JP6127673B2 - Simulation apparatus and simulation method - Google Patents

Description

  The disclosed embodiment relates to a simulation apparatus, a simulation method, and the like.

  When designing an antenna of a wireless communication apparatus such as a mobile phone, the antenna performance is evaluated by performing an electromagnetic field simulation (simply called “simulation” if there is no risk of confusion). Antenna performance includes, but is not limited to, for example, consistency, antenna efficiency (or gain) in transmission or reception, and the like. Although not related to an antenna, an example of a conventional simulation method is described in Patent Document 1.

  The electromagnetic field simulation may be executed by various methods, but typically, a time domain finite difference (Finite Difference Time Domain: FDTD) method, a finite integration (Finite Integration: FI) method, or the like is used. In the FDTD method, a space is subdivided into small volume parts called Yee cells or Yee lattices, and Maxwell's equations are discretized or differentiated to obtain solutions sequentially in the time domain.

JP 2006-293569 A

  In the electromagnetic field simulation, it is assumed that a matching circuit using an ideal lumped element is connected to the antenna. Such an ideal matching circuit is essentially used to make the antenna impedance including the influence of the matching circuit viewed from the wave source a predetermined matching impedance that is the internal impedance of the wave source. For this reason, in the prior art, electromagnetic field simulation is performed by simply adding the impedance of such a matching circuit. However, in the special case of Maxwell's equations discretized using FDTD, FI, etc., elements that do not exist in the actual physical circuit but seem to exist during simulation (elements other than the matching circuit) The resulting impedance also occurs. For this reason, in the prior art that considers only the impedance of the matching circuit using an ideal lumped element, the matching characteristics of the antenna indicated by the simulation results are not sufficient. As a result, in the prior art, the impedance of the lumped element has to be adjusted again and the simulation has to be performed again. The inventors of the present application have found such problems of the prior art in the basic research of this case.

  The problem of the disclosed embodiment is not only the impedance of the matching circuit idealized by the lumped element, but also the impedance caused by elements other than the matching circuit in the electromagnetic field simulation solving the discretized Maxwell equation Is to provide an apparatus or a method that can realize the desired matching characteristics of the antenna by setting the impedance of the matching element in consideration of the above.

The simulation apparatus according to the disclosed embodiment
The antenna impedance seen from the wave source when the matching circuit formed by the lumped constant element is not connected to the antenna, the antenna considering the wiring seen from the wave source when the matching circuit is connected to the antenna through the wiring An impedance determination unit that determines the impedance of the matching circuit so as to be equal to the sum of the impedance and the internal impedance of the wave source;
An electromagnetic field simulator that executes an electromagnetic field simulation for the antenna to which the matching circuit having the determined impedance is connected by solving a discretized Maxwell equation.

  According to the disclosed embodiment, in the electromagnetic field simulation for solving the discretized Maxwell equation, not only the impedance of the matching circuit idealized by the lumped element, but also the impedance caused by elements other than the matching circuit By setting the impedance of the matching element in consideration of the above, it is possible to provide an apparatus or method that can realize the desired matching characteristics of the antenna.

The figure which shows the basic structure assumed by the electromagnetic field simulation of an antenna. The equivalent circuit diagram when a matching circuit is connected in series with a wave source. The equivalent circuit diagram when the matching circuit is connected in parallel to the wave source. The figure which shows the relationship between the impedance seen from the wave source, and matching impedance with a Smith chart. The figure which shows the design procedure of the conventional antenna. The figure which shows a mode that the three-dimensional structure was discretized by the grid. The figure which shows the electric field component along the edge | side of a Yee cell, and a magnetic field component perpendicular | vertical to the surface of a Yee cell. The figure which shows a mode that the circuit element which is a lumped constant element exists in the center of a Yee cell. The figure for demonstrating the example which calculates | requires the magnetic field component Hy around the thin wire conductor along az axis. The figure for demonstrating the example which calculates | requires the magnetic field component Hy around the thin wire | line conductor which has a circular cross section with a radius R. FIG. The figure which shows the structure where the matching circuit is connected in series between the wave source and the antenna. Sectional drawing regarding the yz plane of the structure shown in FIG. FIG. 12 is a cross-sectional view regarding the zx plane of the structure shown in FIG. The figure which shows the structure where the matching circuit connected to an antenna is connected in parallel with the wave source. FIG. 15 is a cross-sectional view regarding the yz plane of the structure shown in FIG. The figure which shows an example of the structure where the some matching circuit from which the connection method with respect to a wave source differs is used. The flowchart of the simulation method by embodiment. The figure which shows the antenna impedance at the time of connecting a matching circuit to an antenna. The functional block diagram of the simulation apparatus by embodiment.

The embodiment will be described from the following viewpoints.
1. Matching circuit 2. Analysis method 3. 3. Lumped constant element 4. Consider wiring. 5. When matching circuit is connected in series with wave source 6. When matching circuit is connected in parallel to wave source 7. When there are a plurality of matching circuits 8. Simulation method Hereinafter, embodiments will be described with reference to the accompanying drawings. In the figures, similar elements are given the same reference numbers. It should be noted that when terms such as “embodiment”, “one embodiment”, and “embodiment” are used herein, they do not necessarily all refer to the same form.

<1. Matching circuit>
Fig. 1 shows the basic structure assumed in the electromagnetic field simulation of an antenna. FIG. 1 shows a substrate 11, an antenna 12, and a wave source and matching circuit 13 that are used in a wireless communication apparatus. A conductive path (not shown) is formed on one side (front surface, front surface, front surface) of the substrate 11. A ground plate (not shown) is provided on the other side (back surface, back surface) of the substrate 11. The ground plane is any suitable conductive layer that provides a reference potential, and may be referred to as a ground plate or ground (GND). The antenna 12 is used for transmitting and receiving wireless signals by the wireless communication device. The radio signal is carried by an 11 GHz radio wave as an example, but the frequency value is arbitrary. The antenna 12 is an inverted L antenna in the illustrated example, but may be any other antenna such as a monopole antenna.

  The wireless communication device is typically a mobile phone, but may be another device. For example, the wireless communication device may be a user device, an information terminal, a high-performance mobile phone, a smartphone, a tablet computer, a personal digital assistant (PDA), a portable personal computer, a palmtop computer, a laptop computer, a desktop computer, or the like. Alternatively, it may be a base station, a relay station, an access point, etc., but is not limited thereto.

  FIG. 2 shows an example of an equivalent circuit of the basic structure shown in FIG. The substrate 11 is represented by GND. A wave source 21 and a matching circuit 22 are provided between the antenna 12 and the substrate 11 (GND). In the example shown in FIG. 2, the wave source 21 and the matching circuit 22 are connected in series between the substrate 11 (GND) and the antenna 12. However, this is not essential, and the matching circuit 22 may be connected to the wave source 21 in parallel as shown in FIG.

  In the wireless communication device, the antenna impedance including the influence of the matching circuit 22 viewed from the wave source 21 needs to be equal to the internal impedance of the wave source 21 so that a radio signal can be appropriately transmitted and received through the antenna. The internal impedance is typically 50 ohms and is called the matching impedance.

  FIG. 4 shows how matching the impedance seen from the wave source to the matching impedance moves on the Smith chart. Generally, in the Smith chart, the origin corresponds to the matching impedance. A group of circles perpendicular to the x-axis at point A and centered on the x-axis show how the impedance changes when the reactance is changed while the resistance or resistance (Ω) is constant. . A group of circles that are in contact with the x-axis at the point A (1, 0) and have a center on a straight line of x = 1, how the impedance changes when the resistance is changed while keeping the reactance constant. Indicate. These groups of circles are called impedance charts. Similarly, the circle that intersects perpendicularly with the x-axis at the point B (-1, 0) and has the center on the x-axis shows how the admittance changes when the susceptance is changed while keeping the conductance constant. Indicates. A circle that is in contact with the x-axis at the point B and has a center on a straight line of x = −1 indicates how the admittance changes when the conductance is changed while the susceptance is kept constant. These groups of circles are called admittance charts.

  Assume that the antenna impedance viewed from the wave source corresponds to the point U in the Smith chart shown in FIG. 4 in a structure in which no matching circuit is provided. In this case, for example, the point U can be moved to the point V by changing the reactance while keeping the resistance constant, and then the point U can be moved to the origin by changing the susceptance while keeping the conductance constant. Therefore, by connecting a matching circuit having reactance and susceptance that moves from point U to point V to the origin, the antenna impedance including the influence of the matching circuit seen from the wave source can be matched to the matching impedance. . Note that there is not one way to change the impedance or admittance in the Smith chart. For example, in the above example, the point U may be moved to the point W by changing the resistance while keeping the reactance constant, and then the point W may be moved to the origin by changing the reactance while keeping the resistance constant. . However, this method is unlikely to be used in actual design because the efficiency of the antenna is likely to deteriorate. In any case, the impedance or admittance of the matching circuit is determined to appropriately change one or more of resistance, reactance, conductance, and susceptance.

  Next, in order to facilitate understanding of the disclosed embodiment, first, a conventional antenna design procedure will be described with reference to FIG.

  In step 1, a state where no matching circuit is connected to the antenna 12 is set. Alternatively, the impedance of the matching circuit may be set to zero.

  In step 2, the antenna impedance viewed from the wave source is obtained. In the illustrated example, the antenna impedance corresponds to the point U on the Smith chart. Next, the amount of change in impedance necessary to move the point U to a desired point on the Smith chart is obtained. For convenience of explanation, the amount of change in impedance necessary to move the point U to the point V is obtained. As described with reference to FIG. 4, finally, it is necessary to match the antenna impedance including the influence of the matching circuit to the matching impedance. In step 2 of FIG. 5, if the reactance can be changed by (Xm) while keeping the resistance constant, it can be seen that the point U moves to the point V.

  Therefore, in the prior art, in step 3, the reactance of the matching circuit connected to the antenna is set to the reactance (Xm) obtained in step 2, and electromagnetic field simulation is performed. In the electromagnetic field simulation, the matching circuit is treated as an ideal lumped element. However, in practice, not only an ideal matching circuit using such a lumped constant element but also an impedance caused by elements other than the matching circuit exists. Specifically, there is an influence caused by the wiring, line or wire between the matching circuit and the wave source. For this reason, the matching characteristics of the obtained antenna are not sufficient in the prior art in which only a matching circuit using an ideal lumped element is considered.

  As a result, as shown in step 4, the antenna impedance including the influence of the matching circuit as viewed from the wave source has moved from point U to point W instead of point V. Therefore, after this simulation, the impedance of the matching circuit must be adjusted again so as to move the point W to the point V, and the simulation must be performed again. As described above, in the conventional technique, it is necessary to reset the impedance to be set in the matching circuit and repeat the simulation until the antenna impedance including the influence of the matching circuit matches the desired impedance.

  In the embodiment, the desired matching of the antenna is set by setting the impedance of the matching circuit in consideration of not only the ideal lumped element matching circuit but also the wiring, line, or wire between the wave source and the matching circuit. Characteristics can be realized.

<2. Analysis method>
Next, an analysis method that is the basis of the electromagnetic field simulation method used in the embodiment will be described. This analysis method can be applied to any method for solving the Maxwell equation by discretizing in time and space, such as the time domain finite difference (FDTD) method and the wire integration (FI) method.

  Assuming that the medium assumed in the electromagnetic field simulation is a linear and isotropic continuous medium with no electric charge, the Maxwell equation can be written as follows.

ここで、Eは電界ベクトルを表し、カーテシアン座標系ではE=(Ex，Ey，Ez)のように表現される。Hは磁界ベクトルを表し、カーテシアン座標系ではH=(Hx，Hy，Hz)のように表現される。▽はベクトル微分演算子(grad)を表し、▽=(∂/∂x，∂/∂y，∂/∂y)である。「▽×」はローテーション又は回転(rot)の演算を表す。εは媒質の誘電率(F/m)を表す。σは媒質の導電率(S/m)を表す。μは媒質の透磁率(H/m)を表す。ρ*は媒質の磁気抵抗率(Ω/m)を表す。カーテシアン座標系で上記の数式(1a)及び(1b)を成分毎に書けば次のようになる。

Here, E represents an electric field vector, and is expressed as E = (Ex, Ey, Ez) in the Cartesian coordinate system. H represents a magnetic field vector, and is expressed as H = (Hx, Hy, Hz) in the Cartesian coordinate system. ▽ represents a vector differentiation operator (grad), where ▽ = (∂ / ∂x, ∂ / ∂y, ∂ / ∂y). “▽ ×” represents a calculation of rotation or rotation. ε represents the dielectric constant (F / m) of the medium. σ represents the conductivity (S / m) of the medium. μ represents the magnetic permeability (H / m) of the medium. ρ * represents the magnetic resistivity (Ω / m) of the medium. If the above mathematical formulas (1a) and (1b) are written for each component in the Cartesian coordinate system, they are as follows.

  In order to solve the partial differential equation expressed by the mathematical formulas (2a)-(2f), the space to be analyzed is discretized into small cubes called `` Yee cells '' or `` Yee lattices '', and the time is also discretized. The A Yee cell or Yee lattice may be referred to as a voxel. Assuming that the units of discretization on the x-axis, y-axis, and z-axis of space are Δx, Δy, and Δz, respectively, and that the unit of discretization on the time axis is Δt, any function F (x, y in time and space , Z, t), the discretized form Fn can be written as

Fn (i, j, k) = F (iΔx, jΔy, kΔz, nΔt) (3)
As shown in FIG. 6, an arbitrary three-dimensional structure is discretized into a grid whose lengths in the x, y, and z axis directions are Xmax, Ymax, and Zmax, respectively. As shown in FIG. 7, it is assumed that each component of the electric field vector E exists along the side of the Yee cell, and each component of the magnetic field vector H exists along a direction perpendicular to the plane of the Yee cell.

  When calculating the value of the discretized function F, as an example, a central difference scheme can be used as shown below.

数式(4a)は、t=nΔtにおいて座標(iΔx，jΔy，kΔz)での関数Fのxに関する偏微分係数が、座標((i+1/2)Δx，jΔy，kΔz)での関数Fの値と座標((i-1/2)Δx，jΔy，kΔz)での関数Fの値との差分をΔxで除算することで近似できることを示す。ただし、必要に応じて他の近似が使用されてもよい。数式(4a)はxに関する偏微分係数を表すが、y及びzに関する偏微分係数も同様に近似できる。数式(4b)は、t=nΔtにおける関数Fのtに関する偏微分係数が、t=(n+1/2)Δtでの関数Fの値とt=(n-1/2)Δtでの関数Fの値との差分をΔtで除算することで近似できることを示す。ただし、必要に応じて他の近似が使用されてもよい。数式(4a)及び(4b)の関係式を、マックスウェル方程式の成分毎の数式(2a)−(2f)に適用すると、次のような離散化された方程式又は差分方程式が得られる。

Equation (4a) shows that the partial differential coefficient with respect to x of the function F at the coordinates (iΔx, jΔy, kΔz) at t = nΔt is the function F of the function F at the coordinates ((i + 1/2) Δx, jΔy, kΔz). It shows that the difference between the value and the value of the function F at the coordinates ((i-1 / 2) Δx, jΔy, kΔz) can be approximated by dividing by Δx. However, other approximations may be used as needed. Equation (4a) represents the partial differential coefficient for x, but the partial differential coefficients for y and z can be similarly approximated. Equation (4b) shows that the partial differential coefficient with respect to t of function F at t = nΔt is the value of function F at t = (n + 1/2) Δt and the function at t = (n−1 / 2) Δt. It shows that it can be approximated by dividing the difference from the value of F by Δt. However, other approximations may be used as needed. When the relational expressions of the equations (4a) and (4b) are applied to the equations (2a)-(2f) for each component of the Maxwell equation, the following discretized equations or difference equations are obtained.

数式(5a)−(5f)のような差分方程式により電磁界を逐次求めるアルゴリズムは、「蛙跳び(leap−frog)」アルゴリズムと呼ばれている。なお、数式(5a)−(5f)を導出する際に、次のような平均化の近似が使用されている。

An algorithm for sequentially obtaining an electromagnetic field by a differential equation such as Equations (5a)-(5f) is called a “leap-frog” algorithm. It should be noted that the following averaging approximation is used when deriving the equations (5a)-(5f).

数式(6)は、t=nΔtにおける関数Hの値は、t=(n+1/2)Δtでの関数Fの値とt=(n-1/2)Δtでの関数Fの値との算術平均で近似できることを示す。算術平均に限らず、重み付け平均が使用されてもよい。

Equation (6) shows that the value of the function H at t = nΔt is the value of the function F at t = (n + 1/2) Δt and the value of the function F at t = (n−1 / 2) Δt. It can be approximated by the arithmetic mean of. Not only an arithmetic average but a weighted average may be used.

<3. Lumped constant element>
Next, how to handle the lumped element in “2. Analysis method” will be described. The dimension of the lumped element is sufficiently smaller than the wavelength of the target electromagnetic wave. It is assumed that a circuit element which is a lumped constant element exists in a Yee cell as shown in FIG. If the current density flowing through the circuit element is JL and the approximation of the formula (4b) is used for the Maxwell equation shown in the formula (1b), the z component of the electric field E can be written as follows.

ただし、JLは、

However, JL

により表現され、ここでz^はz軸方向の単位ベクトルを示す。電流の正の向きはz軸のプラス方向である。

Where z ^ represents a unit vector in the z-axis direction. The positive direction of the current is the positive direction of the z axis.

<< resistance >>
It is assumed that the circuit element which is a lumped constant element is a resistor having a resistance value R or resistance (Ω). In this case, if the voltage applied to both ends of the circuit element is VL, VL = Ez · Δz, so the current IL flowing through the circuit element is
IL = VL / R = Ez ・ Δz / R (9)
Can be written. Therefore, the current ILn−1 / 2 at the time of t = (n−1 / 2) Δt can be written as follows.

この数式(10)を数式(7)に代入すると、次式が得られる。

Substituting this equation (10) into equation (7) yields:

なお、数式(10)及び(11)において電界成分及び電流の値に対応する場所の座標は、(i，j，k+1/2)に対応する(iΔx，jΔy，(k+1/2)Δz)であるが、全ての項に共通するので具体的には明記されていない点に留意を要する。

In the equations (10) and (11), the coordinates of the location corresponding to the electric field component and the current value correspond to (iΔx, jΔy, (k + 1/2) corresponding to (i, j, k + 1/2). ) Δz), but it should be noted that it is not specified because it is common to all terms.

<< Capacitor >>
It is assumed that the circuit element which is a lumped constant element is a capacitor whose capacitance is C. In this case, the following equation is established between the current IL flowing through the capacitor and the voltage VL applied to the capacitor.

IL = C (dVL / dt) ... (12)
Therefore, the current ILn-1 / 2 at the time of t = (n-1 / 2) Δt is
ILn-1 / 2 = C (Δz / Δt) (Ezn−Ezn-1) (13)
Substituting this equation (13) into equation (7) yields:

＜＜インダクタ＞＞
集中定数素子である回路素子が、インダクタンスがLであるインダクタであったとする。この場合、インダクタに流れる電流ILとインダクタに印加される電圧VLとの間には次式が成立する。

<< Inductor >>
It is assumed that the circuit element which is a lumped constant element is an inductor whose inductance is L. In this case, the following equation is established between the current IL flowing through the inductor and the voltage VL applied to the inductor.

従って、t=(n-1/2)Δtの時点の電流ILn-1/2は、

Therefore, the current ILn-1 / 2 at the time of t = (n-1 / 2) Δt is

と書ける。数式(16)における積分は、次のようにして計算できる。

Can be written. The integral in equation (16) can be calculated as follows.

例えば、数式(17a)を数式(7)に代入すると、次式が得られる。

For example, when the formula (17a) is substituted into the formula (7), the following formula is obtained.

数式(17a)の代わりに数式(17b)が使用されてもよい。

Equation (17b) may be used instead of equation (17a).

  In this way, when the lumped constant element is a resistor, Formula (11) is used, when it is a capacitor, Formula (14) is used, and when it is an inductor, Formula (18) is used. The electric field can be obtained by a difference equation.

<4. Consider wiring>
Next, consider the magnetic field component Hy around the thin wire conductor along the z-axis as shown in FIG. In FIG. 9, (i, j, k) represents coordinates (iΔx, jΔy, kΔz). For convenience of explanation, it is assumed that the thin wire conductor is a perfect conductor having a resistance value of 0 and a magnetoresistance value ρ * of 0, but the generality is not lost. In this case, the electric field component along the central axis of the thin wire conductor can be considered as zero. Ez (i, j, k + 1/2) = 0. Therefore, using the formula (5b), coordinates ((i + 1/2) Δx, jΔy, (k + 1/2) Δz) corresponding to (i + 1/2, j, k + 1/2) The magnetic field Hy at can be written as:

  In deriving Equation (19), the thickness or radius of the thin wire conductor was not taken into account, but to consider the radius of the thin wire conductor, the electric and magnetic fields were attenuated so that they were inversely proportional to the distance from the thin wire conductor. In addition, the assumption that there is no change in the length direction (z-axis direction) of the thin wire conductor can be used. Specifically, when the distance from the center (z axis) of the thin wire conductor is r, the x component Ex of the electric field E and the y component Hy of the magnetic field H as shown in FIG. 10 can be written as follows.

数式(20)の左辺カッコ内の(r，j，k)において、rは細線導体からの距離を表し、j及びkはYeeセルのインデックスを表すので、(r，j，k)は座標(r，jΔy，kΔz)に対応することに留意を要する。同様に、数式(21)の左辺カッコ内の(r，j，k＋1/2)は座標(r，jΔy，(k+1/2)Δz)に対応する。図10に示すような細線導体の太さを考慮する場合、数式(5b)を使用するよりも、マックスウェル方程式の数式(1a)に遡って考察した方が、計算が容易になる。そこで、閉曲線Cに沿って電界を線積分したものが、磁界を時間に関して偏微分したものに等しくなること(ファラデーの法則又はストークス(Stokes)の定理)を利用すると、次式が得られる。

In (r, j, k) in the left parenthesis of Equation (20), r represents the distance from the thin wire conductor, and j and k represent the Yee cell index, so (r, j, k) is the coordinate ( Note that it corresponds to r, jΔy, kΔz). Similarly, (r, j, k + 1/2) in the left parenthesis of Equation (21) corresponds to coordinates (r, jΔy, (k + 1/2) Δz). When considering the thickness of the thin wire conductor as shown in FIG. 10, it is easier to calculate by considering retrospectively the equation (1a) of the Maxwell equation rather than using the equation (5b). Therefore, if the fact that the line integral of the electric field along the closed curve C is equal to the partial differentiation of the magnetic field with respect to time (Faraday's law or Stokes's theorem) is used, the following equation is obtained.

∫(dx/x)=ln(x)(自然対数)であるので、数式(22)から次式が得られる。

Since ∫ (dx / x) = ln (x) (natural logarithm), the following equation is obtained from Equation (22).

  Equation (23) shows the y component of the magnetic field when the thickness of the thin wire conductor is taken into account. Compared with Equation (23) considering the thickness of the thin wire conductor and Equation (19) not considering the thickness of the thin wire conductor, the first and second terms of the three terms on the right side of each equation It can be seen that only the third term differs by a factor of 2 / (ln (Δx / R), so R = Δx / e2 ≒ Δx / 7.39 ≒ 0.135Δx In this case, the formula (19) that does not consider the thickness of the thin wire conductor is the same as the formula (23) that considers the thickness of the thin wire conductor, in other words, when the thickness R of the thin wire conductor is ignored. Even so, the result of the electromagnetic field simulation is the same as when a conductor having a thickness of R = 0.135Δx exists.

  The conventional technology does not consider the apparently thin wire conductors in this way, and electromagnetic field simulation is performed exclusively considering only the lumped constant elements (Equations (11), (14), (18)). Yes. As a result, it is difficult to obtain appropriate antenna matching due to the apparently thin wire conductor. Unlike the prior art, the disclosed embodiment can improve the efficiency of electromagnetic field simulation by taking into consideration the influence of a thin wire conductor that appears in this way. When considering the influence of the thin wire conductor, the handling is different depending on whether the matching circuit is connected in series to the wave source or in parallel, so each case will be described below.

<5. When matching circuit is connected in series with wave source>
FIG. 11 shows a state in which the matching circuit 22 is connected in series between the wave source 21 and the antenna 12. FIG. 12 shows a cross-sectional view along the y-axis. An equivalent circuit diagram of this structure is as shown in FIG. In the case of the illustrated example, the dielectric layer 121 is provided on the substrate 11 including the ground plane, and the antenna 12 and the matching circuit 22 are provided on the surface of the dielectric layer 121. Further, the wiring existing on the dielectric layer 121 between the wave source 21 and the matching circuit 22 and the wiring existing between the matching circuit 22 and the antenna 12 are indicated by reference numeral 123. The influence of this wiring, line or wire 123 on the electromagnetic field simulation has not been sufficiently considered in the past. As described below, in the disclosed embodiment, the electromagnetic field simulation is performed in consideration of the influence of the wiring.

  FIG. 13 shows a cross-sectional view along the x-axis including the wiring 123. The wiring, line or wire has a radius R and forms a cylinder extending in the y-axis direction. As described above, the radius R of this wiring has a magnitude of 0.0135Δ. Therefore, when performing an electromagnetic field simulation, it is necessary to consider not only the matching circuit 22 (FIGS. 11 and 12) but also the influence of this wiring. Specifically, the matching is performed so that the antenna impedance (Zm) including the effect of the matching circuit viewed from the wave source 21 is equal to the sum of the impedance (Zm ′) of the matching circuit 22 and the wiring impedance (Zw) of the wiring. The impedance (Zm ′) of the circuit 22 needs to be set (Zm = Zm ′ + Zw). In general, the wiring 123 has resistance, capacitance, and inductance, but it is the inductance (Lw) of the wiring that has a particularly great influence in the electromagnetic field simulation. Accordingly, the wiring inductance (Lw) caused by the wiring 123 is obtained, and the matching circuit 22 has an inductance (Xm ′) and a wiring inductance (Lw) that are equal to the antenna inductance (Xm). By setting the inductance (Xm ′) (Xm = Xm ′ + Lw), the electromagnetic field simulation can be appropriately executed.

  It is easier to obtain the inductance of a microstrip line (MSL) formed of a quadrangular prism conductor than to obtain the inductance of a cylindrical conductor. Therefore, as shown in the lower side of FIG. 13, the line having a cross-sectional contour circumscribing the circular cross-section has the inductance of the microstrip line 124 existing on the dielectric layer 121 having a thickness of Δz-R. It may be approximated to be an inductance of 123.

  The inductance (Lw) of a microstrip line may be obtained by various methods. For example, Antonije R. et, al., "Closed-Form Formulas for Frequency-Dependent Resistantce and Inductance per Unit Legth of Microstrip and Strip It can be obtained according to equations (52)-(54) described in “Transmission Lines”.

ここで、L'(f)は任意の周波数に対するインダクタンスである。R∞'(fs)は表皮効果の抵抗である。L0'は上記の文献のセクションIIから導出されるマイクロストリップラインの単位長さ当たりのインダクタンスである。ただし、マイクロストリップの場合はkr＝0.2であり、ストリップラインの場合はkr＝0.4である。また、fsは次式により算出される近似的な遷移周波数である。

Here, L ′ (f) is an inductance for an arbitrary frequency. R∞ '(fs) is the resistance of the skin effect. L0 ′ is the inductance per unit length of the microstrip line derived from section II of the above document. However, kr = 0.2 for microstrip and kr = 0.4 for stripline. Fs is an approximate transition frequency calculated by the following equation.

fs = (ks + (10t / w) / (1 + w / h)) / (πμ0σt2)
Here, ks is 1.6 for the microstrip line and 2.4 for the strip line. t is the thickness of the conductor. w is the width of the conductor. σ is the conductivity of the conductor. μ0 is the vacuum permeability.

  Note that a ground plane is not provided on the opposite side (back side) of the dielectric layer 121 to the side where the antenna 12 is provided, but this is not essential, and the antenna 12 and the ground plane 11 have any suitable shape. It may be formed. Further, it is not essential to approximate the cylindrical conductor 123 as shown in the upper side of FIG. It may be approximated by a line having any suitable cross-sectional shape. For example, the wiring 123 may be approximated by a line having a trapezoidal cross-sectional shape.

<6. When matching circuit is connected in parallel to wave source>
FIG. 14 shows a state in which the matching circuit 22 connected to the antenna 12 is connected to the wave source 21 in parallel. FIG. 15 shows a cross-sectional view along the y-axis. An equivalent circuit diagram of this structure is as shown in FIG. In the case of the illustrated example, a dielectric layer 121 is provided on the substrate 11 including the ground plane, and the antenna 12 and the wiring are provided on the surface of the dielectric layer 121. The wave source 21 is connected to the ground plane 11 at a point P, and is connected to the antenna 12 and the matching circuit 22 at a point Q. The matching circuit 22 is connected to the ground plane 11 at a point S, and is connected to the antenna 12 and the wave source 21 at a point R. For this reason, the wiring passing through the points P, Q, R, and S forms a loop, ring, or ring. The influence of this wiring, line or wire 123 on the electromagnetic field simulation has not been sufficiently considered in the past. As described below, in the disclosed embodiment, the electromagnetic field simulation is performed in consideration of the influence of the wiring.

  Specifically, the matching is performed so that the antenna impedance (Zm) including the influence of the matching circuit viewed from the wave source 21 is equal to the sum of the impedance (Zm ′) of the matching circuit 22 and the wiring impedance (Zw) of the wiring. The impedance (Zm ′) of the circuit 22 needs to be set (Zm = Zm ′ + Zw). In general, the wiring 123 has resistance, capacitance, and inductance, but it is the inductance of the wiring that has a particularly great influence in the electromagnetic field simulation. Accordingly, the wiring inductance (Lw) is obtained, and the inductance (Xm ′) of the matching circuit 22 is set so that the sum of the inductance (Xm ′) of the matching circuit 22 and the wiring inductance (Lw) is equal to the antenna inductance (Xm). By setting (Xm = Xm ′ + Lw), the electromagnetic field simulation can be appropriately executed. The wiring inductance (Lw) is obtained by subtracting the self-inductance LPQ existing between the points P and Q from the loop inductance (loop inductance) LPQRQ formed by the wiring passing through the points P, Q, R, and S. (LW = LPQRS−LPQ). There are various ways to obtain the loop inductance LPQRS. As an example, it can be obtained according to the following equation. This is described, for example, in “Detailed Electromagnetics Exercise”, Kyoritsu Shuppan Co., Ltd., p.277-278.

ここで、Liは線路の自己インダクタンスである。Leは外部インダクタンスである。Mは長方形ループの内側と外側の間の相互インダクタンスである。a、bはループの辺の長さである。μ0は透磁率である。logは自然対数である。rはループをなす導体の半径である。

Here, Li is the self-inductance of the line. Le is the external inductance. M is the mutual inductance between the inside and outside of the rectangular loop. a and b are the lengths of the sides of the loop. μ0 is the magnetic permeability. log is the natural logarithm. r is the radius of the conductor forming the loop.

  Note that a ground plane is not provided on the opposite side (back side) of the dielectric layer 121 to the side where the antenna 12 is provided, but this is not essential, and the antenna 12 and the ground plane 11 have any suitable shape. It may be formed.

<7. When there are multiple matching circuits>
In the description of “6.”, the matching circuit is connected in series between the wave source 21 and the antenna 12. In the description of “7.”, the matching circuit is connected to the wave source 21 in parallel. These may be used alone or in combination.

  FIG. 16 shows an example in which the first matching circuit 22_1 is connected in series between the wave source 21 and the antenna 12, and the second matching circuit 22_2 is connected in parallel to the wave source 21. The disclosed embodiment is not limited to the illustrated example, and may be any suitable form in which one or more matching circuits are provided in series and / or in parallel.

<8. Simulation method>
FIG. 17 shows a flowchart of the simulation method according to the embodiment. The flow begins at step 171. In step 171, a state where no matching circuit is connected to the antenna 12 is set. Alternatively, the impedance of the matching circuit may be set to zero.

  In step 172, the antenna impedance (Zm) including the influence of the matching circuit viewed from the wave source 21 is obtained. The antenna impedance including the influence of the matching circuit corresponds to the point U on the Smith chart as shown in FIG.

  In step 173, the amount of change in impedance necessary for moving the point U to a desired point on the Smith chart is obtained. For convenience of explanation, the amount of change in impedance necessary to move the point U to the point Videal is obtained. As described with reference to FIG. 4, it is necessary to finally match the antenna impedance (Zm) including the influence of the matching circuit to the internal impedance of the wave source. In step 173 of FIG. 17, if the reactance can be changed by Xm while keeping the resistance constant (more generally, if the impedance can be changed by (Zm)), the point U can move to the point Videal. I understand. Unlike the prior art, in the embodiment, the reactance (Xm ′) of the matching circuit necessary for realizing the reactance (Xm) is required. Specifically, the reactance (Xm ′) of the matching circuit is determined so that the reactance (Xm) becomes equal to the sum of the reactance (Xm ′) of the matching circuit and the reactance (Lw) of the wiring. More generally, the impedance (Zm ′) of the matching circuit is determined so that the impedance (Zm) becomes equal to the sum of the impedance (Zm ′) of the matching circuit and the impedance Zw due to the wiring. The reactance (Lw) of the wiring (or the impedance (Zw) of the wiring) can be calculated by the method described in “5.” and “6.” above.

  In step 174, the reactance (Xm ′) (or impedance (Zm ′)) obtained in step 172 is set in the matching circuit connected to the antenna, and electromagnetic field simulation is performed. Since the electromagnetic field simulation is performed in consideration of the reactance (or impedance) of the accompanying wiring in addition to the reactance of the matching circuit, an appropriate matching characteristic can be obtained. As shown in FIG. 18, since the reactance of the matching circuit was conventionally set to (Xm), the antenna impedance including the effect of the matching circuit shown as a result of simulation shows the value indicated by the point W. It was. However, since the reactance of the matching circuit is set to Xm ′ (= Xm−Lw) in the embodiment, the antenna impedance shown as a result of the simulation shows the value indicated by the point Vactual. In this way, the point U can be moved to a point Vactual that is substantially equal to the target point Videal.

<9. Simulation device>
FIG. 19 shows a functional block diagram of a simulation apparatus 190 that executes the method shown in FIG. The simulation apparatus 190 includes an input unit 191, an impedance determination unit 192, an electromagnetic field simulator 193, and an output unit 194.

  The input unit 191 receives various parameter values necessary for performing an electromagnetic field simulation with the simulation apparatus 190. For example, parameters that specify electromagnetic wave frequency, dielectric constant, electrical conductivity, magnetic permeability, magnetic resistance, substrate dimensions (length, thickness, width), wiring dimensions (length, thickness, width), antenna shape, etc. The value of is entered. The input may be performed manually by the user, or may be performed by receiving a value output from some device.

  The impedance determination unit 192 measures the antenna impedance including the effect of the matching circuit as viewed from the wave source when the matching circuit is not connected, and determines the impedance of the matching circuit while considering the impedance of the wiring. The impedance determining unit 192 can determine not only the impedance but also the admittance.

  The electromagnetic field simulator 193 performs electromagnetic field simulation under the condition that the impedance determined by the impedance determination unit is the impedance of the matching circuit. The simulation method (analysis method) may be any suitable method, but is typically the TDFD method or the FI method.

  The output unit 194 visually displays the result of the electromagnetic field simulation, prints it on paper, or outputs the result by any other method. This output also includes electronically transferring the results to other devices.

  As described above, according to the disclosed embodiment, not only the matching circuit but also the impedance of the wiring accompanying the matching circuit is taken into consideration so that the matching circuit can be appropriately modeled in the antenna design stage or the upstream basic examination stage. To be able to do that. Thereby, the trouble of adjusting the impedance of the matching circuit again or performing the electromagnetic field simulation again can be substantially eliminated.

  The method and apparatus for setting the impedance of the matching circuit in consideration of not only the matching circuit but also the influence of the wiring have been described above, but the disclosed embodiments are not limited to such embodiments, and those skilled in the art Will understand various variations, modifications, alternatives, substitutions, and the like. For example, although the description has been made using the Cartesian coordinate system, it is obvious to those skilled in the art that the embodiment can be used for other coordinate systems. Although specific numerical examples have been described to facilitate understanding of the embodiment, these numerical values are merely examples, and any appropriate values may be used unless otherwise specified. In addition, although specific mathematical formulas have been used to facilitate understanding of the embodiment, these mathematical formulas are only examples unless otherwise specified, and other mathematical formulas that yield similar results are used. Also good. The classification of items in the above description is not essential to the disclosed embodiment, and the items described in two or more items may be used in combination as necessary, or are described in a certain item. A matter may apply to a matter described in another item (unless it conflicts). The boundaries between functional units or processing units in the functional block diagram do not necessarily correspond to physical component boundaries. The operations of a plurality of functional units may be physically performed by one component, or the operations of one functional unit may be physically performed by a plurality of components.

It should be noted that in the above description, when terms such as “embodiment”, “one embodiment”, and “embodiment” are used, they do not necessarily all refer to the same form. The disclosed embodiments are not limited to the above-described embodiments, and various modifications, modifications, alternatives, substitutions, and the like will be apparent to those skilled in the art without departing from the spirit of the disclosed embodiments. Such variations, modifications, alternatives, substitutions and the like are intended to be included within the scope of the appended claims.
(Appendix 1)
The antenna impedance seen from the wave source when the matching circuit formed by the lumped constant element is not connected to the antenna, the antenna considering the wiring seen from the wave source when the matching circuit is connected to the antenna through the wiring An impedance determination unit that determines the impedance of the matching circuit so as to be equal to the sum of the impedance and the internal impedance of the wave source;
A simulation apparatus comprising: an electromagnetic field simulator that performs an electromagnetic field simulation on the antenna to which the matching circuit having the determined impedance is connected by solving a discretized Maxwell equation.
(Appendix 2)
The simulation apparatus according to appendix 1, wherein the lumped constant element includes one or more of a resistor, an inductor, and a capacitor.
(Appendix 3)
The simulation device according to appendix 1 or 2, wherein the matching circuit is connected in series between the antenna and the wave source.
(Appendix 4)
The simulation apparatus according to claim 3, wherein an impedance generated by the wiring is approximated by an impedance of a microstrip line.
(Appendix 5)
The simulation device according to appendix 1 or 2, wherein the matching circuit is connected in parallel to the wave source.
(Appendix 6)
The simulation apparatus according to claim 5, wherein the impedance generated by the wiring is obtained by subtracting a self-inductance related to the wave source from an inductance of a loop including the wave source, the wiring, and the matching circuit.
(Appendix 7)
The matching item 1 or 2, wherein the matching circuit includes a first matching circuit connected in series between the antenna and the wave source, and a second matching circuit connected in parallel to the wave source. The simulation apparatus described in 1.
(Appendix 8)
The electromagnetic field simulator uses the time-domain finite difference method or the finite integration method to solve the discretized Maxwell equation, thereby electromagnetically controlling the antenna to which the matching circuit having the determined impedance is connected. 8. The simulation apparatus according to any one of additional items 1 to 7, which executes a boundary simulation.
(Appendix 9)
The simulation device according to any one of appendices 1 to 8, wherein a radius of the wiring is substantially equal to e1 / 2 of a unit length when the Maxwell equation is discretized.
(Appendix 10)
The antenna impedance seen from the wave source when the matching circuit formed by the lumped constant element is not connected to the antenna, the antenna considering the wiring seen from the wave source when the matching circuit is connected to the antenna through the wiring Determining the impedance of the matching circuit to be equal to the sum of the impedance and the internal impedance of the wave source;
A simulation method comprising: performing electromagnetic field simulation on the antenna to which the matching circuit having the determined impedance is connected by solving the discretized Maxwell equation.

11 Board
12 Antenna
13 Wave source and matching circuit
21 wave source
22 Matching circuit
121 Dielectric layer
123 Wiring
190 Simulation equipment
191 Input section
192 Impedance determination unit
193 Electromagnetic simulator
194 Output section

Claims (5)

The antenna impedance seen from the wave source when the matching circuit formed by the lumped constant element is not connected to the antenna, the antenna considering the wiring seen from the wave source when the matching circuit is connected to the antenna through the wiring An impedance determination unit that determines the impedance of the matching circuit so as to be equal to the sum of the impedance and the internal impedance of the wave source;
A simulation apparatus comprising: an electromagnetic field simulator that performs an electromagnetic field simulation on the antenna to which the matching circuit having the determined impedance is connected by solving a discretized Maxwell equation.   The simulation apparatus according to claim 1, wherein the lumped constant element includes one or more of a resistor, an inductor, and a capacitor.   The simulation apparatus according to claim 1, wherein the matching circuit is connected in series between the antenna and the wave source.   The simulation device according to claim 1, wherein the matching circuit is connected in parallel to the wave source. The antenna impedance seen from the wave source when the matching circuit formed by the lumped constant element is not connected to the antenna, the antenna considering the wiring seen from the wave source when the matching circuit is connected to the antenna through the wiring An impedance determining unit determining an impedance of the matching circuit to be equal to a sum of an impedance and an internal impedance of the wave source;
An electromagnetic field simulator executing an electromagnetic field simulation on the antenna to which the matching circuit having the determined impedance is connected by solving a discretized Maxwell equation.

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