Antenna device

Abstract

Provided is an antenna device disposed on an object having a transmission part and a non-transmission part, wherein: the antenna device comprises a power-feeding unit, and a film antenna that is capacitively coupled to the power-feeding unit; and when viewed in a direction normal to the obverse surface of the film antenna, the power-feeding unit overlaps the non-transmission part.

Description

Antenna device

[0001] The present invention relates to an antenna device.

[0002] Patent Document 1 describes an antenna device that is placed on the glass of a vehicle. The antenna device described in Patent Document 1 includes a power supply unit and a film antenna having a radiating element sandwiched between films.

[0003] Patent No. 5067289

[0004] However, in the antenna device described in Patent Document 1, when viewed in a plane, the power supply section is located on the glass portion of the film antenna, which can reduce visibility when viewing an object through the glass portion.

[0005] An example of an object of the present invention is to suppress the influence of an antenna device on the transparency of a transparent portion of an object. Other objects of the present invention will become apparent from the description of this specification.

[0006] One aspect of the present invention is an antenna device that is placed on an object having a transparent portion and an opaque portion, and that includes a power supply portion and a film antenna that is capacitively coupled to the power supply portion, and when viewed in the normal direction to the front surface of the film antenna, at least a portion of the power supply portion overlaps with the opaque portion.

[0007] According to the above aspect of the present invention, it is possible to suppress the influence of the antenna device on the transparency of the transparent portion of the object.

[0008] 1 is an explanatory diagram of an object 100A on which the antenna device 10 of the present embodiment is disposed. It is an enlarged view of the dashed line portion in FIG. 1 . It is an explanatory diagram of an object 100B on which the antenna device 10 of the present embodiment is disposed. It is a perspective view of the antenna device 10 of the present embodiment. It is an enlarged view of the dashed line portion in FIG. 4 . It is an explanatory diagram showing a cross section of the antenna device 10. It is an explanatory diagram showing an enlarged view of a part of a conductor portion 126 when viewed in the Z direction. It is an explanatory diagram showing an equivalent circuit of the antenna device 10. It is a diagram showing an example of a change in VSWR under condition 1 for a normalized capacitance Cs, and a predetermined range based on VSWR = 10.0. It is a diagram showing an example of a change in VSWR under condition 2 for a normalized capacitance Cs, and a predetermined range based on VSWR = 10.0. It is a diagram showing an example of a change in VSWR under condition 3 for a normalized capacitance Cs, and a predetermined range based on VSWR = 10.0. It is a diagram showing an example of a change in VSWR under condition 4 for a normalized capacitance Cs, and a predetermined range based on VSWR = 10.0. 1 is a diagram showing an example of a change in VSWR under condition 1 for normalized capacitance Cs, and a predetermined range based on VSWR=3.0; FIG. 2 is a diagram showing an example of a change in VSWR under condition 2 for normalized capacitance Cs, and a predetermined range based on VSWR=3.0; FIG. 3 is a diagram showing an example of a change in VSWR under condition 1 for capacitance C, and a predetermined range based on VSWR=10.0; FIG. 4 is a diagram showing an example of a change in VSWR under condition 2 for capacitance C, and a predetermined range based on VSWR=10.0; FIG. 5 is a diagram showing an example of a change in VSWR under condition 3 for capacitance C, and a predetermined range based on VSWR=10.0; FIG. 6 is a diagram showing an example of a change in VSWR under condition 4 for capacitance C, and a predetermined range based on VSWR=10.0; FIG. 7 is a diagram showing an example of a change in VSWR under condition 1 for capacitance C, and a predetermined range based on VSWR=3.0. 21 is a diagram showing an example of the amount of change in VSWR under condition 2 for capacitance C, and a predetermined range with VSWR = 3.0 as a reference. FIG. 22 is a perspective view of an antenna device 10A of a first modified example. FIG. 23 is an enlarged view of the dashed line portion of FIG. 21. FIG. 24 is an explanatory diagram showing a cross section of an antenna device 10A of a first modified example. FIG. 25 is an explanatory diagram showing a cross section of an antenna device 10B of a second modified example. FIG. 26 is an explanatory diagram showing a cross section of an antenna device 10C of a third modified example. FIG. 27 is an enlarged perspective view of the vicinity of a base portion 125 of the antenna device 10C.Fig. 10C is an enlarged cross-sectional perspective view of the vicinity of a base portion 125 of the antenna device 10C. Fig. 11 is an explanatory diagram showing a cross section of an antenna device 10D of a fourth modified example.

[0009] At least the following matters will become clear from the description of this specification and the accompanying drawings.

[0010] Hereinafter, preferred embodiments of the present invention will be described with reference to the drawings. The same or equivalent components, members, etc. shown in the drawings will be designated by the same reference numerals, and redundant explanations will be omitted where appropriate.

[0011] 1 is an explanatory diagram of an object 100A on which an antenna device 10 of this embodiment is disposed. FIG. 2 is an enlarged view of the dashed line portion of FIG.

[0012] <<Definition of Directions, Etc.>> First, directions, etc. in the antenna device 10 of this embodiment will be defined with reference to FIGS.

[0013] 1 and 2, directions parallel to the plane on which the power feed unit 11 (described later) of the antenna device 10 is arranged and perpendicular to each other are defined as the "+X direction" and the "+Y direction." In this embodiment, the plane on which the power feed unit 11 of the antenna device 10 is arranged is the front surface of the ground unit (described later) of the antenna device 10. In the antenna device 10 of this embodiment, the +X direction is also the direction from the power feed unit 11 (described later) toward the film antenna 12, as shown in FIG. 2. The direction perpendicular to the +X direction and the +Y direction is defined as the "+Z direction."

[0014] The +X direction, -X direction, +Y direction, -Y direction, +Z direction, and -Z direction are each a fixed direction. Rather than being fixed directions as described above, both the +X direction and the -X direction may be simply referred to as the "X direction." Similarly, both the +Y direction and the -Y direction may be simply referred to as the "Y direction." Furthermore, both the +Z direction and the -Z direction may be simply referred to as the "Z direction." Furthermore, the Z direction may be referred to as the "up-down direction," and the direction perpendicular to the Z direction may be referred to as the "horizontal direction." Furthermore, the Z direction is the normal direction to the front surface of the film antenna 12.

[0015] 1 and 2, the +X direction, +Y direction, and +Z direction are each represented by a line segment with an arrow to facilitate understanding of directions, etc. in the antenna device 10. Note that the intersection of these line segments with an arrow does not indicate the origin of the coordinate system.

[0016] The above definitions of directions and the like are common to other embodiments in this specification unless otherwise specified.

[0017] <<Outline of Antenna Device 10 >> Next, an outline of the antenna device 10 of this embodiment will be described with reference again to FIGS. 1 and 2 described above.

[0018] As shown in Fig. 1, the antenna device 10 is an antenna device that is disposed on an object 100A. In the example shown in Figs. 1 and 2, the object 100A is a vehicle. Here, "vehicle" refers to a vehicle having wheels. However, the object 100A is not limited to the vehicle shown in Figs. 1 and 2, and may be a moving object that does not have wheels, such as construction machinery, agricultural machinery, a ship, an aircraft, or a drone.

[0019] The object 100A has a transparent portion 101A and an opaque portion 102A. The transparent portion 101A is a material that allows visible light or infrared light to pass through, in other words, a material that is transparent to visible light or infrared light. For example, when an internal space and an external space are separated by the transparent portion 101A, an object in the external space can be visually recognized or sensed by infrared light from the internal space through the transparent portion 101A. Conversely, an object in the internal space can be visually recognized or sensed by infrared light from the external space through the transparent portion 101A. Furthermore, the opaque portion 102A is a portion that is more difficult for visible light and infrared light to pass through than the transparent portion 101A, and is therefore more difficult for objects to be visually recognized or sensed by infrared light through the opaque portion 102A than the transparent portion 101A.

[0020] In the object 100A of this embodiment, the transmissive portion 101A is made of a material such as glass, acrylic, etc. The non-transmissive portion 102A is made of a conductive material such as metal, and is used as a ground portion of the film antenna 12 together with the external conductor side power supply portion 112 of the power supply portion 11.

[0021] In the object 100A of this embodiment, the transmissive portion 101A and the opaque portion 102A are located adjacent to each other, and the antenna device 10 of this embodiment is disposed across the transmissive portion 101A and the opaque portion 102A, as shown in Fig. 2. In other words, the antenna device 10 of this embodiment is disposed at the boundary between the transmissive portion 101A and the opaque portion 102A.

[0022] 1 and 2, the transmissive portion 101A is, for example, a vehicle windshield, and the opaque portion 102A is a pillar adjacent to the windshield, for example, an A-pillar (front pillar). Alternatively, the transmissive portion 101A may be a vehicle side glass, and the opaque portion 102A may be a pillar adjacent to the side glass, for example, an A-pillar (front pillar) or a B-pillar (center pillar). Furthermore, for example, if the roof of the vehicle is made of glass, the transmissive portion 101A may be a roof made of glass, and the opaque portion 102A may be a vehicle body frame that supports the roof.

[0023] As shown in FIG. 2, the antenna device 10 includes a power supply unit 11 and a film antenna 12 .

[0024] The power supply unit 11 is a component that includes the power supply point of the film antenna 12. When viewed in the Z direction (the normal direction to the front surface of the film antenna 12), the power supply unit 11 overlaps with the opaque portion 102A. In the antenna device 10 of this embodiment, when viewed in the Z direction, the entire power supply unit 11 overlaps with the opaque portion 102A. In other words, as shown in Figure 2, the entire power supply unit 11 is located on the +Z direction side of the opaque portion 102A. In Figure 2, the outline of the power supply unit 11 hidden by the opaque portion 102A is shown by a dashed line.

[0025] However, a part of the power supply unit 11 may overlap with the opaque portion 102A. In other words, it is sufficient that at least a part of the power supply unit 11 overlaps with the opaque portion 102A when viewed in the Z direction. Also, a part of the film antenna 12, which will be described later, may overlap with the opaque portion 102A.

[0026] The power supply unit 11 is formed of, for example, a conductor. Therefore, if the power supply unit 11 is placed in the transmissive portion 101, it may affect the transmittance of visible light and infrared rays in the transmissive portion 101. As described above, the antenna device 10 is placed across the transmissive portion 101A and the non-transmissive portion 102A. By positioning at least a portion of the power supply unit 11 in the antenna device 10 so that it overlaps with the non-transmissive portion 102A, the overlapping area of ​​the power supply unit 11 with the transmissive portion 101A can be reduced. In other words, the influence of the power supply unit 11 on the transmittance of visible light and infrared rays in the transmissive portion 101A can be reduced. Therefore, when the antenna device 10 is placed on an object 100A (here, a vehicle) having the transmissive portion 101A, the influence of the antenna device 10 on the transmittance of the transmissive portion 101A of the object 100A can be reduced.

[0027] Furthermore, when the object 100A on which the antenna device 10 is disposed is viewed from the −Z direction side, at least a part of the power supply unit 11 is hidden on the +Z direction side of the opaque portion 102A, as shown in Fig. 2. This makes it possible to prevent deterioration in the aesthetic appearance of the object 100A on which the antenna device 10 is disposed due to the power supply unit 11 being visible.

[0028] The power supply unit 11 has an inner conductor side power supply unit 111 and an outer conductor side power supply unit 112. The inner conductor side power supply unit 111 is a portion to which the inner conductor 91 (e.g., a core wire) of the coaxial cable 90 is connected. The outer conductor side power supply unit 112 is a portion to which the outer conductor 92 (e.g., a ground wire) of the coaxial cable 90 is connected. When the antenna device 10 is installed on an opaque portion 102A of an object 100A, which is the installation target, the outer conductor side power supply unit 112 of the power supply unit 11 is connected to the opaque portion 102A of the object 100A with adhesive or tape. In this embodiment, the power supply structure of the antenna device 10 is described as a power supply structure using the coaxial cable 90. However, the power supply structure of the antenna device 10 may be a power supply structure other than a power supply structure using the coaxial cable 90, for example, a power supply structure using a transmission line or a power supply structure using a microstrip line.

[0029] The film antenna 12 is an antenna that can be attached to the object 100A. The film antenna 12 will be described in detail later.

[0030] The object 100A on which the antenna device 10 is disposed in the above-described embodiment is a vehicle. However, the object on which the antenna device 10 is disposed may be an object other than a vehicle, as shown in FIG. 3, which will be described later.

[0031] FIG. 3 is an explanatory diagram of an object 100B on which the antenna device 10 of this embodiment is disposed.

[0032] In the example shown in FIG. 3 , the object 100B is a vending machine. The transparent portion 101B of the object 100B is, for example, an acrylic plate on the front of the vending machine, allowing users of the vending machine to view product samples and the like placed inside through the acrylic plate on the front. The opaque portion 102B is a housing portion adjacent to the acrylic plate on the front. In the example of the object 100B (vending machine) shown in FIG. 3 , at least a portion of the power supply unit 11 (not shown in FIG. 3 ) overlaps with the opaque portion 102B when viewed in the Z direction. This makes it possible to suppress the influence of the antenna device 10 on the transparency of the transparent portion 101B of the object 100B when the antenna device 10 is placed on the object 100B (here, a vending machine) having the transparent portion 101B.

[0033] <<Details of Antenna Device 10>> Next, details of the antenna device 10 of this embodiment will be described with reference to Figures 4 to 7. In the following description, the object on which the antenna device 10 is placed will be referred to as "object 100," representing the above-mentioned objects 100A and 100B. Furthermore, the transparent portion of the object 100 will be referred to as "transparent portion 101," representing the above-mentioned transparent portion 101A and transparent portion 101B, and the non-transparent portion of the object 100 will be referred to as "non-transparent portion 102," representing the above-mentioned non-transparent portion 102A and non-transparent portion 102B.

[0034] Fig. 4 is a perspective view of the antenna device 10 of this embodiment. Fig. 5 is an enlarged view of the dashed line portion in Fig. 4. Fig. 6 is an explanatory diagram showing a cross section of the antenna device 10. Fig. 7 is an enlarged explanatory diagram of a portion of the conductor portion 126 when viewed in the Z direction.

[0035] As shown in FIG. 4 , the film antenna 12 has a main body portion 121 and a root portion 122. The main body portion 121 has a circular shape when viewed in the Z direction. However, the shape of the main body portion 121 when viewed in the Z direction may be other than circular, such as an ellipse or a polygon including a substantially quadrilateral. The root portion 122 is located between the main body portion 121 and the internal conductor side feed portion 111 of the power supply unit 11. The root portion 122 (specifically, the conductor portion 126) is capacitively coupled to the internal conductor side feed portion 111. This allows the root portion 122 (specifically, the conductor portion 126) to be electrically connected to the internal conductor side feed portion 111 without directly connecting them by solder or the like. Therefore, deformation of the film antenna 12 due to heat from soldering, pressure from pressing with a soldering iron, and the like can be suppressed compared to when the film antenna 12 and the power supply unit 11 are directly connected by solder or the like.

[0036] 5 and 6, the main body portion 121 and the root portion 122 both extend parallel to the XY plane (a plane parallel to the X and Y directions). However, the main body portion 121 and the root portion 122 may extend at a predetermined angle with respect to the XY plane. Furthermore, as will be explained in the first, second, and third modified examples described later, the root portion 122 of the film antenna 12 may be bent.

[0037] As shown in Figures 5 and 6, the root portion 122 of the film antenna 12 is located between the internal conductor side feeding portion 111 of the power feeding unit 11 and the opaque portion 102. In this embodiment, the root portion 122 is located so as to be sandwiched between the internal conductor side feeding portion 111 of the power feeding unit 11 and the opaque portion 102. However, the root portion 122 of the film antenna 12 does not have to be located between the internal conductor side feeding portion 111 of the power feeding unit 11 and the opaque portion 102. As will be described in a second modified example below, the root portion 122 of the film antenna 12 may be located on the +X direction side of the internal conductor side feeding portion 111 of the power feeding unit 11. Furthermore, as will be described in a third modified example below, the root portion 122 of the film antenna 12 may be located on the +Z direction side of the internal conductor side feeding portion 111 of the power feeding unit 11.

[0038] That is, the root portion 122 of the film antenna 12 faces the internal conductor side feeding portion 111 of the feeding portion 11. Furthermore, the root portion 122 of the film antenna 12 faces not only the internal conductor side feeding portion 111 but also the opaque portion 102 used as a ground portion. That is, the root portion 122 of the film antenna 12 faces at least one of the feeding portion 11 and the opaque portion 102.

[0039] 6, the film antenna 12 has a conductor portion 126 and a film portion 127. The conductor portion 126 is an element of the film antenna 12, and has a shape corresponding to the desired frequency band of the film antenna 12. In this embodiment, the conductor portion 126 is formed in a mesh structure using conductor wires.

[0040] In this embodiment, the mesh structure of the conductor portion 126 is composed of, for example, conductor lines 128 extending in the Y direction and conductor lines 129 extending in the X direction, as shown in FIG. 7 . A plurality of conductor lines 128 are arranged in the X direction, and a plurality of conductor lines 129 are arranged in the Y direction. The area surrounded by the conductor lines 128 and 129 forms the opening 130. Here, the width W of the conductor lines 128 and 129 is preferably, for example, 30 μm. Furthermore, the pitch P at which the plurality of conductor lines 128 and 129 are arranged is preferably, for example, 300 μm. In this case, the size of the opening 130 surrounded by the conductor lines 128 and 129 in the X and Y directions is larger than the width W of the conductor lines 128 and 129. Conversely, the width W of the conductor lines 128 and 129 is smaller than the size of the opening 130 in the X and Y directions. Therefore, the influence of the conductor lines 128 and 129 on the transparency of the transmissive portion 101 can be reduced.

[0041] This makes it possible to suppress the influence on the transparency of the transparent portion 101 even when the film antenna 12 is placed in the transparent portion 101 of the object 100. However, the extending direction, arranging direction, pitch P, and width W of the conductor wires 128 and 129 are not limited to those shown in Fig. 7. Furthermore, the conductor portion 126 may be formed in a structure other than a mesh structure using conductor wires, as long as the influence on the transparency of the transparent portion 101 can be suppressed.

[0042] The film portion 127 is a member that covers the conductor portion 126 and is located on both the +Z and −Z sides of the conductor portion 126. In this embodiment, the film portion 127 is formed of an insulating film that is transparent to visible light or infrared light. However, the film portion 127 may also be, for example, a rust-proof coating placed on the conductor portion 126. Even in this case, the internal conductor side power supply portion 111 of the power supply unit 11 and the conductor portion 126 are not directly connected, and the internal conductor side power supply portion 111 of the power supply unit 11 and the conductor portion 126 are capacitively coupled. Furthermore, the film portion 127 does not necessarily need to cover the entire conductor portion 126; a portion of the conductor portion 126 may be exposed.

[0043] Furthermore, film portion 127 may be arranged on only one of the +Z direction side and the −Z direction side of conductor portion 126. However, if film portion 127 is not arranged on the +Z direction side of conductor portion 126, internal conductor side power supply portion 111 of power supply unit 11 and conductor portion 126 may be spaced apart so that they are not directly connected to each other.

[0044] The base portion 122 of the film antenna 12 and the internal-conductor-side power feeding portion 111 of the power feeding unit 11 are positioned so that the +Z-direction surface of the film portion 127 located on the +Z-direction side of the conductor portion 126 comes into contact with the −Z-direction surface of the internal-conductor-side power feeding portion 111. Even in this case, the internal-conductor-side power feeding portion 111 of the power feeding unit 11 and the conductor portion 126 are not directly electrically connected, and the internal-conductor-side power feeding portion 111 of the power feeding unit 11 and the conductor portion 126 are capacitively coupled. However, the base portion 122 of the film antenna 12 and the internal-conductor-side power feeding portion 111 of the power feeding unit 11 may be positioned so that the +Z-direction surface of the film portion 127 located on the +Z-direction side of the conductor portion 126 is spaced apart from the −Z-direction surface of the internal-conductor-side power feeding portion 111.

[0045] 6 , the distance between the conductor portion 126 of the film antenna 12 and the internal-conductor-side power supply portion 111 is defined as d1. The distance between the conductor portion 126 of the film antenna 12 and the non-transparent portion 102 is defined as d2. In this embodiment, the +Z-direction surface of the film portion 127 on the +Z-direction side is in contact with the −Z-direction surface of the internal-conductor-side power supply portion 111, and therefore the distance d1 is approximately equal to the thickness of the film portion 127 on the +Z-direction side.

[0046] <<Equivalent Circuit of Antenna Device 10>> As described above, in the antenna device 10 of this embodiment, the power feeding unit 11 overlaps with the non-transparent portion 102 when viewed in the Z direction. Furthermore, in the antenna device 10 of this embodiment, the root portion 122 of the film antenna 12 is capacitively coupled with the internal conductor side power feeding unit 111 of the power feeding unit 11. At this time, the root portion 122 of the film antenna 12 faces not only the internal conductor side power feeding unit 111 but also the non-transparent portion 102 used as a ground portion, and may thereby form capacitive coupling with the non-transparent portion 102.

[0047] Therefore, in the antenna device 10 of this embodiment, it is necessary to consider degradation of antenna characteristics due to capacitive coupling between the base portion 122 of the film antenna 12 and the non-transparent portion 102. Below, first, the equivalent circuit of the antenna device 10 will be described, and then the antenna device 10 that can reduce degradation of antenna characteristics due to capacitive coupling between the base portion 122 of the film antenna 12 and the non-transparent portion 102 will be described.

[0048] FIG. 8 is an explanatory diagram showing an equivalent circuit of the antenna device 10. As shown in FIG.

[0049] As shown in Fig. 8, in the equivalent circuit of the antenna device 10, the characteristic impedance of the coaxial cable 90 is Z0, and the load impedance of the film antenna 12 is ZL. Furthermore, the electrostatic capacitance between the power feeding portion 11 and the film antenna 12 (hereinafter sometimes referred to as the first capacitance) is C1, and the electrostatic capacitance between the film antenna 12 and the opaque portion 102 (hereinafter sometimes referred to as the second capacitance) is C2. As shown in Fig. 8, the portion constituting the first capacitance C1 can be considered to be connected in series to the load impedance ZL in the antenna device 10, and the portion constituting the second capacitance C2 can be considered to be connected in parallel to the load impedance ZL.

[0050] <<Operation Principle of Antenna Device 10 >> Next, the operation principle of the antenna device 10 will be described using the characteristic impedance Z0, the load impedance ZL, the first capacitance C1, and the second capacitance C2 described above.

[0051] Generally, a capacitance C including a first capacitance C1 and a second capacitance C2 is expressed by the following Equation 1 using an area S, a dielectric constant ε, and a distance d.

[0052]

[0053] That is, the first capacitance C1 between the film antenna 12 and the power supply unit 11 is determined by the opposing area, dielectric constant, and distance (here, separation distance d1) between the film antenna 12 and the power supply unit 11. Also, the second capacitance C2 between the film antenna 12 and the opaque portion 102 is determined by the opposing area, dielectric constant, and distance (here, separation distance d2) between the film antenna 12 and the opaque portion 102.

[0054] Here, the normalized capacitance Cs obtained by normalizing the capacitance C by the wavelength λ is expressed by the following equation 2.

[0055]

[0056] Since the VSWR characteristics of the film antenna 12 vary depending on the desired frequency band, the desired antenna characteristics independent of frequency can be verified by verifying the antenna characteristics (here, the VSWR characteristics) using the normalized capacitance Cs in the above-mentioned equation 2.

[0057] Here, the capacitive reactance Xc of the antenna device 10 is calculated by the above-mentioned normalized capacitance Cs and phase velocity V p Using the above, it is expressed by the following Equation 3.

[0058]

[0059] Therefore, the total impedance Ztotal of the film antenna 12 is expressed in complex notation using the imaginary unit j as in the following Equation 4.

[0060]

[0061] Then, the reflection coefficient Γ of the film antenna 12 is expressed by the following equation 5.

[0062]

[0063] Therefore, the VSWR of the film antenna 12 is expressed by the following equation 6 using the reflection coefficient Γ.

[0064]

[0065] <<Regarding the Range of Capacity Satisfying Desired VSWR Characteristics>> Below, the range of capacity that satisfies the desired VSWR characteristics will be verified by simulation using the antenna device 10 under the following conditions 1 to 4.

[0066] (Condition 1) Frequency f: 600 MHz Characteristic impedance Z0: 50 Ω Load impedance ZL: 50 Ω (Condition 2) Frequency f: 3000 MHz Characteristic impedance Z0: 50 Ω Load impedance ZL: 50 Ω (Condition 3) Frequency f: 600 MHz Characteristic impedance Z0: 50 Ω Load impedance ZL: 25 Ω (Condition 4) Frequency f: 3000 MHz Characteristic impedance Z0: 50 Ω Load impedance ZL: 25 Ω

[0067] Condition 1 and condition 2 have the same characteristic impedance Z0 value (50 Ω) and load impedance ZL value (50 Ω), while condition 3 and condition 4 have the same characteristic impedance Z0 value (50 Ω) and load impedance ZL value (25 Ω). Condition 1 and condition 3 also have the same frequency f value (600 MHz), while condition 2 and condition 4 have the same frequency f value (3000 MHz).

[0068] <Study using normalized capacitance Cs> Fig. 9 is a diagram showing an example of the amount of change in VSWR under condition 1 for normalized capacitance Cs, and a predetermined range based on VSWR = 10.0. Fig. 10 is a diagram showing an example of the amount of change in VSWR under condition 2 for normalized capacitance Cs, and a predetermined range based on VSWR = 10.0.

[0069] 9 and 10 , the VSWR values ​​are plotted for each color brightness, with the horizontal axis representing the first normalized capacitance C1s and the vertical axis representing the second normalized capacitance C2s. The first normalized capacitance C1s is the normalized capacitance Cs at a separation distance d1, and the second normalized capacitance C2s is the normalized capacitance Cs at a separation distance d2. In each of FIGS. 9 and 10 , the set of values ​​of the first normalized capacitance C1s and the second normalized capacitance C2s corresponding to a VSWR of 10.0 is represented by a solid line.

[0070] As described above, the values ​​of frequency f are different between condition 1, whose results are shown in Fig. 9, and condition 2, whose results are shown in Fig. 10, with the value of frequency f being 600 MHz under condition 1 and the value of frequency f being 3000 MHz under condition 2. However, because the values ​​of the first normalized capacitance C1s and the second normalized capacitance C2s are normalized capacitances normalized by the wavelength λ, the amount of change in VSWR is similar in Fig. 9 and Fig. 10.

[0071] In the antenna device 10 of this embodiment, the set of values ​​of the first normalized capacitance C1s and the second normalized capacitance C2s to the right of the solid line corresponding to VSWR = 10.0 is a desirable range. That is, it is preferable that the VSWR calculated using the first normalized capacitance C1s, the second normalized capacitance C2s, the characteristic impedance Z0 of the film antenna 12, and the load impedance ZL is 10.0 or less. In this case, it is possible to reduce degradation of the antenna characteristics due to capacitive coupling between the film antenna 12 and the opaque portion 102.

[0072] In the following description, the range of the set of values ​​of the first standardized capacitance C1s (or the first capacitance C1) and the second standardized capacitance C2s (or the second capacitance C2) that result in a desirable VSWR range for the film antenna 12 may be referred to as the "predetermined range."

[0073] 11 is a diagram showing an example of the amount of change in VSWR under condition 3 for normalized capacitance Cs, and a predetermined range based on VSWR=10.0. FIG. 12 is a diagram showing an example of the amount of change in VSWR under condition 4 for normalized capacitance Cs, and a predetermined range based on VSWR=10.0.

[0074] 11 and 12, the VSWR values ​​are plotted for each color brightness, with the horizontal axis representing the first normalized capacitance C1s and the vertical axis representing the second normalized capacitance C2s. In each of Fig. 11 and 12, the set of values ​​of the first normalized capacitance C1s and the second normalized capacitance C2s corresponding to VSWR = 10.0 is represented by a solid line.

[0075] As described above, the values ​​of frequency f under condition 3, whose results are shown in Fig. 11, and condition 4, whose results are shown in Fig. 12, are different from each other: the value of frequency f is 600 MHz under condition 3, and the value of frequency f is 3000 MHz under condition 4. However, because the values ​​of the first normalized capacitance C1s and the second normalized capacitance C2s are normalized capacitances normalized by the wavelength λ, the amount of change in VSWR is similar in Fig. 11 and Fig. 12.

[0076] In the antenna device 10 of this embodiment, the set of values ​​of the first normalized capacitance C1s and the second normalized capacitance C2s on the right side of the solid line corresponding to VSWR=10.0 is within a desirable range (i.e., a predetermined range). That is, it is preferable that the VSWR calculated using the first normalized capacitance C1s, the second normalized capacitance C2s, the characteristic impedance Z0 of the film antenna 12, and the load impedance ZL is 10.0 or less. In this case, it is possible to reduce degradation of the antenna characteristics due to capacitive coupling between the film antenna 12 and the opaque portion 102.

[0077] 13 is a diagram showing an example of the amount of change in VSWR under condition 1 for normalized capacitance Cs, and a predetermined range based on VSWR=3.0. FIG. 14 is a diagram showing an example of the amount of change in VSWR under condition 2 for normalized capacitance Cs, and a predetermined range based on VSWR=3.0.

[0078] 13 and 14, the VSWR values ​​are plotted for each color brightness, with the horizontal axis representing the first normalized capacitance C1s and the vertical axis representing the second normalized capacitance C2s. In each of Figs. 13 and 14, the set of values ​​of the first normalized capacitance C1s and the second normalized capacitance C2s corresponding to VSWR = 3.0 is represented by a solid line.

[0079] In the antenna device 10 of this embodiment, the set of values ​​of the first normalized capacitance C1s and the second normalized capacitance C2s to the right of the solid line corresponding to VSWR=3.0 is a more desirable range (i.e., a predetermined range). That is, it is more preferable that the VSWR calculated using the first normalized capacitance C1s, the second normalized capacitance C2s, the characteristic impedance Z0 of the film antenna 12, and the load impedance ZL is 3.0 or less. In this case, it is possible to further reduce the degradation of the antenna characteristics due to capacitive coupling between the film antenna 12 and the opaque portion 102.

[0080] <Study Using Characteristic Evaluation Parameter tan Θ> The inventors focused on the characteristic evaluation parameter tan Θ, which is calculated by C2 / C1, as described below. Specifically, the inventors found a characteristic evaluation parameter tan Θ that includes a range (i.e., a predetermined range) of a set of desirable values ​​of the first capacitance C1 and the second capacitance C2. In other words, when the characteristic evaluation parameter tan Θ is equal to or less than a predetermined threshold (here, tan Θ≦2, or even tan Θ≦0.31, as described below), it is possible to reduce degradation of the antenna characteristics due to capacitive coupling between the film antenna 12 and the non-transparent portion 102.

[0081] By using the characteristic evaluation parameter tan Θ, it is possible to consider a range (i.e., a predetermined range) of a set of desirable values ​​of the first capacitance C1 and the second capacitance C2, regardless of the frequency band of radio waves supported by the film antenna 12. Therefore, even if the film antenna 12 is an antenna that supports a wide frequency band, it is possible to determine a predetermined range that can reduce deterioration of the antenna characteristics due to capacitive coupling between the base portion 122 of the film antenna 12 and the non-transparent portion 102.

[0082] The predetermined threshold value of the characteristic evaluation parameter tan Θ will be explained below along with the amount of change in VSWR under each condition for the capacitance C.

[0083] 15 is a diagram showing an example of the amount of change in VSWR under condition 1 for capacitance C, and a predetermined range based on VSWR=10.0. Fig. 16 is a diagram showing an example of the amount of change in VSWR under condition 2 for capacitance C, and a predetermined range based on VSWR=10.0.

[0084] 15 and 16, the VSWR values ​​are plotted for each color brightness, with the horizontal axis representing the first capacitance C1 and the vertical axis representing the second capacitance C2. In each of FIGS. 15 and 16, a set of values ​​of the first capacitance C1 and the second capacitance C2 corresponding to a VSWR of 10.0 is represented by a solid line, and a line (with a slope of 1.4775) passing through the origin, which is tangent to the solid line, is represented by a dashed line. The first capacitance C1 and the second capacitance C2 used in FIGS. 15 and 16 are not normalized by wavelength λ.

[0085] The characteristic evaluation parameter tan Θ in this embodiment is expressed by the following equation 7 using the first capacitance C1 and the second capacitance C2.

[0086]

[0087] Then, from Equation 7, the angle Θ of the characteristic evaluation parameter tan Θ can be considered as the angle of inclination of a line passing through the origin in Figures 15 and 16, where the horizontal axis represents the first capacitance C1 and the vertical axis represents the second capacitance C2.

[0088] Note that we consider the case where the opposing area S between the power supply unit 11 and the film antenna 12 and the opposing area S between the film antenna 12 and the opaque portion 102 are the same or very close to each other. Furthermore, we consider the case where the dielectric constant ε between the power supply unit 11 and the film antenna 12 and the dielectric constant ε between the film antenna 12 and the opaque portion 102 are the same or very close to each other. In these cases, from the above-mentioned Equation 1, the first capacitance C1 is proportional to the reciprocal of the separation distance d1, and the second capacitance C2 is proportional to the reciprocal of the separation distance d2. Therefore, the first capacitance C1 and the second capacitance C2 have the relationship shown in the following Equation 8.

[0089]

[0090] Therefore, the characteristic evaluation parameter tan Θ in this embodiment can also be expressed by the following Equation 9 using the separation distance d1 and the separation distance d2.

[0091]

[0092] In this embodiment, if at least the characteristic evaluation parameter tan Θ≦2, the predetermined range based on VSWR=10.0 is included. In other words, the set of values ​​of the first capacitance C1 and the second capacitance C2 on the right side of the line corresponding to tan Θ=2 is the desirable range. Here, tan Θ=2 is expressed as a set of points on a line expressed by the function C2=2×C1 when the horizontal axis represents the first capacitance C1 and the vertical axis represents the second capacitance C2 in FIGS. 15 and 16 .

[0093] In Figures 15 and 16, the desirable set of values ​​for the first capacitance C1 and the second capacitance C2 is the range of the dashed line tangent to the set (solid line) of values ​​for the first capacitance C1 and the second capacitance C2 corresponding to VSWR = 10.0, with a slope of 1.4775 or less. Therefore, if the characteristic evaluation parameter tan Θ is in the range of 2 or less, the range of the dashed line with a slope of 1.4775 or less can be covered. In other words, the set of points (C1, C2) in the region to the right of the line expressed by the function C2 = 2 × C1 includes VSWR = 10.0 or less. Therefore, the coefficient 2 of the function C2 = 2 × C1 is a predetermined threshold set to include VSWR = 10.0 or less.

[0094] 17 is a diagram showing an example of the amount of change in VSWR under condition 3 for capacitance C, and a predetermined range based on VSWR=10.0. FIG. 18 is a diagram showing an example of the amount of change in VSWR under condition 4 for capacitance C, and a predetermined range based on VSWR=10.0.

[0095] 17 and 18, the VSWR values ​​are plotted for each color brightness, with the horizontal axis representing the first capacitance C1 and the vertical axis representing the second capacitance C2. In each of FIGS. 17 and 18, a set of values ​​of the first capacitance C1 and the second capacitance C2 corresponding to a VSWR of 10.0 is represented by a solid line, and a line (with a slope of 1.9126) passing through the origin among the tangents to the solid line is represented by a dashed line. The first capacitance C1 and the second capacitance C2 used in FIGS. 17 and 18 are not normalized by the wavelength λ.

[0096] 17 and 18, under Conditions 3 and 4, the set of values ​​of the first capacitance C1 and the second capacitance C2 to the right of the straight line expressed by the function C2 = 2 × C1 corresponding to tan Θ = 2 is the desirable range. That is, in FIGS. 17 and 18, the desirable set of values ​​of the first capacitance C1 and the second capacitance C2 is the range of the dashed line tangent to the set of values ​​of the first capacitance C1 and the second capacitance C2 corresponding to VSWR = 10.0 (solid line) with a slope of 1.9126 or less. Therefore, if the characteristic evaluation parameter tan Θ is in the range of 2 or less, the range of the dashed line with a slope of 1.9126 or less can be covered.

[0097] 19 is a diagram showing an example of the amount of change in VSWR under condition 1 for capacitance C, and a predetermined range based on VSWR=3.0. Fig. 20 is a diagram showing an example of the amount of change in VSWR under condition 2 for capacitance C, and a predetermined range based on VSWR=3.0.

[0098] 19 and 20, the VSWR values ​​are plotted for each color brightness, with the horizontal axis representing the first capacitance C1 and the vertical axis representing the second capacitance C2. In each of FIGS. 19 and 20, a set of values ​​of the first capacitance C1 and the second capacitance C2 corresponding to a VSWR of 3.0 is represented by a solid line, and a line (with a slope of 0.3081) passing through the origin, which is tangent to the solid line, is represented by a dashed line. The first capacitance C1 and the second capacitance C2 used in FIGS. 19 and 20 are not normalized by the wavelength λ.

[0099] 19 and 20, the set of values ​​of the first capacitance C1 and the second capacitance C2 to the right of the straight line expressed by C2 = 0.31 × C1 corresponding to tan Θ = 0.31 is a more desirable range. That is, the more desirable set of values ​​of the first capacitance C1 and the second capacitance C2 is the range of the dashed line tangent to the set of values ​​of the first capacitance C1 and the second capacitance C2 corresponding to VSWR = 3.0 (solid line) with a slope of 0.3081 or less. Therefore, if the characteristic evaluation parameter tan Θ is in the range of 0.31 or less, the range of the dashed line with a slope of 0.3081 or less can be covered.

[0100] <<First Modification>> Fig. 21 is a perspective view of an antenna device 10A of a first modification. Fig. 22 is an enlarged view of the dashed line portion in Fig. 21. Fig. 23 is an explanatory diagram showing a cross section of the antenna device 10A of the first modification.

[0101] In the film antenna 12 of the present embodiment described above, both the main body portion 121 and the base portion 122 extend parallel to the XY plane. However, the shape of the film antenna 12 is not limited to this and may be other shapes.

[0102] 21, 22, and 23, in the film antenna 12A in the first modified example, the base portion 123 may be bent. Also, the main body portion 121 has a circular shape like the film antenna 12 in this embodiment, but as shown in Fig. 23, it is in contact with the transparent portion 101. In this way, the film antenna 12A is supported by the transparent portion 101.

[0103] The base portion 123 of the film antenna 12A and the internal conductor side power feeding portion 111 of the power feeding unit 11 are positioned so that the +Z direction surface of the film portion 127 on the +Z direction side comes into contact with the −Z direction surface of the internal conductor side power feeding portion 111. However, the base portion 123 of the film antenna 12A and the internal conductor side power feeding portion 111 of the power feeding unit 11 may be positioned so that the +Z direction surface of the film portion 127 on the +Z direction side is separated from the −Z direction surface of the internal conductor side power feeding portion 111.

[0104] Even the antenna device 10A of the first modification can suppress the influence of the antenna device 10A on the transparency of the transparent portion 101 of the object 100 when it is placed on the object 100 having the transparent portion 101. Furthermore, it is possible to reduce the deterioration of the antenna characteristics due to the capacitive coupling between the film antenna 12A and the non-transparent portion 102.

[0105] <<Second Modification>> FIG. 24 is an explanatory diagram showing a cross section of an antenna device 10B of a second modification.

[0106] In the film antenna 12 of the present embodiment described above, the root portion 122 is located so as to be sandwiched between the internal conductor side feeding portion 111 of the feeding portion 11 and the opaque portion 102. However, in the film antenna 12B of the second modified example, the root portion 124 is not sandwiched between the internal conductor side feeding portion 111 and the opaque portion 102, and is located on the +X direction side of the internal conductor side feeding portion 111 of the feeding portion 11.

[0107] Even the film antenna 12B in the second modified example can suppress the influence of the antenna device 10B on the transparency of the transparent portion 101 of the object 100 when it is placed on the object 100 having the transparent portion 101. Furthermore, it is possible to reduce the deterioration of the antenna characteristics due to the capacitive coupling between the film antenna 12B and the non-transparent portion 102.

[0108] <<Third Modification>> Fig. 25 is an explanatory diagram showing a cross section of an antenna device 10C of a third modification. Fig. 26 is an enlarged perspective view of the vicinity of a base portion 125 of the antenna device 10C. Fig. 27 is an enlarged perspective view of the vicinity of the base portion 125 of the antenna device 10C.

[0109] The antenna device 10C of the third modified example has a film antenna 12, a support member 103, a support member 104, and a substrate 105. Among the drawings showing the third modified example, the support member 103, the support member 104, and the substrate 105 are omitted in Fig. 25.

[0110] Like the film antenna 12 of the present embodiment described above, the film antenna 12C is an antenna that can be attached to the object 100. In the film antenna 12 described above, the root portion 122 is located between the internal conductor side feeding portion 111 of the feeding unit 11 and the opaque portion 102. However, as in the film antenna 12C of the third modified example, the root portion 125 may be located on the +Z direction side of the internal conductor side feeding portion 111 of the feeding unit 11.

[0111] The support member 103 is disposed at a position overlapping the transmissive portion 101 of the object 100 when viewed in the Z direction, and supports the root portion 125 as shown in FIGS. 26 and 27 . The support member 103 is formed, for example, from a resin. The support member 103 is preferably formed from a transparent material. This can suppress the influence of the support member 103 on the transparency of visible light and infrared light in the transmissive portion 101. The support member 103 supports the bent root portion 125, thereby separating the root portion 125 from the non-transmissive portion 102 in the Z direction. The dimensions of the support member 103 are determined taking into consideration the antenna characteristics of the film antenna 12C.

[0112] When viewed in the Z direction, the support member 104 is disposed at a position overlapping the opaque portion 102 of the object 100, and supports the base portion 125 and the substrate 105, as shown in Figures 26 and 27. In Figures 26 and 27, the support member 103 and the support member 104 are formed separately, but the support member 103 and the support member 104 may also be formed integrally.

[0113] The substrate 105 is a member on which an electronic circuit configured with a conductor pattern or the like, electronic components, etc. are arranged. The substrate 105 is, for example, a printed circuit board (PCB) or a flexible printed circuit (FPC). The substrate 105 is supported by the support member 104.

[0114] Even the film antenna 12C in the third modified example can suppress the influence of the antenna device 10C on the transparency of the transparent portion 101 of the object 100 when it is placed on the object 100 having the transparent portion 101. Furthermore, it can reduce the deterioration of the antenna characteristics due to the capacitive coupling between the film antenna 12C and the non-transparent portion 102.

[0115] <<Fourth Modification>> FIG. 28 is an explanatory diagram showing a cross section of an antenna device 10D of a fourth modification.

[0116] As described above, in the antenna device 10 of this embodiment, when the antenna device 10 is installed on the opaque portion 102 of the object 100, which is the installation target, the external conductor side feeding portion 112 of the feeding portion 11 is connected to the opaque portion 102 of the object 100 with adhesive or tape. At this time, depending on the thickness of the adhesive or tape used to connect the external conductor side feeding portion 112 and the opaque portion 102, the separation distance d2 between the conductor portion 126 of the film antenna 12 and the opaque portion 102 may differ from the desired separation distance. As a result, when the antenna device 10 is installed on the object 100, which is the installation target, a separate adjustment may be required to ensure desired antenna characteristics.

[0117] Therefore, in the antenna device 10D of the fourth modification, the power supply unit 11 has a conductive member 113 on the −Z direction side of the outer conductor side power supply unit 112 in the antenna device 10 of the present embodiment. The conductive member 113 is a portion to which the outer conductor 92 of the coaxial cable 90 is electrically connected, similar to the outer conductor side power supply unit 112. In the antenna device 10D of the fourth modification, the conductive member 113 is formed of a conductive material such as metal, and is electrically connected to the opaque portion 102 via capacitive coupling. In the antenna device 10D, the conductive member 113 is disposed so that the distance between the conductive member 113 and the conductor portion 126 of the film antenna 12 is constant. This makes it easy to ensure the desired antenna characteristics of the antenna device 10D when the antenna device 10D is installed on the object 100 to which it is to be installed.

[0118] <<Other Modifications>> In the above-described embodiment, examples have been described in which the antenna device 10 is disposed in a vehicle or a vending machine as an example of the object 100. However, the object 100 on which the antenna device 10 is disposed is not limited to the above-described examples. For example, the antenna device 10 may be used in a building. In this case, the transmissive portion 101 is a window glass portion of the building, and the non-transmissive portion 102 is a window frame portion of the building. The antenna device 10 may also be disposed in other devices, such as a PC, a mobile terminal (smartphone, tablet, POS, etc.), or a home appliance (refrigerator, air conditioner, rice cooker, etc.).

[0119] In the above embodiment, an example has been described in which the +Z direction surfaces of the transparent portion 101 and the non-transparent portion 102 of the object 100 are flush with each other when viewed from a direction parallel to the XY plane (i.e., the boundary between the transparent portion 101 and the non-transparent portion 102 is flush with each other). However, a step may be formed at the boundary between the transparent portion 101 and the non-transparent portion 102 of the object 100. Even when a step is formed at the boundary, it is possible to make appropriate adjustments using a support member or the like so that the film antenna 12 is stably held.

[0120] Summary According to the present specification, there is provided an antenna device having the following aspects.

[0121] (Aspect 1) Aspect 1 is an antenna device that is placed on an object having a transparent portion and an opaque portion, and includes a power supply portion and a film antenna that is capacitively coupled to the power supply portion, and when viewed in the normal direction to the front surface of the film antenna, at least a portion of the power supply portion overlaps with the opaque portion.

[0122] According to the above-described aspect, it is possible to suppress the influence of the antenna device on the transparency of the transparent portion of the object. Also, it is possible to suppress deterioration of the aesthetic appearance of the object on which the antenna device is placed due to the power supply unit being visible. Furthermore, since the film antenna is connected to the power supply unit by capacitive coupling, it is possible to suppress deformation of the film antenna compared to when the film antenna is directly connected to the power supply unit by soldering or the like.

[0123] (Aspect 2) In aspect 2, the film antenna faces at least one of the power feeding portion and the non-transparent portion.

[0124] According to the above-described aspect, it is possible to suppress the influence of the antenna device on the transparency of the transparent portion of the object.

[0125] (Aspect 3) In aspect 3, the film antenna is positioned so as to be sandwiched between the feeding portion and the opaque portion.

[0126] According to the above-described aspect, it is possible to suppress the influence of the antenna device on the transparency of the transparent portion of the object.

[0127] (Aspect 4) In aspect 4, the VSWR calculated from a first normalized capacitance C1s obtained by normalizing the capacitance C1 between the power supply section and the film antenna by wavelength, a second normalized capacitance C2s obtained by normalizing the capacitance C2 between the film antenna and the opaque section by wavelength, and the characteristic impedance Z0 and load impedance ZL of the film antenna is 10.0 or less.

[0128] According to the above-described aspect, it is possible to reduce deterioration of antenna characteristics due to capacitive coupling between the film antenna and the non-transparent portion.

[0129] (Aspect 5) In aspect 5, the VSWR is 3.0 or less.

[0130] According to the above-described aspect, it is possible to further reduce the deterioration of the antenna characteristics due to the capacitive coupling between the film antenna and the non-transparent portion.

[0131] (Aspect 6) In aspect 6, when the capacitance between the power supply section and the film antenna is C1, the capacitance between the film antenna and the opaque section is C2, and the characteristic evaluation parameter of the film antenna is tanΘ=C2 / C1, tanΘ≦2.

[0132] According to the above-described aspect, it is possible to reduce deterioration of antenna characteristics due to capacitive coupling between the film antenna and the non-transparent portion.

[0133] (Embodiment 7) In embodiment 7, tan Θ≦0.31.

[0134] According to the above-described aspect, it is possible to further reduce the deterioration of the antenna characteristics due to the capacitive coupling between the film antenna and the non-transparent portion.

[0135] The above-described embodiments are intended to facilitate understanding of the present invention and are not intended to limit the present invention. Furthermore, the present invention may be modified or improved without departing from the spirit thereof, and the present invention includes equivalents thereof.

[0136] 10, 10A, 10B, 10C, 10D Antenna device 11 Power supply portion 12, 12A, 12B, 12C, 12D Film antenna 100, 100A, 100B Object 101, 101A, 101B Transparent portion 102, 102A, 102B Non-transparent portion

Claims

1. An antenna device to be placed on an object having a transparent portion and a non-transparent portion, comprising: a power supply portion; and a film antenna that is capacitively coupled to the power supply portion, wherein at least a portion of the power supply portion overlaps with the non-transparent portion when viewed in the normal direction of the front surface of the film antenna.

2. The antenna device according to claim 1, wherein the film antenna faces at least one of the power supply section and the opaque section.

3. The antenna device according to claim 2, wherein the film antenna is positioned so as to be sandwiched between the power supply section and the opaque section.

4. The antenna device according to claim 2, wherein a VSWR calculated using a first normalized capacitance C1s obtained by normalizing the capacitance C1 between the power supply unit and the film antenna by wavelength, a second normalized capacitance C2s obtained by normalizing the capacitance C2 between the film antenna and the opaque unit by wavelength, and the characteristic impedance Z0 and load impedance ZL of the film antenna is 10.0 or less.

5. The antenna device according to claim 4, wherein the VSWR is 3 or less.

6. The antenna device according to claim 2, wherein when the capacitance between the power supply section and the film antenna is C1, the capacitance between the film antenna and the opaque section is C2, and a characteristic evaluation parameter of the film antenna is tanΘ=C2 / C1, then tanΘ≦2.

7. The antenna device according to claim 6, wherein tan Θ≦0.31.

Images