JP2009093327A - Apparatus, method and program for analyzing microstrip line - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide an apparatus, a method and a program for analyzing a microstrip line which analyze the characteristic impedance of a microstrip line at high speed with less computer resources, and calculating the cross-sectional size required to achieve a predetermined characteristic impedance. <P>SOLUTION: The apparatus for analyzing a microstrip line 1 includes a base 11 with a dielectric constant ε<SB>sub</SB>and a thickness (h), a surface wiring 13 with a width (w) and a thickness (t), and a surface dielectric 10 with a dielectric constant ε<SB>sr</SB>and a thickness T. The apparatus for analyzing the microstrip line 1 has at least either a first computing means for calculating the effective dielectric constant ε<SB>eff</SB>of the microstrip line 1 using a predetermined relational expression or a second computing means for calculating an undecided structural parameter among structure parameters with a dielectric constant ε<SB>sub</SB>, a thickness (h), a width (w), a thickness (t), a dielectric constant ε<SB>sr</SB>, and a thickness T. <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

  The present invention relates to a microstrip line analysis device, a microstrip line analysis method, and a microstrip line analysis program.

  Among the transmission lines used for printed circuit boards, microstrip lines consisting of a substrate, a surface layer wiring formed on the surface of the substrate, and a ground plane formed on the back surface of the substrate are easily manufactured and densely wired. It is excellent in that it can be used and is widely used.

  Since the surface layer wiring of the microstrip line is located on the surface layer of the substrate, an unintended short circuit or deterioration is likely to occur due to contact with solder or air. For this reason, in order to avoid these short circuits and deterioration, it is common to employ a structure in which a surface layer dielectric is provided on the substrate surface and the surface of the surface layer wiring to protect the wiring. An example of such a surface layer dielectric is a solder resist layer having a thickness of about several tens of μm. The presence of the solder resist layer changes the effective dielectric constant felt by the microwave transmitted to the transmission line, so that the characteristic impedance of the microstrip line changes as compared with the case without the solder resist layer.

  Despite changes in the characteristic impedance when such a solder resist layer is provided, in the microstrip line having the solder resist layer, the microstrip is calculated using a formula for calculating the effective dielectric constant and the characteristic impedance without considering the presence of the solder resist layer. Line characteristic impedance design has been performed. This is due to the following two reasons.

  First, in signal transmission in the low frequency region that has been performed so far, the amount of signal reflection at the characteristic impedance mismatch point is small, and the need for strict impedance design is small.

  Secondly, there are various formulas for calculating the effective dielectric constant in the microstrip line without the solder resist layer, such as analysis by Wheeler using the conformal mapping method and function approximation by MV Schneider (see Non-Patent Document 1). This is because there is no formula generally used as a formula for calculating the effective dielectric constant of the microstrip line provided with the solder resist layer. This is because the presence of a surface layer dielectric such as a solder resist layer makes the boundary conditions very complicated, and it is difficult to analytically determine the electromagnetic field distribution.

  However, with the recent increase in the speed of electronic devices and devices, there is an increasing need to transmit high-frequency signals exceeding 1 GHz to the transmission line on the printed circuit board, and in order to suppress signal reflection due to impedance mismatch, a microstrip line is required. However, it is becoming necessary to design impedance with high accuracy in consideration of the influence of the solder resist layer.

In response to this requirement, for example, Polar Instruments' characteristic impedance calculation software "Si9000" calculates the characteristic impedance of a transmission line with a complex cross-sectional structure by performing a two-dimensional electromagnetic field analysis using the boundary element method. (See Non-Patent Document 2).
M.M. V. MV Schneider, "Microstrip Lines for Microwave Integrated Circuits", Bell Systems Technical Journal, (USA), Vol. 48, 1969, pp. 1421-1444 Polar Instruments, “PCB transmission line field solver for extracting RLGC and s-parameters” [online], [searched on June 28, 2007], Internet <URL http://www.polarinstruments.com/jp/ index.html>

  However, the electromagnetic field analysis method described above can calculate the characteristic impedance of the line from the cross-sectional model of the transmission line, but conversely, in order to obtain the characteristic impedance desired by the designer, the surface wiring or solder resist layer There is a problem that it is not possible to directly calculate what value the cross-sectional dimension should be. As a result, in order to obtain the optimum cross-sectional dimensions of the surface wiring and the solder resist layer, it was necessary to analyze a large number of models having different cross-sectional dimensions and find a model that gives a result close to a desired characteristic impedance.

  Further, the above-described electromagnetic field analysis method has a problem in that it uses a relatively large amount of computer resources and requires a long calculation time.

  The first object of the present invention is to solve the above problems. More specifically, a microstrip line analysis device that can analyze the characteristic impedance of a microstrip line whose surface layer wiring is covered with a surface layer dielectric such as a solder resist layer at a high speed with a small amount of computer resources. An object is to provide a stripline analysis method and a microstripline analysis program.

  Furthermore, the second object of the present invention is made to solve the above-mentioned problems. More specifically, in a microstrip line whose surface layer wiring is covered with a surface layer dielectric such as a solder resist layer, a microstrip line capable of calculating a cross-sectional dimension necessary for realizing a predetermined characteristic impedance An analysis apparatus, a microstrip line analysis method, and a microstrip line analysis program are provided.

A first microstrip line analyzing apparatus of the present invention for solving the above-described problem is a substrate having a thickness h having a relative dielectric constant of ε _sub and a thickness having a width of w provided on the substrate. a microstrip line analysis device having a surface wiring of t and a surface dielectric of thickness T having a relative dielectric constant of ε _sr provided on the surface wiring and the substrate, wherein the relative dielectric constant is The effective dielectric constant ε1 _eff , the relative dielectric constant ε ′, the relative dielectric constant ε _sub when the dielectric having an infinite thickness of ε ′ is provided instead of the surface layer dielectric, When the first relational expression established between the thickness h, the width w, and the thickness t matches the effective dielectric constant ε1 _eff and the effective dielectric constant ε _{eff of the} microstrip line, the relative dielectric constant epsilon ', the dielectric constant epsilon _sub, said thickness h The width w, the thickness t, the relative permittivity epsilon _sr, and using a second relational expression holds between the thickness T, a first calculation for calculating the effective dielectric constant epsilon _eff Means, or among the structural parameters of the relative permittivity ε _sub , the thickness h, the width w, the thickness t, the relative permittivity ε _sr , and the thickness T, there are undecided structural parameters. In this case, the undetermined structural parameter is calculated from the structural parameter other than the undetermined structural parameter and the value of the characteristic impedance of the microstrip line or the value of the effective dielectric constant ε _eff of the microstrip line. It is characterized by having at least one of the calculation means.

A second microstrip line analyzing apparatus of the present invention for solving the above-described problems is a substrate having a thickness h having a relative dielectric constant of ε _sub and a thickness having a width of w provided on the substrate. a microstrip line analyzing apparatus, comprising: a surface layer wiring of t; and a surface layer dielectric having a relative dielectric constant of ε _sr and provided on the surface layer wiring and the substrate; First effective means for calculating the effective dielectric constant ε _{eff of the following} using the following equations (1), (2), (3), or the relative dielectric constant ε _sub , the thickness h, the width w, When there are undecided structural parameters among the structural parameters of the thickness t, the relative dielectric constant ε _sr , and the thickness T, the structural parameters other than the undecided structural parameters, the characteristics of the microstrip line Impedance value or before Effective dielectric constant epsilon _eff value of the microstrip line, and the following formula (1), (2), having the second calculating means for calculating the structural parameters of the pending, at least one of using (3) It is characterized by that.

In a preferred aspect of the microstrip line analysis device of the present invention, when the microstrip line analysis device includes the first calculation unit, the first structural parameter input unit inputs the structural parameter; First calculation result output means for outputting at least the effective dielectric constant ε _eff calculated by the first calculation means.

In a preferred aspect of the microstrip line analysis device of the present invention, the first calculation means has a function of obtaining the characteristic impedance of the microstrip line using the obtained effective dielectric constant ε _eff .

In a preferred aspect of the microstrip line analyzing apparatus of the present invention, the first computing means at least calculates the effective dielectric constant ε from the values of the relative dielectric constant ε _sub and the relative dielectric constant ε _sr for each frequency. _It has a function for _obtaining the frequency dependence of _eff .

In a preferred aspect of the microstrip line analysis device according to the present invention, when the microstrip line analysis device has the second calculation means, a second structure parameter is input to input a structural parameter other than the undetermined structural parameter. At least the structural parameter input means, the characteristic impedance / effective dielectric constant input means for inputting the characteristic impedance or effective dielectric constant ε _eff of the microstrip line, and the undetermined structural parameter calculated by the second computing means And a second calculation result output means for outputting.

The first microstrip line analysis method of the present invention for solving the above-described problem is a substrate having a thickness h having a relative dielectric constant of ε _sub and a thickness having a width of w provided on the substrate. a microstrip line analysis method comprising: a surface wiring of t; and a surface dielectric of thickness T having a relative dielectric constant of ε _sr provided on the surface wiring and the substrate, wherein the relative dielectric constant is The effective dielectric constant ε1 _eff , the relative dielectric constant ε ′, the relative dielectric constant ε _sub when the dielectric having an infinite thickness of ε ′ is provided instead of the surface layer dielectric, When the first relational expression established between the thickness h, the width w, and the thickness t matches the effective dielectric constant ε1 _eff and the effective dielectric constant ε _{eff of the} microstrip line, the relative dielectric constant epsilon ', the dielectric constant epsilon _sub, said thickness h The width w, the thickness t, the relative permittivity epsilon _sr, and using a second relational expression holds between the thickness T, a first calculation for calculating the effective dielectric constant epsilon _eff There are undecided structural parameters among the structural parameters of the step or the relative dielectric constant ε _sub , the thickness h, the width w, the thickness t, the relative dielectric constant ε _sr , and the thickness T. In this case, the undetermined structural parameter is calculated from the structural parameter other than the undetermined structural parameter and the value of the characteristic impedance of the microstrip line or the value of the effective dielectric constant ε _eff of the microstrip line. At least one of the following calculation steps.

The second microstrip line analysis method of the present invention for solving the above-described problem is a substrate having a thickness h having a relative dielectric constant of _εsub and a thickness having a width of w provided on the substrate. a microstrip line analysis method comprising: a surface layer wiring of t; and a surface layer dielectric having a relative dielectric constant of ε _sr and provided on the surface layer wiring and the substrate. A first calculation step of calculating an effective dielectric constant ε _{eff of the following} using the following formulas (1), (2), and (3), or the relative dielectric constant ε _sub , the thickness h, the width w, When there are undecided structural parameters among the structural parameters of the thickness t, the relative dielectric constant ε _sr , and the thickness T, the structural parameters other than the undecided structural parameters, the characteristics of the microstrip line Impedance value or Effective dielectric constant epsilon _eff value of the microstrip line, and the following formula (1), the undetermined second calculation step of calculating the structural parameters of at least one of using (2), (3) It is characterized by having.

In a preferred aspect of the microstrip line analysis method of the present invention, when the microstrip line analysis method includes the first calculation step, the first structural parameter input step for inputting the structural parameter; And a first calculation result output step for outputting at least the effective dielectric constant ε _eff calculated in the first calculation step.

In a preferred aspect of the microstrip line analysis method of the present invention, the first calculation step has a function of obtaining the characteristic impedance of the microstrip line using the obtained effective dielectric constant ε _eff .

In a preferred aspect of the microstrip line analysis method of the present invention, the first calculation step includes at least the effective permittivity ε from the values of the relative permittivity ε _sub and the relative permittivity ε _sr for each frequency. _It has a function for _obtaining the frequency dependence of _eff .

In a preferred aspect of the microstrip line analysis method of the present invention, when the microstrip line analysis method includes the second calculation step, a second structural parameter other than the undetermined structural parameter is input. At least the structure parameter input step, the characteristic impedance / effective dielectric constant input step for inputting the characteristic impedance or effective dielectric constant ε _eff of the microstrip line, and the undetermined structural parameter calculated in the second calculation step And a second calculation result output step of outputting.

A first microstrip line analysis program of the present invention for solving the above-described problem is a substrate having a thickness h having a relative dielectric constant of _εsub and a thickness having a width of w provided on the substrate. A microstrip line analysis program comprising a surface wiring of t and a surface dielectric having a thickness T and having a relative dielectric constant of ε _sr provided on the surface wiring and the substrate, The effective dielectric constant ε1 _eff , the relative dielectric constant ε ′, and the relative dielectric constant when a dielectric having an infinite thickness of ε ′ and an infinite thickness is provided instead of the surface layer dielectric The first relational expression established between ε _sub , the thickness h, the width w, and the thickness t matches the effective dielectric constant ε1 _eff and the effective dielectric constant ε _{eff of the} microstrip line. The relative dielectric constant ε ′, the Permittivity epsilon _sub, said thickness h, using a second relational expression holds between the width w, the thickness t, the relative permittivity epsilon _sr, and the thickness T, the effective dielectric A first calculation processing procedure for calculating a rate ε _eff , or a structure of the relative permittivity ε _sub , the thickness h, the width w, the thickness t, the relative permittivity ε _sr , and the thickness T When there is an undecided structural parameter among the parameters, from the structural parameter other than the undecided structural parameter and the value of the characteristic impedance of the microstrip line or the value of the effective dielectric constant ε _eff of the microstrip line, At least one of a second calculation processing procedure for calculating the undetermined structural parameter is executed.

A second microstrip line analysis program of the present invention for solving the above-described problem is a substrate having a thickness h having a relative dielectric constant of ε _sub and a thickness having a width of w provided on the substrate. A microstrip line analysis program comprising a surface wiring of t and a surface dielectric of thickness T having a relative dielectric constant of ε _sr provided on the surface wiring and the substrate, The first calculation processing procedure for calculating the effective dielectric constant ε _eff of the microstrip line using the equations (1), (2), (3), or the relative dielectric constant ε _sub , the thickness h, If there are undecided structural parameters among the structural parameters of width w, thickness t, relative permittivity ε _sr , and thickness T, structural parameters other than the undecided structural parameters, the microstrip line The characteristic impedance value or effective permittivity epsilon _eff value of the microstrip line, and the following formula (1), (2), the second arithmetic processing procedure for calculating the structural parameters of the non determined using (3) , At least one of the above is executed.

In a preferred aspect of the microstrip line analysis program of the present invention, the first structure parameter for inputting the structure parameter when the microstrip line analysis program causes the computer to execute the first arithmetic processing procedure. The computer is further caused to execute an input processing procedure and a first calculation result output processing procedure for outputting at least the effective dielectric constant ε _eff calculated in the first arithmetic processing procedure.

In a preferred aspect of the microstrip line analysis program of the present invention, in the first calculation processing procedure, the process for obtaining the characteristic impedance of the microstrip line using the obtained effective permittivity ε _eff is performed in the computer. To run.

In a preferred aspect of the microstrip line analysis program of the present invention, in the first arithmetic processing procedure, at least the effective dielectric constant is calculated from the values of the relative dielectric constant ε _sub and the relative dielectric constant ε _sr for each frequency. The computer is caused to execute processing for determining the frequency dependence of ε _eff .

In a preferred aspect of the microstrip line analysis program of the present invention, when the microstrip line analysis program causes the computer to execute the second arithmetic processing procedure, a structural parameter other than the undetermined structural parameter is set. The second structural parameter input processing procedure to be inputted, the characteristic impedance / effective dielectric constant input processing procedure to input the characteristic impedance or effective dielectric constant ε _eff of the microstrip line, and the second arithmetic processing procedure were used. And causing the computer to further execute a second calculation result output processing procedure for outputting at least the undetermined structural parameter.

According to the microstrip line analyzing apparatus of the present invention, since the first calculating means for calculating the effective dielectric constant ε _eff using a predetermined relational expression is provided, the boundary element method used in the method based on the electromagnetic field analysis, etc. As a result, there is provided a microstrip line analysis apparatus capable of performing effective dielectric constant and characteristic impedance analysis of a microstrip line provided with a surface layer dielectric at high speed with less computer resources without performing any complicated calculations. be able to.

According to the microstrip line analyzing apparatus of the present invention, an undecided structure among the structural parameters of relative permittivity ε _sub , thickness h, width w, thickness t, relative permittivity ε _sr , and thickness T. When there is a parameter, from the structural parameter other than this undecided structural parameter, the value of the characteristic impedance of the microstrip line or the value of the effective dielectric constant ε _eff of the microstrip line, using the predetermined relational expression, Since the second calculation means for calculating the undetermined structural parameter is provided, the optimum cross-sectional dimension and material constant that cannot be directly obtained by the electromagnetic field analysis method can be obtained. As a result, the predetermined characteristic impedance can be obtained. A microphone that can directly calculate the cross-sectional dimensions and material constants necessary to realize It is possible to provide an analysis apparatus of the strip line.

According to the microstrip line analysis method of the present invention, since the first calculation step for calculating the effective dielectric constant ε _eff using a predetermined relational expression is included, the boundary element method used in the method based on the electromagnetic field analysis, etc. As a result, there is provided a microstrip line analysis method capable of performing effective dielectric constant and characteristic impedance analysis of a microstrip line provided with a surface layer dielectric at high speed with less computer resources without performing any complicated calculation. be able to.

According to the microstrip line analysis method of the present invention, an undecided structure among the structural parameters of relative permittivity ε _sub , thickness h, width w, thickness t, relative permittivity ε _sr , and thickness T. When there is a parameter, from the structural parameter other than this undecided structural parameter, the value of the characteristic impedance of the microstrip line or the value of the effective dielectric constant ε _eff of the microstrip line, using the predetermined relational expression, Since it has a second calculation step for calculating an undetermined structural parameter, it is possible to obtain the optimum cross-sectional dimensions and material constants that could not be obtained directly by the electromagnetic field analysis method. This makes it possible to directly calculate the cross-sectional dimensions and material constants necessary to realize a high-accuracy line. It is possible to provide a method of analysis cross trip line.

According to the microstrip line analysis program of the present invention, the computer is caused to execute the first calculation processing procedure for calculating the effective dielectric constant ε _eff using a predetermined relational expression. As a result, the effective permittivity and characteristic impedance analysis of the microstrip line provided with the surface dielectric can be performed at high speed with few computer resources without any complicated calculations such as the boundary element method. An analysis program can be provided.

According to the microstrip line analysis program of the present invention, a computer is used to determine whether the relative dielectric constant ε _sub , the thickness h, the width w, the thickness t, the relative dielectric constant ε _sr , and the thickness T are not set. When there is a structural parameter to be determined, from a structural parameter other than this undecided structural parameter and the value of the characteristic impedance of the microstrip line or the value of the effective dielectric constant ε _eff of the microstrip line, using a predetermined relational expression Because the second calculation processing procedure for calculating the above-mentioned undetermined structural parameters is executed, the optimum cross-sectional dimensions and material constants that could not be obtained directly by the electromagnetic field analysis method can be obtained. Therefore, it is possible to directly calculate the cross-sectional dimensions and material constants necessary to achieve a predetermined characteristic impedance, and to handle highly accurate lines. It is possible to provide an analysis program of the microstrip line can be designed.

  Hereinafter, examples of the present invention will be described, but the present invention is not limited to the following examples, and can be arbitrarily modified and implemented without departing from the gist of the present invention.

[Principle of analysis]
FIG. 1 is an example of a schematic cross-sectional view of a microstrip line to be analyzed by a microstrip line analysis apparatus, analysis method, and analysis program of the present invention. As shown in FIG. 1, a microstrip line 1 includes a substrate 11 having a thickness h having a relative dielectric constant ε _sub and a surface layer wiring having a thickness t having a width w provided on one surface of the substrate 11. 13 and a surface layer dielectric 10 having a thickness T and a dielectric constant of ε _sr provided on the surface layer wiring 13 and the substrate 11. In the microstrip line 1, a ground plane 12 is formed on the other surface of the substrate 11 where the surface layer wiring 13 or the like is not provided. The relative dielectric constant ε _{sub of} the substrate 11, the thickness h of the substrate 11, the width w of the surface wiring 13, the thickness t of the surface wiring 13, the relative dielectric constant ε _{sr of} the surface dielectric 10, and the surface dielectric 10 The thickness T is a structural parameter.

  FIG. 2 is a schematic cross-sectional view of a microstrip line having a dielectric having a relative dielectric constant of ε ′ and an infinite thickness instead of a surface dielectric. FIG. 2 is obtained by replacing the surface dielectric 10 in the microstrip line 1 of FIG.

In the microstrip line analysis apparatus, analysis method, and analysis program of the present invention, instead of the surface dielectric 10 of the microstrip line 1 of FIG. 1, the relative dielectric constant shown in FIG. When the infinite dielectric 20 is provided, the effective dielectric constant ε1 _eff of the microstrip line 2, the relative dielectric constant ε ′ of the dielectric 20, the relative dielectric constant ε _sub of the substrate 11, the thickness h of the substrate, and the surface layer A first relational expression established between the width w of the wiring 13 and the thickness t of the surface wiring 13 is used. Furthermore, in the case where the effective dielectric constant epsilon _eff the effective permittivity .epsilon.1 _eff and the microstrip line 1 of the microstrip line 2 is matched, the relative dielectric constant of the dielectric 20 epsilon ', the dielectric constant of the substrate 11 epsilon _sub, substrate 11, a thickness w of the surface layer wiring 13, a thickness t of the surface layer wiring 13, a relative dielectric constant ε _{sr of} the surface layer dielectric 10 and a thickness T of the surface layer dielectric 10. Use an expression. Therefore, the principle of the first calculation for calculating the effective dielectric constant ε _eff and the characteristic impedance using the first relational expression and the second relational expression will be described below. Thereafter, when there is an undetermined structural parameter among the structural parameters, the principle of the second calculation for calculating the undetermined structural parameter using the first relational expression and the second relational expression will be described. .

(Principle of the first calculation)
In the first calculation principle, the effective dielectric constant ε _eff of the microstrip line 1 is calculated. Further, the characteristic impedance Zc of the microstrip line 1 can be further obtained using the effective dielectric constant ε _eff . Therefore, a specific method for calculating the effective dielectric constant ε _eff and the characteristic impedance Zc will be described.

The characteristic impedance Zc can be expressed by the following equation (4) using the effective dielectric constant ε _eff .

In Expression (4), Z ₀ is a characteristic impedance when elements other than the ground plane 12 and the surface wiring 13 are removed and the ground plane 12 and the surface wiring 13 are placed in a vacuum in FIG. 1 or FIG. Equation (4) is established between the characteristic impedance Z _{0 in} vacuum and the characteristic impedance Zc when the ground plane 12 and the surface layer wiring 13 are placed in a uniform medium having an effective relative dielectric constant ε _eff. It is a general relational expression.

Several methods for obtaining the characteristic impedance Z ₀ of the microstrip line placed in a vacuum are known. For example, approximate expressions such as the following expressions (5) and (6) are used. Formula (7) is a correction formula for the wiring width of the surface layer wiring.

The characteristic impedance when a microstrip line having a characteristic impedance Z ₀ in a vacuum is placed in a medium having an effective dielectric constant (effective relative dielectric constant) ε _eff is given by the above equation (4). Therefore, in order to obtain the characteristic impedance of a microstrip line in a non-uniform medium, such as a normal microstrip line in which surface layer wiring is formed on a substrate, the effective relative dielectric constant of the microstrip line due to the distribution of the dielectric material is obtained. What is necessary is _just to obtain _| require a ratio (effective dielectric constant) and substitute the value to Formula (4) as (epsilon) _eff .

The effective relative dielectric constant (effective dielectric constant) when the surface layer wiring 13 is not covered with the dielectric 20 or the surface layer dielectric 10, that is, when the substrate 11 and the surface layer wiring 13 are in contact with air. ε _eff ′ V. It is given by Schneider as an approximate expression shown in the following expression (8).

When the surface layer wiring 13 is exposed to air, the transmitted microwave medium is a substrate having a relative dielectric constant ε _sub and air having a relative dielectric constant of 1. In the equation (8), the first term is an arithmetic average of ε _sub and 1, and the second term which is a correction term based on the structural parameter and the correction for the thickness t of the surface wiring 13 being a finite value. It consists of the third term.

In the present invention, first, a case where the air portion is filled with a dielectric having a relative dielectric constant ε ′ will be considered. This is a state in which a dielectric 20 having a relative dielectric constant ε ′ and an infinite thickness is provided on the surface wiring 13 and the substrate 11 as in the microstrip line 2 of FIG. In the microstrip line 1, a dielectric 20 having a relative dielectric constant ε ′ and an infinite thickness is provided in place of the surface dielectric 10. In this case, the effective relative dielectric constant (effective dielectric constant) ε1 _eff is obtained by extending Equation (8) to the form of Equation (9), which is obtained by adding a correction term to the arithmetic mean of ε _sub and ε ′. It can be expressed as

As described above, the microstrip line 2 in FIG. 2 is a model of electromagnetic field analysis performed to confirm the above idea, and the region above the surface wiring 13 is formed by the dielectric 20 having a relative dielectric constant ε ′. Fully covered. FIG. 3 is a graph in which the relative dielectric constant ε ′ obtained from the electromagnetic analysis model setting value and the relative dielectric constant ε ′ calculated from the approximate expression are plotted. Specifically, in FIG. 3, the horizontal axis represents the value of the relative permittivity ε ′ set in the dielectric 20 during the electromagnetic field analysis, and the vertical axis represents the relationship of Equation (4) from the characteristic impedance of the electromagnetic field analysis result. Further, the values obtained for the relative dielectric constant ε ′ using the formula (5) or the formula (6), the formula (7), and the formula (9) are plotted, respectively. If equation (9) is valid, these two ε's match and the plot should be on a straight line with slope 1. Actually, if FIG. 3 is seen, both plots are almost completely on a straight line with a slope of 1. From this, it can be seen that the expansion of equation (9) is sufficiently valid. Equation (9) indicates that the dielectric 20 having a relative dielectric constant ε ′ and an infinite thickness is provided in place of the surface dielectric 10, and the effective dielectric constant ε1 _eff , ratio It can be seen that this is the first relational expression that holds among the dielectric constant ε ′, the relative dielectric constant ε _sub , the thickness h, the width w, and the thickness t. The structural parameters used in the electromagnetic field analysis are ε _sub = 4.29, h = 200 μm, w = 90 μm, t = 35 μm.

On the other hand, since the surface dielectric 10 such as the solder resist layer has a finite thickness T as shown in FIG. 1, the relative dielectric constant ε _sr of the surface dielectric 10 is directly used as the relative dielectric constant in the equation (9). Cannot be used as ε '. However, the transmission characteristics of the microstrip line 1 of FIG. 1 covered with the surface dielectric 10 having a finite thickness T and relative dielectric constant ε _sr and the surface dielectric 10 are removed, and the thickness is infinite and the relative dielectric constant. When the transmission characteristics of the microstrip line 2 in FIG. 2 replaced by the dielectric 20 having the rate ε ′ coincide with each other, more specifically, the effective dielectric constant ε1 _eff of the equation (9) and the microstrip line 1 If the relative permittivity ε ′ of the dielectric 20 when the effective permittivity ε _eff matches can be expressed as a function of the relative permittivity ε _sr and the thickness T of the surface dielectric 10, its function ε ′ ( By substituting ε _sr , T) into equation (9), the effective dielectric constant ε _eff can be obtained from the structural parameters of the surface dielectric 10.

  In the present invention, the formula (2) and the formula (3) are used as a monotonically increasing function regarding the thickness T of the surface dielectric 10, and the formula (9) can be expanded as the formula (1).

  In the expressions (2) and (3), α, β, a, b, c, and d are constants. More specifically, α, β, a, b, c, and d are constants that do not depend on structural parameters, which are introduced in order to match the calculation result of this approximate expression with the actual measurement value or the result of electromagnetic field analysis. is there. The parameters α and β can be appropriately determined by actual measurement or electromagnetic field analysis. Here, α = 2.2 and β = −0.2. Parameters a, b, c, and d are also determined by actual measurement or electromagnetic field analysis. An example of the determination method will be described below.

  First, with respect to four microstrip lines having different values of T / t, from the characteristic impedance calculated by measuring the reflected signal in the time domain or performing electromagnetic field analysis, the equations (4), (1), ( 5) or using the formula (6) and the formula (7), the relative dielectric constant ε ′ corresponding to four different structures is calculated. Next, the parameters a, b, c, and d can be determined by substituting these four sets of structural parameters and the relative dielectric constant ε ′ into the equations (2) and (3) to solve the simultaneous equations.

FIG. 4 is a graph showing the relationship between T / t and effective dielectric constant ε _eff, and FIG. 5 is another graph showing the relationship between T / t and effective dielectric constant ε _eff . Specifically, FIGS. 4 and 5 show the case where the parameters a, b, c, and d obtained by the above method are 0.076, 0.291, 0.135, and 1.651, respectively. equation (1), equation (2), and that the effective permittivity epsilon _{eff (approximate} expression calculation result) calculated from equation (3), the effective dielectric constant epsilon _{eff (electromagnetic} calculated from S parameter of the electromagnetic field analysis results (Analysis results) are shown in comparison with each other.

The curves drawn in FIGS. 4 and 5 represent the dependence of the effective dielectric constant ε _eff calculated from the equations (1), (2), and (3) on the thickness T of the surface dielectric 10. On the other hand, the points plotted in FIGS. 4 and 5 are the effective dielectrics calculated from the electromagnetic field analysis S-parameters obtained by setting the thickness T of the surface dielectric 10 to several values in the microstrip line 1 of FIG. The rate ε _eff is plotted. 4 and 5 show the analysis results when the relative dielectric constant ε _sr of the surface dielectric 10 is 4 and 5. The different types of curves in FIG. 4 represent the results when the width w of the surface wiring 13 is changed. 4 and 5, the relative dielectric constant ε _{sub of} the substrate 11 and the thickness h of the substrate 11 are ε _sub = 4.29 and h = 200 μm, respectively.

4 and 5, the effective dielectric constant ε _eff calculated using the equations (1), (2), and (3) is a structural parameter T / t, w that defines the microstrip line 1. It can be seen that even when / t and ε _sr are changed, it matches the effective dielectric constant ε _eff obtained from the electromagnetic field analysis with very high accuracy. Then, equation (1) to (3), if the effective dielectric constant epsilon _eff the effective permittivity .epsilon.1 _eff and the microstrip line 1 of the microstrip line 2 is matched, the relative dielectric constant epsilon ', the dielectric constant epsilon _It can be seen that the second relational expression is established among _sub , thickness h, width w, thickness t, relative dielectric constant ε _sr , and thickness T.

Therefore, the microstrip line analysis apparatus, the microstrip line analysis method, and the microstrip line analysis program according to the present invention are performed using the method for calculating the effective dielectric constant ε _eff using the analysis principle described above. And the effective dielectric constant ε _eff calculated from the formula (1), the formula (2), and the formula (3), the characteristic impedance Z _{0 in} vacuum obtained by the formula (5) or the formula (6), Is used to calculate the characteristic impedance Zc with high accuracy from the data such as the structural parameters of the microstrip line 1. However, the calculation of the characteristic impedance Z ₀ of the vacuum is not necessarily the formula (5) need not be determined by Equation (6) may be used a formula other methods known to the other general.

In addition, the values of the parameters α, β, a, b, c, and d used here closely reproduce the effective dielectric constant ε _eff calculated from the electromagnetic field analysis. It is not restricted to the value shown by. Even when other values are used, although there is a difference in accuracy, there is no influence on the essential effect of the present invention that the characteristic impedance Zc is calculated at high speed using an approximate expression.

  Furthermore, in the above description, by replacing the relative permittivity 1 of air with the relative permittivity ε ′ of the dielectric 20, the approximate expression of the effective permittivity of the generally known formula (8) is changed to the form of the formula (9). Further, the equations (2) and (3) are used as monotonically increasing functions related to the thickness T of the surface dielectric 10, and the equation (9) is expanded as the equation (1). Such an extension enables analysis of the microstrip line 1 having the surface dielectric 10. However, the approximate expression for the effective dielectric constant is not necessarily in the form of the equation (8), and other approximate expressions for the effective dielectric constant can naturally be extended by the same concept. Also in this case, the value of ε ′ may be obtained by using the equations (2) and (3).

(Principle of the second calculation)
The principle of the second calculation is used when determining the structural parameters of the microstrip line 1. That is, in the principle of the second calculation, structural parameters (relative permittivity ε _sub of substrate 11, thickness h of substrate 11, width w of surface wiring 13, thickness t of surface wiring 13, surface dielectric 10 The undetermined structural parameters of the dielectric constant ε _sr and the thickness T of the surface dielectric 10 are determined. Here, “undecided structural parameter” means an undecided structural parameter, an unknown structural parameter, or the like. Then, the undetermined structural parameter is calculated from the structural parameter other than the undetermined structural parameter and the value of the characteristic impedance Zc of the microstrip line 1 or the value of the effective dielectric constant ε _eff of the microstrip line. The characteristic impedance Zc and the effective dielectric constant ε _eff may be determined as a desired value (design target value) for the microstrip line 1 or may be obtained by actual measurement.

The undetermined structural parameters are the relative dielectric constant ε _{sub of} the substrate 11, the thickness h of the substrate 11, the width w of the surface wiring 13, the thickness t of the surface wiring 13, the relative dielectric constant ε _sr of the surface dielectric 10, and Any of the thickness T of the surface dielectric 10 may be sufficient. Therefore, hereinafter, as a specific example, a case where the width w of the surface layer wiring 13 is an undetermined structural parameter and a case where the relative dielectric constant ε _sr of the surface layer dielectric 10 is an undetermined structural parameter will be described.

When designing the microstrip line 1 of FIG. 1, the relative permittivity ε _{sub of} the substrate 11, the thickness h of the substrate 11, the height t of the surface layer wiring 13, and the ratio of the surface layer dielectric 10 are actually used for the convenience of materials. The dielectric constant ε _sr and the thickness T of the surface dielectric 10 are often not easily changed. In such a case, a desired characteristic impedance Zc is often realized by setting the width w of the surface layer wiring 13 to an optimum value. In such a case, using the first relational expression and the second relational expression, the width w of the surface layer wiring 13 which is an undetermined structural parameter is set as the remaining structural parameter (relative dielectric constant ε of the substrate 11). _sub , thickness h of the substrate 11, height t of the surface layer wiring 13, relative dielectric constant ε _{sr of} the surface layer dielectric 10, and thickness T of the surface layer dielectric 10) and the desired impedance Zc for the microstrip line 1 Is calculated from the value of (design target value). Thereby, the optimum width w of the surface layer wiring 13 for realizing the characteristic impedance Zc required for the microstrip line 1 can be determined.

In the actually manufactured microstrip line 1, the relative dielectric constant ε _sr of the surface dielectric 10 used may be unknown. In such a case, using the first relational expression and the second relational expression, the relative dielectric constant ε _sr that is an undetermined structural parameter is changed to the remaining structural parameter (the relative dielectric constant ε _{sub of} the substrate 11, The thickness h of the substrate 11, the width w of the surface wiring 13, the height t of the surface wiring 13, and the thickness T of the surface dielectric 10, and the characteristic impedance Zc of the microstrip line 1 obtained by actual measurement or It is calculated from the value of the effective dielectric constant ε _eff of the microstrip line obtained by actual measurement. By using the data of the characteristic impedance Zc or the effective dielectric constant ε _eff thus measured, the relative dielectric constant ε _sr of the surface dielectric 10 can be known.

Since the first relational expression and the second relational expression are as described above, the description here is omitted to avoid duplication of explanation. Specifically, the structural parameters other than the undecided structural parameters and the characteristic impedance Zc or effective dielectric constant ε _eff of the microstrip line 1 are substituted into the above equations (1) to (4), respectively, and the equations ( 5) or by substituting predetermined data into the characteristic impedance Z ₀ in vacuum represented by the formula (6) and solving these simultaneous equations for the undecided structural parameters, the optimum undecided structural parameters or unknown The undetermined structural parameters that were Using this analysis principle, the microstrip line analysis device, microstrip line analysis method, and microstrip line analysis program of the present invention may be configured.

Note that the calculation of the characteristic impedance Z ₀ in vacuum is not necessarily calculated by the equations (5) and (6), and other generally known calculation equations and other methods may be used. This is the same as the case of the principle.

  Furthermore, in the calculation of the undetermined structural parameter, by replacing the relative dielectric constant 1 of air with the relative dielectric constant ε ′ of the dielectric 20, an approximate expression for the effective dielectric constant of the generally known expression (8) 9), and using equations (2) and (3) as a monotonically increasing function with respect to the thickness T of the surface dielectric 10, the equation (9) is expanded to the equation (1) Yes. Such an extension enables analysis of the microstrip line 1 having the surface dielectric 10. However, as in the case of the first calculation principle, the original approximate expression of the effective dielectric constant does not necessarily need to be in the form of the expression (8). Naturally, expansion is also conceivable. Also in this case, the value of ε ′ may be obtained by using the equations (2) and (3).

[Microstrip line analyzer]
The microstrip line analyzing apparatus of the present invention is intended to analyze the microstrip line 1 of FIG. Then, as described in the principle of the first calculation and the principle of the second calculation, the first calculation for calculating the effective dielectric constant ε _eff using the first relational expression and the second relational expression. If there is an undecided structural parameter among the means or structural parameters, the structural parameter other than the undecided structural parameter, the characteristic impedance value of the microstrip line or the effective dielectric constant ε _eff At least one of the second calculation means for calculating the undetermined structural parameter. In other words, the microstrip line analyzing apparatus of the present invention has either one of the first calculation means and the second calculation means, or both the first calculation means and the second calculation means. .

The principle of calculation for calculating the effective dielectric constant ε _eff by the first calculation means using the first relational expression and the second relational expression described above is as described above. More specifically, the relationship between the effective dielectric constant ε _eff and the characteristic impedance Zc of the microstrip line 1 in which the surface layer wiring 13 is covered with the surface layer dielectric 10 shown in FIG. A relational expression that approximately represents is prepared. Then, using this relational expression, predetermined parameters are input, and the corresponding dielectric constant ε _eff and characteristic impedance Zc are calculated.

Further, the principle of calculation for calculating the undetermined structural parameter by the second calculation means using the first relational expression and the second relational expression described above is also as described above. Specifically, the relationship between the effective dielectric constant ε _eff and characteristic impedance Zc of the microstrip line 1 in which the surface wiring 13 is covered with the surface dielectric 10 shown in FIG. Prepare a relational expression expressed approximately. Then, using this relational expression, the characteristic impedance Zc or effective dielectric constant ε _eff , which is a design target value or an actual measurement value, and each data of known structural parameters are input, and a predetermined characteristic impedance Zc or effective dielectric constant ε _eff is obtained. Calculate the undetermined structural parameters necessary for realization.

  Therefore, specific examples of the microstrip line analysis device having the first calculation means and the microstrip line analysis device having the second calculation means using the above principle will be described below.

(A microstrip line analyzing device having a first computing means)
FIG. 6 is a block diagram functionally showing a configuration of an example of a microstrip line analyzing apparatus having the first arithmetic means. The microstrip line analysis apparatus 100 having the first calculation means includes first structural parameter input means, first calculation means, and first calculation result output means.

The first structural parameter input means has a function of inputting a structural parameter. More specifically, in the first structural parameter input means, the structural parameters of the microstrip line 1 of FIG. 1 (relative permittivity ε _{sub of} the substrate 11, thickness h of the substrate 11, width w of the surface wiring 13, surface layer) Input and recognition of the height t of the wiring 13, the relative dielectric constant ε _{sr of} the surface dielectric 10, and the thickness T of the surface dielectric 10 are performed. Here, the frequency dependence of the relative permittivity ε _sub of the substrate 11 and the relative permittivity ε _sr of the surface dielectric 10 is input, and the first structure parameter input means inputs the relative permittivity ε _sub and the ratio for each frequency. The value of the dielectric constant ε _sr may be recognized.

The first calculation means has a function of calculating the effective dielectric constant ε _eff using the first relational expression and the second relational expression described above. Specifically, the first calculation means calculates the effective dielectric constant ε _eff of the microstrip line 1 using equations (1), (2), and (3). The first calculation means has a function of further obtaining the characteristic impedance Zc of the microstrip line 1 using the obtained effective dielectric constant ε _eff . More specifically, the first calculation means includes the characteristic impedance Zc from the equation (5) or (6), the equation (7), the equation (4), and the value of the obtained effective dielectric constant ε _eff. The function to calculate is added. The frequency dependence of the relative dielectric constant ε _sub of the substrate 11 and the relative dielectric constant ε _sr of the surface dielectric 10 is input, and the first structural parameter input means performs the relative dielectric constant ε _sub and relative dielectric constant for each frequency. When the input of the data of the rate ε _sr is recognized, the first calculation means repeatedly calculates the effective dielectric constant ε _eff and the characteristic impedance Zc for each frequency. As described above, the first calculation means also has a function of obtaining the frequency dependence of the effective dielectric constant ε _eff and the characteristic impedance Zc.

The first calculation result output unit has a function of outputting the effective dielectric constant ε _eff and the characteristic impedance Zc calculated by the first calculation unit.

  FIG. 7 is a schematic explanatory diagram illustrating an example of a hardware configuration of a microstrip line analyzer. The microstrip line analysis apparatus 100 having the first calculation means includes a recording medium 206 on which a microstrip line analysis program or data of the present invention is recorded, and an analysis apparatus 200. The analysis device 200 includes an input / output device 201 that inputs and outputs data, a memory 202 that records a read program or data, an arithmetic device 203 that controls the entire analysis device 200 and performs processing such as calculation. , And a display device 204 that outputs a calculation result. A path 205 indicates a path for connecting the above units.

  The first structural parameter input means includes an input / output device 201 in the microstrip line analysis apparatus 100 having the first arithmetic means. The input / output device 201 inputs data values such as structure parameters and recognizes the input.

  The first calculation means includes a memory 202, a recording medium 206, and a calculation device 203 in the microstrip line analysis device 100 having the first calculation means. The various functions of the first computing means are performed by the computing device 203 executing command processing according to the commands described in the microstrip line analysis program of the present invention recorded in the memory 202 or the recording medium 206. Realized.

The first calculation result output means includes the display device 204 and the input / output device 201 in the microstrip line analysis device 100 having the first calculation means. Then, the calculated effective dielectric constant ε _eff and characteristic impedance Zc are displayed on the display device 204 in the form of a numerical value or a graph such as frequency dependency. Further, a printer or the like may be used as an output device of the input / output device 201, and the calculated results of the effective dielectric constant ε _eff and the characteristic impedance Zc may be printed.

FIG. 9 is a flowchart showing the processing procedure of the microstrip line analyzer having the first computing means. In the flowchart of FIG. 9, first, information related to the structure parameter is input (step S301). In step S301, the frequency dependence of the relative dielectric constant ε _sub of the substrate 11 and the relative dielectric constant ε _sr of the surface dielectric 10 may be input. Next, the effective dielectric constant ε _eff and characteristic impedance Zc are calculated based on the given structural parameters (step S302). Here, if the values of the relative dielectric constants ε _sub and ε _sr are input in step S301 for each frequency, it is determined in step S303 whether the calculation has been completed for all frequencies, and uncalculated frequencies. If there is, the calculation in step S302 is repeated. The calculated effective dielectric constant ε _eff and characteristic impedance are output (step S304), and all the processes are terminated. In step 304, the effective dielectric constant ε _eff and characteristic impedance Zc at each frequency may be output.

(A microstrip line analysis device having a second calculation means)
FIG. 8 is a block diagram functionally showing a configuration of an example of a microstrip line analyzing apparatus having the second arithmetic means. The microstrip line analyzing apparatus 101 having the second calculation means includes a second structural parameter input means, a characteristic impedance / effective dielectric constant input means, a second calculation means, and a second calculation result output means. Have. As shown in FIG. 7, the hardware configuration of the microstrip line analysis apparatus 101 having the second calculation means is the same as that of the microstrip line analysis apparatus 100 having the first calculation means. Can do.

  The second structural parameter input means has a function of inputting values of structural parameters (determined structural parameters) other than undecided structural parameters. Specifically, the second structural parameter input means inputs and recognizes the structural parameter determined in the microstrip line 1 of FIG. On the hardware configuration of the microstrip line analysis apparatus 101 having the second calculation means, the input / recognition of the determined structural parameter is performed by the input / output apparatus 201 of FIG.

The characteristic impedance / effective dielectric constant input means is a value of the characteristic impedance Zc as a design target value or actual measurement value of the microstrip line 1, or a value of the effective dielectric constant ε _eff as a design target value or actual measurement value of the microstrip line 1. Has the function of inputting. Here, the design target value is a value of the desired characteristic impedance Zc that the microstrip line 1 should have or a value of the effective dielectric constant ε _eff , and the actually measured value is actually obtained in the obtained microstrip line 1. It refers to the value of the characteristic impedance Zc to be measured or the value of the effective dielectric constant ε _eff . Specifically, the characteristic impedance / effective dielectric constant input means inputs and recognizes the value of the characteristic impedance Zc or the value of the effective dielectric constant ε _eff . On the hardware configuration of the microstrip line analysis device 101 having the second calculation means, the input / recognition device 201 in FIG. 7 inputs and recognizes the value of the characteristic impedance Zc or the value of the effective dielectric constant ε _eff .

The second computing means uses the first relational expression and the second relational expression described above, and when there is an undecided structural parameter in the structural parameter, a structural parameter other than the undecided structural parameter, And the function of calculating the above-mentioned undetermined structural parameter from the value of the characteristic impedance Zc of the microstrip line 1 or the value of the effective dielectric constant ε _eff of the microstrip line 1. Specifically, in the second calculation means, the structural parameter other than the undecided structural parameter, the value of the characteristic impedance of the microstrip line 1 or the value of the effective dielectric constant ε _eff of the microstrip line 1, and the formula (1) , (2), (3) are used to calculate undetermined structural parameters. The details of the calculation method are as described above, but the formulas (1) to (4) and the formula for calculating the characteristic impedance Z ₀ in vacuum represented by formula (5) or formula (6) Substituting the data input to, and solving these simultaneous equations for undetermined parameters, undetermined structural parameters are obtained. On the hardware configuration of the microstrip line analysis apparatus 101 having the second arithmetic means, the function of the second arithmetic means is that of the microstrip line of the present invention recorded in the memory 202 or the recording medium 206 of FIG. This is realized by the arithmetic unit 203 executing instruction processing in accordance with instructions described in the analysis program.

  The second calculation result output unit has a function of outputting the undetermined structural parameter calculated by the second calculation unit. On the hardware configuration of the microstrip line analysis device 101 having the second calculation means, the function of the second calculation result output means is to display the calculated undecided structural parameters on the display device 204 in FIG. It is realized by displaying in the form of etc. In addition, the function of the second calculation result output unit may print the result of the calculated undetermined structural parameter using a printer or the like as the output device of the input / output device 201.

FIG. 10 is a flowchart showing a processing procedure of the microstrip line analyzing apparatus having the second calculating means. In the flowchart of FIG. 10, first, a structural parameter that has already been determined, a characteristic impedance Zc, or an effective dielectric constant ε _eff are input (step S401). Here, a design target value or an actual measurement value is used for the characteristic impedance Zc and the effective dielectric constant ε _eff . Next, based on the given structural parameter and the characteristic impedance Zc or effective dielectric constant ε _eff , calculation of the value of the undetermined structural parameter (step S402) is executed. Then, the calculated undetermined structural parameter is output (step S403), and all the processes are terminated.

[Microstrip line analysis method]
The microstrip line analysis method of the present invention is intended to analyze the microstrip line 1 of FIG. Then, using the first relational expression and the second relational expression described above, there is an undecided structural parameter in the first calculation step for calculating the effective dielectric constant ε _eff or the structural parameter. In this case, the undetermined structural parameter is calculated from the structural parameter other than the undetermined structural parameter and the value of the characteristic impedance of the microstrip line 1 or the effective dielectric constant ε _eff of the microstrip line 1. And at least one of two calculation steps. That is, the microstrip line analysis method of the present invention includes either one of the first calculation step and the second calculation step, or both the first calculation step and the second calculation step. .

The principle of calculation for calculating the effective dielectric constant ε _eff in the first calculation step using the first relational expression and the second relational expression is as described above. For this reason, description here is abbreviate | omitted in order to avoid duplication of description.

  Further, the principle of the calculation for calculating the undetermined structural parameter in the second calculation step using the first relational expression and the second relational expression is also as described above. For this reason, description here is abbreviate | omitted in order to avoid duplication of description.

  The microstrip line analysis method of the present invention can be implemented by operating the microstrip line analysis apparatus of the present invention described above. For example, the first calculation means in the microstrip line analysis device 100 shown in FIGS. 6 and 7 operates to function as a first calculation step, and the microstrip line analysis device shown in FIGS. The second calculation means in 101 functions, and functions as a second calculation step. Various other means also function as various steps by operating each other. More specifically, the microstrip line analysis method is realized by executing a prepared microstrip line analysis program of the present invention on a computer such as a personal computer or a workstation. The above program is recorded on a computer-readable recording medium such as a hard disk, CD-ROM, or DVD, and is executed by being read from the recording medium by the computer. In the following, in order to avoid duplication with the description of the microstrip line analysis device, typical methods in the microstrip line analysis method having the first calculation step and the microstrip line analysis method having the second calculation step are used. Explain matters.

(Method for analyzing microstrip line having first calculation step)
The microstrip line analysis method having the first calculation step includes a first structural parameter input step, a first calculation step, and a first calculation result output step. In the first structural parameter input step, structural parameters are input. In the first calculation step, the effective dielectric constant ε _eff is calculated using the first relational expression and the second relational expression described above. Specifically, in the first calculation step, the effective dielectric constant ε _eff of the microstrip line 1 is calculated using equations (1), (2), and (3). In the first calculation result output step, at least the effective dielectric constant ε _eff calculated in the first calculation step is output.

In the microstrip line analysis method having the first calculation step, the first calculation step has a function of obtaining the characteristic impedance Zc of the microstrip line 1 using the obtained effective dielectric constant ε _eff. Good. In the first calculation step, the frequency dependence of the effective dielectric constant ε _eff is obtained from the values of the relative dielectric constant ε _sub of the substrate 11 and the relative dielectric constant ε _sr of the surface layer dielectric 10 for each input frequency. Further, the frequency dependence of the characteristic impedance Zc may be obtained. Then, in the first calculation result output step, the characteristic impedance Zc calculated in the first calculation step may be output.

(Method for analyzing microstrip line having second calculation step)
A microstrip line analysis method having a second calculation step includes a second structural parameter input step, a characteristic impedance / effective dielectric constant input step, a second calculation step, a second calculation result output step, Have

In the second structural parameter input step, structural parameters other than the undecided structural parameters are input. In the characteristic impedance / effective dielectric constant input step, the value of the characteristic impedance Zc or the value of the effective dielectric constant ε _eff as the design target value or the actual measurement value of the microstrip line 1 is input. Here, the design target value is a value of the desired characteristic impedance Zc that the microstrip line 1 should have or a value of the effective dielectric constant ε _eff , and the actually measured value is actually obtained in the obtained microstrip line 1. It refers to the value of the characteristic impedance Zc to be measured or the value of the effective dielectric constant ε _eff .

In the second calculation step, when there is an undecided structural parameter using the first relational expression and the second relational expression described above, a structural parameter other than the undecided structural parameter, Then, the above-described undetermined structural parameter is calculated from the value of the characteristic impedance Zc of the microstrip line 1 or the value of the effective dielectric constant ε _eff . More specifically, in the second calculation step, the structural parameters other than the undecided structural parameters, the value of the characteristic impedance Zc or the value of the effective dielectric constant ε _eff of the microstrip line 1, and the expressions (1) and (2 ) And (3) are used to calculate undetermined structural parameters. In the second calculation result output step, the undetermined structure parameter calculated in the second calculation step is output.

[Microstrip line analysis program]
The microstrip line analysis program of the present invention analyzes the microstrip line 1 of FIG. Then, the computer uses the first relational expression and the second relational expression described above, and the first arithmetic processing procedure for calculating the effective dielectric constant ε _eff , or the structure parameter that has not yet been determined. When there is a structural parameter, the second structural parameter is calculated from the structural parameter other than the undecided structural parameter and the value of the characteristic impedance or effective dielectric constant ε _eff of the microstrip line. At least one of the arithmetic processing procedures is executed. In other words, the microstrip line analysis program of the present invention allows a computer to execute either the first arithmetic processing procedure or the second arithmetic processing procedure, or the first arithmetic processing procedure and the second arithmetic processing procedure. Both are supposed to be executed.

The principle of the calculation for calculating the effective dielectric constant ε _eff in the first calculation processing procedure using the first relational expression and the second relational expression is as described above. More specifically, the relationship between the effective dielectric constant ε _eff and the characteristic impedance Zc of the microstrip line 1 in which the surface layer wiring 13 is covered with the surface layer dielectric 10 shown in FIG. A relational expression that approximately represents is prepared. Then, the computer is caused to execute processing for calculating the corresponding dielectric constant ε _eff and characteristic impedance Zc from the input predetermined parameters using the above relational expression.

Further, the principle of calculation for calculating an undetermined structural parameter in the second calculation processing procedure using the first relational expression and the second relational expression is also as described above. Specifically, the relationship between the effective dielectric constant ε _eff and characteristic impedance Zc of the microstrip line 1 in which the surface wiring 13 is covered with the surface dielectric 10 shown in FIG. Prepare a relational expression expressed approximately. Then, using the above relational expression, the computer inputs a predetermined characteristic impedance Zc or effective dielectric constant ε _{eff from} a characteristic impedance Zc or effective dielectric constant ε _eff that is an inputted design target value or actual measurement value and a known structural parameter. A process for calculating an undetermined structural parameter necessary for realizing _eff is executed.

  The microstrip line analysis program of the present invention is used to operate the microstrip line analysis apparatus of the present invention described above. Then, the microstrip line analysis apparatus of the present invention operates, and the microstrip line analysis method of the present invention is implemented. For example, when the computer executes the first calculation processing procedure, the first calculation means in the microstrip line analysis apparatus 100 shown in FIGS. 6 and 7 operates, and the microstrip line analysis method of the present invention is performed. The first calculation step will be performed. Similarly, when the computer executes the second calculation processing procedure, the second calculation means in the microstrip line analysis apparatus 101 shown in FIGS. 7 and 8 operates, and the microstrip line of the present invention is operated. The second calculation step of the analysis method will be performed. The relationship between other various processing procedures and means and steps is also the same. More specifically, the microstrip line analysis program is realized by being executed by a computer such as a personal computer or a workstation. This program is recorded on a computer-readable recording medium such as a hard disk, CD-ROM, or DVD, and is executed by being read from the recording medium by the computer. In the following, in order to avoid duplication with the description of the microstrip line analysis device, a representative of the microstrip line analysis program having the first arithmetic processing procedure and the microstrip line analysis program having the second arithmetic processing procedure Explain specific matters.

(A microstrip line analysis program having a first arithmetic processing procedure)
A microstrip line analysis program having a first arithmetic processing procedure causes a computer to execute a first structural parameter input processing procedure, a first arithmetic processing procedure, and a first calculation result output processing procedure. .

  In the first structural parameter input processing means, the structural parameters are input and recognized by a computer.

In the first calculation processing procedure, a process for causing the computer to calculate the effective dielectric constant ε _eff using the first relational expression and the second relational expression described above is performed. Specifically, in the first calculation processing procedure, processing is performed for causing the computer to calculate the effective dielectric constant ε _eff of the microstrip line 1 using the equations (1), (2), and (3). In the first calculation result output processing procedure, the computer causes at least the output processing of the effective dielectric constant ε _eff calculated in the first calculation processing procedure.

The microstrip line analysis program having the first calculation processing procedure uses a computer to perform a process for obtaining the characteristic impedance Zc of the microstrip line 1 using the effective dielectric constant ε _eff obtained in the first calculation processing procedure. It may be executed. Further, in the first calculation processing procedure, at least the frequency dependence of the effective dielectric constant ε _eff from the input values of the relative dielectric constant ε _sub of the substrate 11 and the relative dielectric constant ε _sr of the surface dielectric 10. May be executed by the computer, and further, the computer may be executed to determine the frequency dependence of the characteristic impedance Zc. Then, in the first calculation result output processing procedure, the computer may output the characteristic impedance Zc calculated in the first calculation processing procedure.

(A microstrip line analysis program having a second arithmetic processing procedure)
A microstrip line analysis program having a second arithmetic processing procedure is stored in a computer by a second structural parameter input processing procedure, a characteristic impedance / effective dielectric constant input processing procedure, a second arithmetic processing procedure, The calculation result output processing procedure is executed.

In the second structural parameter input processing procedure, a structural parameter other than an undetermined structural parameter is input to and recognized by the computer. In the characteristic impedance / effective dielectric constant input processing procedure, the computer inputs and recognizes the value of the characteristic impedance Zc or the value of the effective dielectric constant ε _eff as the design target value or actually measured value of the microstrip line 1. Here, the design target value and the actual measurement value are as described above.

In the second calculation processing procedure, when there are undecided structural parameters in the structural parameter using the first relational expression and the second relational expression described above, the computer other than the undecided structural parameters. Calculation of the above-mentioned undetermined structural parameter is executed from the value of the structural parameter and the value of the characteristic impedance Zc of the microstrip line 1 or the value of the effective dielectric constant ε _eff . More specifically, in the second arithmetic processing procedure, the computer is caused to receive a structural parameter other than the undecided structural parameter, the value of the characteristic impedance Zc of the microstrip line 1 or the value of the effective dielectric constant ε _eff , and the formula (1 ), (2), and (3) are used to calculate an undecided structure parameter. In the second calculation result output processing procedure, the computer is caused to execute a process of outputting at least the undetermined structural parameter calculated by the second calculation processing procedure.

1 is an example of a schematic cross-sectional view of a microstrip line to be analyzed by a microstrip line analysis apparatus, analysis method, and analysis program of the present invention. FIG. 5 is a schematic cross-sectional view of a microstrip line having a dielectric having a relative dielectric constant of ε ′ and an infinite thickness instead of a surface dielectric. It is the graph which plotted the dielectric constant (epsilon) 'calculated | required from the electromagnetic analysis model setting value, and the dielectric constant (epsilon)' calculated from the approximate expression. It is a graph which shows the relationship between T / t and effective dielectric constant (epsilon) _eff . It is another graph which shows the relationship between T / t and effective dielectric constant (epsilon) _eff . It is a block diagram which shows functionally the structure of an example of the analysis apparatus of a microstrip line which has a 1st calculating means. It is typical explanatory drawing which shows an example of the hardware constitutions of the analysis apparatus of a microstrip line. It is a block diagram which shows functionally the structure of an example of the analysis apparatus of the microstrip line which has a 2nd calculating means. It is a flowchart which shows the process sequence of the analyzer of a microstrip line which has a 1st calculating means. It is a flowchart which shows the process sequence of the analyzer of a microstrip line which has a 2nd calculating means.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1, 2 Microstrip line 10 Surface layer dielectric 11 Board | substrate 12 Ground plane 13 Surface layer wiring 20 Dielectric 100 Microstrip line analysis apparatus 101 which has 1st calculating means 101 Microstrip line analysis apparatus 200 which has 2nd calculation procedure 200 Analysis device 201 Input / output device 202 Memory 203 Arithmetic device 204 Display device 205 Path 206 Storage medium

Claims (18)

A substrate having a relative dielectric constant of ε _sub and a thickness of h, a surface layer wiring having a thickness of t having a width of w, and the surface layer wiring and the substrate having a relative dielectric constant of a microstrip line analysis device having a surface dielectric with a thickness T of ε _sr ,
Effective dielectric constant ε1 _eff , relative dielectric constant ε ′, and relative dielectric constant in the case where a dielectric having a relative dielectric constant of ε ′ and an infinite thickness is provided instead of the surface dielectric A first relational expression established between the rate ε _sub , the thickness h, the width w, and the thickness t;
When the effective dielectric constant ε1 _eff matches the effective dielectric constant ε _eff of the microstrip line, the relative dielectric constant ε ′, the relative dielectric constant ε _sub , the thickness h, the width w, the thickness a second relational expression established between t, the relative dielectric constant ε _sr , and the thickness T;
Using,
First calculating means for calculating the effective dielectric constant ε _eff ;
Or
When there are undecided structural parameters among the structural parameters of the relative dielectric constant ε _sub , the thickness h, the width w, the thickness t, the relative dielectric constant ε _sr , and the thickness T, Second calculation means for calculating the undetermined structural parameter from a structural parameter other than the undetermined structural parameter and a value of the characteristic impedance of the microstrip line or an effective dielectric constant ε _eff of the microstrip line;
An apparatus for analyzing a microstrip line, comprising at least one of the following. A substrate having a relative dielectric constant of ε _sub and a thickness of h, a surface layer wiring having a thickness of t having a width of w, and the surface layer wiring and the substrate having a relative dielectric constant of a microstrip line analysis device having a surface dielectric with a thickness T of ε _sr ,
A first calculating means for calculating an effective dielectric constant ε _eff of the microstrip line using the following equations (1), (2), (3);
Or
When there are undecided structural parameters among the structural parameters of the relative dielectric constant ε _sub , the thickness h, the width w, the thickness t, the relative dielectric constant ε _sr , and the thickness T, Using structural parameters other than undecided structural parameters, the value of the characteristic impedance of the microstrip line or the value of the effective dielectric constant ε _eff of the microstrip line, and the following equations (1), (2), (3) Second computing means for calculating the undetermined structural parameter;
An apparatus for analyzing a microstrip line, comprising at least one of the following.

When the microstrip line analyzing apparatus has the first calculation means, the first structural parameter input means for inputting the structural parameters, and the effective dielectric constant ε _eff calculated by the first calculation means. 3. The microstrip line analysis device according to claim 1, further comprising: a first calculation result output unit that outputs at least the first calculation result output unit. The microstrip line according to any one of claims 1 to 3, wherein the first calculation means has a function of obtaining a characteristic impedance of the microstrip line by using the obtained effective dielectric constant ε _eff. Analysis device. 2. The function according to claim 1, wherein the first computing unit has a function of obtaining at least frequency dependence of the effective dielectric constant ε _eff from the values of the relative dielectric constant ε _sub and the relative dielectric constant ε _sr for each frequency. 5. The microstrip line analyzer according to any one of 4 above. When the microstrip line analyzing apparatus has the second computing means, second structural parameter input means for inputting a structural parameter other than the undetermined structural parameter, and characteristic impedance or effective of the microstrip line Characteristic impedance / effective dielectric constant input means for inputting a dielectric constant ε _eff, and second calculation result output means for outputting at least the undetermined structural parameter calculated by the second calculation means, The microstrip line analyzing apparatus according to claim 1 or 2. A substrate having a relative dielectric constant of ε _sub and a thickness of h, a surface layer wiring having a thickness of t having a width of w, and the surface layer wiring and the substrate having a relative dielectric constant of a method of analyzing a microstrip line having a surface dielectric with a thickness T that is ε _sr ,
Effective dielectric constant ε1 _eff , relative dielectric constant ε ′, and relative dielectric constant in the case where a dielectric having a relative dielectric constant of ε ′ and an infinite thickness is provided instead of the surface dielectric A first relational expression established between the rate ε _sub , the thickness h, the width w, and the thickness t;
When the effective dielectric constant ε1 _eff matches the effective dielectric constant ε _eff of the microstrip line, the relative dielectric constant ε ′, the relative dielectric constant ε _sub , the thickness h, the width w, the thickness a second relational expression established between t, the relative dielectric constant ε _sr , and the thickness T;
Using,
A first calculation step for calculating the effective dielectric constant ε _eff ;
Or
When there are undecided structural parameters among the structural parameters of the relative dielectric constant ε _sub , the thickness h, the width w, the thickness t, the relative dielectric constant ε _sr , and the thickness T, A second calculation step of calculating the undetermined structural parameter from a structural parameter other than the undetermined structural parameter and a value of a characteristic impedance of the microstrip line or a value of an effective dielectric constant ε _eff of the microstrip line;
A method for analyzing a microstrip line, comprising at least one of the following. A substrate having a relative dielectric constant of ε _sub and a thickness of h, a surface layer wiring having a thickness of t having a width of w, and the surface layer wiring and the substrate having a relative dielectric constant of a method of analyzing a microstrip line having a surface dielectric with a thickness T that is ε _sr ,
A first calculation step of calculating an effective dielectric constant ε _eff of the microstrip line using the following equations (1), (2), (3):
Or
When there are undecided structural parameters among the structural parameters of the relative dielectric constant ε _sub , the thickness h, the width w, the thickness t, the relative dielectric constant ε _sr , and the thickness T, Using structural parameters other than undecided structural parameters, the value of the characteristic impedance of the microstrip line or the value of the effective dielectric constant ε _eff of the microstrip line, and the following equations (1), (2), (3) A second calculation step for calculating the undetermined structural parameter;
A method for analyzing a microstrip line, comprising at least one of the following.

When the microstrip line analysis method includes the first calculation step, the first structural parameter input step for inputting the structural parameter, and the effective dielectric constant ε _eff calculated in the first calculation step 9. The microstrip line analysis method according to claim 7, further comprising a first calculation result output step of outputting at least a first calculation result output step. 10. The microstrip line according to claim 7, wherein the first calculation step has a function of obtaining a characteristic impedance of the microstrip line by using the obtained effective dielectric constant ε _eff. Analysis method. The first calculation step has a function of _obtaining a frequency dependency of at least the effective dielectric constant ε _eff from values of the relative dielectric constant ε _sub and the relative dielectric constant ε _sr for each frequency. The method for analyzing a microstrip line according to any one of 10. When the microstrip line analysis method includes the second calculation step, a second structural parameter input step for inputting a structural parameter other than the undetermined structural parameter; and a characteristic impedance or effective of the microstrip line A characteristic impedance / effective dielectric constant input step for inputting a dielectric constant ε _eff; and a second calculation result output step for outputting at least the undetermined structural parameter calculated in the second calculation step. The method for analyzing a microstrip line according to claim 7 or 8. A substrate having a relative dielectric constant of ε _sub and a thickness of h, a surface layer wiring having a thickness of t having a width of w, and the surface layer wiring and the substrate having a relative dielectric constant of a microstrip line analysis program having a surface dielectric with a thickness T of ε _sr ,
On the computer,
Effective dielectric constant ε1 _eff , relative dielectric constant ε ′, and relative dielectric constant in the case where a dielectric having a relative dielectric constant of ε ′ and an infinite thickness is provided instead of the surface dielectric A first relational expression established between the rate ε _sub , the thickness h, the width w, and the thickness t;
When the effective dielectric constant ε1 _eff matches the effective dielectric constant ε _eff of the microstrip line, the relative dielectric constant ε ′, the relative dielectric constant ε _sub , the thickness h, the width w, the thickness a second relational expression established between t, the relative dielectric constant ε _sr , and the thickness T;
Using,
A first calculation processing procedure for calculating the effective dielectric constant ε _eff ;
Or
When there are undecided structural parameters among the structural parameters of the relative dielectric constant ε _sub , the thickness h, the width w, the thickness t, the relative dielectric constant ε _sr , and the thickness T, Second calculation processing procedure for calculating the undetermined structural parameter from the structural parameter other than the undetermined structural parameter and the value of the characteristic impedance of the microstrip line or the effective dielectric constant ε _eff of the microstrip line. ,
A program for analyzing a microstrip line, wherein at least one of the above is executed. A substrate having a relative dielectric constant of ε _sub and a thickness of h, a surface layer wiring having a thickness of t having a width of w, and the surface layer wiring and the substrate having a relative dielectric constant of a microstrip line analysis program having a surface dielectric with a thickness T of ε _sr ,
On the computer,
A first calculation processing procedure for calculating an effective dielectric constant ε _eff of the microstrip line using the following equations (1), (2), (3);
Or
When there are undecided structural parameters among the structural parameters of the relative dielectric constant ε _sub , the thickness h, the width w, the thickness t, the relative dielectric constant ε _sr , and the thickness T, Using structural parameters other than undecided structural parameters, the value of the characteristic impedance of the microstrip line or the value of the effective dielectric constant ε _eff of the microstrip line, and the following equations (1), (2), (3) A second arithmetic processing procedure for calculating the undetermined structural parameter;
A program for analyzing a microstrip line, wherein at least one of the above is executed.

When the microstrip line analysis program causes the computer to execute the first arithmetic processing procedure, the microstrip line analysis program is calculated by a first structural parameter input processing procedure for inputting the structural parameter, and the first arithmetic processing procedure. The microstrip line analysis program according to claim 13 or 14, further causing the computer to further execute a first calculation result output processing procedure for outputting at least the effective dielectric constant ε _eff . _{16. The} method according to claim 13, wherein, in the first calculation processing procedure, the computer is caused to execute a process of obtaining a characteristic impedance of the microstrip line using the obtained effective dielectric constant ε _eff. The microstrip line analysis program described. In the first calculation processing procedure, the computer is caused to execute processing for _obtaining at least the frequency dependence of the effective permittivity ε _eff from the values of the relative permittivity ε _sub and the relative permittivity ε _sr for each frequency. The microstrip line analysis program according to any one of claims 13 to 16. A second structural parameter input processing procedure for inputting a structural parameter other than the undetermined structural parameter when the microstrip line analysis program causes the computer to execute the second arithmetic processing procedure; A characteristic impedance / effective dielectric constant input processing procedure for inputting the characteristic impedance or effective dielectric constant ε _eff of the line, and a second calculation result for outputting at least the undetermined structural parameter calculated in the second arithmetic processing procedure The microstrip line analysis program according to claim 13 or 14, further causing the computer to execute an output processing procedure.

Images