JP3942087B2 - In-vehicle millimeter-wave radar antenna - Google Patents

Description

[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a vehicle-mounted radar antenna, and particularly to a vehicle-mounted millimeter-wave radar antenna using an electromagnetic horn.
[0002]
[Prior art]
Conventionally, as radar antennas for in-vehicle radars, an antenna having an array configuration in which a plurality of unit antennas are arranged in a horizontal direction has been adopted, and various antenna systems have been considered based on the principle of antennas that transmit and receive electromagnetic waves. . Typical examples of radar antennas for in-vehicle radars include a printed antenna configuration using a patch array or the like, and a slot array configuration in which a slot is provided on a waveguide tube wall.
[0003]
The antenna mounted on the satellite is a horn array antenna that can use linearly polarized waves and circularly polarized radio waves, with low thermal noise, and is arranged in an array of horns (horn elements). A horn array antenna configured to connect a waveguide and synthesize the waveguide is known (see, for example, Patent Document 1). Note that the general characteristics and the like of the horn antenna are described in Non-Patent Documents 2-3.
[0004]
[Patent Document 1]
JP-A-2-214307 [Non-Patent Document 1]
Susumu Miwa, 1 other author, "Antenna and Radio Wave Propagation" 1st Edition, September 26, 1999, Tokyo Denki University Press, P.I. 62-65
[Non-Patent Document 2]
Saburo Adachi, 1 author, “Radio Optics”, Morikita Publishing Co., Ltd., June 30, 1998, 1st Edition, P.I. 68-71
[Non-Patent Document 3]
Edited by the Institute of Electrical Communication, "Microwave Engineering", first edition, Corona Co., Ltd., July 10, 1933; 99-103, 164-167
[0005]
[Problems to be solved by the invention]
Printed antennas are suitable for in-vehicle use because they are thin and can be reduced in weight, but because they need to have a multilayer structure of conductors and dielectrics, they are generally more expensive, heat resistant, mechanical deformation, etc. There is a problem that the entire outer shape is enlarged, such as weakness and the need for an outer frame for holding and fixing the antenna, which is separate from the device housing, and the loss of the feed circuit is also large in terms of characteristics Therefore, the antenna efficiency is low, and the minimum unit of the element is determined, so that there is a difficulty in that the beam width cannot be arbitrarily selected.
[0006]
The slot array antenna is thicker than the printed antenna, but has a merit that a sufficiently thin antenna can be obtained because the waveguide size is small in the millimeter wave band, and the feed loss can be made relatively small. However, the mechanism structure is complicated and high accuracy is required, and the cost is generally increased. The effect of the accuracy of the slot size and interval greatly appears on the characteristics. Further, since a beam tilt in which the beam is tilted from several degrees to several tens of degrees from the direction perpendicular to the antenna surface occurs, the assembling mechanism is complicated and high accuracy is required, and the capacity is increased. Furthermore, the leakage coupling of the waveguide has a direct influence on the characteristics, and there is a problem that a welded or screw-use structure is provided, and the beam width cannot be arbitrarily selected like a printed antenna.
[0007]
As an in-vehicle radar antenna, in addition to the above-mentioned antenna, it is conceivable to apply an antenna of various principles, and it is conceivable to use a horn array antenna as described in Patent Document 1. The application of the horn array antenna has a very difficult problem. In other words, miniaturization of the device is indispensable for in-vehicle radar, and in particular, it is strongly required to reduce the height of the antenna in the elevation direction, and the required narrow beam characteristics are required as antenna characteristics. Therefore, in order to obtain the required narrow beam characteristics, there is a limit to the reduction in height, and the horn elements of the horn array antenna itself have sidelobe peaks. There is a problem that a high peak occurs due to a lobe (a side lobe of an orientation in-phase synthesized), and it is difficult to obtain low side lobe characteristics.
[0008]
(Object of invention)
An object of the present invention is to provide a vehicle-mounted radar antenna having a horn array configuration that can reduce the size of an antenna and realize low sidelobe characteristics.
[0009]
[Means for Solving the Problems]
The in-vehicle radar antenna of the present invention is applied to a multi-horn antenna in an in-vehicle millimeter wave radar, and the configuration and number of elements of the multi-horn for transmission / reception and the dimensions / intervals of each horn element are selected to predetermined appropriate values. It is possible to downsize (realize a smaller antenna height for obtaining a narrow beam characteristic in a predetermined elevation angle direction) and to realize a low sidelobe characteristic.
[0010]
The vehicle-mounted radar antenna of the present invention is a vehicle-mounted millimeter-wave radar antenna having a transmission and reception unit antenna constituted by a multihorn. Among the transmission and reception unit antennas, one unit antenna is in an elevation direction. And the two inner elements of the four-element multihorn have the same width in the elevation angle direction, and the other unit antenna has at least two elements arranged in the elevation angle direction. The two elements are characterized by having the same width in the elevation direction. The distance Do between the central axes of the two elements of the unit antenna of the two-element multihorn is about 0.55 Ho with respect to the elevation length Ho of the unit antenna composed of the four-element multihorn. And
[0011]
In each of the above inventions, the ratio W1 / W2 of the elevation direction width W1 of the two inner elements of the unit antenna consisting of the four-element multihorn and the elevation direction width W2 of the two outer elements is about ½, or The ratio D1 / D2 of the distance D1 between the central axes of the two inner elements of the unit antenna composed of multihorns and the distance D2 between the central axes of the two outer elements is about 1/4, or the four elements The ratio W1 / W2 of the elevation direction width W1 of the inner two elements of the multi-horn unit antenna to the elevation direction width W2 of the two outer elements is about 2, or the inner two elements of the unit antenna composed of the four-element multihorn The ratio D1 / D2 of the distance D1 between the central axes of the two elements and the distance D2 between the central axes of the two outer elements is about 1 / 2.5.
The unit antennas are arranged in an array in the horizontal direction, and the entire radar antenna or the radar apparatus housing and at least a part of the radar antenna are manufactured integrally.
[0012]
(Function)
When applying an electromagnetic horn to an in-vehicle millimeter-wave radar antenna, each of the transmitting and receiving antennas has a multi-horn configuration, and one of the multi-horns has a two-element configuration to reduce the height of the antenna in the elevation direction. The radar antenna is reduced in size, and the other multihorn is made up of four elements, and a main directivity characteristic as a desired antenna is realized by a combination of radiation characteristics of transmission and reception by each multihorn. The directivity is set by the size and arrangement in the elevation direction of each of the two and four elements.
[0013]
DETAILED DESCRIPTION OF THE INVENTION
Embodiments of an on-vehicle radar antenna according to the present invention will be described in detail with reference to the drawings.
(First embodiment)
(Description of configuration)
FIG. 1 is a block diagram showing the configuration of the first embodiment. FIG. 1A is an arrangement of rectangular electromagnetic horns (electromagnetic horns) as viewed from the front of the antenna opening surface, and FIG. It is the waveguide branch structure for arrangement | positioning of the electromagnetic horn seen from the side surface side of the antenna, and the electromagnetic wave electric power feeding to each electromagnetic horn. Each antenna (unit antenna) on the transmitting side and the receiving side is composed of a plurality of electromagnetic horns (elements), and the transmitting side and the receiving side differ in the size, number and arrangement of elements.
[0014]
As shown in FIG. 1A, the antenna arrangement of the radar antenna of the present embodiment is such that the transmitting side has two elements (TX11 and TX12, TX21 and TX22; two-element multi-horn), and each unit antenna (TX1, TX2). ), And the receiving side forms unit antennas (RX1, RX2) with four elements (RX11, RX12, RX13, and RX14, RX21, RX22, RX23, and RX24; four-element multi-horn).
[0015]
The two elements of each unit antenna on the transmission side have the same height in the elevation direction (referred to as “elevation direction width”), that is, have openings with the same elevation direction width W0. the two outer elements of the elevation direction (height direction) (RX11 and RX14, RX21 and RX24) has an opening of the same elevation width W 2, the two inner elements (and RX12 RX13, RX22 and RX23) Have openings having the same elevation angle direction width W 1 ( < W 2 ), and are arranged without providing a gap in the elevation direction (height) direction on the opening surface of each element. Further, as shown in FIG. 1B, each element (electromagnetic horn) is provided with a waveguide for coupling electromagnetic waves at a feeding point. The waveguide includes a waveguide CT that electromagnetically couples with the two feeding points of the transmission unit antenna, and a waveguide CR that couples with the four feeding points of the reception unit antenna. Each of the tubes CT and CR includes a branching unit or a combining unit B for coupling with the feeding point.
[0016]
FIG. 2 is a diagram showing a more detailed arrangement relationship seen from the opening surface side of the horn antenna used in the present embodiment, and FIG. 2 (a) is a relationship between a horn of one element and a multi-horn of two elements, FIG. 2B shows a relationship with a similar four-element multihorn.
[0017]
As shown in FIG. 2 (a), the two-element unit antenna for transmission according to the present embodiment has an interval between the elevation angle direction intermediate portions (referred to as “center axis”) of the opening having the elevation angle direction width W0. The two elements are arranged vertically with a distance D0 between the central axes. In this case, the height of the two-element unit antenna is Hd (= D0 + W0). In addition, as shown in FIG. 2B, the four-element unit antenna has two elements (horns) having an elevation angle direction width W1 arranged in the vertical direction with a distance D1 between its central axes, and an elevation angle on the outer side. Two elements (horns) having a directional width W2 (> W1) are arranged vertically with a distance D2 between their central axes. The height of the 4-element unit antenna in this case is assumed to be Ho.
[0018]
FIG. 3 is a diagram illustrating a configuration example of a switching circuit for a radar antenna and an example of switching control according to the present embodiment. FIG. 3A is a configuration example of a switching circuit having two transmission unit antennas (transmission antennas) (TX1, TX2) and two reception unit antennas (reception antennas) (RX1, RX2). FIG. 3B shows an example of switching in that case. The two transmitting antennas (TX1, TX2) are supplied with detection electromagnetic waves (radio waves) by switching them with a switch S1, and the two receiving antennas (RX1, RX2) switch reflected waves from the detection direction. Switching is received at S2. Detection of obstacles by forming a beam in the azimuth direction (horizontal direction) by receiving reflected waves from all combinations of two transmitting antennas (TX1, TX2) and two receiving antennas (RX1, RX2). Do. As radio waves to be transmitted and received, for example, a signal frequency-modulated by a triangular wave signal can be used. In this case, for example, in synchronization with the rising point of the triangular wave signal, the switch S1 is switched every one period of the triangular wave signal to transmit radio waves from the transmission antennas (TX1, TX2), and the transmission antennas (TX1, TX2) are switched. The switch S2 is switched every cycle 2T period, which is a cycle of one cycle, and the reflected wave is received from the two receiving antennas (RX1, RX2).
[0019]
(Description of operation)
Next, the operation of the present embodiment will be described in detail with reference to FIGS. The radar antenna has an array configuration in which a plurality of unit antennas are arranged in the horizontal direction. In general, a radar antenna is required to have a wide-angle characteristic with a beam width of 20 ° to 30 ° or more in the horizontal direction, and a narrow-angle characteristic with a beam width of about 3 ° to 5 ° in the elevation angle direction. An opening such as a rectangle is required. In the present invention, the antenna is miniaturized by using a two-element multihorn and the side lobe is reduced by using a four-element multihorn.
[0020]
[Miniaturization with two-element multihorn]
First, the radiation characteristics (directivity characteristics) of the one-element horn and the two-element multihorn will be described.
Looking at the radiation characteristics of a 1-element horn, assuming that the elevation width H of the 1-element horn (in the case of 1 element, the height of the antenna is also H), the elevation angle θ, and the wavelength λ of the radio wave, a rectangular aperture with a uniform electric field distribution The radiation characteristics from
Fo (θ) = sin (Uh) / Uh (1)
However, Uh = πH / λ · sin (θ)
Represented as:
[0021]
On the other hand, the radiation characteristic of a multihorn in which two elements having an elevation width W0 are arranged at a distance D0 is
Fd (θ) = sin (Uw) / Uw · cos (Vd) (2)
However,
Uw = πW0 / λ · sin (θ), Vd = πD0 / λ · sin (θ)
Represented as:
[0022]
When the height Hd that makes the beam widths represented by the above formulas (1) and (2) the same in the case of the 1-element horn and the case of the 2-element multihorn is calculated by a specific example, for example, the elevation angle When the respective heights H and Hd for realizing the beam width of 3.3 ° (degrees) are obtained, in the case of one element, H = 15.4λ (aperture length) is obtained. = 4λ, the height Hd = 12.5λ (<15.4λ).
[0023]
In general, a one-element horn and a two-element multihorn exhibit radiation characteristics with substantially the same beam width, that is, the conditions under which the radiation characteristics Fo and Fd can be made substantially equal are:
Considering a practical range regarding the relationship between the height H of the 1-element horn and the elevation direction (height direction) width W0 of each horn of the 2-element multihorn, W0 = 0.2H to 0.4H. , D0 = 0.56H to 0.53H.
[0024]
That is, the relationship between the height Hd (= D0 + W0) in the case of the two-element multihorn and the height H in the case of the one-element horn is Hd = 0.76H to 0.93H. If used, the same beam width as a one-element horn can be realized at a low (small) height, and the antenna can be downsized by using a two-element multihorn.
[Reduction of side lobe by 4-element multi-horn]
Next, radiation characteristics of the four-element multihorn will be described.
The radiation characteristic Fq of the 4-element multihorn is
Fq (θ) = W1 ^1/2 · sin (Uw1) / Uw1 · cos (Vd1)
+ W2 ^1/2 · sin (Uw2) / Uw2 · cos (Vd2) (3)
However,
Uw1 = πW1 / λ · sin (θ), Vd1 = πD1 / λ · sin (θ)
Uw2 = πW2 / λ · sin (θ), Vd2 = πD2 / λ · sin (θ)
Represented as:
[0025]
Since the directivity characteristic (radar antenna characteristic) Fr as a radar antenna is determined by the combination of each unit antenna for transmission and reception, the radiation characteristic Fq of the four-element multi-horn of Expression (3) and Expression (2) It is given by the product (Fr = Fq × Fd) with the radiation characteristic Fd of the two-element multihorn. Here, the best low side lobe characteristic can be obtained by selecting a relationship in which the side lobe peaks and nulls of the radiation characteristics Fq and Fd cancel each other.
[0026]
FIG. 4 is a diagram illustrating a calculation example of the directivity characteristic Fr according to the present embodiment. This figure shows the directivity characteristics with the E (electric field) plane as the elevation angle direction, and the ratio W1 / W2 of the elevation angle widths W1 and W2 on the inside and outside with the height Ho of the four-element multihorn constant. Shows the radar antenna characteristics when is changed to 1/3, 1/2, 1 / 1.4, 1/1, and 2/1. In each case, the element spacing of the two-element multihorn is set to the side lobe. It is selected so that the peak is minimized.
[0027]
In the directivity shown in FIG. 4, when the ratio W1 / W2 of W1 and W2 is W1 / W2 = 2/1, the side lobe is the highest, and W1 / W2 = 1/1, 1/1. The side lobes are lowered in order of 4, 1/2, and 1/3, and are minimized. As a result, the best low sidelobe characteristic is obtained when W1 / W2 is about 1/3. However, the beam width characteristic is the narrowest when the ratio W1 / W2 of W1 and W2 is 2/1, and W1 / W2 = 1/1, 1 / 1.4, 1/2, and 1/3 in this order. If it is large and remarkably large, it becomes difficult to obtain narrow beam characteristics, and problems such as a significant decrease in antenna efficiency occur. When W1 / W2 is about ½, a sufficiently low sidelobe characteristic can be obtained for on-vehicle radar applications, and the antenna in this case can obtain an optimum characteristic comprehensively.
[0028]
FIG. 5 and FIG. 6 are diagrams showing similar calculation examples for the directivity with the H plane as the elevation angle direction. The element dimensions / intervals of the 4-element multihorn are fixed, and the element-intervals of the 2-element multihorn are changed to obtain conditions for canceling side lobes. As shown in this figure, the elevation direction widths W1, W2 are obtained. Can be used as the characteristics of the radar antenna by the combination of the element spacing settings of two elements, whether they are the same or larger.
[0029]
In the case of FIG. 5, good low sidelobe characteristics are obtained when W1: W2 is about 2: 1. In the case of FIG. 6, the sidelobe peak is lowest when W1: W2 = 1: 2 to 1: 3. In this case, the peak level is higher than in the case of FIGS. 4 and 5, but there is an advantage that narrow-angle beam characteristics can be obtained with the same antenna height.
[0030]
The above calculation is based on the condition that the lag phase of the horn can be ignored (the horn length is sufficiently large). However, the actual horn has a limited horn length and affects the efficiency and radiation characteristics of a single unit. Therefore, the calculation is much more complicated, but the same tendency can be obtained by a detailed calculation in which the opening area is applied in consideration of the slow phase.
[0031]
In general, in a multihorn, if the number of elements (number of divisions) is increased with the horn length being constant (up to a certain limit), the antenna efficiency is improved, but the loss of the branch circuit is increased. In particular, in millimeter waves, the influence of waveguide loss is large, and it is necessary to design the path length as short as possible with a circuit configuration as simple as possible. Considering these, in order to achieve an elevation beam characteristic of 5 ° to 3 ° required for in-vehicle radar and to obtain an appropriate gain, a combination of 4 elements / 2 elements is optimal as a unit antenna configuration.
[0032]
(Second Embodiment)
In the above embodiment, the configuration in which the opening of each horn is arranged without providing a gap in the elevation angle direction with respect to the multi-horn consisting of four elements has been shown. However, the present invention is not limited to such an arrangement. It is possible to realize similar characteristics by satisfying the conditions.
[0033]
FIG. 7 is a view showing an embodiment in which a gap is provided between openings of a horn of a unit antenna composed of a four-element multihorn. The unit antenna consisting of a two-element multi-horn is the same as in the first embodiment, but the unit antenna consisting of a four-element multi-horn has a horn arrangement in which gaps of the same interval are provided between the openings, The feeding points of the horn elements are all connected to the opening of the waveguide.
[0034]
In the case of the present embodiment, the ratio D1 / D2 of the distance D1 between the center axes of the two inner elements of the four-element multihorn and the distance D2 between the center axes of the two outer elements is set to about 1/4. 4 is the same as the directivity characteristic when W1: W2 = 1: 2 for the E plane shown in FIG. 4, and the same as the directivity characteristic when W1: W2 = 1: 2 for the H plane shown in FIGS. These characteristics can be realized.
[0035]
Further, the ratio D1 / D2 of the distance D1 between the central axes of the two inner elements of the four-element multihorn and the distance D2 between the central axes of the two outer elements is set to about 1/2. When the ratio W1 / W2 of the elevation direction width W1 of the two inner elements of the multihorn to the elevation direction width W2 of the two outer elements is about 2, the same characteristics as the directivity characteristics for the E plane shown in FIG. Realization of characteristics similar to the directional characteristics for the H plane shown in FIGS. 5 and 6 when the ratio W1 / W2 of the elevation angle direction width W1 of the two inner elements of the multi-horn and the elevation direction width W2 of the two outer elements is about 2. Is possible.
[0036]
(Other embodiments)
In the above embodiment, the combination configuration of the horn elements of only two elements and four elements has been described as the unit antenna. However, each unit antenna has a main characteristic according to the present invention that is a combination of the horn elements of two elements or four elements. That is, it is shown as determining the basic desired characteristics, and as long as such main characteristics can be realized by two or four elements, an additional or auxiliary horn element is combined with either or both of them. It goes without saying that it is possible.
[0037]
The radar antenna as a whole has a configuration in which a large number of horn antennas are arranged vertically and horizontally, and the mechanism of the above embodiment is suitable for a die-cast manufacturing method or the like. Further, it is possible to manufacture the entire device housing or a part of the device housing and the antenna integrally. By adopting this manufacturing method, the entire device can be reduced in size and cost.
FIG. 8 is a diagram illustrating an example in which an antenna is integrally manufactured by a die casting method. This example shows a structure on the premise of the antenna arrangement of the first embodiment shown in FIG. 1, and is for fixing to a vehicle member on a plane corresponding to the position of the feeding point of each unit antenna. This is a structure in which an antenna mounting substrate provided with a plurality of holes is arranged.
The horn of each unit antenna has an outer shape configured as a box and is formed in an integrated structure with the substrate. Such a structure can be easily formed by using two molds that can be divided in the surface direction of the substrate. It is obvious that the antenna of the second embodiment shown in FIG. 7 can be manufactured by the same manufacturing method.
[0038]
In the above embodiment, an example in which a 2-element unit antenna is used for transmission and a 4-element unit antenna is used for reception has been described. However, a 4-element unit antenna is used for transmission. The fact that the antenna can be used for reception is apparent from the fact that the main characteristic of the present invention is realized by transmission / reception of a combination of two elements and four elements, and further the unit antenna of the present invention. In the array arrangement, the combination of transmission and reception of 2 elements and 4 elements can be performed by switching control of the switch switching circuit as described above, and whether or not to set fixedly for transmission and reception is arbitrary. it is obvious.
[0039]
【The invention's effect】
According to the present invention, a horn element is used as an in-vehicle millimeter wave antenna, and a unit antenna composed of multi-horns is a combination of two elements and four elements, and the main directivity is realized by transmitting and receiving these combinations. In addition, since the height of the two-element unit antenna in the elevation angle direction can be reduced by using a single horn element, the entire radar antenna can be reduced in size.
[0040]
Further, a combination of 2 elements and 4 elements can realize a miniaturized radar antenna, and can also realize a narrow-angle beam characteristic as a directivity characteristic (radar antenna characteristic).
[0041]
Furthermore, according to the present invention, the in-vehicle millimeter wave antenna has a horn array antenna configuration, so that a radar antenna including an array antenna or a casing can be manufactured by die-casting or the like by integral molding.
[Brief description of the drawings]
FIG. 1 is a diagram showing a first embodiment of the present invention.
FIG. 2 is a diagram showing a relationship between a 2-element and 4-element unit antenna and a 1-element horn according to the present embodiment.
FIG. 3 is a diagram illustrating a configuration example of a radar antenna switching circuit according to the present embodiment;
FIG. 4 is a diagram illustrating a calculation example of directivity (E plane is an elevation angle direction).
FIG. 5 is a diagram illustrating a calculation example of directivity (H plane is an elevation angle direction).
FIG. 6 is a diagram illustrating a calculation example of directivity (H plane is an elevation angle direction).
FIG. 7 is a diagram showing a second embodiment of the present invention.
FIG. 8 is a diagram showing an antenna structure manufactured integrally by a die-cast manufacturing method.
[Explanation of symbols]
TX1, TX2 Two-element unit antenna RX1, RX2 Four-element unit antenna CT, RT Waveguide B Branch S1, S2 Changeover switch

Claims (5)

In a vehicle-mounted millimeter-wave radar antenna having a unit antenna for transmission and reception configured by a multihorn,
Of the unit antennas for transmission and reception, one unit antenna is composed of a four-element multihorn that determines the main characteristics arranged in the elevation angle direction, and the two inner elements and the two outer elements of the four-element multihorn. The widths in the elevation direction are the same size , and the ratio W1 / W2 of the elevation direction width W1 of the two inner elements to the elevation direction width W2 of the two outer elements is about 1/2, or between the central axes of the two inner elements. The ratio D1 / D2 of the distance D1 and the distance D2 between the center axes of the two outer elements is about 1/4 , and the other unit antenna is a two-element multihorn that determines the main characteristics arranged in the elevation direction. The in-vehicle millimeter-wave radar antenna, wherein the two elements have the same height in the elevation direction. In a vehicle-mounted millimeter-wave radar antenna having a unit antenna for transmission and reception configured by a multihorn,
Of the unit antennas for transmission and reception, one unit antenna is composed of a four-element multihorn that determines the main characteristics arranged in the elevation angle direction, and the two inner elements and the two outer elements of the four-element multihorn. The width W1 of the inner two elements and the width W2 of the outer two elements are about 2 or the distance D1 between the central axes of the two inner elements. The ratio D1 / D2 of the distance D2 between the central axes of the two outer elements is about 1 / 2.5, and the other unit antenna is a two-element multihorn that determines the main characteristics arranged in the elevation direction. The in- vehicle millimeter-wave radar antenna, wherein the two elements have the same height in the elevation direction . The interval Do between the central axes of the two elements of the unit antenna of the two-element multihorn is about 0.55 Ho with respect to the elevation length Ho of the unit antenna composed of the four-element multihorn. The in- vehicle millimeter wave radar antenna according to claim 1 or 2 . 4. The on- vehicle millimeter-wave radar antenna according to claim 1, wherein the unit antennas are arrayed in a horizontal direction . The in-vehicle millimeter-wave radar antenna according to any one of claims 1 to 4, wherein the entire radar antenna or the radar apparatus housing and at least a part of the radar antenna are manufactured integrally .

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