WO2011118170A1

WO2011118170A1 - Antenna

Info

Publication number: WO2011118170A1
Application number: PCT/JP2011/001598
Authority: WO
Inventors: 工藤敏夫; 湖東雅弘; 柏原一之; 中村智一; 阿部真之
Original assignee: 三菱電線工業株式会社
Priority date: 2010-03-23
Filing date: 2011-03-17
Publication date: 2011-09-29
Also published as: JP5635787B2; JP2011199715A; TW201203700A

Abstract

At least three thin-layer shaped antenna elements (1) formed from conductive material are arranged so as to be rotationally symmetrical around a single point (C) and so as to be close to one-another whilst having a minute gap (3) there-between. The thin-layer shaped antenna elements (1) are provided with an outer-most corner section (10) at the point furthest from the single point (C), and have a radial slit (2) which goes from the single point (C) toward the outer-most corner section (10), and the inner edges of which are continuous with the inner edges of the minute gaps (3).

Description

antenna

The present invention relates to an antenna.

In order to be able to use mobile phones and PHS in each building and underground mall, systems that introduce radio waves from outdoor mobile phones and relay them using indoor small output antennas have been introduced in various places.

Conventionally, as the small output antenna for this system, a dipole antenna or a monopole antenna has been used because the antenna is required to have omnidirectional characteristics for designing an indoor conversation area (Patent Document) 1).

JP 2007-215133 A

Conventional antennas have to have a three-dimensional shape in order to obtain omnidirectional characteristics, and when the antenna is installed on a ceiling or the like, the antenna protrudes from the ceiling and has a disadvantage of poor appearance.

In order to solve this problem, a planar omnidirectional loop antenna has been proposed. One example is a crowbar antenna having a plurality of linear loops. Since this crowbar type antenna is composed of a linear loop, it can only deal with a single frequency band, and the frequency range where a predetermined VSWR value can be obtained is limited to a narrow band. Therefore, with a conventional crowbar antenna, it is difficult to cover all of a plurality of frequencies in a frequency division duplex (FDD) of a mobile phone with a single antenna.

Therefore, the present invention provides an antenna that exhibits excellent VSWR (voltage standing wave ratio) characteristics in a wide frequency band and that can radiate radio waves uniformly over a wide range. The purpose is to provide.

In the antenna according to the present invention, the thin-sided antenna element is formed by arranging three or more thin-sided antenna elements made of a conductive material in rotational symmetry around one point and close to each other with a minute gap. Has an outermost corner portion at a position farthest from the one point, and has a radial slit from the one point to the outermost corner portion, and the inner end of the radial slit is at the inner end of the minute gap portion. It is continuous.

The one point is used as a common first feeding point for the three or more antenna elements, and the second feeding point is arranged at an inner corner where the inner end of the radial slit and the inner end of the minute gap portion are continuous. It is set.

An imaginary path connecting the first feeding point and the second feeding point along the outer peripheral edge of the antenna element is an outer loop, and the first feeding point and the second feeding point are the antenna. Assuming that an imaginary path connected along the inner peripheral edge of the element is an inner peripheral loop, the outer peripheral path length dimension of the outer peripheral loop is 1.8 to 2.2 times the electrical wavelength corresponding to the lower limit frequency of the required frequency band. The inner circumference path length dimension of the inner circumference loop is 1.3 times to 1.7 times the electrical wavelength corresponding to the upper limit frequency of the required frequency band.

According to the antenna of the present invention, it becomes possible to deal with a plurality of radio waves having different frequency ranges without impairing omnidirectional characteristics (broadband), and a plurality of relay antennas can be integrated into one antenna. Therefore, it is possible to radiate radio waves efficiently and uniformly over a wide range with a small number of installations. Moreover, since it is planar, it does not protrude from the ceiling or the like, and can be installed without conspicuous, improving the practicality.

It is the figure which showed the structure of 1st Embodiment, Comprising: (a) is a top view, (b) is an enlarged view of the outermost corner part vicinity, (c) is principal part explanatory drawing. It is the figure which showed the structure of 2nd Embodiment, Comprising: (a) is a top view, (b) is an enlarged view of the outermost corner part vicinity. It is the figure which showed the structure of 3rd Embodiment, Comprising: (a) is a top view, (b) is an enlarged view of the outermost corner part vicinity. It is the simple figure which showed the example of installation of the antenna. It is the simple top view which showed the example of installation of an antenna. It is the graph which showed the VSWR characteristic of the antenna. It is the graph which showed the directivity and gain characteristic of an antenna. It is the top view which showed the antenna of the comparative example. It is the graph which showed the VSWR characteristic of the antenna of a comparative example. It is the graph which showed the VSWR characteristic based on the measurement data of various antennas. It is the graph which showed the VSWR characteristic based on the measurement data of various antennas.

Hereinafter, a detailed description will be given based on the drawings showing the embodiments.

1, 2, and 3, the configuration common to all of the first embodiment, the second embodiment, and the third embodiment of the antenna A will be described. A thin single-sided antenna element 1 made of a conductive material is rotationally symmetric about one point C and is arranged close to each other with a minute gap 3. Further, the thin single-sided antenna element 1 includes an outermost corner portion 10 at a position farthest from one point C, and has a radial slit 2 extending from the one point C toward the outermost corner portion 10. Further, the inner end of the radial slit 2 is continuous with the inner end of the minute gap 3.

Further, the antenna A has a single point C as a common first feeding point E1 for three or more antenna elements 1, and the antenna A is connected to the inner corner 12 where the inner end of the radial slit 2 and the inner end of the minute gap 3 are continuous. Two feeding points E2 are arranged. A conducting wire (not shown) is connected to the antenna A so as to energize from the first feeding point E1 to the second feeding point E2.

The three or more thin single-sided antenna elements 1 are preferably composed of a single thin metal plate. Specifically, the antenna element 1 can be a thin metal plate (metal foil) such as Cu, Al, Ag, or Au, and can be used by being attached to glass, a resin sheet and a resin film, an electronic substrate, or the like.

In addition, a metal film, a transparent conductive film and a conductive paint film can be used by directly forming them on glass and an electronic substrate, or a film once formed on a resin sheet, a resin film, etc. is further stretched on the glass and the electronic substrate. Can also be used.

As the metal film, Au, Ag, Cu, Al, Pd, Pt and alloys containing them can be used. As the transparent conductive film, metal oxides such as ITO, zinc oxide and tin oxide can be used. It can be manufactured by sputtering, plating, electrodeposition or the like.

As the conductive paint film, metal paste or carbon paste can be used, and can be manufactured by screen printing, roll coating, transfer, or the like.

When it is used while being stretched on a glass surface such as a window glass, it is desirable that the visible light transmittance is 70% or more. In applications where such transparency is required, a metal mesh type, extremely thin (for example, 0) (.05 μm) metal foil, or a transparent conductive film or metal translucent film. As the metal translucent film, Ag—Cu, Ag—Pd, Ni—Au or the like can be used.

In addition, tensioning or tensioning means tensioning the outer surface of the glass surface with an adhesive or pressure-sensitive adhesive, etc., or baking and laminating, or otherwise sandwiching or sandwiching between glass layers. Include.

In each antenna element 1, if an imaginary path connecting the first feeding point E 1 and the second feeding point E 2 along the outer peripheral edge 13 of the antenna element 1 is an outer loop 18, the outer loop 18 The outer peripheral path length dimension L18 is configured to be approximately twice as long as the electrical wavelength λeL corresponding to the lower limit frequency FL of the required frequency band. The outer peripheral path length dimension L18 is preferably set to 1.8 times to 2.2 times the electrical wavelength λeL, and more specifically set to 1.9 times to 2.1 times. . On the other hand, when an imaginary path connecting the first feeding point E1 and the second feeding point E2 along the inner peripheral edge portion 14 of the antenna element 1 is an inner peripheral loop 19, an inner peripheral path length dimension L19 of the inner peripheral loop 19 is shown. However, the length is about 1.5 times the electrical wavelength λeH corresponding to the upper limit frequency FH of the required frequency band. The inner circumferential path length dimension L19 is preferably set to 1.3 times to 1.7 times the electrical wavelength λeH, and more specifically, set to 1.4 times to 1.6 times. preferable. As a result, VSWR characteristics corresponding to a plurality of types of radio wave frequency ranges can be obtained.

Here, in the antenna element 1, the outer peripheral edge 13 means a range excluding the radial slit 2 in the outline of the antenna element 1, and the inner peripheral edge 14 is a radial in the outline of the antenna element 1. The range of the slit 2 is meant.

Further, the electrical wavelength λe (mm) is a wavelength in a state where the current of the frequency F (GHz) flows through the antenna element 1 having the wavelength shortening rate K (%), and is represented by the following equation.

λe = (300 / F) * K
The inner circumferential path length dimension L19 of the inner circumferential loop 19 can be adjusted by appropriately setting the length dimension L2 from the inner end to the outer end of the radial slit 2.

Further, the outer peripheral path length dimension L18 of the outer peripheral loop 18 is such that the

adjacent corner portions

11 and 11 of the thin-sided antenna element 1 forming the outer end portion of the minute gap portion 3 are chamfered in an arc shape, and the radius of curvature R11 of the arc is set. Can be adjusted by appropriately setting.

The outermost corner 10 is formed between the outer end of the radial slit 2 and the remainder of 0.5 mm to 2.0 mm. The outermost corner 10 may have an appropriate radius of curvature, and may be formed, for example, so that the radius of curvature is 0.5 mm.

The width dimension W2 of the radial slit 2 is preferably set to 1.0 mm to 5.0 mm, and the gap dimension W3 of the minute gap 3 is preferably set to 0.5 mm to 2.0 mm. Although the outer end of the radial slit 2 is illustrated as having a tapered shape, it may have an appropriate radius of curvature and may be sharp. The inner end of the radial slit 2 is tapered and decreases to the same width as the inner end of the minute gap 3, and continues to the inner end of the minute gap 3. A portion where the radial slit 2 and the minute gap portion 3 are continuous is a curved shape, and an arc-shaped inner corner portion 12 is formed.

Next, each embodiment will be described. The antenna A according to the first embodiment shown in FIG. 1 includes four square-shaped single-sided antenna elements 1 and is formed into a square shape as a whole. The outermost corner portions 10 disposed at the four corners of the antenna A are formed at right angles and sharply. The antenna A integrally connects the four thin plane antenna elements 1 by a central connecting portion having a first feeding point E1 (one point C).

The antenna A according to the second embodiment shown in FIG. 2 includes three rectangular thin-sided antenna elements 1 and is formed into a regular triangle shape as a whole. The outermost corner portion 10 disposed at each apex of the antenna A is formed with an angle of 60 ° and a sharp shape. The antenna A integrally connects the three thin-plate antenna elements 1 by a central connecting portion having a first feeding point E1 (one point C).

The antenna A according to the third embodiment shown in FIG. 3 includes three regular hexagonal thin single-sided antenna elements 1 and is formed in a three-pronged shape as a whole. The three lamellar planar antenna elements 1 are formed so that each outermost corner portion 10 is formed at an angle of 120 ° and sharp, and is integrally connected by a central connecting portion having a first feeding point E1 (one point C). .

The method (action) of using the antenna described above will be described.

As shown in FIG. 4, the antenna A is connected to an indoor relay antenna 30 for drawing mobile phone radio waves indoors, and the outdoor radio waves are transmitted to closed indoor spaces such as a building interior 31 and an underground mall 32. Relay to reach. The antenna A is installed on the ceiling of the indoor space 31 of the building or the indoor space of the underground mall 32 without protruding.

The antenna A is used in two-way wireless communication of a cellular phone, for example, frequency division duplex (FDD) reception radio waves (frequency: 1.94 GHz to 1.96 GHz) and transmission radio waves (frequency: 2.13 GHz to 2.13 GHz). 15 GHz).

As shown in FIG. 5, a plurality of antennas A are arranged at predetermined equal intervals on the ceiling of an indoor space such as the room 31 of the building, and the service areas S supplemented by the respective antennas A are overlapped with each other. Design so that there are as few areas in the indoor space as possible that are not affected by radio waves. The antenna A has a non-directional characteristic that uniformly radiates and absorbs radio waves, and generates the service area S in a circular shape in plan view. That is, the omnidirectional antenna A efficiently forms a service area S in a wide range with a small number of installations. Further, since frequency division duplex (FDD) is handled by one antenna A, the number of installations can be further reduced.

Next, the graph shown in FIG. 6 is the first embodiment shown in FIG. 1, and the material is Cu, the thickness dimension is 35 μm, the length dimension L0 between the

outermost corner portions

10 and 10 is 100 mm, The width dimension W2 of the radial slit 2 is 3.0 mm, the gap dimension W3 of the minute gap portion 3 is 1.0 mm, the length dimension L2 of the radial slit 2 is 65 mm, and the radius of curvature R11 of the adjacent corner portion 11 is 7.5 mm. As an example, measured data when an antenna is formed on a 1.6 mm thick epoxy glass substrate (wavelength shortening rate K = 62%) is shown, with the horizontal axis representing frequency (GHz) and the vertical axis representing VSWR value (voltage Standing wave ratio).

The antenna 100 of the comparative example shown in FIG. 8 is formed by improving a conventional crowbar type antenna into a flat plate shape (foil shape). The antenna 100 of the comparative example includes four linear loop elements 101. The four linear loop elements 101 are arranged rotationally symmetrical around one point and close to each other with a minute gap. The outer diameter Ld is 100 mm.

The graph shown in FIG. 9 is the antenna 100 of the comparative example, when the material is set to Cu and the thickness dimension is 35 μm, and it is formed on a 1.6 mm thick epoxy glass substrate (wavelength reduction rate K = 62%). The measured data is shown, with the horizontal axis representing the frequency (GHz) and the vertical axis representing the VSWR value (voltage standing wave ratio).

In FIG. 6, it can be seen that the frequency band in which the antenna of the example shows a VSWR value of 2.0 or less is sufficiently wide. It has a first deepest portion P1 in the vicinity of the frequency (1.94 GHz) of the received radio wave, and a second deepest portion P2 in the vicinity of the frequency (2.15 GHz) of the transmitted radio wave. That is, the graph showing the VSWR characteristics of the antenna of the embodiment draws a bimodal locus in which the first deepest portion P1 and the second deepest portion P2 exist, and the frequency of two types of radio waves of frequency division duplex (FDD). It can be said that an effective VSWR was obtained over a wide band corresponding to.

On the other hand, in FIG. 9, the antenna of the comparative example has a very narrow frequency band showing a VSWR value of 2.0 or less, and the frequency of the received radio wave (1.94 GHz) and the frequency of the transmitted radio wave (2.15 GHz). It can be seen that the VSWR characteristics are unimodal (only one minimum peak of the VSWR value) that cannot correspond to both.

Next, the graph shown in FIG. 7 illustrates the evaluation result of the directivity of the antenna of the example. In FIG. 7, it can be seen that the antenna of the example has non-directional characteristics. That is, radio waves are radiated uniformly in both the frequency range of the received radio wave (1.94 GHz) and the frequency of the transmit radio wave (2.15 GHz) corresponding to frequency division duplex (FDD). It is confirmed that the directivity is not impaired.

10 and 11, the antenna {prototype (i)} having the same configuration as that of the above-described embodiment and the antenna of the embodiment have a length dimension L0 between the

outermost corner portions

10 and 10. A plurality of types of antennas {prototypes (ii) to (vii)} set so that at least one of the radius of curvature R11 of the adjacent corner portion 11 and the length dimension L2 of the radial slit 2 is different, and the four corners of the antenna of the embodiment VSWR characteristics obtained by forming an antenna {prototypes (viii) to (ix)} with chamfered outermost corners 10 on a 1.6 mm thick epoxy glass substrate (wavelength reduction rate K = 62%) The graph lines are shown as graph lines (i) to (ix), where the horizontal axis represents the frequency (GHz) and the vertical axis represents the VSWR value (voltage standing wave ratio).

Conditions for each antenna are as shown in Table 1 and Table 2 below.
Further, in each antenna, the magnification between the outer circumference path length dimension L18 and the electrical wavelength λeL corresponding to the lower limit frequency FL, and the magnification between the inner circumference path length dimension L19 and the electrical wavelength λeH corresponding to the upper limit frequency FH, Is shown in Table 3.

10 and 11, a measurement graph line (i) is a VSWR characteristic obtained from an antenna {prototype (i)} having the same configuration as that of the example. Hereinafter, the measurement graph lines (ii) to (ix) are VSWR characteristics obtained from the corresponding prototypes (ii) to (ix).

In FIG. 10, the measurement graph line (i) and the measurement graph line (ii) show the VSWR characteristics obtained from the antenna in which the length L0 between the

outermost corner portions

10 and 10 is set to different conditions. Yes. It can be seen that the graph showing the VSWR characteristic shifts to the high frequency side as a whole by setting the length L0 between the

outermost corner portions

10 and 10 short.

The measurement graph line (ii) to the measurement graph line (v) indicate the VSWR characteristics obtained from the antennas in which the curvature radii R11 of the adjacent corner portions 11 are set to different conditions. It can be seen that by setting the radius of curvature R11 of the close corner 11 large, only the matching frequency on the low frequency side of the graph showing the VSWR characteristics is shifted to the high frequency side.

Next, in FIG. 11, the measurement graph line (i), the measurement graph line (vi), and the measurement graph line (vii) are obtained from the antenna in which the length dimension L2 of the radial slit 2 is set to different conditions. VSWR characteristics are shown. It can be seen that by setting the length dimension L2 of the radial slit 2 large, only the matching frequency on the high frequency side of the graph showing the VSWR characteristics is shifted to the low frequency side.

Further, the measurement graph line (viii) shows the VSWR characteristics obtained from an antenna which is the same antenna as that of the example but whose outermost corner portions 10 at the four corners are chamfered by 2 mm. The measurement graph line (ix) shows the VSWR characteristics obtained from the antenna in which the outermost corner portions 10 at the four corners of the antenna of the example are chamfered by 5 mm. It can be seen that chamfering the outermost corners 10 at the four corners hardly affects the VSWR characteristics of the antenna.

As described above, when the VSWR characteristics of the antenna shown in Tables 1 to 3 and measurement graph line (i) to measurement graph line (ix) are verified, the length dimension L0 between two adjacent

outermost corner portions

10 and 10 is It is confirmed that an antenna corresponding to a required frequency band can be obtained by appropriately setting the radius of curvature R11 of the close corner 11 and the length dimension L2 of the radial slit 2. In other words, setting of frequency bands corresponding to both reception radio waves (frequency: 1.94 GHz to 1.96 GHz) and transmission radio waves (frequency: 2.13 GHz to 2.15 GHz) in frequency division duplex (FDD) of mobile phones. The outer circumference path length dimension L18 of the outer circumference loop 18 is set to about twice the electrical wavelength corresponding to the frequency of the received radio wave, and the inner circumference path length dimension L19 of the inner circumference loop 19 is set to an electric power corresponding to the frequency of the transmission radio wave. This is achieved by setting it to about 1.5 times the target wavelength.

As described above, in the present embodiment, the single-sided antenna element 1 made of three or more conductive materials is rotationally symmetric about one point C and arranged close to each other with the minute gap portion 3. The lamellar planar antenna element 1 includes an outermost corner 10 at a position farthest from one point C, and has a radial slit 2 from the point C to the outermost corner 10, and the inner end of the radial slit 2 is Since it is continuous to the inner end of the minute gap 3, it can handle multiple radio waves with different frequency ranges without impairing the omnidirectional characteristics (broadband). Multiple relay antennas can be combined into one antenna. Can be integrated. Therefore, with a small number of installations, radio waves can be radiated or received uniformly and efficiently over a wide range without being noticeable. Moreover, since it is planar, it does not protrude from the ceiling or the like, and can be installed without conspicuous, improving the practicality.

One point C is a common first feeding point E1 for three or more antenna elements 1, and the second feeding point is connected to the inner corner 12 where the inner end of the radial slit 2 and the inner end of the minute gap 3 are continuous. Since E2 is disposed, the entire antenna can be reduced in size, and a high-performance antenna with a wide band can be obtained without impairing omnidirectionality.

An imaginary path connecting the first feeding point E1 and the second feeding point E2 along the outer peripheral edge portion 13 of the antenna element 1 is defined as an outer peripheral loop 18, and the first feeding point E1 and the second feeding point E2 are Assuming that an imaginary path connected along the inner peripheral edge portion 14 of the antenna element 1 is an inner peripheral loop 19, the outer peripheral path length dimension L18 of the outer peripheral loop 18 is 1 of the electrical wavelength λeL corresponding to the lower limit frequency FL of the required frequency band. .8 times to 2.2 times so that the inner circumference path length dimension L19 of the inner circumference loop 19 is 1.3 times to 1.7 times the electrical wavelength λeH corresponding to the upper limit frequency FH of the required frequency band. Since it comprised, it can respond | correspond suitably to the desired frequency band containing two or more types of different frequencies with one antenna.

The present invention is useful for antennas.

DESCRIPTION OF SYMBOLS 1 Thin plane antenna element 2 Radial slit 3 Minute gap part 10 Outermost corner part 11 Proximal corner part 12 Inner corner part 13 Outer peripheral edge part 14 Inner peripheral edge part 18 Outer peripheral loop 19 Inner peripheral loop C One point E1 First feeding point E2 Second feeding Point L0 Length dimension L18 Outer circumference path length dimension FL Lower limit frequency λeL Electrical wavelength L19 Inner circumference path length dimension FH Upper limit frequency λeH Electrical wavelength

Claims

Three thin plane antenna elements (1) made of three or more conductive materials are arranged rotationally symmetrical around one point (C) and close to each other with a minute gap (3),
The flaky antenna element (1) includes an outermost corner (10) at a position farthest from the one point (C) and a radial slit (10) from the one point (C) toward the outermost corner (10). 2)
Furthermore, the inner end of the radial slit (2) is continuous with the inner end of the minute gap (3).
The one point (C) is a common first feeding point (E1) for the three or more antenna elements (1), and the inner end of the radial slit (2) and the inner end of the minute gap portion (3). The antenna according to claim 1, wherein the second feeding point (E2) is disposed at an inner corner (12) where the two are continuous.
An imaginary path connecting the first feeding point (E1) and the second feeding point (E2) along the outer peripheral edge (13) of the antenna element (1) is defined as an outer loop (18). When an imaginary path connecting one feeding point (E1) and the second feeding point (E2) along the inner peripheral edge (14) of the antenna element (1) is an inner peripheral loop (19),
The outer circumference path length dimension (L18) of the outer circumference loop (18) is 1.8 to 2.2 times the electrical wavelength (λeL) corresponding to the lower limit frequency (FL) of the required frequency band, and the inner circumference loop ( The inner circumference path length dimension (L19) of 19) is configured to be 1.3 to 1.7 times the electrical wavelength (λeH) corresponding to the upper limit frequency (FH) of the required frequency band. Antenna.
The antenna according to any one of claims 1 to 3, wherein the thin single-sided antenna element (1) is composed of a thin metal plate, a metal film, a transparent conductive film, or a conductive paint film.
The antenna according to any one of claims 1 to 4, wherein the thin-sided antenna element (1) is attached to glass, a resin sheet, a resin film, or an electronic substrate.
The antenna according to any one of claims 1 to 5, wherein the thin-sided antenna element (1) is formed of a mesh.
The antenna according to any one of claims 1 to 6, wherein the thin-sided antenna element (1) is transparent or translucent.
The antenna according to any one of claims 1 to 7, wherein the outermost corner (10) is formed with a remaining portion of 0.5 mm to 2.0 mm between the outer end of the radial slit (2). .
The antenna according to any one of claims 1 to 8, wherein a width dimension of the radial slit (2) is 1.0 mm to 5.0 mm.
The antenna according to any one of claims 1 to 9, wherein a gap dimension of the minute gap (3) is 0.5 mm to 2.0 mm.
The antenna according to any one of claims 1 to 10, wherein an outer end of the radial slit (2) is pointed.
The inner end of the radial slit (2) decreases to the same width as the inner end of the minute gap (3) and continues to the inner end of the minute gap (3). The antenna according to Crab.
The antenna according to any one of claims 1 to 12, wherein a portion where the radial slit (2) and the minute gap portion (3) are continuous is curved.
The lamellar planar antenna element (1) is formed in a square shape and includes four square lamellar planar antenna elements (1), and the four lamellar planar antenna elements (1) have four corners. The antenna according to claim 1, wherein the antenna is formed in a square shape as a whole.
The lamellar planar antenna element (1) is formed in a quadrangular shape and includes three rectangular lamellar planar antenna elements (1). The three lamellar planar antenna elements (1) The antenna according to claim 1, wherein the antenna is formed in an equilateral triangle shape.
The lamellar planar antenna element (1) is formed in a regular hexagonal shape and includes three regular hexagonal lamellar planar antenna elements (1), and the three lamellar planar antenna elements (1). The antenna according to any one of claims 1 to 13, wherein the antenna is entirely formed in a trigeminal shape.