.2 and equal to or smaller than 0.2.

Additional (m−2) surface functions, where m is a positive integer equal to or greater than three, may be combined with the first and second corrected surface functions by being weighted and averaged with the first and second corrected surface functions. Any additional n-th reflector is expressed by a parabolic function or a corrected surface function in a coordinate system defined by a horizontal axis Xn, a vertical axis Yn and an axis Zn perpendicular to the plane defined by the Xn and Yn axes, where n is a positive integer equal to or greater than 3 and equal to or smaller than m, with the axis Zn disposed along the direction from which an n-th electromagnetic wave comes.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS.

1

(

a

) and

1

(

b

) respectively illustrate how electromagnetic waves are reflected from a reflector according to a basic corrected surface function of the present invention and from a prior art offset paraboloidal reflector.

FIGS.

2

(

a

) through

2

(

d

) illustrate convergence of equiphase points of the reflector according to the basic corrected surface function of the present invention and the prior art offset paraboloidal reflector.

FIG. 3

illustrates how convergence of equiphase points change when a coefficient k is changed in the reflector according to the basic corrected surface function of the present invention.

FIG. 4

shows a relationship between a beam deviation angle and a relative gain in the reflector according to the basic corrected surface function of the present invention.

FIG. 5

is perspective view of a multibeam antenna reflector according to one embodiment of the present invention.

FIG. 6

is a plan view of the multibeam antenna reflector of FIG.

5

.

FIG. 7

shows a simulation of aberration generated in the multibeam antenna reflector of

FIG. 5

when the beam deviation angle is 10 degrees.

FIG. 8

shows a simulation of aberration generated in an ordinary paraboloidal reflector when the beam deviation angle is 10 degrees.

FIG. 9

shows a relationship between a beam deviation angle and a relative efficiency as simulated and as actually measured for the multibeam antenna reflector of FIG.

5

.

FIG. 10

shows a relationship between the beam deviation angle and a relative efficiency as actually measured and as simulated for each of the multibeam antenna reflector of FIG.

5

and the conventional offset paraboloidal reflector.

FIG. 11

is a perspective view of a multibeam antenna reflector according to another embodiment of the present invention.

DETAILED DESCRIPTION OF EMBODIMENTS

According to the present invention, a multibeam antenna reflector has a reflecting surface expressed by a function which is a combination of at least two corrected surface function. First, the corrected surface functions are described. However, before that, a conventional paraboloidal reflector receiving an electromagnetic wave from a diagonal direction is described.

As shown in FIGS.

1

(

a

) and

1

(

b

) which are plan and side views of an offset paraboloidal reflector

2

, in the reflection surface of the offset paraboloidal reflector

2

, a coordinate system is defined by a horizontal axis X

1

, a vertical axis Y

1

, and an axis Z

1

perpendicular to the plane defined by the X

1

and Y

1

axes. The focal point of the reflector

2

on the Z

1

axis is defined as the origin of the coordinate system. The angle between the electromagnetic wave E as projected onto the X

1

-Z

1

plane and the Z

1

axis is defined as a beam deviation angle θb. The reflection surface of the reflector

2

is expressed by the following expression (1), in which F

1

is the focal length of the reflector.

z

1

=[−(x

1

2

+y

1

2

)/4F

1

]+F

1

(1)

A plane M resulting from projecting the offset paraboloidal reflector onto a plane perpendicular to the electromagnetic wave vector E can be considered to be an equiphase surface of the electromagnetic wave E corresponding to the aperture plane of the reflector

2

.

Let it be assumed that the upper and lower ends of the reflector

2

along the Y

1

axis are Pa and Pu, respectively, that the positive and negative side ends along the X

1

axis are Pl and Pr, respectively, and the corresponding points on the equiphase surface are Ma, Mu, Mr and Ml, respectively. Since the points Ma, Mu, Mr and Ml are points on the equiphase surface M, the electric fields at these points are in phase.

The field which has passed through a point, e.g. the point Ma, in the equiphase surface M propagates in parallel with the direction of the wave E and is reflected from a point, e.g. Pa, on the reflector

2

toward a point in the vicinity of the focal point F of the reflector

2

.

A set of points on the propagation paths at the same distance from the equiphase surface M is a set of equiphase points. Equiphase points which are in the vicinity of the focal point F and correspond to the points Ma, Mu, Mr and Ml on the equiphase surface are designated as Fa, Fu, Fr and Fl in FIGS.

1

(

a

) and

1

(

b

). The electric field passing through the center Mc of the equiphase surface M reaches the center point Pc of the reflector

2

and is reflected in a direction E′. The line interconnecting the origin O and the equiphase point Fc in the E′ direction corresponding to the points Mc and Pc forms an angle θb′ (feed displacement angle) with the Z

1

axis (FIG.

1

(

a

)). When the equiphase points Fc, Fa, Fu, Fr and Fl converge most, they spread about Fc in the projection on the Z

1

-X

1

plane, and are dispersed on a curved plane extending generally perpendicular to the direction E′ when viewed in the projection on the Y

1

-Z

1

plane. The line interconnecting Pc and Fc forms an angle θo (offset paraboloidal reflector offset angle) with respect to the Z

1

axis (FIG.

1

(

b

)).

Let the points Pr and Pl be selected as being representative of any points in the right and left halves of the reflector

2

. The line interconnecting Mr and Pr is in parallel with the line interconnecting Ml and Pl. When an electromagnetic wave E enters into the reflector

2

from a location whose X

1

and Z

1

coordinates are negative as shown in FIG.

1

(

a

), the line segment MrPr<the line segment MlPl and, therefore, the line segment PrFr>the line segment PlFl, because the line segment MrFr is equal to the line segment MlFl, the line segment MrFr consists of the line segments MrPr and PrFr, and the line segment MlFl consists of the line segments MlPl and PlFl.

When the offset angle θo> the beam deviation angle θb, the line segment PrFr is substantially symmetrical with the line segment PlFl with respect to the direction E′ (i.e. the line interconnecting Pc and Fc). Accordingly, as shown in FIGS.

1

(

a

) and

1

(

b

), the points Fr and Fl on the projection on the X

1

-Z

1

plane are displaced less in the direction along the axis X

1

, but they are dispersed largely in both the Y

1

and Z

1

directions and, particularly, in the Y

1

direction when projected onto the Y

1

-Z

1

plane.

Similarly, the points Pa and Pu are considered to represent any points on the upper and lower halves of the reflector

2

. The line segment PaF minus the line segment PaFa is larger than the segment PuF minus the segment PuFu. Also, as shown in FIGS.

1

(

a

) and

1

(

b

), the points Pc, Pa and Pu are in the same curved plane, and Fc, Fa and Fu are on the same curved plane, and the points Fa and Fu are on opposite sides of the line segment PcFc in the example shown in FIGS.

1

(

a

) and

1

(

b

), with the point Fu being more positive in the X

1

direction and more negative in the Y

1

direction, than Fc.

Accordingly, the points Fa, Fc and Fu are spread along a line which is curved but almost straight, and, accordingly, equiphase points are dispersed in the respective directions X

1

, Y

1

and Z

1

on a curved but almost flat plane. The dispersion of the equiphase points is shown in FIGS.

2

(

a

) and 2(

b

).

For reducing such dispersion of equiphase points, a correcting function g(x

1

, y

1

) is utilized. For example, let it be assumed that the following equation (2) is used as the correcting function g(x

1

, y

1

).

g(x

1

, y

1

)=k|x

1

| (2)

where k is greater than 0. Then, the corrected surface function expressing the reflector surface is:

z

1

=[−(x

1

2

+y

1

2

)/4(F

1

+k|x

1

|)]+F

1

(3)

where k is a coefficient having a positive value. The reflector surface expressed by the equation (3) is generally shallow dish-shaped as indicated by a dash-and-dot line in FIG.

1

(

a

), in which as the value x

1

increases the value z

1

is smaller than in the conventional paraboloidal reflector. The distance of the right end Pr′ of the reflector from the corresponding point on the equiphase surface, and the distance of the left end Pl′ of the reflector from the corresponding point on the equiphase surface are both increased. Also, the normals at Pr′ and Pl′ are closer to the Z

1

axis or the normal at Pc than the normals at Pr and Pl. Accordingly, Fr′ and Fl′ are nearer to Fc′, which means that the density of equiphase points around Fc′ is higher. Thus, the gain is improved.

By using the following function (4) as the correcting function g(x

1

, y

1

), the position of the origin or vertex of the paraboloid can be changed along the X

1

axis.

g(x

1

, yl)=k|x

1

|+β (4)

where |β| is equal to or smaller than D/2, and D is an aperture of the paraboloidal reflector. By properly selecting β, it is possible to further increase the density of equiphase points around Fc′, or to deal with electromagnetic waves coming from, for example, two different directions.

Next, the employment of the following expression (5) as the correcting function g(x

1

, y

1

) is considered.

g(x

1

, y

1

)=k(y

1

—of−D/2) (5)

where k is a value smaller than 0. As described above, in the example shown in FIGS.

1

(

a

) and

1

(

b

), with the line Pc-Fc used as the reference, Fu is more positive than Fc along the X

1

axis, and is more negative than Fc along the Y

1

axis. Also, Fa is more negative along the X

1

axis than Fc and is more positive along the Y

1

axis. For the entire reflector, the set of equiphase points corresponding to respective points on the lower half surface of the reflector

2

are more positive along the X

1

axis than Fc and more negative along the Y

1

axis, while the set of equiphase points corresponding to respective point on the upper half surface of the reflector

2

are more negative along the X

1

axis than Fc and more positive along the Y

1

axis.

The corrected surface function in which the correcting function g(x

1

, y

1

) is incorporated is:

z

1

=[−(x

1

2

+y

1

2

)/4(F

1

+g(x

1

, y

1

))]+F

1

(6)

If g(x

1

, y

1

)>0 for a particular (x

1

, y

1

), the value of z

1

is smaller than z

1

=−[(x

1

2

+y

1

2

)/4F

1

]+F

1

, and if g(x

1

, y

1

)<0 for a particular (x

1

, y

1

), the value of z

1

is larger than z

1

=−[(x1

2

+y1

2

)/4F

1

]+F

1

.

When the equation (5) is adopted as g(x

1

, y

1

), g(x

1

, y

1

)>0 when y

1

<(of+D/2), and g(x

1

, y

1

)<0 when y

1

>(of+D/2). Accordingly, the corrected surface function (6) is a stack of a plurality of paraboloids having successively and smoothly decreasing focal lengths with y

1

as it changes from y

1

= of toward y

1

=of+D/2. When y

1

=of+D/2, g(x

1

, y

1

)=0, which results in the conventional parabolic function. When y

1

>of+D/2, g(x

1

, y

1

)<0. As y

1

increases, the focal length gradually decreases, and the angle formed between E and normals at the respective points becomes larger than in the conventional parabolic function. Therefore, the equiphase points come closer to Fc′ than the conventional parabolic function. In other words, the position where the modification of the focal length starts is the point y

1

=of+D/2.

When y<of+D/2, g(x

1

, y

1

)>0. As y

1

increases, the focal length gradually decreases and, at the same time, the angle formed between the direction of the wave E and the normal at each point becomes smaller than in the conventional parabolic function. Thus, the equiphase points are closer to Fc′ than the ones of the parabolic function. The shape of the reflection surface is indicated by a dash-and-dot line in FIG.

1

(

b

), in which the equiphase point corresponding to the upper end Pa′ of the reflection surface is indicated by Fa′, and the one corresponding to the lower end Pu′ is the point Fu′. As is understood, the range over which equiphase points are dispersed is narrow. That is, the density of equiphase points increases, resulting in increase of the gain. FIGS.

2

(

c

) and

2

(

d

) illustrate how equiphase points are dispersed when k=−0.02 in the expression (5). Comparing FIGS.

2

(

a

) and 2(

b

) with FIGS.

2

(

c

) and

2

(

d

), respectively, it will be understood that the employment of the expression (5) for the correcting function g(x

1

, y

1

) can provide more improvement on the convergence of equiphase points.

Next, the use of the following expression (7) as the correcting function g(x

1

, y

1

) is considered.

g(x

1

, y

1

)=k(y

1

+α) (7)

where |α| is equal to or smaller than of+D. If α=—of−D/2, the expression (7) is the same as the expression (5). Accordingly, by selecting the value for a from the range of |α| is equal to or smaller than of +D, it is possible to place the point where the focal length starts to be corrected at any location on the reflection surface. The dispersion of the equiphase points can be further reduced by selecting a proper value for α. Then, the density of the equiphase points can be further improved, and electromagnetic waves coming from, for example, two different directions can be handled by the reflector.

The combination of the two correcting functions (2) and (5), i.e. the following expression (8), may be used as the correcting function g(x

1

, y

1

).

g(x

1

, y

1

)=k(y

1

-of−D/2+|x|) (8)

In this case, by selecting a proper value for k, all of Fr, Fl, Fa and Fu can be made to locate in the vicinity of Fc.

FIG. 3

shows how the equiphase points can converge when the correcting functions (2), (5) and (8) are employed, and θb=10 degrees, with k varied from a value near −0.2 to a value near +0.2. In

FIG. 3

, the vertical axis is for the density of equiphase points converted into the antenna efficiency. The antenna efficiency is unity when an electromagnetic wave enters into the conventional paraboloidal antenna from the front. By selecting a value from a range of from about −0.2 to about +0.2 for k, good results was obtained. In particular, when θb=10°, the peak is within a range of from about −0.1 to about +0.1 of k. More specifically, the peaks when the functions (5) and (8) are employed are in the vicinity of −0.05, and the peak when the function (2) is employed is in the vicinity of +0.05. These peak densities are about 0.64.

FIG. 4

shows how the relative gain of the reflector expressed by the corrected surface function employing the correcting function (5), in which D=755 mm, F=453 mm, of =0 and k=−0.02, and the relative gain of a conventional paraboloidal reflector having the same dimensions change, with the beam deviation angle θb changing from 0°. It is seen from

FIG. 4

, the present invention can provide a wider effective deviation angle than the conventional paraboloidal reflector.

Generalizing all of the above-described correcting functions results in the following correcting function (9).

g(x

1

, y

1

)=k

1

(y

1

+α)+k

2

(|x

1

|+β) (9)

where |α| is equal to or smaller than (of+D), and |β| is equal to or smaller than D/2. The coefficients k

1

and k

2

may have any value, but they may preferably have a value within a range of from −0.2 to +0.2, as discussed with reference to FIG.

3

. In

FIG. 3

, θb is 10°,but the beam deviation angle θb of any different value may be handled by selecting proper values for α, k

1

and k

2

and selecting one or more appropriate correcting functions.

Two reflectors prepared in accordance with the above-described corrected surface functions are combined or merged together to form a reflector

4

shown in

FIGS. 5 and 6

. Referring to

FIG. 5

, the corrected surface function

1

for a reflector mainly reflecting an electromagnetic wave

6

from a satellite

1

may be expressed by the following equation (10), for example, in a right handed coordinate system which has its origin at the focal point f

1

of the reflector, the Z

1

axis extending in the positive direction through the origin toward the reflector expressed by the corrected surface function 1, the horizontal X

1

axis, and the vertical Y

1

axis. In the expression (10), g(x

1

, y

1

) =k(y

1

−D/2−of), and F

1

represents the focal length.

z

1

=[−(x

1

2

+y

1

2

)/4(F

1

+g(x

1

, y

1

))]+F

1

(10)

Similarly, the corrected surface function 2 for a reflector mainly reflecting an electromagnetic wave

8

from a satellite

2

may be expressed by the following equation (11), for example, in a right handed coordinate system which has its origin at the focal point f

2

of the reflector, the Z

2

axis extending in the positive direction through the origin toward the reflector expressed by the corrected surface function

2

, the horizontal X

2

axis, and the vertical Y

2

axis. In the expression (11), g(x

2

, y

2

)=k(y

2

−D/2—of), and F

2

represents the focal length.

z

2

=[−(x

2

2

+y

2

2

)/4(F

2

+g(x

2

, y

2

))]+F

2

(11)

These two coordinate systems are arranged in a coordinate system including the X, Y and Z axes as shown in FIG.

6

. In the coordinate system shown in

FIG. 6

, the two focal points f

1

and f

2

are spaced by a distance d

1

+d

2

from each other so that the angle between the waves from the satellites

1

and

2

is equally divided into two parts, namely, δ

1

and δ

2

, that the coordinate values at the combination center Mp of the two corrected surface functions 1 and 2 are the same, and that the normal to the combination center Mp of the two corrected surface functions 1 and 2 are aligned. The X axis extends in the positive direction through the focal points f

2

and f

1

in the name order with the origin O of the coordinate system being located at the midpoint between the points f

1

and f

2

. The Z axis extends in the positive direction generally coincident with the directions of propagation of the waves from the satellites

1

and

2

. The Z axis extends orthogonal to the X axis. It extends through the origin O and lies in the plane in which the lines interconnecting the combination center Mp and the satellites

1

and

2

, respectively, lie. Thus, the Z axis bisects the angle between the electromagnetic waves from the satellites

1

and

2

into the angles δ

1

and δ

1

. In other words, the angles δ

1

and δ

2

are beam deviation angles. The Y axis is such that the coordinate system with the X, Y and Z axes is a right handed coordinate system.

Considering the corrected surface functions in the coordinate system with the X, Y and Z axes, the corrected surface function 1 is the function expressed by the equation (10) as rotated by δ

1

from the positive direction of the Z axis toward the positive direction of the X axis and translated by d

1

in the positive direction along the X axis in the X-Z plane, while the corrected surface function

2

is the function expressed by the equation (11) as rotated by δ

2

from the positive direction of the Z axis toward the negative direction of the X axis and translated by d

2

in the negative direction along the X axis, in the X-Z plane.

The corrected surface function 1 is weighted by W

1

, and the corrected surface function 2 is weighted by W

2

. Then, the weighted, corrected surface functions 1 and 2 are averaged to form a combined function, which defines a reflection surface. The weight WI is expressed by the following equation (12). The weight W

2

is 1−W

1

. The weights W

1

and W

2

are positive values.

W

1

=||x−D/2|−D|/D (12)

Thus, when x=0, i.e. in the Y-Z plane, W

1

and W

2

are equal to 0.5. When x is D/2, W

1

=1 and W

2

=0. When x=−D/2, W

1

=0 and W

2

=1. Then, the combined function has a value intermediate between the corrected surface functions 1 and 2 when x=0,has a value as expressed by the corrected surface function 1 when x=D/2, and has a value as expressed by the corrected surface function 2 when x=−D/2.

FIG. 7

shows the result of simulation conducted for the generation of aberration at the beam deviation angle of 10 degrees of a reflector formed according to combined corrected surface functions, in which D=457.2 mm, the focal lengths F

1

=F

2

=274.32 mm, g(x

1

, y

1

)=−0.01(y

1

−D/2), g(x

2

, y

2

)=−0.01(y

2

−D/2), δ

1

=−10°, δ

2

=10°, W

1

=||x−D/2|−D|/D, and of=0. For the purpose of comparison,

FIG. 8

shows the result of simulation on aberration at the beam deviation angle of 10 degrees of an offset paraboloidal reflector having a focal length of 230 mm, an aperture of 457.2 mm and an amount of offset of 30 mm. The comparison of

FIG. 7

with

FIG. 8

evidences the fact that the reflector shown in

FIG. 7

has smaller aberration than the reflector of FIG.

8

. It is also known that the antenna gain is 33.5 dB in

FIG. 7

, whereas the antenna gain of the reflector of

FIG. 8

is 32.9 dB, which means that the reflector of

FIG. 7

is improved in antenna gain by about 0.6 dB relative to the reflector of FIG.

8

.

The relative efficiency changing with the beam deviation angle of the reflector expressed by the combined corrected surface functions was simulated. Also, a reflector having the above-described combined, corrected surface functions, having a horizontal diameter of 472.6 mm and a vertical diameter of 445.3 mm was experimentally made, and the relative efficiency changing with the beam deviation angle was actually measured. The results of the simulation and the actual measurement are shown in FIG.

9

. The solid line curve is a curve resulting from the simulation for a primary radiator positioned at the focal point f

1

which is adapted to receive waves coming at a beam deviation angle of from −25° to 0°, and the x'es are the actual measurements for the radiator positioned at the point f

1

. The broken line curve and triangles are for a primary radiator positioned at the focal point f

2

which is adapted to receive waves coming at a beam deviation angle of from 0° to 20°. The actually measured values and the simulated values are generally coincident with each other within the deviation angle range of about ±15°.

The simulated and actually measured values shown in

FIG. 9

are also shown in

FIG. 10

together with the simulated and actually measured values of relative efficiency changing with the deviation angle of the above-mentioned offset paraboloidal reflector.

It is seen from

FIG. 10

that both the simulated and actually measured reductions of efficiency are less in the reflector defined by the combined corrected surface functions than in the conventional offset paraboloidal reflector over a wide range of beam deviation angles. The combined corrected surface function reflector with a beam width of about 3.7° has reduction of efficiency of only about 2.0 dB at a location remote by six times the beam width. In other words, the combined corrected surface function reflector can be used with a beam displaced up to six times the beam width. In contrast, the reduction of efficiency of about 2.0 dB results when the beam deviation angle is about 14° in the conventional offset paraboloidal reflector. In other words, the conventional offset paraboloidal reflector can efficiently receive a wave within a range of only about 3.5 times the beam width.

It is because the corrected surface functions 1 and 2 are combined that a larger beam deviation angle can be obtained. Because of a larger beam deviation angle, the multibeam antenna reflector according to the present invention can receive electromagnetic waves coming into it from various directions.

The present invention has been described by means of a multibeam antenna reflector formed by combining the two corrected surface functions 1 and 2. However, (m−2) additional corrected surface functions or parabolic functions may be combined with the functions 1 and 2, where the number m is a positive integer greater than 3. For example,

FIG. 11

shows focal points f

1

, f

2

and fn of the first, second and n-th corrected surface functions

1

,

2

and n out of the m functions combined. In this case, δ

1

=δ

2

, and the beam deviation angle δn is smaller than δ

1

or δ

2

. The parabolic function or n-th corrected surface function can be expressed, with respect to a coordinate system defined by an Xn axis extending horizontally with respect to the reflector surface, a vertically extending Yn axis and a Zn axis extending toward the reflector surface, by zn=[−(xn

2

+yn

2

)/4Fn]+Fn or zn=[−(xn

2

+yn

2

)/4(Fn+g(xn, yn))+Fn, where g(xn, yn) is expressed as k

1

(yn+α)+k

2

(|xn|+β), as previously described. In the last expression, α is not smaller than −(of +D) and not greater than (of+D), β is not smaller than −D/2 and not greater than D/2, of is the offset amount of the reflector which is not smaller than 0, D is the diameter of a circle resulting from projecting a desired area of the n-th function onto the Xn-Yn plane, Fn is the focal length of the n-th corrected surface function or parabolic function, and k

1

and k

2

are coefficients.

The weights W

1

-Wn used in weighted-averaging these functions are all positive values. The weights W

1

and W

2

are expressed by the following expressions (13) and (14), with the sum of W

3

through Wm being smaller than unity.

\begin{matrix} W1 = (1 - \sum_{t = 3}^{n} W_{i}) \frac{&LeftBracketingBar; &LeftBracketingBar; x - \frac{D}{2} &RightBracketingBar; - D &RightBracketingBar;}{D} & (13) \\ W2 = 1 - W1 - \sum_{t = 3}^{n} W_{i} & (14) \end{matrix}

Number	Name	Date
4603334	Mizuguchi et al.	Jul 1986
5140337	Rappaport	Aug 1992
5283591	Delmas	Feb 1994
5790777	Luh et al.	Aug 1998
5828344	Alder et al.	Oct 1998
5859619	Wu et al.	Jan 1999
5913151	Lusignan	Jun 1999
5949594	Iglseder et al.	Sep 1999

Multibeam antenna reflector

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