Multiconductor transmission line system analysis method and design method

Abstract

To enable the analysis of noise characteristics of a multiconductor transmission line system having branches to be easily carried out.SOLUTION: The present invention analyzes the noise characteristic of a multiconductor transmission line system including a plurality of conductor lines 12, 13, each having branches, by using a propagation model in which it is assumed that a noise signal propagates by being multiple reflected between a first terminal network 31 and a second terminal network 32 via a uniform line group 30. The propagation model constitutes the uniform line group 30 by lines 33-39 bridging over between the first terminal network 31 and the second terminal network 32, and the first terminal network 31 and the second terminal network 32 are constituted by terminal elements located on both sides of it, when it is assumed that each of conductor lines 12, 13 is laid so as to reciprocate between the first terminal network 31 and the second terminal network 32, taking a characteristic impedance change position including branches 20, 21 from a parallel-running section 14 as a turnaround point.SELECTED DRAWING: Figure 2

Description

[Technical Field]

[0001] The present invention relates to a method for analyzing and designing a multi-conductor transmission line system. [Background technology]

[0002] A system configured with a ground plane and multiple conductor lines, such as an in-vehicle wire harness or a pattern wiring on a circuit board, is a multi-conductor transmission line system. In such a multi-conductor transmission line system, noise may become apparent due to resonance. Patent Document 1 describes a technology for suppressing the appearance of noise in an in-vehicle wire harness. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Japanese Patent Application Publication No. 2019-55686 Summary of the Invention [Problem to be solved by the invention]

[0004] The technology described in Patent Document 1 is limited to application to automotive wire harnesses in which multiple wires are bundled together, and therefore cannot be applied to multi-conductor transmission line systems with branches. Noise suppression in multi-conductor transmission line systems requires analysis of noise characteristics. However, a simple method for analyzing noise characteristics in multi-conductor transmission line systems with branches has not yet been established. As a result, it has been difficult to design a multi-conductor transmission line system that can suppress the manifestation of noise. [Means for solving the problem]

[0005] A method for analyzing a multi-conductor transmission line system that solves the above-mentioned problems is a method for analyzing noise characteristics of a multi-conductor transmission line system that is composed of a ground plane and a plurality of conductor lines and has a parallel-running section in which the plurality of conductor lines run in parallel, and analyzes the noise characteristics of the multi-conductor transmission line system using a propagation model that assumes that a noise signal input to the multi-conductor transmission line system propagates through a uniform line group with multiple reflections between a first terminal circuit network and a second terminal circuit network. The propagation model assumes that each of the plurality of conductor lines is wired so as to travel back and forth between the first terminal circuit network and the second terminal circuit network, with a turning point being a position where characteristic impedance changes, including a branch point from the parallel-running section, and the uniform line group is constituted by each line that spans between the first terminal circuit network and the second terminal circuit network, and the terminal loads and the turning points of each of the plurality of conductor lines that are located at one end of the uniform line group constitute the first terminal circuit network, and the second terminal circuit network constitutes the second terminal circuit network, respectively,

[0006] A design method for a multi-conductor transmission line system that solves the above-mentioned problems is a method for designing a multi-conductor transmission line system that is composed of a ground plane and a plurality of conductor lines and has a parallel section in which the plurality of conductor lines run parallel, and that designs the multi-conductor transmission line system through the following steps: using the analysis method described in claim 1 to perform eigenvalue analysis of components of the multi-conductor transmission line system; extracting components of the multi-conductor transmission line system that have large eigenvalues ​​at problematic frequencies based on the results of the eigenvalue analysis; and changing the design values ​​of the extracted components so that the characteristic impedance of the extracted components changes.

[0007] Another method for designing a multi-conductor transmission line system that solves the above-mentioned problems is a method for designing a multi-conductor transmission line system that is composed of a ground plane and a plurality of conductor lines and has a parallel section in which the plurality of conductor lines run parallel to one another, and that uses the analysis method set forth in claim 1 to design the multi-conductor transmission line system through the steps of: calculating noise peak frequencies of components of the multi-conductor transmission line system; and, if the calculated peak frequency is a problematic frequency, changing the height of one or more of the lines from the ground plane. [Effects of the Invention]

[0008] The above-described method for analyzing a multi-conductor transmission line system has the advantage of being able to easily analyze the noise characteristics of a multi-conductor transmission line system having branches. The above-described method for designing a multi-conductor transmission line system has the advantage of facilitating the design of a multi-conductor transmission line system. [Brief explanation of the drawings]

[0009] [Figure 1] FIG. 1 is a diagram illustrating a configuration of an example of a multi-conductor transmission line system. [Figure 2] FIG. 2 is a circuit diagram of a noise signal propagation model of the multi-conductor transmission line system of FIG. [Figure 3] FIG. 10 is a diagram schematically illustrating another configuration example of a multi-conductor transmission line system. [Figure 4] FIG. 4 is a circuit diagram of a noise signal propagation model of the multi-conductor transmission line system of FIG. 3. [Figure 5] FIG. 10 is a diagram schematically illustrating another configuration example of a multi-conductor transmission line system. [Figure 6] FIG. 6 is a circuit diagram of a propagation model of a noise signal in the multi-conductor transmission line system of FIG. 5. DETAILED DESCRIPTION OF THE INVENTION

[0010] An embodiment of a method for analyzing a multi-conductor transmission line system will be described in detail below with reference to FIGS. <Configuration of multiconductor transmission line system> First, with reference to FIG. 1, the configuration of a multi-conductor transmission line system that is the subject of noise characteristic analysis in this embodiment will be described.

[0011] The multi-conductor transmission line system 10 shown in FIG. 1 is composed of a ground plane 11 and two conductor lines, a first conductor line 12 and a second conductor line 13, laid on the ground plane 11. The conductors and insulating coatings of the first conductor line 12 and the second conductor line 13 are made of the same material and have the same cross-sectional shape. The multi-conductor transmission line system 10 has a parallel section 14 in which the first conductor line 12 and the second conductor line 13 run adjacent to each other. The first conductor line 12 and the second conductor line 13 branch off from each other at both ends of the parallel section 14. In the following description, one end of the parallel section 14 will be referred to as a first branch section 20, and the other end as a second branch section 21. The portions of the first conductor line 12 and the second conductor line 13 that branch off from the parallel section 14 and are laid independently will be referred to as single-wire sections.

[0012] Both ends of the first conductor line 12 are grounded to the ground plane 11 via a first terminal load 15 and a third terminal load 17, respectively. Similarly, both ends of the second conductor line 13 are grounded to the ground plane 11 via a second terminal load 16 and a fourth terminal load 18, respectively. The first conductor line and the second conductor line 13 are laid at a certain height H1 above the ground plane 11, with the exception of a portion of the second conductor line 13 between the second branch 21 and the fourth terminal load 18, which is laid at a height H2 (>H1) above the ground plane 11. Note that, among the lines showing the first conductor line 12 and the second conductor line 13 in FIG. 1 , the length of the line extending perpendicular to the ground plane 11 does not represent the physical length of the conductor line, but represents the height from the ground plane 11.

[0013] In the case of the multi-conductor transmission line system 10 in Fig. 1, a noise source 19 is connected to the terminal of the first conductor line 12 on the side where the first terminal load 15 is located. The noise source 19 represents, for example, a noise source included in the first terminal load 15. Another example of the noise source 19 is a noise generated in the first conductor line 12 by induction of external noise, represented as an equivalent terminal noise source.

[0014] Examples of such a multi-conductor transmission line system 10 include wire harnesses and busbar modules installed in transportation equipment such as vehicles and aircraft. In this case, the ground plane 11 is the conductor body of the transportation equipment, and the first conductor line 12 and the second conductor line 13 are electric wires or busbars. Another example of a multi-conductor transmission line system 10 is the wiring pattern of a circuit board. In this case, the ground plane 11 is the GND plane of the circuit board, and the first conductor line 12 and the second conductor line 13 are the pattern wiring of the circuit board.

[0015] <Noise propagation model for multi-conductor transmission lines> The analysis method of this embodiment uses the following noise propagation model to analyze the noise characteristics of the multi-conductor transmission line system 10. In this propagation model, the multi-conductor transmission line system 10 in Fig. 1 is replaced with a multi-conductor transmission line system in which multiple lines without branches are arranged in parallel, and noise propagation is modeled.

[0016] Figure 2 shows a substitution circuit for the multi-conductor transmission line system 10 used in the propagation model. This substitution circuit is composed of a first terminal circuit network 31, a second terminal circuit network 32, and a group of uniform lines 30 stretched between them. This substitution circuit is created by replacing the multi-conductor transmission line system 10 in Figure 1 in the following manner.

[0017] Assume that the first conductor line 12 and the second conductor line 13 are wired to travel back and forth between the first terminal circuit network 31 and the second terminal circuit network 32, with the characteristic impedance change positions, including the branch sections (first branch section 20 and second branch section 21) from the parallel running section 14, as turning points. In the case of the multi-conductor transmission line system 10 of FIG. 1 , the characteristic impedance change positions of the first conductor line 12 and the second conductor line 13 are the first branch section 20 and the second branch section 21. If there are other portions where the cross-sectional shape of the conductor of the conductor line or the height from the ground plane 11 changes along the way, those portions also become characteristic impedance change positions. As a result, a plurality of juxtaposed lines 33 to 39 are spanned between the first terminal circuit network 31 and the second terminal circuit network 32. As described above, when replaced with a replacement circuit, the first conductor line 12 and the second conductor line 13 are turned back at the characteristic impedance change positions. Therefore, each of the lines 33 to 39 spanning between the first terminal circuit network 31 and the second terminal circuit network 32 has a uniform characteristic impedance over its entire length. The uniform line group 30 is made up of the lines 33 to 39 spanning between the first terminal circuit network 31 and the second terminal circuit network 32 in parallel.

[0018] In the case of FIG. 2 , in order to include the noise source 19 in the first terminal network 31, the first conductor line 12 is folded back once more at the midpoint of the single-wire section between the first terminal load 15 and the first branch 20. In the following description, this folding position will be referred to as a folding point 22. The line length of the section of the first conductor line 12 between the noise source 19 and the first terminal load 15 and the folding point 22 is set to be sufficiently shorter than the line length of the section between the first branch 20 and the folding point 22. In this propagation model, the first terminal network 31 is composed of the first terminal load 15, the third terminal load 17, the fourth terminal load 18, the first branch 20, and the noise source 19. The second terminal network 32 is composed of the folding point 22, the second terminal load 16, and the second branch 21. The first branch 20, the second branch 21, and the turning point 22 are represented as short-circuit lines connecting the terminals of the two lines.

[0019] 2, the uniform line group 30 is composed of seven lines 33 to 39 arranged in parallel. The line 33 corresponds to the portion of the second conductor line 13 between the second branch 21 and the fourth terminal load 18. The line 34 corresponds to the portion of the first conductor line 12 between the second branch 21 and the third terminal load 17. The line 35 corresponds to the portion of the second conductor line 13 between the first branch 20 and the second branch 21. The line 36 corresponds to the portion of the first conductor line 12 between the first branch 20 and the second branch 21. The line 37 corresponds to the portion of the second conductor line 13 between the second terminal load 16 and the first branch 20. The line 38 corresponds to the portion of the first conductor line 12 between the turn-back point 22 and the first branch 20. The line 39 corresponds to the portion of the first conductor line 12 between the terminal load 15 and the noise source 19 and the turning point 22. Of these, the lines 35 and 36 are the parallel running section 14, and the other lines 33, 34, 37 to 39 are single track sections.

[0020] In this embodiment, when analyzing noise characteristics, the multi-conductor transmission line system 10 having branches as shown in FIG. 1 is replaced with a multi-conductor transmission line system without branches as shown in FIG. 2. Then, the noise characteristics are analyzed using a noise propagation model in the replaced multi-conductor transmission line system. The analysis of noise characteristics in a multi-conductor transmission line system without branches consisting of multiple transmission lines as shown in FIG. 2 is described in detail in a reference (Clayton R. Paul, "Analysis of Multiconductor Transmission Lines", 2nd Edition, Wiley). Therefore, a brief overview will be given here.

[0021] When analyzing noise characteristics, it is first necessary to determine the unit length impedance, propagation constant, and voltage mode conversion coefficient of each of the lines 33 to 39. These values ​​can be calculated from the unit length inductance, unit length capacitance, etc. of each of the lines 33 to 39. The unit length inductance and unit length capacitance of each of the lines 33 to 39 can be calculated by electromagnetic field simulation based on the cross-sectional shape of the conductor of each of the lines 33 to 39.

[0022] In this embodiment, the cross-sectional shape of the conductor of each of the lines 33 to 39 is the same. In this case, the unit length inductance and unit length capacitance of each of the lines 33, 34, 37 to 39 in the single-wire section are the same if they are at the same height from the ground plane 11. The line 33 is laid at a height H2 from the ground plane 11, and the lines 34, 37 to 39 are laid at a height H1 from the ground plane 11. Therefore, the unit length impedance, propagation constant, and voltage-mode conversion coefficient of each of the lines 34, 37 to 39 other than the line 33, which is at a different height from the ground plane 11, are the same. In the following description, the unit length impedance of the lines 34, 37 to 39 is referred to as "Z1," the propagation constant as "γ1," and the voltage-mode conversion coefficient as "Tv1." Furthermore, the unit length impedance of the line 33 is referred to as "Z3," the propagation constant as "γ3," and the voltage-mode conversion coefficient as "Tv3." In addition, in single-track sections, the noise propagation mode can be considered to be single, so the values ​​of Tv1 and Tv3 are formally "1".

[0023] Meanwhile, the unit length impedance, propagation constant, and voltage-mode conversion coefficient of the parallel section 14 are obtained by modeling it as a multi-conductor transmission line system based on the capacitive coupling and mutual inductance coupling between the conductors of the parallel lines 35 and 36. The unit length impedance, propagation constant, and voltage-mode conversion coefficient of the parallel section 14 are expressed as square quadratic matrices. In the following explanation, the unit length impedance matrix of the parallel section 14 is referred to as "Z2," the propagation constant matrix as "γ2," and the voltage-mode conversion coefficient matrix as "Tv2." Incidentally, the unit length impedance, propagation constant, and voltage-mode conversion coefficient of a parallel section consisting of N parallel lines are each expressed as a square Nth-order matrix.

[0024] In this embodiment, the electrical resistance of the conductors of the lines 33 to 39 and the dielectric loss of the wire coating, etc. are sufficiently small values, so these are ignored when calculating the above parameters. If more precise calculations are required or if the electrical resistance and dielectric loss are too large to be ignored, it is advisable to calculate the above parameters taking into account the electrical resistance of the conductors and the dielectric loss of the wire coating, etc.

[0025] In reality, the unit length impedance, propagation constant, and voltage mode conversion coefficient have frequency characteristics. However, in practice, there are many cases where the frequency characteristics can be ignored without causing any problems. In this embodiment, the frequency characteristics are taken into consideration only when calculating the unit length impedance. Specifically, the unit length impedance value is calculated as a value obtained by applying frequency correction that takes into account the skin effect to the unit length impedance value at low frequencies.

[0026] When analyzing noise characteristics, it is necessary to express the first terminal circuit network 31 and the second terminal circuit network 32 using modal reflection coefficient matrices. These expressions using modal reflection coefficient matrices are performed as follows.

[0027] First, the first terminal circuit network 31 is represented by admittance matrices Y1 and Y2 as shown in equation (1). In the admittance matrix Y1, the admittances of the first terminal load 15, the third terminal load 17, and the fourth terminal load 18 included in the first terminal circuit network 31 are arranged as diagonal elements. Furthermore, for the load elements connecting the lines 33 to 39 within the first terminal circuit network 31, the admittances are arranged as diagonal elements, and the sign-inverted values ​​of the admittances are arranged as off-diagonal elements in the admittance matrix Y1. The corresponding parts are enclosed by dotted lines in the equation. In the first terminal circuit network 31, short-circuit lines between the lines 35 and 37 and between the lines 36 and 38 in the first branch section 20 exist as load elements connecting the lines 33 to 39. The inductance of these short-circuit lines is actually "0," but this would result in an infinite admittance. Therefore, here, the admittance values ​​of these short-circuit lines are set to values ​​st that are sufficiently smaller than the admittances of the terminal loads 15 to 18, and are arranged in the admittance matrix Y1.

[0028]

number

[0029] On the other hand, the second terminal circuit network 32 has a second terminal load 16 as a load element connected to the terminals of the lines 33 to 39. The second terminal circuit network 32 also has a short-circuit line between the lines 38, 38 at the turnaround point 22, and short-circuit lines between the lines 33, 35 and between the lines 34, 36 at the second branch section 21 as load elements connecting the lines 33 to 39. By arranging these admittances in a matrix in the same way as in the case of equation (1), the admittance matrix Y2 of the second terminal circuit network 32 as shown in equation (2) can be obtained.

[0030]

number

[0031] Next, a unit length impedance matrix Z of the entire uniform line group 30 is created as shown in equation (3). This unit length impedance matrix Z is obtained by arranging the unit length impedances of the lines 33 to 39 that make up the uniform line group 30 as diagonal elements.

[0032]

number

[0033] Also, a voltage mode conversion coefficient matrix Tv is created for the entire uniform line group 30 as shown in equation (4). This voltage mode conversion coefficient matrix Tv is obtained by arranging the voltage mode conversion coefficients of the lines 33 to 39 that make up the uniform line group 30 as diagonal elements.

[0034]

number

[0035] Furthermore, a propagation coefficient matrix γ is created for the entire uniform line group 30 as shown in equation (5). This propagation coefficient matrix γ is obtained by arranging the propagation coefficients of the lines 33 to 39 that make up the uniform line group 30 as diagonal elements.

[0036]

number

[0037] In addition, a line length matrix d is created for the entire uniform line group 30 as shown in equation (6). This line length matrix d is obtained by arranging the line lengths d1 to d7 of the lines 33 to 39 that make up the uniform line group 30 as diagonal elements.

[0038]

number

[0039] Using the above, the characteristic admittance matrix Y0 of the entire uniform line group 30 can be derived as shown in equation (7).

[0040]

number

[0041] Then, when the admittance matrix of the first terminal circuit network 31 is Y1 and the noise source 19 is a current source J, the real input voltage wave Ass from the first terminal circuit network 31 is found as the value shown in equation (8). Note that if the noise source 19 is defined as a voltage source, the real input voltage wave Ass can be found by converting it into a current source using a Norton equivalent circuit.

[0042]

number

[0043] The real input voltage wave Ass can be converted into the modal incident voltage wave vector Amss as shown in equation (9).

[0044]

number

[0045] Furthermore, the real voltage reflection coefficient matrix S1 of the first terminal network 31 is expressed in the form shown in equation (10).

[0046]

number

[0047] When this is transformed into modal space, the modal reflection coefficient matrix Sm1 of the first terminal circuit network 31 shown in equation (11) can be found. In a similar manner, the modal reflection coefficient matrix Sm2 of the second terminal circuit network 32 can also be found.

[0048]

number

[0049] Here, noise propagation in the substitution circuit of the multi-conductor transmission line system 10 in Fig. 2 is considered as the propagation of a modal voltage wave in the uniform line group 30 and modal reflection at the first terminal circuit network 31 and the second terminal circuit network 32. In this case, the noise injected from the noise source 19 has a modal incident voltage wave vector Amss. The injected noise then circulates around the multi-conductor transmission line system 10, following the following steps in order: (a) propagation through the uniform line group 30, (b) reflection at the second terminal circuit network 32, (c) propagation through the uniform line group 30, and (d) reflection at the first terminal circuit network 31. The attenuation and phase delay of the noise during propagation in (a) and (c) can be calculated as the vector AT shown in equation (12).

[0050]

number

[0051] On the other hand, as described above, the noise reflection at the first terminal circuit network 31 and the second terminal circuit network 32 is expressed by the modal reflection coefficient matrices Sm1 and Sm2. Therefore, the noise propagation that makes a loop around the multi-conductor transmission line system 10 is expressed as the loop propagation Smc shown in equation (13).

[0052]

number

[0053] In the multi-conductor transmission line system 10, this loop propagation Smc is repeated infinitely. The accumulation of these multiple reflections and propagations results in the final propagation. Therefore, noise propagation in the multi-conductor transmission line system 10 can be expressed as the sum of a geometric infinite series matrix in which the loop propagation Smc of equation (13) is the common ratio matrix. Note that, since reflections at the terminal networks 31 and 32 are usually accompanied by attenuation, this geometric infinite series matrix does not diverge.

[0054] From the above, the mode voltage wave vector Am1 of the noise incident on the uniform line group 30 from the first terminal network 31 can be expressed as in equation (14).

[0055]

number

[0056] Then, the modal multiple reflection infinite series matrix Sms of the multi-conductor transmission line system 10 is obtained as shown in equation (15). Since the sum of this modal multiple reflection infinite series matrix Sms is a vectorized infinite geometric series of a scalar, the method of derivation is the same as for the scalar.

[0057]

number

[0058] The modal multi-reflection infinite series matrix Sms of equation (15) contains information about noise propagation for all of the components of the multi-conductor transmission line system 10, and represents the multiple reflections of noise injected into the multi-conductor transmission line system 10. Therefore, it is possible to analyze the noise characteristics of the multi-conductor transmission line system 10 using this modal multi-reflection infinite series matrix Sms.

[0059] <Actions and Effects of the Embodiment> The operation and effects of the method for analyzing the multi-conductor transmission line system 10 of this embodiment will be described. The multi-conductor transmission line system 10 to be analyzed in this embodiment has a plurality of conductor lines with branches, making it difficult to analyze the noise characteristics as is. In the analysis method of this embodiment, the noise characteristics of the multi-conductor transmission line system 10 are analyzed using a propagation model that assumes that a noise signal input to the multi-conductor transmission line system 10 propagates through a uniform line group 30, undergoing multiple reflections between a first terminal circuit network 31 and a second terminal circuit network 32. The propagation model assumes that each of the conductor lines (12, 13) of the multi-conductor transmission line system 10 is wired to travel back and forth between the first terminal circuit network 31 and the second terminal circuit network 32, with the turning points being positions where the characteristic impedance changes, including branch points (20, 21) from the parallel running section 14. The uniform line group 30 in the propagation model is composed of lines 33 to 39 that are laid between the first terminal circuit network 31 and the second terminal circuit network 32. The first terminal circuit network 31 and the second terminal circuit network 32 in the propagation model are respectively composed of terminal loads 15-18 of the multiple conductor lines (12, 13) and elements connected to the terminals of the lines 33-39 constituting the uniform line group 30, among the terminal elements of the turnaround points (20-22). In this propagation model, the multi-conductor transmission line system 10 is replaced by a virtual multi-conductor transmission line system composed of multiple lines 33-39 with no branches, which are juxtaposed and spanned between the first terminal circuit network 31 and the second terminal circuit network 32. Existing analysis methods can be used to analyze the noise characteristics of such a virtual multi-conductor transmission line system.

[0060] According to the above-described method for analyzing the multi-conductor transmission line system 10 of this embodiment, the following effects can be achieved. (1) In the analysis method of this embodiment, the noise characteristics are analyzed by virtually replacing multi-conductor transmission line system 10 with a branchless multi-conductor transmission line system, which makes it easy to analyze the noise characteristics of multi-conductor transmission line system 10 with branches.

[0061] (2) The analysis method of this embodiment can individually determine the noise characteristics of each section of the first conductor line 12 and the second conductor line 13, which are divided based on the difference in characteristic impedance. This allows for detailed analysis of noise characteristics.

[0062] (Method for designing a multi-conductor transmission line system using the analysis method of the above embodiment) By reflecting the results of an analysis of noise characteristics using the modal multiple reflection infinite series matrix Sms, it becomes possible to easily design a multi-conductor transmission line system 10 that suppresses the manifestation of noise. Below, examples 1 to 4 of a design method for such a multi-conductor transmission line system 10 will be described.

[0063] Example 1 A prototype multi-conductor transmission line system 10 was fabricated by setting the line lengths d1 to d7 of the lines 33 to 39 so that the line length matrix d = [390, 390, [740, 740], 470, 470, 1] (all units in mm). The line 39 was provided for the convenience of calculations in order to include the noise source 19 in the first terminal circuit network 31 in the substitution circuit of Figure 2. Therefore, here, the line length d7 of the line 39 was set to a length (1 mm) that is sufficiently shorter than the other lines 33 to 38. In addition, in this prototype, all of the terminal loads 15 to 18 have a load resistance of 50 Ω.

[0064] A noise signal was injected from noise source 19 into a prototype of multi-conductor transmission line system 10, with the terminal voltage of first conductor line 12 connected to first terminal load 15 set to 1 V across the entire frequency band. Then, the current at second branch 21 of second conductor line 13 was measured while the noise signal was injected. A measurement antenna was also installed near the prototype to measure the electric field strength at the installation point. The current measurement results confirmed that the current had a resonant peak at 537 Hz. Accordingly, it was also confirmed that the electromagnetic waves radiated from the prototype also had a peak at 537 Hz. However, the 537 Hz electromagnetic waves may have an undesirable effect on the operation of equipment in which this multi-conductor transmission line system 10 is installed. Therefore, the design of multi-conductor transmission line system 10 needs to be modified to shift the frequency of the current resonant peak away from 537 Hz.

[0065] Here, the modal multi-reflection infinite series matrix Sms in equation (15) represents the steady state of the response of the multi-conductor transmission line system 10 to an incident noise signal. Therefore, the eigenvalues ​​of the modal multi-reflection infinite series matrix Sms represent the natural vibrations of the multi-conductor transmission line system 10. Therefore, an eigenvalue analysis of the prototype is performed using the modal multi-reflection infinite series matrix Sms that reflects the prototype design values ​​and noise signal as described above. The results of the eigenvalue analysis are obtained as eigenvectors E for each frequency. The eigenvector E at a specific frequency is obtained as shown in equation (16). The subscript "T" in equation (16) and each equation described below indicates transposition, indicating that the vectors in the equations are actually vertical vectors. The elements e1 to e6 of the eigenvector E correspond to the eigenvalues ​​of lines 33 to 38, respectively. Note that, in reality, the eigenvector E also includes an element corresponding to the eigenvalue of line 39, but this is omitted in equation (16).

[0066]

number

[0067] Here, the maximum value among the elements e1 to e6 of the eigenvector E at a specific frequency is defined as the maximum eigenvalue. The frequency at which the maximum eigenvalue reaches its peak (maximum) is defined as the peak frequency of the maximum eigenvalue. The results of the eigenvalue analysis confirmed that the peak frequency of the maximum eigenvalue is 558 Hz, which is close to the 537 Hz resonant peak frequency of the current in question. The results of the eigenvalue analysis using the modal multi-reflection infinite series matrix Sms contain some errors due to circuit substitution. Therefore, although the frequencies do not match perfectly, it is highly likely that the peak frequency of the maximum eigenvalue at 558 Hz is related to the 537 Hz peak frequency of the current and electromagnetic waves.

[0068] The results of the eigenvalue analysis confirmed that, among the elements e1 to e6 of the eigenvector E at 558 Hz, elements e1, e4, and e6 are larger than the other elements e2, e3, and e5. Therefore, in order to shift the peak frequency at 537 Hz, it is considered effective to change the characteristic impedance of lines 33, 36, and 38 corresponding to elements e1, e4, and e6. Therefore, in this study, we decided to change the line lengths d1 to d4 of four lines 33 to 36, including two of lines 33, 36, and 38. This change was made so that the line length matrix d after the change became [510, 510, [620, 620], 470, 470, 1] (all units are in mm).

[0069] The results of eigenvalue analysis using the mode multi-reflection infinite series matrix Sms that reflects these changes in line lengths d1 to d4 show that the peak frequency of the maximum eigenvalue deviates from 558 Hz. Furthermore, when the current and electromagnetic strength were measured in the multi-conductor transmission line system 10 with the line lengths d1 to d4 changed, as in the prototype, it was confirmed that the resonance peaks of the current and electromagnetic waves also deviated from 537 Hz.

[0070] As described above, in Example 1, the multi-conductor transmission line system 10 is designed through the following first to third steps. The first step is a step of performing eigenvalue analysis on each of the lines 33 to 38, which are components of the multi-conductor transmission line system 10, using the analysis method of this embodiment. The second step is a step of extracting lines 33 to 38 that have large eigenvalues ​​at problematic frequencies based on the results of the eigenvalue analysis. The third step is a step of changing the design values ​​(line lengths in Example 1) of the extracted lines (lines 33 and 36 in Example 1) so as to change the characteristic impedance of the extracted lines. Note that the characteristic impedance of the lines 33 to 38 can also be changed by changing the cross-sectional shape of the conductors or the height from the ground plane 11. Therefore, the third step may be performed by changing the cross-sectional shape of the conductors of the extracted lines or by changing the height from the ground plane 11 of the extracted lines.

[0071] It is also possible to design the multi-conductor transmission line system 10 by changing the load resistance of the terminal loads 15-18 as follows. In this case, in the first step, the eigenvalues ​​of the terminal loads 15-18 for each frequency are found by eigenvalue analysis using the analysis method of this embodiment. In the second step, the terminal loads 15-18 with large eigenvalues ​​at the problematic frequency are extracted. In the third step, the load resistances of the extracted terminal loads 15-18 are changed so as to change the characteristic impedance.

[0072] <Example 2> In the case of Example 2, the prototype of multi-conductor transmission line system 10 has line lengths d1 to d7 of each of lines 33 to 39 set so that the line length matrix d = [390, 390, [740, 740], 470, 470, 1] (all units are mm) is satisfied, as in Example 1. Furthermore, each of terminal loads 15 to 18 of this prototype has a load resistance of 50 Ω. Meanwhile, in the prototype of multi-conductor transmission line system 10 in Example 2, each of lines 33 to 39 is laid at a certain height H1 from ground plane 11.

[0073] A noise signal was injected from noise source 19 into a prototype of multi-conductor transmission line system 10 of Example 2, with the noise signal set so that the terminal voltage of first conductor line 12 connected to first terminal load 15 was 1 V across the entire frequency band. Then, with the noise signal injected, the voltage value V3 of third terminal load 17 and the voltage value V4 of fourth terminal load 18 were measured. From the measurement results of voltage values ​​V3 and V4, multiple frequencies of voltage resonance peaks were confirmed. The multiple confirmed frequencies included 413 Hz, a frequency that has an undesirable effect on the operation of a device connected as fourth terminal load 18. Therefore, it was necessary to change the design of multi-conductor transmission line system 10 so that the frequency of the voltage resonance peak was shifted from 413 Hz.

[0074] On the other hand, the results of eigenvalue analysis of this prototype confirmed that the peak frequencies of the eigenvalue with the largest absolute value and the eigenvalue with the second largest absolute value appear to overlap roughly with the frequency of the voltage resonance peak. In the eigenvector corresponding to the eigenvalue with the largest absolute value at 413 Hz, the first, fifth, and sixth elements e1, e5, and e6 show larger values ​​than the other elements e2 to e4. Furthermore, in the eigenvector corresponding to the eigenvalue with the second largest absolute value at 413 Hz, the first, second, and fourth elements e1, e2, and e4 show larger values ​​than the other elements e3, e5, and e6.

[0075] Here, we consider changing the second largest eigenvalue at 413 Hz as a countermeasure. From the results of the above eigenvalue analysis, it is considered effective to change the characteristic impedances of the lines 33, 34, and 36 corresponding to the first, second, and fourth elements e1, e2, and e4. Here, as in the first embodiment, we decided to change the line lengths d1 to d4 of the lines 33 to 36 so that the changed line length matrix d becomes [510, 510, [620, 620], 470, 470, 1] (all units are mm).

[0076] The results of eigenvalue analysis using the modal multiple reflection infinite series matrix Sms that reflects these changes in line lengths d1 to d4 show that the frequency of the voltage resonance peak deviates from 558 Hz. Furthermore, when the voltage values ​​V3 and V4 were measured in the same manner as in the prototype for the multi-conductor transmission line system 10 in which the line lengths d1 to d4 were changed, it was confirmed that the voltage resonance peak of the fourth terminal load 18 also deviated from 537 Hz.

[0077] Instead of changing the line length, the height of each of the lines 33 to 39 from the ground plane 11 may be changed to change the frequency of the resonance peak. In this case, the design of the multi-conductor transmission line system 10 is performed through the following fourth and fifth steps. The fourth step is a step of calculating the noise peak frequency of the components of the multi-conductor transmission line system 10 using the analysis method of the above embodiment. The fifth step is a step of changing the height of one or more of the lines 33 to 39 from the ground plane 11 if the calculated peak frequency is a problematic frequency.

[0078] Example 3 The voltage value of each terminal load 15-18 when noise is injected can be calculated using the modal multi-reflection infinite series matrix Sms of equation (15). By using the calculation results of the voltage values ​​of the terminal loads 15-18, it is possible to design the multi-conductor transmission line system 10 so as to reduce a specific frequency component of the noise voltage in any of the terminal loads 15-18.

[0079] From equation (15), the mode voltage wave vector Am1 of the noise incident on the uniform line group 30 from the first terminal network 31 can be determined. The noise incident on the uniform line group 30 from the first terminal network 31 propagates through the uniform line group 30 and is incident on the second terminal network 32. As described above, the attenuation and phase delay and attenuation associated with propagation through the uniform line group 30 can be expressed by the vector AT in equation (12). Therefore, the mode voltage wave vector Bm2 of the noise that is emitted from the first terminal network 31, propagates through the uniform line group 30, and is incident on the second terminal network 32 can be determined as shown in equation (17).

[0080]

number

[0081] The modal voltage wave vector Am2 of the noise that is then reflected by the second terminal network 32 and re-enters the uniform line group 30 can be expressed as in equation (18) using the modal reflection coefficient matrix Sm2 at the second terminal network 32.

[0082]

number

[0083] Furthermore, the mode voltage wave vector Bm1 of the noise that propagates through the uniform line group 30 after re-incursion and re-incurs the first terminal circuit network 31 can be expressed as in equation (19) using vector AT of equation (12) which indicates the attenuation and phase delay associated with propagation through the uniform line group 30.

[0084]

number

[0085] As described above, all of the incident and reflected voltage waves of the first terminal network 31 and the second terminal network 32 are calculated. From these, the modal voltage vectors Vm1 and Vm2 of the first terminal network 31 and the second terminal network 32 are calculated. The modal voltage vector Vm1 of the first terminal network 31 can be expressed as the sum of the modal voltage wave vector Am1 and the modal voltage wave vector Bm1 (Vm1 = Am1 + Bm1). The modal voltage vector Vm2 of the second terminal network 32 can be expressed as the sum of the modal voltage wave vector Am2 and the modal voltage wave vector Bm2 (Vm2 = Am2 + Bm2). The voltage values ​​of each terminal load 15-18 can be calculated by multiplying the modal voltage vectors Vm1 and Vm2 by the modal conversion matrix Pv. In the third embodiment, the multi-conductor transmission line system 10 is designed using the results of these voltage value calculations.

[0086] In this Example 3, two design proposals 1 and 2 for a multi-conductor transmission line system 10 are compared and examined. The design proposals differ only in the height from the ground plane 11 of the single-wire section of the second conductor line 13 corresponding to the line 33 in FIG. 2 . The height from the ground plane 11 of the single-wire section corresponding to the line 33 in Design Proposal 1 is "H1," while the height from the ground plane 11 of the single-wire section corresponding to the line 33 in Design Proposal 2 is "H2." It has been confirmed that 500 MHz noise has an undesirable effect on the operation of a device connected as the fourth terminal load 18 in the multi-conductor transmission line system 10 being designed. Therefore, the merits of Design Proposals 1 and 2 are determined based on the magnitude of the 500 MHz noise generated in the fourth terminal load 18.

[0087] In the comparative study, first, for each of the multi-conductor transmission line systems 10 of design proposals 1 and 2, the voltage value of the fourth terminal load 18 when a noise signal similar to that in Examples 1 and 2 was incident was calculated using the above analysis method. As a result, it was confirmed that there are bands in which the frequency characteristics of the noise generated at the fourth terminal load 18 differ greatly between design proposals 1 and 2. For the 500 MHz noise in question, design proposal 1 was smaller than design proposal 2, so it was decided to adopt design proposal 1.

[0088] Example 4 In Example 4, the following three prototypes 1 to 3 of a multi-conductor transmission line system 10 were prepared. Prototypes 1 to 3 differ only in the height from ground plane 11 on which first conductor line 12 and second conductor line 13 are laid. Prototype 1 is a multi-conductor transmission line system 10 in which the entire first conductor line 12 and second conductor line 13 are laid at a height H1 from ground plane 11. Prototype 2 is a multi-conductor transmission line system 10 in which the entire first conductor line 12 and second conductor line 13 are laid at a height H2 (>H1) from ground plane 11. Prototype 3 is a multi-conductor transmission line system 10 in which the entire first conductor line 12 and second conductor line 13 are laid in close contact with ground plane 11.

[0089] In this Example 4, the noise voltage of the fourth terminal load 18 for each of Prototypes 1 to 3 was calculated using the analysis method of Example 3. Furthermore, the noise voltage of the fourth terminal load 18 for each of Prototypes 1 to 3 was actually measured and compared with the results of calculation using the analysis method. As a result, for Prototype 1, the calculation results generally agreed with the actual measurement results, except for some frequency bands. In contrast, for Prototypes 2 and 3, the calculation results deviated significantly from the actual measurement results in more than half of the frequency bands.

[0090] This is thought to be due to the following reasons: When a conductor line is installed at a position more than a certain distance from the ground plane 11, the coupling between the conductor of the conductor line and the ground plane 11 becomes weak. Also, radiation from the conductor line increases. Therefore, when the height from the ground plane 11 of the installation position of the conductor line becomes higher than a certain level, it is thought that the analysis results of noise characteristics using the analysis method of the above embodiment will not easily match the results of actual measurements. On the other hand, when the conductor line is installed in close contact with the ground plane 11, the distance between the conductor of the conductor line and the ground plane 11 is determined by the thickness of the insulating film of the conductor line. In this case, the noise characteristics change significantly due to deformation of the insulating film, so it is thought that the analysis results will easily deviate from the results of actual measurements.

[0091] From the results of such analysis and comparison of actual measurements, the inventors have come to the following finding: It is desirable to set the height of the conductor lines from ground plane 11 in multi-conductor transmission line system 10 so as to satisfy the following requirements 1 and 2. Requirement 1 is that the height from ground plane 11 must be at least twice the thickness of the dielectric covering of the conductor lines. Requirement 2 is that the height from ground plane 11 must be sufficiently smaller than the wavelength of the noise signal with the maximum frequency among the noise signals to be analyzed. These requirements 1 and 2 define the effective application range of the analysis method of the above embodiment.

[0092] (Other embodiments) The analysis method of the above embodiment and the design method of each of the above examples can also be applied to multi-conductor transmission line systems with configurations different from those shown in FIG. 1, as long as the multi-conductor transmission line system has branches made up of multiple conductor lines. For example, they can also be applied to multi-conductor transmission line systems made up of three or more conductor lines or multi-conductor transmission line systems with multiple parallel sections. Below, configuration examples 1 and 2 of multi-conductor transmission line systems to which the analysis method of the above embodiment can be applied are described.

[0093] <Configuration example 1> A multi-conductor transmission line system 100 of configuration example 1 shown in FIG. 3 includes a ground plane 101 and three conductor lines 102-104. In this multi-conductor transmission line system 100, conductor lines 103 and 104 are laid so as to run parallel to each other in close proximity over their entire length. Furthermore, the multi-conductor transmission line system 100 includes a three-wire parallel section 105 in which the three conductor lines 102-104 run parallel to each other. Both ends of the three-wire parallel section 105 are branched into branch sections 120 and 121, which branch into a single-wire section of conductor line 102 and two-wire parallel sections 106 and 107 of conductor lines 103 and 104. Both ends of conductor line 102 are grounded to ground plane 11 via terminal loads 108 and 111, respectively. Both ends of conductor line 103 are grounded to ground plane 11 via terminal loads 109 and 112, respectively. Both ends of the conductor line 104 are grounded to the ground plane 11 via terminal loads 110 and 113, respectively. In this multi-conductor transmission line system 100, the noise source 19 is connected to the terminal of the conductor line 102 that is connected to the terminal load 108.

[0094] The cross-sectional shape of the conductor of conductor line 102 changes midway through the single-wire section between branch 120 and terminal load 108. In Fig. 3, the difference in the cross-sectional shape of the conductor is represented by the difference in thickness of the line representing conductor line 102. In the following description, the position where the cross-sectional shape of the conductor of conductor line 102 changes is referred to as change point 114.

[0095] Fig. 4 shows a circuit diagram of a substitution circuit that virtually replaces the multi-conductor transmission line system 100 of Fig. 3 when applying the analysis method of the above embodiment. Similar to the above embodiment, this substitution circuit is created by virtually wiring each of the conductor lines 102-104 so that they travel back and forth between the first terminal circuit network 131 and the second terminal circuit network 132, with the positions of change in characteristic impedance, including branch points 120 and 121 from the parallel running section (105), as turning points. In the case of the multi-conductor transmission line system 100 of Fig. 3, in addition to the branch points 120 and 121, the positions of change in characteristic impedance also include the change point 114 in the cross-sectional shape of the conductor in the conductor line 102. In this case, the uniform line group 230 is composed of ten lines 133-142, each of which has a uniform characteristic impedance over its entire length. The modal multiple reflection infinite series matrix Sms of equation (15) can be applied to the multi-conductor transmission line system 100 of Fig. 3 by virtually replacing it with the substitution circuit of Fig. 4. Therefore, the noise characteristics of the multi-conductor transmission line system 100 of configuration example 1 can also be easily analyzed using the analysis method of the above embodiment.

[0096] <Configuration example 2> Multi-conductor transmission line system 200 of configuration example 2 shown in Fig. 5 includes ground plane 201 and three conductor lines 202 to 204. This multi-conductor transmission line system 200 has two parallel sections 205 and 206. Parallel section 205 is a section where two conductor lines 202 and 203 run parallel to each other in close proximity. Parallel section 206 is a section where two conductor lines 202 and 204 run parallel to each other in close proximity. Both ends of parallel section 205 are branch sections 220 and 221 where conductor lines 202 and 203 branch off. Both ends of parallel section 206 are branch sections 220 and 221 where conductor lines 202 and 204 branch off. Of the three conductor lines 202 to 204, only conductor line 202 is laid through both parallel sections 205 and 206. Both ends of conductor line 202 are grounded to ground plane 11 via terminal loads 207 and 210, respectively. Both ends of conductor line 203 are grounded to ground plane 11 via terminal loads 208 and 211, respectively. Both ends of conductor line 204 are grounded to ground plane 11 via terminal loads 209 and 212, respectively. In the case of this multi-conductor transmission line system 200, noise source 19 is connected to the terminal of conductor line 202 that is connected to terminal load 207.

[0097] FIG. 6 shows a circuit diagram of a substitution circuit that virtually replaces the multi-conductor transmission line system 200 of FIG. 4 when applying the analysis method of the above embodiment. In the case of the multi-conductor transmission line system 200 of FIG. 5, the branch points 220-223 of the conductor lines 202-204 from both parallel sections 205 and 206 are the locations where the characteristic impedance of each conductor line 202-204 changes. The substitution circuit of FIG. 5 is created by virtually wiring each conductor line 202-204 so that it travels back and forth between the first terminal circuit network 231 and the second terminal circuit network 232, with the branch points 220-223 from the parallel sections 205 and 206 as turning points. In this case, the uniform line group 230 is composed of eleven lines 233-243. By virtually replacing the multi-conductor transmission line system 200 of FIG. 5 with the substitution circuit of FIG. 6, the modal multiple reflection infinite series matrix Sms of Equation (15) can be applied. Therefore, the noise characteristics of the multi-conductor transmission line system 200 of Configuration Example 2 can also be easily analyzed using the analysis method of the above embodiment. [Explanation of symbols]

[0098] 10...multi-conductor transmission line system, 11...ground plane, 12, 13...conductor line, 14...parallel running section, 15-18...terminal load, 19...noise source, 20, 21...branch section, 22...turn point, 30...uniform line group, 31...first terminal circuit network, 32...second terminal circuit network, 33-39...line.

Claims

1. A method for analyzing noise characteristics of a multi-conductor transmission line system that is configured by a ground plane and a plurality of conductor lines and has a parallel running section in which the plurality of conductor lines run parallel to each other, comprising: a propagation model is used to assume that a noise signal input to the multi-conductor transmission line system propagates through a group of uniform lines, with multiple reflections between a first terminal circuit network and a second terminal circuit network, and the noise characteristics of the multi-conductor transmission line system are analyzed; The propagation model is such that, assuming that each of the plurality of conductor lines is wired so as to travel back and forth between the first terminal circuit network and the second terminal circuit network, with a turning point being a position where a characteristic impedance changes, including a branch point from the parallel running section, the uniform line group is constituted by each line spanning between the first terminal circuit network and the second terminal circuit network, and among the terminal loads of each of the plurality of conductor lines and the terminal elements at the turning points, the first terminal circuit network is constituted by an element connected to one end of the uniform line group, and the second terminal circuit network is constituted by an element connected to the other end. Analysis methods for multiconductor transmission line systems.

2. 2. The method for analyzing a multi-conductor transmission line system according to claim 1, wherein the ground plane is a conductor body of a transportation device.

3. 2. The method for analyzing a multi-conductor transmission line system according to claim 1, wherein the conductor line is an electric wire or a bus bar.

4. A method for designing a multi-conductor transmission line system that is configured by a ground plane and a plurality of conductor lines and has a parallel running section in which the plurality of conductor lines run parallel to each other, comprising: performing an eigenvalue analysis of components of the multi-conductor transmission line system using the analysis method according to claim 1; extracting, from among the components of the multi-conductor transmission line system, components having large eigenvalues ​​at problematic frequencies based on the results of the eigenvalue analysis; and changing the design values ​​of the extracted components so that the characteristic impedance of the components changes; The multi-conductor transmission line system is designed through Design methods for multiconductor transmission line systems.

5. A method for designing a multi-conductor transmission line system that is configured by a ground plane and a plurality of conductor lines and has a parallel running section in which the plurality of conductor lines run parallel to each other, comprising: calculating a peak frequency of noise from a component of the multi-conductor transmission line system using the analysis method according to claim 1; if the calculated peak frequency is a frequency of interest, varying the height of one or more of the lines from the ground plane; The multi-conductor transmission line system is designed through Design methods for multiconductor transmission line systems.

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