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CN113959564A - Temperature compensated microstrip sensor for microfluidics - Google Patents

Temperature compensated microstrip sensor for microfluidics Download PDF

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CN113959564A
CN113959564A CN202111091675.8A CN202111091675A CN113959564A CN 113959564 A CN113959564 A CN 113959564A CN 202111091675 A CN202111091675 A CN 202111091675A CN 113959564 A CN113959564 A CN 113959564A
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temperature
liquid
microstrip
split ring
substrate
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CN113959564B (en
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方宇浩
赵文生
吴文敬
王大伟
袁博
王高峰
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Hangzhou Dianzi University
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Abstract

The invention discloses a temperature compensation microstrip sensor for microfluid, which comprises a dielectric substrate, wherein a split ring resonator is etched on the bottom surface of the substrate and is provided with a microstrip part, the microstrip part comprises two main microstrip lines and two branch microstrip lines, the two branch microstrip lines surround to form a rectangular shape, two sides of the two branch microstrip lines respectively form a T-shaped junction with the main microstrip lines on the same side, and the other end of the main microstrip line is a port; etching two complementary split ring resonators on the top layer of the substrate, and respectively exciting one complementary split ring resonator by each branch microstrip line; the complementary split ring resonator is provided with a liquid injection port and a liquid outflow port, and a zigzag groove is etched on the medium substrate between the liquid injection port and the liquid outflow port; the PDMS microfluidic channel substrate is arranged above the two complementary split ring resonators, the PDMS microfluidic channel substrate is provided with a test channel and a reference channel, the test channel and the reference channel are respectively overlapped and strictly aligned with the meandering grooves of the two complementary split ring resonators, the reference channel is used as a reference, and the test channel is used for testing when a binary mixed liquid is injected.

Description

Temperature compensated microstrip sensor for microfluidics
Technical Field
The invention belongs to the technical field of microwave sensor design, and particularly relates to a temperature compensation microstrip sensor for microfluid.
Background
In the past years, many microwave sensors based on split-ring resonators (split-ring resonators), complementary split-ring resonators (complementary split-ring resonators), and their modified structures have been proposed for detecting solid substances or binary liquid mixtures.
It is well known that unwanted or uncontrolled ambient environmental factors (e.g., temperature, air pressure, humidity, etc.) can affect the dielectric constants of the dielectric substrate of the dielectric, the PDMS, and the liquid sample, resulting in a resonant frequency shift and corresponding measurement error. In order to suppress the influence of environmental factors, several compensation techniques have been developed. Among them, the differential sensor is based on this birth, however, although the differential sensor can effectively suppress the environmental influence, it cannot recognize the liquid because the dielectric constant of the liquid is highly dependent on the temperature. Recently, microwave sensors have been introduced that employ machine learning algorithms to eliminate temperature effects in SRR-based applications. However, the compiling process of the algorithm is complex, and the trained ANN model is only suitable for binary liquid with the characteristic parameters being trained in advance, so that the application range of the algorithm is greatly limited. Furthermore, this technique cannot exclude other environmental influences than temperature.
Therefore, it is very important to develop a microwave microfluidic sensor structure to deal with the above mentioned problem of influence of complex multidimensional environment variables.
Disclosure of Invention
The invention provides a temperature compensation microstrip sensor for microfluid, which can realize higher measurement precision and better inhibition effect by adding an SRR structure to detect the variable of temperature while inhibiting the influence of complex environment through an improved differential microwave sensor structure.
In order to solve the technical problems, the invention adopts the following technical scheme:
a temperature compensated microstrip sensor for microfluidics, comprising: the micro-strip micro-fluidic chip comprises a dielectric substrate, a micro-strip part, a Split Ring Resonator (SRR), a Complementary Split Ring Resonator (CSRR) and a PDMS micro-fluidic channel substrate; the bottom surface of the dielectric substrate is etched with the Split Ring Resonator (SRR) and is provided with a microstrip part, the microstrip part comprises two main microstrip lines and two branch microstrip lines, the two branch microstrip lines surround to form a rectangular shape, two sides of the two branch microstrip lines respectively form T-shaped junctions with the main microstrip lines on the same side, and the other ends of the two main microstrip lines are respectively a first port and a second port; etching two CSRRs on the top layer of the dielectric substrate, and respectively exciting one CSRR by each branch microstrip line; the Complementary Split Ring Resonator (CSRR) is provided with a liquid injection port and a liquid outflow port, and a zigzag groove is etched on the medium substrate between the liquid injection port and the liquid outflow port; the Polydimethylsiloxane (PDMS) microfluidic channel substrate is arranged above the two Complementary Split Ring Resonators (CSRR), the PDMS microfluidic channel substrate is provided with a test channel and a reference channel, the test channel and the reference channel are respectively overlapped and strictly aligned with the zigzag grooves of the two Complementary Split Ring Resonators (CSRR), the reference channel is used as a reference, and the test channel is used for testing when binary mixed liquid is injected.
Preferably, the dielectric substrate is made of Rogers RT/Duroid 4350, and has a thickness of 0.762mm, a relative dielectric constant of 3.66 and a loss tangent of 0.004. Preferably, a quarter-wave impedance conversion line with a characteristic impedance of 35.35 ohms is cascaded between the two 50 ohm ports and the corresponding T-junctions.
Preferably, according to the Maxwell-Garnett expression, the complex dielectric constant of the binary liquid mixed liquid is expressed as follows:
Figure BDA0003267604210000031
wherein epsilonmAnd εfIs the dielectric constant of the host medium and the second liquid, vfIs the volume fraction of the second liquid.
Preferably, the liquid dielectric constant can be described using a single Debye model, which is expressed as follows:
Figure BDA0003267604210000032
wherein epsilon0(T) and ε(T) is a dielectric constant in the low and high frequency ranges, respectively, and τ (T) represents a relaxation time, and the expression for pure water τ (T) is:
Figure BDA0003267604210000033
wherein a is 1.37 × 10-13s,d=651℃,T0=133℃,TwaterRepresents the temperature of the water;
preferably, temperature has a significant effect on the properties of the liquid, and it is necessary to specify the complex dielectric constants of the liquid at different temperatures according to Kirkwood theory for pure fluids, the relationship of the dielectric constant of the liquid to temperature is described as follows:
Figure BDA0003267604210000034
wherein M iswDenotes molecular weight, ρ denotes density, α is molecular polarizability, NAIndicates that the Avogadro constant μ indicates the dipole moment of the molecule, kBRepresenting the boltzmann constant, g characterizes a correlation factor for the relative orientation between adjacent molecules.
Preferably, the temperature can be restored by a change in the SRR resonant frequency. A fitted expression is applied to describe the relationship between temperature and resonant frequency as follows:
T=83.36-452.78fr+1570.76fr 2-2832.13fr 3
wherein f isrIs relative to a reference frequency fref,SRRThe expression of (a) is as follows:
Figure BDA0003267604210000035
wherein f isSRRIndicating different temperaturesResonant frequency of the lower SRR, reference frequency fref,SRRSet to 1.52 GHz;
preferably, in general, the fluid properties can be retrieved by relative resonance frequency shift and normalized figure of merit, as follows:
Figure BDA0003267604210000041
Figure BDA0003267604210000042
wherein f isCSRR,LAnd QCSRR,LRespectively expressed as the resonant frequency and quality factor, f, of the lower branch reference CSRRCSRR,UAnd QCSRR,URespectively representing the resonant frequency and the quality factor of the CSRR in which the liquid to be measured is added into the upper branch.
Preferably, the sensitivity of the sensor is defined as:
Figure BDA0003267604210000043
preferably, a machine learning method is used to retrieve the dielectric constant of the liquid at different temperatures. A back propagation neural network (BP-NN) optimized based on Genetic Algorithm (GA) was used to reconstruct the relationship between measured data and fluid properties. During the training process, the GA searches for initial weights, which the BP-NN uses to find the optimal solution. The node of the hidden layer is set to 10 to shift f from the resonance according to the kolmogorov lawrmAnd temperature T as input data, liquid dielectric constant ε'rThe real part of' as output. Weight of the network (w)ijAnd VjI 1,2, j 1,2, …,10) and a threshold (t)jAnd a0J-1, 2, …,10) through a training data set (f)rmAnd T) is obtained. After obtaining the NN model, all the training data f are combinedrmAnd T as test data to verify the reliability of the model. Extracting epsilon'rThereafter, BP-NN was applied to search for the loss tangent tan. delta. It has three inputsVariable (ε'r,T,and Qnor) And an output variable (tan δ). Similarly, the network weight (w)kpAnd VpK 1,2,3 and p 1,2, …,10) and a threshold (t)pand b0P-1, 2, …,10) is trained to obtain a data set (ε'r,T,QnorAnd tan δ). From above, training data ε'rT, and QnorThe rationality of the NN model was also verified as test data.
The invention has the beneficial effects that: the invention relates to a temperature compensation microstrip sensor for microfluid, which can inhibit complex environmental influence by an improved differential microwave sensor structure and simultaneously increase an SRR structure to detect temperature variable. The invention can realize higher measurement precision and better inhibition effect on environmental influence, and has very positive effect on promoting the industrialization process of the microwave sensor.
Drawings
FIG. 1 is a schematic diagram of a temperature compensated microstrip sensor configuration for microfluidic applications according to an embodiment of the present invention;
FIG. 2 is a top view of a temperature compensated microstrip sensor structure for microfluidic applications according to an embodiment of the present invention;
FIG. 3 is a bottom view of a temperature compensated microstrip sensor structure for microfluidic applications according to an embodiment of the present invention;
FIG. 4 is an equivalent circuit model of a temperature compensated microstrip sensor structure for microfluidic applications according to an embodiment of the present invention;
FIG. 5 is a schematic diagram of one of the neural networks of an embodiment of the present invention;
FIG. 6 is a schematic diagram of one of the neural networks of an embodiment of the present invention;
FIG. 7 is a graph showing the results of an experiment according to an embodiment of the present invention.
In the figure, a 1-dielectric substrate, a 1-1-zigzag slot, a 2-microstrip part, a 2-1 main microstrip line, a 2-2 branch microstrip line, a 2-1-1-port I, a 20-1-2-port II, a 3-Split Ring Resonator (SRR), a 4-Complementary Split Ring Resonator (CSRR), a 4-1-liquid injection port, a 4-2-liquid outflow port, a 4-3-test channel, a 4-4-reference channel and a 5-PDMS microfluidic channel substrate.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and examples.
The invention provides a temperature compensation type microwave micro-fluidic sensor, a micro-strip part is used for realizing differential sensing, and two symmetrical Complementary Split Ring Resonators (CSRR)4 are etched on a ground plane. A Polydimethylsiloxane (PDMS) substrate 5 is connected to the ground plane. To enhance electric field confinement, a meandering channel is added to the CSRR and the microfluidic channel is aligned with the meandering channel. In addition, a Split Ring Resonator (SRR)3 and peripheral circuitry are added to capture ambient temperature. The extracted temperature and the changes in the resonant frequency and the quality factor of the CSRR are used as input data for training the neural network model. The result shows that the dielectric constant of the liquid predicted by the trained neural network is very consistent with the reference value. The sensor provided by the invention has excellent performance, small volume, high sensitivity and temperature compensation capability, and becomes a good candidate in the field of microfluidic detection.
Referring to fig. 1-6, the present invention provides an improved differential microwave sensor structure to suppress complex environmental impact and simultaneously add an SRR structure to detect a temperature variable, fig. 1 is a schematic diagram of a temperature compensation microstrip sensor structure for microfluidic application according to an embodiment of the present invention, including a dielectric substrate 1, a microstrip portion 2, a split ring resonator 3, a complementary split ring resonator 4, and a PDMS channel substrate 5; the bottom surface of the dielectric substrate 1 etches the split-ring resonator 3 and is provided with a microstrip part 2, and the split-ring resonator 3 is excited by the microstrip line. The microstrip part 2 comprises two main microstrip lines 2-1 and two branch microstrip lines 2-2, the two branch microstrip lines 2-2 enclose a rectangular shape, two sides of the rectangular shape respectively form T-shaped junctions with the main microstrip line 2-1 at the same side, and the other ends of the two main microstrip lines 2-1 are respectively a first port 2-1-1 and a second port 2-1-2; the top layer of the dielectric substrate 1 etches two complementary split-ring resonators 4, which are excited by microstrip lines. Each branch microstrip line 2-2 respectively excites a complementary split ring resonator; the complementary split ring resonator 4 is provided with a liquid injection port 4-1 and a liquid outflow port 4-2, and a zigzag groove 1-1 is etched on the medium substrate between the liquid injection port 4-1 and the liquid outflow port 4-2; the complementary split-ring resonator CSRR, which uses a meander slot to enhance the electric field confinement, is also used as a sensing region on the etched dielectric substrate. The PDMS microfluidic channel substrate 5 is arranged above the two complementary split ring resonators, the PDMS microfluidic channel substrate 5 is provided with a test channel 4-3 and a reference channel 4-4, the test channel 4-3 and the reference channel 4-4 are respectively overlapped and strictly aligned with the zigzag grooves of the two complementary split ring resonators 4, the reference channel 4-4 is used as a reference, and the test channel 4-3 is used for testing when binary mixed liquid is injected.
In this embodiment, a quarter-wave impedance conversion line with a characteristic impedance of 35.35 ohms is cascaded between the first port and the second port of 50 ohms and the T-junction on the same side. The dielectric substrate is made of Rogers RT/Duroid 4350, the thickness of the dielectric substrate is 0.762mm, the relative dielectric constant of the dielectric substrate is 3.66, and the loss tangent of the dielectric substrate is 0.004.
The proposed sensor is shown in top and bottom views in fig. 2 and 3, respectively, according to an embodiment of the present invention. To accurately detect the temperature, the SRR with peripheral circuits is added. As shown in fig. 3, the SRR is loaded with a varactor SMV2023 and a thermistor NCP03XH103J05 RD. Full-wave electromagnetic simulations were performed using commercial software ANSYS HFSS, in which the varactors were modeled as lumped elements with different capacitance values. The values of the parameters of the remaining structural variables of the sensor are determined in both fig. 2 and fig. 3.
An equivalent circuit model of a sensor structure of an embodiment of the present invention is shown in fig. 4.
According to the Maxwell-Garnett expression, the complex dielectric constant of the binary liquid mixture is expressed as follows:
Figure BDA0003267604210000071
wherein epsilonmAnd εfIs the dielectric constant of the host medium and the second liquid, vfIs the volume fraction of the second liquid.
According to an embodiment of the present invention, the liquid dielectric constant may be described using a single Debye model, which is expressed as follows:
Figure BDA0003267604210000081
wherein epsilon0(T) and ε(T) is a dielectric constant in the low and high frequency ranges, respectively, and τ (T) represents a relaxation time, and the expression for pure water τ (T) is:
Figure BDA0003267604210000082
wherein a is 1.37 × 10-13s,d=651℃,T0=133℃,TwaterRepresents the temperature of the water;
according to the embodiments of the present invention, temperature has a significant influence on the liquid properties, and it is required to clarify complex dielectric constants of the liquid at different temperatures according to Kirkwood theory of pure fluid, the relationship between the liquid dielectric constant and the temperature is described as follows:
Figure BDA0003267604210000083
wherein M iswDenotes molecular weight, ρ denotes density, α is molecular polarizability, NAIndicates that the Avogadro constant μ indicates the dipole moment of the molecule, kBRepresenting the boltzmann constant, g characterizes a correlation factor for the relative orientation between adjacent molecules.
According to embodiments of the present invention, temperature may be recovered by a change in the SRR resonant frequency. A fitted expression is applied to describe the relationship between temperature and resonant frequency as follows:
T=83.36-452.78fr+1570.76fr 2-2832.13fr 3
wherein f isrIs relative to a reference frequency fref,SRRThe expression of (a) is as follows:
Figure BDA0003267604210000084
wherein f isSRRRepresenting the resonance frequency, reference frequency f, of the SRR at different temperaturesref,SRRSet to 1.52 GHz;
according to an embodiment of the invention, in general, the fluid properties may be retrieved by relative resonance frequency shift and normalized figure of merit, as follows:
Figure BDA0003267604210000091
Figure BDA0003267604210000092
wherein f isCSRR,LAnd QCSRR,LRespectively expressed as the resonant frequency and quality factor, f, of the lower branch reference CSRRCSRR,U
And QCSRR,URespectively representing the resonant frequency and the quality factor of the CSRR in which the liquid to be measured is added into the upper branch.
According to an embodiment of the invention, the sensitivity of the sensor is defined as:
Figure BDA0003267604210000093
according to an embodiment of the invention, a machine learning method is used to retrieve the dielectric constant of the liquid at different temperatures. A back propagation neural network (BP-NN) optimized based on Genetic Algorithm (GA) was used to reconstruct the relationship between measured data and fluid properties. During the training process, the GA searches for initial weights, which the BP-NN uses to find the optimal solution. The node of the hidden layer is set to 10 according to the kolmogorov law, as shown in fig. 5, 6 with a relative resonance frequency shift frmAnd temperature T as input data, liquid dielectric constant ε'rThe real part of' as output. Weight of the network (w)ijAnd VjI 1,2, j 1,2, …,10) and a threshold (t)jAnd a0J-1, 2, …,10) through a training data set (f)rmAnd T) is obtained. After obtaining the NN model, allTraining data frmAnd T as test data to verify the reliability of the model. Extracting epsilon'rThereafter, the loss tangent tan δ was searched by applying BP-NN shown in FIG. 6. It has three input variables (ε'r,T,and Qnor) And an output variable (tan δ). Similarly, the network weight (w)kpAnd VpK 1,2,3 and p 1,2, …,10) and a threshold (t)pand b0P-1, 2, …,10) is trained to obtain a data set (ε'r,T,QnorAnd tan δ). From above, training data ε'rT, and QnorThe rationality of the NN model was also verified as test data.
Fig. 7 shows a part of the experimental results according to an embodiment of the present invention, in which fig. 7(a), (b), (c), and (d) show a set of water-methanol mixtures injected into the test channel of the proposed sensor at different temperatures, respectively, and the resulting transmission coefficients are recorded. The temperatures shown in FIGS. 7(a), (b), (c) and (d) were 20 deg.C, 25 deg.C, 40 deg.C and 50 deg.C, respectively. It can be seen from fig. 7 that the resonance frequency of the SRR and the CSRR of the reference are hardly changed. The resonant frequency of the upper CSRR decreases with increasing volume fraction of water in the mixture due to the increase in the dielectric constant of the liquid. It is noted that the dielectric constants of the substrate and PDMS are also affected by ambient temperature, but these effects can be suppressed to some extent by the differential structure.
According to the temperature compensation type microwave micro-fluidic sensor, a micro-strip part is used for realizing differential sensing, and two symmetrical Complementary Split Ring Resonators (CSRR) are etched on a ground plane. A Polydimethylsiloxane (PDMS) substrate is connected to the ground plane. To enhance electric field confinement, a meandering channel is added to the CSRR and the microfluidic channel is aligned with the meandering channel. In addition, a Split Ring Resonator (SRR) and peripheral circuitry are added to capture ambient temperature. The extracted temperature and the changes in the resonant frequency and the quality factor of the CSRR are used as input data for training the neural network model. The result shows that the dielectric constant of the liquid predicted by the trained neural network is very consistent with the reference value. The proposed sensor exhibits excellent performance, has small volume, high sensitivity and temperature compensation capability, making it a good candidate in the field of microfluidic detection.
The improved differential microwave sensor of the present invention is proposed to suppress environmental effects and to increase the SRR to detect temperature. The retrieved dielectric constant and temperature are used together to identify the measured Liquid (LUT). On the other hand, the method has a very positive effect on promoting the industrialization process of the microwave sensor.
The above description is only an embodiment of the present invention, and not intended to limit the scope of the present invention, and all modifications of equivalent structures and equivalent processes performed by the present specification and drawings, or directly or indirectly applied to other related technical fields, are included in the scope of the present invention.

Claims (10)

1. A temperature compensated microstrip sensor for microfluidics, comprising: the micro-strip micro-fluidic chip comprises a dielectric substrate (1), a micro-strip part (2), a split ring resonator (3), a complementary split ring resonator (4) and a PDMS micro-fluidic channel substrate (5); the bottom surface of the dielectric substrate (1) is etched with the split ring resonator (3) and is provided with a microstrip part (2), the microstrip part (2) comprises two main microstrip lines (2-1) and two branch microstrip lines (2-2), the two branch microstrip lines (2-2) enclose a rectangular shape, two sides of the rectangular shape and the main microstrip lines (2-1) on the same side form a T-shaped junction, and the other ends of the two main microstrip lines (2-1) are respectively a first port (2-1-1) and a second port (2-1-2); the top layer of the dielectric substrate (1) is etched with two complementary split-ring resonators (4), and each branch microstrip line (2-2) respectively excites one complementary split-ring resonator; the complementary split ring resonator (4) is provided with a liquid injection port (4-1) and a liquid outflow port (4-2), and a zigzag groove (1-1) is etched on a medium substrate between the liquid injection port (4-1) and the liquid outflow port (4-2); the PDMS microfluidic channel substrate (5) is arranged above the two complementary split ring resonators, the PDMS microfluidic channel substrate (5) is provided with a test channel (4-3) and a reference channel (4-4), the test channel (4-3) and the reference channel (4-4) are respectively overlapped with the zigzag grooves of the two complementary split ring resonators (4) and are strictly aligned, the reference channel (4-4) is used as a reference, and the test channel (4-3) is used for testing when binary mixed liquid is injected.
2. The temperature-compensated microstrip sensor according to claim 1 wherein the dielectric substrate is of a material such as Rogers RT/Duroid 4350, having a thickness of 0.762mm, a relative dielectric constant of 3.66 and a loss tangent of 0.004.
3. The temperature-compensated microstrip sensor according to claim 1 wherein a quarter-wave impedance transition line having a characteristic impedance of 35.35 ohms is cascaded between 50 ohms at port one, port two and the same side of the T-junction.
4. The temperature-compensated microstrip sensor according to any of claims 1 to 3 wherein the complex permittivity of the binary liquid mixture is expressed by the following formula according to Maxwell-Garnett expression:
Figure FDA0003267604200000011
wherein epsilonmAnd εfIs the dielectric constant of the host medium and the second liquid, vfIs the volume fraction of the second liquid.
5. The temperature-compensated microstrip sensor for microfluidics according to claim 4 wherein the liquid dielectric constant is described using a single Debye model, expressed as follows:
Figure FDA0003267604200000021
wherein epsilon0(T) and ε(T) is a dielectric constant in the low and high frequency ranges, respectively, and τ (T) represents a relaxation time, and the expression for pure water τ (T) is:
Figure FDA0003267604200000022
whereina=1.37×10-13s,d=651℃,T0=133℃,TwaterIndicating the temperature of the water.
6. The micro-fluidic temperature-compensated microstrip sensor according to claim 5 wherein temperature has a significant effect on the properties of the liquid, and the complex dielectric constants of the liquid at different temperatures are defined according to Kirkwood theory for pure fluids, and the relationship between the dielectric constant of the liquid and the temperature is described as follows:
Figure FDA0003267604200000023
wherein M iswDenotes molecular weight, ρ denotes density, α is molecular polarizability, NAIndicates that the Avogadro constant μ indicates the dipole moment of the molecule, kBRepresenting the boltzmann constant, g characterizes a correlation factor for the relative orientation between adjacent molecules.
7. The temperature-compensated microstrip sensor according to claim 6 wherein temperature is recovered by variation of the SRR resonant frequency and a fitting expression is applied to describe the relationship between temperature and resonant frequency as follows:
T=83.36-452.78fr+1570.76fr 2-2832.13fr 3
wherein f isrIs relative to a reference frequency fref,SRRThe expression of (a) is as follows:
Figure FDA0003267604200000024
wherein f isSRRRepresenting the resonance frequency, reference frequency f, of the SRR at different temperaturesref,SRRIs set to 1.52 GHz.
8. The temperature-compensated microstrip sensor for microfluidics according to claim 7 wherein the fluid properties are retrieved by relative resonance frequency shift and normalized quality factor as follows:
Figure FDA0003267604200000031
Figure FDA0003267604200000032
wherein f isCSRR,LAnd QCSRR,LRespectively expressed as the resonant frequency and quality factor, f, of the lower branch reference CSRRCSRR,UAnd QCSRR,URespectively representing the resonant frequency and the quality factor of the CSRR in which the liquid to be measured is added into the upper branch.
9. The temperature-compensated microstrip sensor for microfluidics according to claim 8 wherein the sensitivity of the sensor is defined as:
Figure FDA0003267604200000033
10. the micro-fluidic temperature-compensated microstrip sensor of claim 9 wherein the node of the hidden layer is set to 10 to shift f relative to the resonance frequency according to kolmogorov's lawrmAnd temperature T as input data, liquid dielectric constant ε'rAs output; weight of the network (w)ijAnd Vj1,2, j 1,2, 10) and a threshold (t)jAnd a0J 1,2, 10) is passed through a training data set (f)rmAnd T) obtaining; after obtaining the NN model, all the training data f are combinedrmAnd T as test data to verify the reliability of the model; extracting epsilon'rThen, BP-NN was applied to search for the loss tangent tan δ; it has three input variables (ε'r,T,and Qnor) And an output variable (tan δ); similarly, network weights(wkpAnd VpK 1,2,3 and p 1,2pand b01,2, 10) are trained to obtain a data set (e'r,T,QnorAnd tan δ); from above, training data ε'rT, and QnorThe rationality of the NN model was also verified as test data.
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