A method for estimating the thickness and dielectric constant of multilayer dielectrics based on time-domain analysis.

Abstract

This invention belongs to the field of microwave measurement technology, specifically a method for estimating the thickness and dielectric constant of multilayer dielectrics based on time-domain analysis. This method uses a reflectometer to measure S-parameters over a wide frequency band, then uses inverse Fourier transform to obtain the waveform in the time domain. Analyzing the time-domain waveform allows for the deduction of the material's thickness and dielectric constant. This method utilizes the physical meaning of the discontinuity of the measured medium in the time domain to separate the dielectric material layer by layer. First, the thickness and dielectric constant of the outermost single layer are calculated, and then the thickness and dielectric constant of each internal layer are analyzed from the outside in. This invention enables the simultaneous measurement of the thickness and dielectric constant of multilayer dielectrics.

Description

Technical Field

[0001] This invention belongs to the field of microwave measurement technology and is a method for estimating the thickness and dielectric constant of multilayer dielectrics based on time-domain analysis. Background Technology

[0002] The measurement of electromagnetic parameters of a medium typically employs the network parameter method, which can be measured over a wide frequency band. This method treats the medium as a single-port or two-port network, measuring its scattering parameters, complex reflection coefficient, and other network parameters, and then calculating the electromagnetic parameters of the medium material. However, processing the measured scattering parameters directly from frequency domain data suffers from complex calculations, high computational load, and the potential for multiple values ​​in the measurement results. Conventional time-domain analysis methods use a time-domain gating method to window the time-domain waveform at discontinuities, then convert it to the frequency domain to calculate the magnitude of the reflection coefficient. The dielectric constant of the medium is then deduced from the relationship between the reflection coefficient and wave impedance in a scenario where a plane wave is perpendicularly incident on the boundary plane of an ideal medium. Finally, the thickness of the medium is calculated using the dielectric constant combined with the time difference between the time-domain discontinuities. This method has many error factors. It is greatly affected by the test bandwidth. Insufficient bandwidth can cause waveforms to overlap at time-domain discontinuities, making time-domain gating impossible. Furthermore, during time-frequency transformation, window functions with different attenuation coefficients are applied to the signal to reduce sidelobes and ringing effects, which can introduce time reading errors when calculating the time difference of time-domain discontinuities. If the medium is multilayer or lossy, the calculation error and difficulty will increase significantly, and the calculation accuracy will also decrease.

[0003] Current time-domain analysis methods primarily target single-layer dielectrics, measuring both thickness and dielectric constant. For example, a dielectric constant estimation method based on time-domain analysis uses a vector network analyzer to measure the S-parameters of two test systems as a reference. After subtracting antenna standing waves from both sets of data, a division operation is performed. The data is then converted to the time domain, and the dielectric thickness is calculated through comparative analysis. The time difference between the time points of discontinuities in the device under test (DUT) is used to determine the time taken for electromagnetic waves to propagate through the dielectric substrate. The dielectric constant is then calculated based on this time and the obtained dielectric thickness. However, this method is only applicable to single-layer dielectrics and cannot simultaneously measure both thickness and dielectric constant. Summary of the Invention

[0004] The present invention provides a method for estimating the thickness and dielectric constant of multilayer dielectrics based on time-domain analysis. This method utilizes a reflectometer to perform broadband S-parameter measurements, then employs inverse Fourier transform to obtain the waveform in the time domain. Analysis of the time-domain waveform allows for the deduction of the material's thickness and dielectric constant. By leveraging the physical meaning of the discontinuities in the measured medium in the time domain, the dielectric material is separated layer by layer. First, the thickness and dielectric constant of the outermost single layer are calculated, and then the internal dielectric conditions are analyzed from the outside in. This invention aims to utilize digital signal processing theory to calculate the thickness and dielectric constant of multilayer dielectric substrates.

[0005] To achieve the above-mentioned objectives, the technical solution of this invention is as follows:

[0006] 1. A method for estimating parameters of multilayer media based on time-domain analysis, characterized by comprising the following steps:

[0007] S1. Set up the dielectric parameter testing system and test the reflection coefficient S at the calibration point of the focused antenna using a vector network analyzer. 11 ;

[0008] S2, Measuring antenna standing wave S 11SW ;

[0009] S3, Frequency Domain Data Processing:

[0010] The effects of antenna standing waves can be removed through calibration.

[0011] S4. Calculate the dielectric constant and thickness of the first to nth dielectric layers sequentially:

[0012] S4.1. Convert the frequency domain data to the time domain, and perform signal sorting on the time axis to obtain multiple reflected signals;

[0013] S4.2 Calculate the dielectric constant and thickness of the first dielectric layer:

[0014] The first layer dielectric reflection signal Г1 is retained, while all other reflection signals are removed; the time-domain data of the reflection signal Г1 is converted to the frequency domain, and the dielectric constant ε of the first layer dielectric is calculated. r1 ;

[0015] The time difference Δt1 between the first and second discontinuities in the time-domain waveform is measured, and then the dielectric constant ε of the first layer of the medium is obtained based on the propagation speed of electromagnetic waves in the medium and step S4.2. r1 The thickness d1 of the first medium layer is calculated.

[0016] S4.3 Calculate the dielectric constant and thickness of the medium from the second layer to the nth layer:

[0017] The reflection signal Г1 from the second dielectric layer is retained, while the remaining reflection signals are removed. The time-domain data of the reflection signal Г2 is converted to the frequency domain and then combined with the dielectric constant ε of the first dielectric layer. r1 The dielectric constant ε of the second layer was calculated. r2 ;

[0018] The time difference Δt2 between the second and third discontinuities in the time-domain waveform is measured, and then the propagation speed of electromagnetic waves in the medium and the dielectric constant ε of the second layer of the medium are used as a basis. r2 The thickness d2 of the second medium layer is calculated.

[0019] Following the layer-by-layer peeling method, the dielectric constant and thickness of each of the remaining dielectric layers are solved one by one from the outside in, following the solution process of the second dielectric parameter and thickness. This yields the thickness and dielectric constant of the third, fourth...nth dielectric layers.

[0020] As a preferred method, the operation of setting the medium parameter test system in step S1 includes:

[0021] The dielectric parameter testing system includes a vector network analyzer, a spotlight antenna, a dielectric substrate under test (DUT), and a metal plate. The vector network analyzer is connected to the calibration point of the spotlight antenna, i.e., the feed receiver port. The DUT is placed against the metal plate, and the spotlight antenna is positioned perpendicular to the DUT. The reflection coefficient S at the calibration point of the spotlight antenna is measured using the vector network analyzer. 11 The test data is recorded as

[0022] As a preferred method, in step S2, the antenna standing wave S is measured. 11SW The specific operations include:

[0023] The reflection coefficient of the focused antenna was measured using a vector network analyzer when there was no substrate or metal plate under test. This reflection coefficient, also known as the antenna standing wave ratio, is denoted as S. 11SW .

[0024] As a preferred approach, the method for frequency domain data processing in step S3 is as follows:

[0025] The reflection coefficient was measured using a medium parameter testing system. Subtract antenna standing wave S 11SW The corresponding impact, and the corresponding data obtained from this, are denoted as...

[0026] As a preferred method, in step S4.2, the time-domain data of the reflected signal Г1 is converted to the frequency domain using a discrete Fourier transform to obtain the reflection coefficients of the first layer, and then combined with the formula... The dielectric constant ε of the first dielectric layer can then be calculated. r1 .

[0027] As a preferred method, the method for calculating the thickness d1 of the first dielectric layer in step S4.2 includes:

[0028] Analyzing the time-domain waveform, the first reflection peak represents the first discontinuity of the measured material, i.e., the first reflection at the interface between the air and the dielectric plate; the second reflection peak represents the second discontinuity of the measured material, i.e., the first reflection at the dielectric surface between the dielectric plate and the metal plate; there is a certain time difference between the first two reflections in the time domain, which is twice the time required for the electromagnetic wave to propagate within the medium at twice the thickness of the medium, as shown in the following formula:

[0029]

[0030] Where d is the thickness of the medium, c is the speed of electromagnetic wave propagation in vacuum, and ε represents the dielectric constant of the dielectric plate under test; the calculation formula is obtained from this formula.

[0031] Measure the time difference Δt1 between the first and second discontinuities in the time-domain waveform, and then use the dielectric constant ε of the first layer of dielectric obtained in step (4) to determine the dielectric constant. r1 Using the formula c is the propagation speed of electromagnetic waves in a vacuum, from which the thickness d1 of the first medium layer can be calculated.

[0032] As a preferred method, in step S4.3, the time-domain data of the reflected signal Г2 is converted to the frequency domain by performing a discrete Fourier transform, and then combined with the dielectric constant ε of the first layer of dielectric. r1 Using the formula The dielectric constant ε of the second layer can then be calculated. r2 .

[0033] As a preferred method, step S4.3, which involves solving for the dielectric constant and thickness of the remaining dielectric layers, includes:

[0034] When calculating the dielectric constant and thickness of the nth dielectric layer, the reflected signal T from the nth dielectric layer is used. n Retain the original signal and remove the rest of the reflected signal. Then, extract the reflected signal Γ. n Perform a DFT on the time-domain data to obtain the reflection coefficient of the nth layer, and then use the dielectric constant ε of the (n-1)th layer as a reference. rn-1 Using the formula The dielectric constant ε of the nth layer can then be calculated. rn The time difference Δt between the nth discontinuity and the (n+1)th discontinuity in the time-domain waveform is measured. n Then, based on the dielectric constant ε of the nth layer... rn Using the formula The thickness d of the nth layer of medium can then be calculated. n .

[0035] The beneficial effects of this invention are as follows: This invention provides a novel method for calculating the thickness and dielectric constant of a medium using time-domain S-parameter analysis. This method is based on wide-band S-parameter measurement using a reflectometer, followed by the use of inverse Fourier transform to obtain the waveform in the time domain. Analysis of the time-domain waveform allows for the deduction of the material's thickness and dielectric constant. In this process, the physical meaning of the discontinuity of the measured medium in the time domain is utilized to separate the medium material layer by layer. First, the thickness and dielectric constant of a single-layer medium are calculated, and then the calculation is extended from the outside in to the case of multi-layer media. Attached Figure Description

[0036] Figure 1 This is a flowchart of the method for estimating the thickness and dielectric constant of a multilayer dielectric in an embodiment;

[0037] Figure 2 This is a diagram of a multilayer media parameter testing system as described in the embodiment;

[0038] Figure 3 This is a diagram of the double-layer dielectric thickness and dielectric constant testing system in the embodiment;

[0039] Figure 4 This is the time-domain waveform diagram obtained by converting the reflection coefficient measured in Example 1 from the frequency domain to the time domain. Detailed Implementation

[0040] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention.

[0041] like Figure 1 As shown, this embodiment provides a method for estimating the thickness and dielectric constant of multilayer dielectrics based on time-domain analysis, including the following steps:

[0042] S1. Setting up the media parameter test system

[0043] Figure 2 A diagram of a multilayer media parameter testing system is shown. Figure 3 This diagram illustrates a system for testing the thickness and dielectric constant of a double-layer dielectric. (For example...) Figure 2 and Figure 3 As shown, the dielectric parameter testing system includes a transceiver antenna, a dielectric substrate under test (DUT), and a metal reflector. A vector network analyzer is connected to the calibration point of the transceiver antenna, i.e., the feed receiver port. The DUT is placed directly behind the metal reflector, and the transceiver antenna is positioned perpendicular to the DUT. The reflection coefficient S at the calibration point of the transceiver antenna is measured using the vector network analyzer. 11The test data is recorded as

[0044] S2, Measuring antenna standing wave S 11SW ;

[0045] The reflection coefficient of the transceiver antenna without a substrate under test and a metal reflector was tested using a vector network analyzer; this reflection coefficient, denoted as the antenna standing wave (S), is denoted as S. 11SW .

[0046] S3, Frequency Domain Data Processing

[0047] The reflection coefficient of the system is tested using medium parameters. Subtract antenna standing wave S 11SW The data obtained later is recorded as

[0048] S4. Calculate the dielectric constant of the first layer dielectric using time-frequency transformation.

[0049] Figure 4 This displays the time-domain waveform of the measured reflectance coefficient after conversion from the frequency domain to the time domain. The first peak represents the reflection between air and the first layer of medium, the second peak represents the reflection between the first and second layers of medium, and the third peak represents the reflection from the metal plate. However, because the magnitude of the reflectance coefficient between the first and second layers is... This value is very small, so the second reflection is not noticeable in the time domain. For example... Figure 4 As shown, the frequency domain data to be analyzed Transforming to the time domain for analysis: Since the reflected signals are of the same frequency in the frequency domain, they cannot be separated by filtering. However, the reflected signals are different in the time domain. Therefore, signal sorting is performed on the time domain, retaining the reflected signal Г2 and removing the rest. Then, a DFT is performed on the time-domain data of the reflected signal Г1 to obtain the reflection coefficients of the first layer, using the formula... The dielectric constant ε of the first dielectric layer can then be calculated. r1 .

[0050] S5. Time-frequency transformation calculation of the thickness of the first layer of medium.

[0051] Analyzing its time-domain waveform, the first reflection peak represents the first discontinuity of the tested material, i.e., the first reflection at the interface between air and the dielectric plate; the second reflection peak represents the second discontinuity of the tested material, i.e., the first reflection at the dielectric surface between the dielectric plate and the metal plate; there is a certain time difference between the first two reflections in the time domain, which is twice the time required for the electromagnetic wave to propagate within the medium at twice the thickness of the medium; measuring the time difference Δt1 between the first and second discontinuities in the time-domain waveform, and then using the dielectric constant ε of the first layer of the dielectric obtained in step S4... r1 Using the formula c is the propagation speed of electromagnetic waves in a vacuum, from which the thickness d1 of the first medium layer can be calculated.

[0052] S6. Calculate the dielectric constant of the second layer dielectric.

[0053] Following step S4, the reflection signal Г2 of the second layer dielectric is retained, while the remaining reflection signals are removed. Then, a DFT is performed on the time-domain data of the reflection signal Г2 to obtain the reflection coefficient of the second layer. Finally, based on the dielectric constant ε of the first layer dielectric obtained in step S4... r1 Using the formula The dielectric constant of the second layer can then be calculated.

[0054] S7. Calculate the thickness of the second layer of medium.

[0055] Measure the time difference Δt2 between the second and third discontinuities in the time-domain waveform according to step S5, and then use the dielectric constant ε of the second layer dielectric obtained in step S6. r2 Using the formula The thickness d2 of the second layer of medium can then be calculated.

[0056] Similarly, for solving multilayer dielectrics, the dielectric constant and thickness of each layer can be solved one by one from the outside to the inside by peeling off the layers. This will give us the thickness and dielectric constant of the third, fourth...nth layers.

[0057] The above embodiments are merely illustrative of the principles and effects of the present invention and are not intended to limit the invention. Any person skilled in the art can modify or alter the above embodiments without departing from the spirit and scope of the present invention. Therefore, all equivalent modifications or alterations made by those skilled in the art without departing from the technical concept disclosed in the present invention should still be covered by the claims of the present invention.

Claims

1. A method for estimating parameters of multilayer media based on time-domain analysis, characterized in that... Includes the following steps: S1, set the medium parameter test system, through the vector network analyzer test the reflection coefficient S of the calibration place of the beam antenna 11 ; S2, measuring antenna standing wave S 11SW ; S3, Frequency Domain Data Processing: The effects of antenna standing waves can be removed through calibration. S4. Calculate the dielectric constant and thickness of the first to nth dielectric layers sequentially: S4.

1. Convert the frequency domain data to the time domain, and perform signal sorting on the time axis to obtain multiple reflected signals; S4.2 Calculate the dielectric constant and thickness of the first dielectric layer: The reflection signal Γ1 from the first layer of the medium is retained, while the remaining reflection signals are removed. The time-domain data of the reflection signal Γ1 is transformed to the frequency domain using a Discrete Fourier Transform to obtain the reflection coefficients of the first layer, and then combined with the formula... The dielectric constant ε of the first dielectric layer can then be calculated. r1 ; Analyzing the time-domain waveform, the first reflection peak represents the first discontinuity of the measured material, i.e., the first reflection at the interface between air and the dielectric plate; the second reflection peak represents the second discontinuity of the measured material, i.e., the first reflection at the dielectric surface between the dielectric plate and the metal plate; there is a certain time difference between the first and second reflections in the time domain; the time difference ∆t1 between the first and second discontinuities in the time-domain waveform is measured, and the time difference ∆t1 is twice the time required for the electromagnetic wave to propagate within the medium at twice the thickness of the medium, as shown in the following formula: ； Where d is the thickness of the medium, c is the speed of electromagnetic wave propagation in vacuum, and ε represents the dielectric constant of the dielectric plate under test; the calculation formula is obtained from this formula: ; According to the time difference At1 between the first discontinuity and the second discontinuity in the measured time-domain waveform, and the dielectric constant ε r1 , Using formula c is the propagation speed of electromagnetic waves in a vacuum, and the thickness d1 of the first medium layer can be calculated. S4.3 Calculate the dielectric constant and thickness of the medium from the second layer to the nth layer: The reflected signal Г1 from the second dielectric layer is retained, while the remaining reflected signals are removed. The time-domain data of the reflected signal Г2 is converted to the frequency domain using a Discrete Fourier Transform, and then combined with the dielectric constant ε of the first dielectric layer. r1 Using the formula The dielectric constant ε of the second layer was calculated. r2 ; The time difference ∆t2 between the second and third discontinuities in the time-domain waveform is measured, and then the propagation speed of electromagnetic waves in the medium and the dielectric constant ε of the second layer of the medium are used as a basis. r2 The thickness d2 of the second medium layer is calculated. Following a layer-by-layer peeling method, the dielectric constant and thickness of each remaining dielectric layer are calculated sequentially from the outside in, following the same process as calculating the parameters and thickness of the second dielectric layer. This yields the thickness and dielectric constant of the third, fourth...nth dielectric layers. The methods for calculating the dielectric constant and thickness of the remaining dielectric layers include: When calculating the dielectric constant and thickness of the nth dielectric layer, the reflected signal T from the nth dielectric layer is used. n Retain the original signal and remove the rest of the reflected signal; then remove the reflected signal Г. n Perform a DFT on the time-domain data to obtain the reflection coefficient of the nth layer, and then use the dielectric constant ε of the (n-1)th layer as a reference. rn-1 Using the formula The dielectric constant ε of the nth layer can then be calculated. rn ;Measure the time difference ∆t between the nth discontinuity and the (n+1)th discontinuity in the time-domain waveform. n Then, based on the dielectric constant ε of the nth layer... rn Using the formula The thickness d of the nth layer of medium can then be calculated. n .

2. The method for estimating the thickness and dielectric constant of multilayer dielectrics based on time-domain analysis according to claim 1, characterized in that, Step S1 involves setting the media parameter test system, including: The dielectric parameter testing system includes a vector network analyzer, a spotlight antenna, a dielectric substrate under test (DUT), and a metal plate. The vector network analyzer is connected to the calibration point of the spotlight antenna, i.e., the feed receiver port. The DUT is placed against the metal plate, and the spotlight antenna is positioned perpendicular to the DUT. The reflection coefficient S at the calibration point of the spotlight antenna is measured using the vector network analyzer. 11 The test data is recorded as .

3. The method for estimating the thickness and dielectric constant of multilayer dielectrics based on time-domain analysis according to claim 1, characterized in that, In step S2, the antenna standing wave S is measured. 11SW The specific operations include: The reflection coefficient of the beam antenna without the medium plate and the metal plate to be tested is tested by a vector network analyzer, and the reflection coefficient, i.e., the antenna standing wave, is denoted as S 11SW .

4. The method for estimating the thickness and dielectric constant of a multilayer dielectric based on time-domain analysis as described in claim 1, characterized in that, The method for frequency domain data processing in step S3 is as follows: The reflection coefficient was measured using a medium parameter testing system. Subtracting antenna standing wave S 11SW The corresponding impact, and the corresponding data obtained from this, are denoted as... .

Images