A method for fitting transmission line losses using linear regression

Abstract

This invention relates to a method for fitting transmission line loss using linear regression, comprising the following steps: obtaining loss factors corresponding to multiple discrete frequency points based on the characteristic data of the substrate used in the transmission line; establishing a correlation equation between the loss factor and frequency using a linear regression algorithm, and configuring the correlation equation as a dynamic loss factor parameter in the transmission line simulation model; performing transmission line loss simulation through the configured simulation model to achieve full-band fitting of transmission line loss. This invention utilizes the dynamic correlation equation between the loss factor and frequency to avoid simulation deviations caused by fixed value settings, significantly improving the reliability of transmission line loss simulation results and achieving a high degree of consistency between simulated data and measured transmission line loss data within the target frequency band. This invention can construct dynamic loss factor parameters based solely on official substrate characteristic data and a linear regression algorithm, with a simple operation process, low implementation cost, and rapid application by circuit designers.

Description

Technical Field

[0001] This invention relates to the field of circuit design, and more specifically, to a method for fitting transmission line losses using linear regression. Background Technology

[0002] Printed circuit boards (PCBs), as the core component supporting the physical structure and signal transmission of electronic products, directly impact the overall performance of the product due to their signal integrity. With the continuous improvement of transmission rates in electronic devices, accurately fitting transmission line losses through simulation is of significant engineering importance for predicting the actual performance of manufactured products and optimizing design schemes. The simulation accuracy of transmission line loss is closely related to the loss factor (DF value, also known as TanD value) of the substrate. This parameter is a key indicator characterizing the energy loss properties of the dielectric material. It is not fixed but exhibits a regular increase with increasing operating frequency. This variation is usually clearly stated in the official technical datasheet of the substrate as typical values ​​corresponding to multiple discrete frequency points.

[0003] In existing electromagnetic simulation software applications, when simulating transmission line loss, only a single fixed value for the loss factor is set. This leads to significant deviations between the simulation results and measured data. Specifically, while setting the loss factor to a typical value corresponding to the low-frequency band can achieve effective fitting in the low-frequency band, the simulated loss deviates greatly from the measured loss in the high-frequency band. Figure 3 If the loss factor is set to a typical value corresponding to the high-frequency band, the problem arises where the high-frequency band fitting is accurate, but the simulated loss deviates significantly from the measured loss in the low-frequency band. (Refer to...) Figure 4 This ultimately led to the failure of the full-band transmission line loss fitting, severely affecting the reliability of the transmission line loss simulation results. Summary of the Invention

[0004] To overcome the problem that existing electromagnetic simulation methods, which only set a single fixed value for the loss factor, lead to the failure of full-band transmission line loss fitting and unreliable simulation results, this invention provides a method for fitting transmission line loss using linear regression. It proposes to replace the fixed value setting by establishing a dynamic correlation between the loss factor and the frequency.

[0005] The technical solution of this invention is as follows:

[0006] A method for fitting transmission line loss using linear regression includes the following steps:

[0007] Step 1: Based on the characteristic data of the board material used in the transmission line, obtain the loss factors corresponding to multiple discrete frequency points respectively;

[0008] Step 2: Use a linear regression algorithm to establish the correlation equation between the loss factor and the frequency, so as to characterize the dynamic law of the loss factor changing with the frequency.

[0009] Step 3: Configure the correlation equation as a dynamic loss factor parameter in the transmission line simulation model;

[0010] Step 4: Perform transmission line loss simulation using the configured simulation model to achieve full-band fitting of transmission line loss.

[0011] By adopting the above technical solution, a dynamic correlation equation is used instead of a single fixed value of the loss factor, which allows the simulation process to match the actual value of the loss factor at different frequencies in real time. This completely solves the problem of failure in fitting transmission line loss across the entire frequency band, improves the fit between simulation data and measured data, and enhances the reliability of transmission line loss simulation results.

[0012] As a preferred technical solution of the present invention, in step 1, the characteristic data of the board material is derived from the technical data sheet of the board material, and the discrete frequency points cover the target full frequency band of the transmission line simulation.

[0013] By adopting the above technical solution, the authority and accuracy of the loss factor data are ensured, avoiding any impact on the accuracy of subsequent modeling. At the same time, the discrete frequency points covering the entire frequency band reflect the overall pattern of the loss factor change with frequency.

[0014] As a preferred technical solution of the present invention, when using the linear regression algorithm, the frequency value of each discrete frequency point is used as the independent variable, and the loss factor data of the corresponding frequency point is used as the dependent variable. The data is imported into the EXCEL software, and the linear regression algorithm is called up to perform the calculation.

[0015] By adopting the above technical solutions, circuit designers can construct correlation equations without relying on professional modeling software or complex testing equipment, and can do so with the help of general office software, which greatly reduces the technical implementation threshold and cost.

[0016] Furthermore, the specific steps for importing the data into Excel and executing the linear regression algorithm include:

[0017] Step A. Open Excel and create a data table with two columns and several rows;

[0018] Step B. Enter several frequency values ​​from the characteristic data in the first column; enter several loss factor values ​​from the characteristic data in the second column;

[0019] Step C. Open the linear regression algorithm program, enter the data from the second column in the dependent variable column, and enter the data from the first column in the independent variable column;

[0020] Step D. Run the linear regression algorithm program to obtain the correlation equation between the loss factor and the frequency.

[0021] By adopting the above technical solutions, the operation process of linear regression calculation is standardized, ensuring the accuracy of data input and algorithm operation, avoiding result deviations caused by operational errors, and the simplified operation steps further reduce the implementation difficulty and improve the practicality of the solution.

[0022] As a preferred technical solution of the present invention, the correlation equation in step 2 is a linear equation, namely DF=a+b×freq, where DF represents the loss factor, a is the intercept term, b is the frequency coefficient, and freq represents the real-time frequency variable in the simulation process.

[0023] Furthermore, in the settings interface of the linear regression algorithm program, the confidence level is set to 95%.

[0024] Furthermore, the characteristic data includes several frequency values: 14GHz, 25GHz, 37GHz, 49GHz, and 60GHz; several loss factor values: 0.0013, 0.0015, 0.0017, 0.0019, and 0.0021; the correlation equation obtained using the linear regression algorithm is: DF = 0.001062259 + 1.72363 × 10 -14 freq.

[0025] As a preferred technical solution of the present invention, the specific steps of configuring the correlation equation in the transmission line simulation model in step 3 are as follows: in the medium parameter setting interface of the transmission line simulation model, first set the loss factor parameter item as a variable, and then assign the variable a value equal to the correlation equation.

[0026] By adopting the above technical solution, the dynamic loss factor can be configured by switching parameter modes and assigning equations. The operation is simple and highly compatible, and it can be adapted to mainstream electromagnetic simulation software such as ADS and HFSS.

[0027] As a preferred technical solution of the present invention, it further includes step 5: verifying whether the simulation results fit the measured results;

[0028] Calculate the absolute value of the deviation between the simulation results and the measured results of the transmission line loss at different frequencies, and determine whether the absolute value of the deviation is ≤0.1dB.

[0029] By adopting the above technical solution, quantitative standards are used to verify the simulation effect, avoiding fuzzy judgments on the fitting effect; and the high-precision threshold of 0.1dB ensures accurate matching between the simulation results and the actual transmission line loss characteristics.

[0030] As a preferred embodiment of the present invention, the transmission line is a high-speed signal transmission line in a printed circuit board, and the electromagnetic simulation software adapted to the transmission line simulation model includes at least one of ADS and HFSS. It should be noted that a signal transmission frequency of 1 GHz or higher can be defined as a high-speed signal.

[0031] According to the above-described solution, the beneficial effects of this invention are as follows:

[0032] This invention replaces the single fixed value of the loss factor used in existing simulation methods with a dynamic correlation equation between the loss factor and frequency. This allows for real-time matching of the loss factor values ​​at different frequencies during the simulation process, achieving a high degree of consistency between the simulated data and the measured transmission line loss data within the target frequency band. The dynamic correlation equation characterizes the inherent law of the loss factor's variation with frequency, avoiding simulation deviations caused by fixed value settings, and significantly improving the reliability and engineering reference value of transmission line loss simulation results. Furthermore, this invention can construct dynamic loss factor parameters based solely on official material characteristic data and a linear regression algorithm, resulting in a simple operation process, low implementation cost, and rapid application by engineering designers. Attached Figure Description

[0033] Figure 1 This is a flowchart of the method of the present invention;

[0034] Figure 2 This is a comparison chart of the simulation results and the measured results of the method of the present invention;

[0035] Figure 3 A comparison chart of simulation and measured results for low-frequency DF values ​​using existing methods;

[0036] Figure 4 A comparison chart of simulation results and measured results for high-frequency corresponding DF values ​​using existing methods is provided. Detailed Implementation

[0037] To better understand the purpose, technical solution, and technical effects of this invention, the invention will be further explained and described below in conjunction with the accompanying drawings and embodiments. It should be noted that similar reference numerals and letters in the following drawings indicate similar items; therefore, once an item is defined in one drawing, it does not need to be further defined and explained in subsequent drawings. It is also stated that the embodiments described below are only for explaining this invention and are not intended to limit this invention.

[0038] It should be noted that when a component is referred to as "fixed to" or "set on" another component, it can be directly on the other component or there may be an intermediate component. When a component is referred to as "connected to" another component, it can be directly connected to the other component or there may be an intermediate component.

[0039] The terms “first” and “second” are used for descriptive purposes only and should not be construed as indicating or implying relative importance or specifying the number of technical features. “Several” means two or more, unless otherwise expressly and specifically defined.

[0040] like Figure 1 As shown, a method for fitting transmission line loss using linear regression is characterized by comprising the following steps:

[0041] Step 1: Based on the characteristic data of the board material used in the transmission line, obtain the loss factors corresponding to multiple discrete frequency points respectively;

[0042] The characteristic data of the board material comes from the technical data sheet of the board material. The discrete frequency points cover the target full frequency band of the transmission line simulation. The target full frequency band refers to the complete frequency range that the simulation needs to cover. In a specific embodiment, the target full frequency band is 0.05GHz to 60GHz. The characteristic data of the board material records the DF (loss factor) value of a 4-layer board as follows: DF is 0.0013 at 14GHz, DF is 0.0015 at 25GHz, DF is 0.0017 at 37GHz, DF is 0.0019 at 49GHz, and DF is 0.0021 at 60GHz.

[0043] This step provides reliable foundational data for establishing the dynamic correlation equation between loss factor and frequency. It fully utilizes the existing discrete frequency data in the material datasheet to directly transform existing data into dynamic equations, ensuring data authority while significantly improving modeling efficiency.

[0044] Step 2: Establish the correlation equation between the loss factor and frequency using a linear regression algorithm to characterize the dynamic law of the loss factor changing with frequency. This step transforms discrete frequency point data into a dynamic simulation model through the linear regression algorithm, that is, converts the scattered frequency-loss factor numerical pairs in the material datasheet into a dynamic correlation equation to replace the fixed DF value. This step overcomes the limitation that discrete data cannot be directly used for continuous frequency band simulation, and realizes that the corresponding DF value can be automatically calculated according to the real-time frequency during the simulation process, instead of relying on a single fixed value.

[0045] When using the linear regression algorithm, the frequency value of each discrete frequency point is used as the independent variable, and the loss factor data of the corresponding frequency point is used as the dependent variable. The data is imported into the EXCEL software, and the linear regression algorithm is called up to perform the calculation.

[0046] The specific steps for importing data into Excel and executing the linear regression algorithm include:

[0047] Step A. Open Excel and create a data table with two columns and several rows;

[0048] Step B. Enter several frequency values ​​from the characteristic data in the first column; enter several loss factor values ​​from the characteristic data in the second column;

[0049] Step C. Open the linear regression algorithm program, enter the data from the second column in the dependent variable column, and enter the data from the first column in the independent variable column;

[0050] Step D. Run the linear regression algorithm program. Excel software will fit an accurate linear equation based on the data in the first and second columns, thus obtaining the correlation equation between the loss factor and the frequency.

[0051] This invention cleverly utilizes the linear regression calculation program in Excel software. Through simple steps—creating a table, filling in data, debugging the algorithm, and generating the equation—it lowers the implementation threshold. Staff can quickly construct the dynamic equation without relying on complex modeling tools. The final correlation equation is a linear equation, DF=a+b×freq, where DF represents the loss factor, a is the intercept term, b is the frequency coefficient, and freq represents the real-time frequency variable during the simulation. This equation clearly characterizes the dynamic law of the loss factor changing with frequency.

[0052] Excel is a general-purpose office software, not a professional electromagnetic simulation or data modeling tool. This step breaks down prejudice and cleverly uses a general-purpose tool to solve the core modeling problems of professional simulations. It avoids relying on complex parameter optimization software, lowers the implementation threshold, and ensures that the output results of Excel linear regression can be directly adapted to the parameter input requirements of the simulation software.

[0053] As can be seen, this invention precisely selects a linear regression algorithm to address the characteristic that DF changes approximately linearly with frequency. It abandons the fixed value setting mindset in conventional modeling methods and the approach of using complex linear modeling software, thus ensuring modeling accuracy while avoiding the implementation difficulties brought about by complex algorithms. For the first time, it combines the common office function of Excel linear regression with the core requirement of high-speed PCB transmission line loss simulation, significantly reducing the technical implementation threshold and cost.

[0054] This invention also includes:

[0055] Step 3: Configure the correlation equation as a dynamic loss factor parameter in the transmission line simulation model;

[0056] The specific steps for configuring the correlation equation in the transmission line simulation model are as follows: In the medium parameter setting interface of the transmission line simulation model, first set the loss factor parameter item as a variable, and change the loss factor item in the medium parameters of the simulation model from the default fixed value input mode to the variable mode; then assign the variable to the correlation equation obtained in step 2. At this time, the DF value in the simulation model is no longer a fixed number, but a calculation result that changes dynamically with frequency.

[0057] Step 4: Perform transmission line loss simulation using the configured simulation model to achieve full-band fitting of transmission line loss.

[0058] In one specific embodiment, the confidence level is set to 95% in the settings interface of the linear regression algorithm program.

[0059] The characteristic data includes several frequency values: 14GHz, 25GHz, 37GHz, 49GHz, and 60GHz; and several loss factor values: 0.0013, 0.0015, 0.0017, 0.0019, and 0.0021. After executing step 2, the correlation equation obtained using the linear regression algorithm is: DF = 0.001062259 + 1.72363 × 10⁻⁶. -14 freq;

[0060] Perform step 3, and enter the variable DF=0.001062259+1.72363×10 in the loss factor parameter field of the medium parameter setting interface. -14 freq;

[0061] Perform step 4 to obtain the following result: Figure 2 The simulation results shown demonstrate the difference between the simulation curves and the measured curves, exhibiting a very high degree of fit for both low and high frequencies.

[0062] This invention also includes step 5, verifying whether the simulation results fit the measured results; calculating the absolute value of the deviation between the simulation results and the measured results of transmission line loss at different frequencies, and determining whether the absolute value of the deviation is ≤0.1dB. Step 5 provides quantitative verification, verifying whether the simulation results of step 4 truly solve the full-band fitting problem through a clear numerical standard. For several key frequencies or several operating frequencies within the target full-band, the absolute value of the deviation between the simulated value and the measured value of transmission line loss at the same frequency can be calculated, and then the standard of "whether the absolute value of the deviation is ≤0.1dB" is used for judgment. This standard is much higher than the 0.5dB value acceptable in conventional engineering.

[0063] In this invention, the transmission line is a high-speed signal transmission line in a printed circuit board, and the signal transmission frequency reaches 1 GHz or above, which can be defined as a high-speed signal.

[0064] In summary, this invention replaces the single fixed value of the loss factor used in existing simulation methods with a dynamic correlation equation between the loss factor and frequency. This allows for real-time matching of the loss factor values ​​at different frequencies during the simulation process, achieving a high degree of consistency between simulated data and measured transmission line loss data within the target frequency band. Furthermore, the dynamic correlation equation characterizes the inherent law of loss factor variation with frequency, avoiding simulation deviations caused by fixed value settings and significantly improving the reliability and engineering reference value of transmission line loss simulation results. Moreover, this invention can construct dynamic loss factor parameters based solely on official material characteristic data and a linear regression algorithm, resulting in a simple operation process, low implementation cost, and rapid application by engineering designers.

[0065] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0066] The above embodiments merely illustrate several implementation methods of the present invention, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention patent should be determined by the appended claims.

Claims

1. A method for fitting transmission line loss using linear regression, characterized in that, Includes the following steps: Step 1: Based on the characteristic data of the board material used in the transmission line, obtain the loss factors corresponding to multiple discrete frequency points respectively; Step 2: Use a linear regression algorithm to establish the correlation equation between the loss factor and the frequency, so as to characterize the dynamic law of the loss factor changing with the frequency. Step 3: Configure the correlation equation as a dynamic loss factor parameter in the transmission line simulation model; Step 4: Perform transmission line loss simulation using the configured simulation model to achieve full-band fitting of transmission line loss.

2. The method for fitting transmission line loss using linear regression according to claim 1, characterized in that, In step 1, the characteristic data of the board material comes from the technical data sheet of the board material, and the discrete frequency points cover the target full frequency band of the transmission line simulation.

3. The method for fitting transmission line loss using linear regression according to claim 1, characterized in that, When using the linear regression algorithm, the frequency value of each discrete frequency point is used as the independent variable, and the loss factor data of the corresponding frequency point is used as the dependent variable. The data is imported into the EXCEL software, and the linear regression algorithm is invoked to perform the calculation.

4. The method for fitting transmission line loss using linear regression according to claim 3, characterized in that, The specific steps for importing data into Excel and executing the linear regression algorithm include: Step A. Open Excel and create a data table with two columns and several rows; Step B. Enter several frequency values ​​from the characteristic data in the first column; enter several loss factor values ​​from the characteristic data in the second column; Step C. Open the linear regression algorithm program, enter the data from the second column in the dependent variable column, and enter the data from the first column in the independent variable column; Step D. Run the linear regression algorithm program to obtain the correlation equation between the loss factor and the frequency.

5. The method for fitting transmission line loss using linear regression according to any one of claims 1 to 4, characterized in that, The correlation equation mentioned in step 2 is a linear equation, namely DF=a+b×freq, where DF represents the loss factor, a is the intercept term, b is the frequency coefficient, and freq represents the real-time frequency variable during the simulation process.

6. The method for fitting transmission line loss using linear regression according to claim 4, characterized in that, In the settings interface of the linear regression algorithm program, set the confidence level to 95%.

7. The method for fitting transmission line loss using linear regression according to claim 6, characterized in that, The characteristic data includes several frequency values: 14GHz, 25GHz, 37GHz, 49GHz, and 60GHz; several loss factor values: 0.0013, 0.0015, 0.0017, 0.0019, and 0.0021; the correlation equation obtained using the linear regression algorithm is: DF = 0.001062259 + 1.72363 × 10 -14 freq.

8. The method for fitting transmission line loss using linear regression according to claim 1 or 7, characterized in that, In step 3, the specific steps for configuring the correlation equation in the transmission line simulation model are as follows: In the medium parameter setting interface of the transmission line simulation model, first set the loss factor parameter as a variable, and then assign the variable a value equal to the correlation equation.

9. The method for fitting transmission line loss using linear regression according to claim 1, characterized in that, It also includes step 5, verifying whether the simulation results fit the measured results; Calculate the absolute value of the deviation between the simulation results and the measured results of the transmission line loss at different frequencies, and determine whether the absolute value of the deviation is ≤0.1dB.

10. The method for fitting transmission line loss using linear regression according to claim 1, characterized in that, The transmission line is a high-speed signal transmission line in a printed circuit board, and the electromagnetic simulation software adapted to the transmission line simulation model includes at least one of ADS and HFSS.

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