JP2017063500A - Loop Antenna - Google Patents

Abstract

PROBLEM TO BE SOLVED: To improve attenuation characteristics of a magnetic field generated by a loop antenna.SOLUTION: A loop antenna includes a pair of single current loops 10 and 20 arranged in parallel by being separated. Values of current Iand Iflowing through the respective current loops 10 and 20 and radiuses aand aof the respective current loops are set so that a term of zamong a plurality of polynomial terms appearing in a formula (4) obtained by Taylor-expanding a formula (1) representing a magnetic field generated by the pair of current loops 10 and 20 becomes zero.SELECTED DRAWING: Figure 1

Description

  The present invention relates to a loop antenna technique.

  There is a loop antenna that generates a magnetic field by passing a current through a current loop (Patent Document 1). A conventional configuration of such a loop antenna is shown in FIG. By arranging N (N ≧ 1) current loops on the same plane and passing a current of an appropriate magnitude through each current loop in an appropriate direction, a magnetic field having an attenuation characteristic of (2N + 1) power can be obtained. it can. Since attenuation characteristics of the third power or higher can be obtained, the magnetic field area can be clearly limited from other areas (see FIG. 4 of Patent Document 1. However, the radius r in FIG. 4 is the radius of the current loop in FIG. 5). a).

JP 2013-223117 A

  According to the above-described prior art, the attenuation characteristic next to the third power is the fifth power (N = 2), the next power is the seventh power (N = 3), and the next power is the ninth power (N = 4). It is. Such a power rule can be theoretically derived from mathematical expressions.

  However, a conventional loop antenna cannot generate a magnetic field having an even power attenuation characteristic such as fourth power or sixth power. When only an odd power attenuation characteristic can be selected in this way, for example, a situation where an intermediate fourth power attenuation is desired, such as “the magnetic field with the third power attenuation is too wide but the magnetic field with the fifth power attenuation is too small”. I can't respond. That is, the attenuation characteristic cannot be arbitrarily selected, and there is a problem that a magnetic field having a space size desired by the user cannot be provided.

  The present invention has been made in view of the above circumstances, and an object thereof is to improve the attenuation characteristic of a magnetic field generated by a loop antenna.

  In order to solve the above problems, a loop antenna includes a pair of single current loops arranged in parallel and spaced apart from each other, and a plurality of expressions appearing in a Taylor expansion of a mathematical expression representing a magnetic field generated by the pair of current loops. The value of the current flowing in each current loop and the radius of each current loop are set so that only the lowest order term is zero or no power term is zero. And

  According to the present loop antenna, a pair of single current loops arranged in parallel with each other are provided, and a mathematical expression representing a magnetic field generated by the pair of current loops is included in a plurality of power terms appearing in a Taylor expanded mathematical expression. Since the value of the current flowing in each current loop and the radius of each current loop are set so that only the lowest order term is zero, a magnetic field having a fourth power attenuation characteristic can be generated. Also, since the value of the current flowing in each current loop and the radius of each current loop are set so that none of the multiple power terms is zero, a magnetic field with a cube attenuation characteristic is generated. can do.

  Further, in the loop antenna, when only the lowest order term is set to zero in the loop antenna, a value obtained by adding the square of the radius of the one current loop to the value of the current flowing in one current loop and the other current The gist is that the value obtained by adding the value of the current flowing in the loop to the value obtained by integrating the square of the radius of the other current loop is zero.

  The loop antenna according to claim 1, in a three-dimensional space orthogonal coordinate system, has a loop forming plane parallel to the XY plane, a loop center point located on the Z axis, and from an origin on the Z axis. A pair of concentric current loop groups spaced apart from each other, and arbitrarily selected from the lowest order terms among a plurality of power terms appearing in a Taylor expansion formula expressing a magnetic field generated by the pair of current loop groups The gist is that the value of the current flowing in each current loop and the radius of each current loop are set so that the higher-order terms of the current loop are zero.

  According to the present invention, in a Cartesian coordinate system of a three-dimensional space, the loop forming surface is parallel to the XY plane, the loop center point is located on the Z axis, and is spaced from the origin on the Z axis at equal intervals. A pair of concentric current loop groups arranged from the lowest order term to any higher order term among a plurality of power terms appearing in a Taylor expansion of a formula representing the magnetic field generated by the pair of current loop groups Since the value of the current flowing in each current loop and the radius of each current loop are set so as to be zero, it is possible to generate a magnetic field having an attenuation characteristic exceeding the third power and even power or odd power it can.

  The loop antenna according to claim 2 is a three-dimensional space orthogonal coordinate system in which a loop forming surface is parallel to an XY plane, a loop center point is located on the Z axis, and the origin on the Z axis is A plurality of single current loops that are spaced apart from each other, and an arbitrary higher-order term from the lowest-order term among a plurality of power terms appearing in a Taylor-expanded mathematical formula representing a magnetic field generated by the plurality of current loops The gist is that the value of the current flowing in each current loop and the radius of each current loop are set so that the current value is zero.

  According to the present invention, in a Cartesian coordinate system of a three-dimensional space, the loop forming surface is parallel to the XY plane, the loop center point is located on the Z axis, and is spaced from the origin on the Z axis at equal intervals. A plurality of single current loops are arranged, and a numerical expression representing a magnetic field generated by the plurality of current loops is expressed as a zero from the lowest order term to any higher order term among a plurality of power terms appearing in a Taylor expansion formula. As described above, since the value of the current flowing through each current loop and the radius of each current loop are set, a magnetic field having an attenuation characteristic exceeding the third power and even power or odd power can be generated.

  The loop antenna according to claim 3 is the loop antenna according to claim 1 or 2, wherein the distance between the current loops arranged in parallel is set so that the lowest order term to any higher order term is zero. It is a summary.

  According to the present invention, it is possible to improve the attenuation characteristic of the magnetic field generated by the loop antenna.

It is a perspective view of the loop antenna which concerns on 1st Embodiment. It is a perspective view of the loop antenna which concerns on 2nd Embodiment. It is a figure which shows the attenuation | damping characteristic of a magnetic field. It is a perspective view of the loop antenna which concerns on 3rd Embodiment. It is a perspective view of the conventional loop antenna.

  Hereinafter, an embodiment for carrying out the present invention will be described with reference to the drawings.

[First Embodiment]
FIG. 1 is a perspective view of a loop antenna 1 according to the first embodiment. The loop antenna 1 includes a pair of single current loops 10 and 20 that are spaced apart in parallel, and a current control unit (not shown) that inputs a current to each of the current loops 10 and 20.

In such a loop antenna 1, a carrier signal of current I ₁ (> 0) is given to one current loop 10, and a carrier signal of current I ₂ (> 0) is given to the other current loop 20. At this time, the magnetic field B on the z axis generated by the loop antenna 1 is expressed by Equation (1).

但し、ａ_１，ａ_２は、各電流ループ１０，２０の半径である。半径ａ_１と半径ａ_２は同じ値でもよいし、異なる値でもよい。また、μ_０は、真空の透磁率である。なお、各電流ループ１０，２０のループ形成面はｘ−ｙ平面に平行であり、各ループ中心点はｚ軸上に位置するものとする。また、各電流ループ１０，２０は、ｚ軸上の原点から「−ｐ」，「＋ｐ」離れて位置するものとする。

However, a ₁ and a ₂ are radii of the current loops 10 and 20. The radius a ₁ and the radius a ₂ may be the same value or different values. Μ ₀ is the magnetic permeability of vacuum. In addition, the loop formation surface of each current loop 10 and 20 is parallel to an xy plane, and each loop center point shall be located on az axis. In addition, the current loops 10 and 20 are assumed to be located at “−p” and “+ p” apart from the origin on the z-axis.

Here, z >> a ₁ , z >> a ₂ , z >> p, that is, the distance from the origin on the z axis to the detection point T of the magnetic field B is the loop radius a ₁ , a _{2 of} each current loop 10, 20, When the distance between the loops (2p) is sufficiently far, each term on the right side of Equation (1) can be expressed as Equation (2) and Equation (3) by Taylor expansion.

ゆえに、磁界Ｂの振る舞いを示した式（１）を式（４）のように書き換えることができる。

Therefore, Equation (1) showing the behavior of the magnetic field B can be rewritten as Equation (4).

なお、式（４）では、簡単のためｚ^５の項よりも高次の項は省略している。

In Equation (4), a higher-order term than the term z ⁵ is omitted for simplicity.

Here, when generating a magnetic field having a fourth power attenuation characteristic, it is necessary to eliminate the term z ^{3 in} the equation (4). That is, the values of the currents I ₁ and I ₂ flowing in the current loops 10 and 20 and the radii a ₁ and a ₂ of the current loops 10 and 20 are set so that the term of z ³ becomes zero. Specifically, they are set so as to satisfy Expression (5).

式（５）を満たすには、例えば、ａ_１＝１［ｍ］，Ｉ_１＝１［Ａ］，ａ_２＝１［ｍ］，Ｉ_２＝−１［Ａ］と設定すればよい。ここで、電流値は、反時計回りに流す場合を正とし、時計回りの場合を負とした。

In order to satisfy Expression (5), for example, a ₁ = 1 [m], I ₁ = 1 [A], a ₂ = 1 [m], and I ₂ = −1 [A] may be set. Here, the current value was positive when flowing counterclockwise and negative when clockwise.

By setting the current and radius of each of the current loops 10 and 20 so as to satisfy the equation (5), the term z ^{3 in} the equation (4) disappears and the magnetic field of the term z ⁴ appears in the space. Become. That is, a magnetic field with a fourth power attenuation characteristic can be generated. Thereby, it is possible to realize a magnetic field having attenuation characteristics exceeding the third power and even power, which could not be realized by the conventional loop antenna.

  If none of the power terms of Equation (4) is zero, a magnetic field having a cube attenuation characteristic is generated. By appropriately adjusting the current and radius of each of the current loops 10 and 20, it is possible to selectively generate a magnetic field having a third or fourth attenuation characteristic.

According to the present embodiment, a pair of single current loops 10 and 20 that are spaced apart in parallel are provided, and the equation (1) that expresses the magnetic field generated by the pair of current loops 10 and 20 is Taylor-expanded. The values of the currents I ₁ and I ₂ flowing in the current loops 10 and 20 and the radius a of the current loops 10 and 20 so that the z ³ term among the plurality of power terms appearing in the equation (4) is zero. _{Since 1} and a ₂ are set, a magnetic field having a fourth power attenuation characteristic can be generated.

Further, according to the present embodiment, the currents I ₁ and I ₂ flowing in the current loops 10 and 20 are set so that none of the power terms among the plurality of power terms appearing in the equation (4) is zero. Since the value and the radii a ₁ and a _{2 of} each current loop are set, a magnetic field having a cube attenuation characteristic can be generated.

[Second Embodiment]
When a magnetic field having an attenuation characteristic exceeding the fourth power is generated using the loop antenna 1 of the first embodiment, for example, for the magnetic field having the fifth power attenuation characteristic, the terms z ³ and z ⁴ in Equation (4). It is necessary to turn off both. Here, in order to eliminate both the z ³ term and the z ⁴ term, the expression (6) must be further satisfied.

しかし、式（５）と式（６）を満たす場合とは、電流Ｉ_１と電流Ｉ_２が共にゼロ以外にない。つまり、電流ループ数が２つの場合では、式（５）と式（６）を同時に満たすことができない。そこで、本実施の形態では、対をなす各電流ループ１０，２０のそれぞれの各同一平面上に複数の電流ループを同心円状にそれぞれ追加する。

However, when the expressions (5) and (6) are satisfied, the currents I ₁ and I ₂ are not other than zero. That is, when the number of current loops is two, Expression (5) and Expression (6) cannot be satisfied simultaneously. Therefore, in the present embodiment, a plurality of current loops are added concentrically on the same plane of each of the current loops 10 and 20 forming a pair.

FIG. 2 is a perspective view of the loop antenna 1 according to the second embodiment. This embodiment is a modification of the first embodiment. In such modification, the radius a ₁ and the current I on the same plane of the composed current loop 10 at _1, the radius a ₁ and different radii have current I ₁ different current flows plurality of current loops (a _3, I ₃ ), ..., ( _a2k-1 , _I2k-1 ), ..., ( _a2M-1 , _I2M-1 ). Further, the radius _{a 2} and the current _I on the same plane of the composed current loop 20 at _2, radius _{a 2} and different radii have current _{I 2} and the different current flows plurality of current loops _{(a 4, I} 4), ..., (a _2k , I _2k ), ..., (a _2M , I _2M ). Others are the same as those in the first embodiment. M is the number of current loops included in the same plane.

  In the case of the loop antenna 1 having such a configuration, the magnetic field B generated in the space is expanded from Equation (1) to Equation (7).

そして、式（６）をテイラー展開すると式（８）となる。式（８）は、式（４）の拡張式といえる。

Then, when Expression (6) is Taylor-expanded, Expression (8) is obtained. Equation (8) can be said to be an extended equation of equation (4).

そして、ループアンテナ１の生成する磁界Ｂ（式（７））の級数展開式（式（８））において、ｚの各累乗項の係数がゼロとなるように、各電流ループに流れる電流Ｉの値と各電流ループの半径ａと電流ループ間の距離ｐとを設定する。

Then, in the series expansion formula (formula (8)) of the magnetic field B (formula (7)) generated by the loop antenna 1, the current I flowing in each current loop is set so that the coefficient of each power term of z becomes zero. The value, the radius a of each current loop and the distance p between the current loops are set.

Hereinafter, a method for generating a magnetic field having attenuation characteristics of the fifth power and the sixth power will be described for M = 2. For example, in order to generate a magnetic field having a fifth power attenuation characteristic, both the z ³ term and the z ⁴ term may be deleted in the equation (8). Here, when M = 2 is substituted into Expression (8), Expression (9) is obtained.

式（９）のｚ^３とｚ^４の項を消すため、以下の式（１０）と式（１１）に示される条件を適用する。

In order to eliminate the terms z ³ and z ⁴ in equation (9), the conditions shown in the following equations (10) and (11) are applied.

式（１０）と式（１１）を同時に満たすには、例えば、ａ_１＝１［ｍ］，Ｉ_１＝１［Ａ］，ａ_２＝１［ｍ］，Ｉ_２＝−１［Ａ］，ａ_３＝０．５［ｍ］，Ｉ_３＝−４［Ａ］，ａ_４＝０．５［ｍ］，Ｉ_４＝４［Ａ］と設定すればよい。式（１０）と式（１１）を満たすことにより、ｚ^３の項とｚ^４の項の両方が消え、ループアンテナ１から放射される磁界は５乗減衰となる。

In order to satisfy Equation (10) and Equation (11) at the same time, for example, a ₁ = 1 [m], I ₁ = 1 [A], a ₂ = 1 [m], I ₂ = −1 [A], _{a 3 = 0.5 [m],} I 3 = -4 [a], a 4 = 0.5 [m], may be set as I 4 = 4 [a]. By satisfying the equations (10) and (11), both the z ³ term and the z ⁴ term disappear, and the magnetic field radiated from the loop antenna 1 is attenuated to the fifth power.

Further, the magnetic field having the sixth power attenuation characteristic can be obtained by eliminating the z ⁵ term in the equation (9). To clear the section z ^5, in addition to the equation (11) and (10), further it is necessary to satisfy the condition represented by the following formula (12).

式（１０）〜式（１２）を同時に満たすには、例えば、ａ_１＝１［ｍ］，Ｉ_１＝１［Ａ］，ａ_２＝１［ｍ］，Ｉ_２＝１［Ａ］，ａ_３＝０．５［ｍ］，Ｉ_３＝−４［Ａ］，ａ_４＝０．５［ｍ］，Ｉ_４＝−４［Ａ］と設定すればよい。式（１０）〜式（１２）を満たすことにより、ｚ^３，ｚ^４，ｚ^５の各項が消え、ループアンテナ１から放射される磁界は６乗減衰となる。

In order to satisfy the expressions (10) to (12) at the same time, for example, a ₁ = 1 [m], I ₁ = 1 [A], a ₂ = 1 [m], I ₂ = 1 [A], a ₃ = 0.5 [m], I ₃ = −4 [A], a ₄ = 0.5 [m], and I ₄ = −4 [A] may be set. When Expressions (10) to (12) are satisfied, the terms z ³ , z ⁴ , and z ⁵ disappear, and the magnetic field radiated from the loop antenna 1 is attenuated to the sixth power.

Up to this point, the method of generating the magnetic field having the fifth and sixth power attenuation characteristics has been described. On the other hand, even the loop antenna 1 according to the present embodiment can generate a magnetic field having a fourth power attenuation characteristic by satisfying only the condition of the expression (10). Therefore, when only Formula (10) is satisfied, when Formula (10) and Formula (11) are satisfied, when Formula (10), Formula (11), and Formula (12) are satisfied, Formula (10) The case where none of the expressions (12) is satisfied can be selected by switching the currents I ₁ , I ₂ , I ₃ , I ₄ or adjusting the magnitude of the current value. A magnetic field with a 3, 4, 5 or 6th power decay characteristic can be selected. Thereby, the attenuation characteristic of the magnetic field can be selected according to the intention of the user, and adjustment such as switching of the attenuation characteristic with time can be performed.

  FIG. 3 shows the attenuation characteristics of the magnetic field generated in the loop antenna 1 according to the present embodiment. By changing the value of the current that can be taken, different attenuation characteristics can be generated from the same loop antenna 1.

According to this embodiment, a pair of concentric current loop groups arranged in parallel and spaced apart from each other, and a Taylor expansion formula (8) representing a magnetic field generated by the pair of current loop groups ( Since the value of the current I flowing through each current loop and the radius a of each current loop are set so that the z ³ term to any higher order term among the plurality of power terms appearing in 9) are set to zero. It is possible to generate a magnetic field exceeding the power and having an attenuation characteristic of even power or odd power.

  Further, according to the present embodiment, the value of the current I flowing in each current loop and the radius of each current loop are set so that none of the multiple power terms appearing in Equation (9) is zero. Since a is set, it is possible to generate a magnetic field having a cube attenuation characteristic.

[Third Embodiment]
FIG. 4 is a perspective view of the loop antenna 1 according to the third embodiment. This embodiment is a modification of the first embodiment. Such a modification includes N pairs of single current loops that are spaced apart in parallel so that the loop center is located on the z-axis. In each of the i-th pair of current loops, the currents flowing through the current loops are I _2i and I _2i−1, and the radii of the current loops are a _2i and a _2i−1 .

  At this time, the magnetic field B generated in the space from the loop antenna 1 is expressed by the sum of the powers of z, and the expression (1) is expanded into the expression (13).

ここで、ｚ≫ａ_２ｋ−１，ｚ≫ａ_２ｋ，ｚ≫ｐ_ｋ（ｋ＝１，２，…，Ｎ）、すなわち、ｚ軸上の原点から磁界Ｂの検出地点Ｔまでの距離が各電流ループのループ半径ａやループ間距離ｐよりも十分に遠い場合、テイラー展開により式（１３）を式（１４）のように表記できる。

Here, z >> a _2k−1 , z >> a _2k , z >> p _k (k = 1, 2,..., N), that is, the distance from the origin on the z axis to the detection point T of the magnetic field B is When the current loop is sufficiently far than the loop radius a and the inter-loop distance p, Expression (13) can be expressed as Expression (14) by Taylor expansion.

なお、式（７）においてｐは各電流ループに共通の値であったが、式（１３）における各ｐ_ｋは同じ値はとらないものとする。

Although p was common value in each current loop in equation (7), each of p _k in equation (13) shall not take the same value.

  Then, in the series expansion formula (formula (14)) of the magnetic field B (formula (13)) generated by the loop antenna 1, the current I flowing in each current loop is set so that the coefficient of each power term of z becomes zero. A value, a radius a of each current loop, and a distance p between the current loops are set.

  Thereby, the loop antenna 1 can generate | occur | produce arbitrarily the magnetic field of the attenuation | damping characteristic of more than normal 3rd power and below (2N + 2) power. That is, when N = 1 (one pair of current loops), the third and fourth power attenuation characteristics, when N = 2, the third to sixth power attenuation characteristics, and when N = 3, the magnetic field has the third to eighth power attenuation characteristics. Can be generated.

  Hereinafter, the case where N = 2 will be described. Substituting N = 2 into equation (14) yields equation (15).

式（１５）において、ｚ^３の項を消すことにより４乗減衰特性の磁界を生成できる。同様に、ｚ^３とｚ^４の項を消せば５乗減衰特性の磁界、ｚ^３とｚ^４とｚ^５の項を消せば６乗減衰特性の磁界を生成できる。

In equation (15), a magnetic field having a fourth power attenuation characteristic can be generated by eliminating the term z ³ . Similarly, it generates a magnetic field of z ³ and the magnetic field of the fifth power attenuation characteristics if indelible the section z ^4, z ³ and z ⁴ and claim the indelible if the sixth power attenuation characteristics of z ^5.

To eliminate the term of z ³ , for example, a ₁ = 1 [m], I ₁ = 1 [A], a ₂ = 1 [m], I ₂ = 1 [A], a ₃ = 1 [m] , I ₃ = −1 [A], a ₄ = 1 [m], and I ₄ = −1 [A].

In order to erase both the terms z ³ and z ⁴ , for example, a ₁ = 1 [m], I ₁ = 1 [A], a ₂ = 1 [m], I ₂ = −1 [A], _{a 3 = 0.5 [m],} I 3 = -4 [a], a 4 = 0.5 [m], may be set as _I 4 = 4 [a].

Further, in order to erase all the terms z ³ , z ⁴ and z ⁵ , for example, a ₁ = 1 [m], I ₁ = 1 [A], a ₂ = 1 [m], I ₂ = 1 [A ], A ₃ = 2 [m], I ₃ = -4 [A], a ₄ = 2 [m], I ₄ = -4 [A], p ₁ = 1 [m], p ₂ = 4 [m] ] Should be set.

  In this manner, higher order attenuation characteristics can be generated by eliminating the polynomial of z in the equation (15) from the low order power term. The present invention is not limited to the conventional (2N + 1) th power attenuation, but can generate both odd power and even power attenuation characteristics, so that the user can provide a magnetic field having optimum attenuation characteristics. Further, unlike the second embodiment, since a multi-winding configuration is not employed, there is an advantage that an electronic component or the like can be included because there is a spatial margin inside the loop antenna 1.

  If none of the power terms in Equation (15) is zero, a magnetic field with a cube attenuation characteristic is generated. By appropriately adjusting the current and radius of each of the current loops 10 and 20, it is possible to selectively generate a magnetic field having a damping characteristic of 3rd power or higher.

According to the present embodiment, a plurality of single current loops arranged in parallel and spaced apart from each other, and a formula (14) expressing a magnetic field generated by the plurality of current loops is expressed by a Taylor expansion formula (14). Since the value of the current I flowing through each current loop and the radius a of each current loop are set so that the z ³ term to any higher-order term among the multiple power terms that appear is zero, it exceeds the third power In addition, it is possible to generate a magnetic field having an attenuation characteristic of even power or odd power.

  Further, according to the present embodiment, the value of the current I flowing in each current loop and the current loop of each current loop are set so that none of the multiple power terms appearing in Equation (14) is zero. Since the radius a is set, a magnetic field with a cube attenuation characteristic can be generated.

  As described above, according to each of the first to third embodiments, it is possible to realize the loop antenna 1 that generates a magnetic field having an attenuation characteristic of an arbitrary power of 3rd power or higher.

1 ... Loop antenna 10, 20 ... Current loop

Claims (3)

In a Cartesian coordinate system in a three-dimensional space, a loop forming surface is parallel to the XY plane, a loop center point is located on the Z axis, and a pair is arranged at equal intervals from the origin on the Z axis With concentric current loops,
The value of the current flowing through each current loop so that the lowest order term to any higher order term among the plurality of power terms appearing in the Taylor expansion formula that expresses the magnetic field generated by the pair of current loop groups is zero. A loop antenna characterized in that the radius of each current loop is set. In the orthogonal coordinate system of the three-dimensional space, the loop forming surface is parallel to the XY plane, the loop center point is located on the Z axis, and a plurality of points arranged at equal intervals from the origin on the Z axis With a single current loop,
The value of the current flowing through each current loop is set so that the lowest order term to any higher order term among the plurality of power terms appearing in the Taylor expansion formula representing the magnetic field generated by the plurality of current loops is zero. A loop antenna characterized in that the radius of each current loop is set.   The loop antenna according to claim 1 or 2, wherein a distance between the current loops arranged in parallel is set so that the lowest order term to any higher order term is zero.

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