WO2020150933A1 - Electrode polarization correction method for open-ended coaxial probe and processing terminal - Google Patents
Electrode polarization correction method for open-ended coaxial probe and processing terminal Download PDFInfo
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- WO2020150933A1 WO2020150933A1 PCT/CN2019/072857 CN2019072857W WO2020150933A1 WO 2020150933 A1 WO2020150933 A1 WO 2020150933A1 CN 2019072857 W CN2019072857 W CN 2019072857W WO 2020150933 A1 WO2020150933 A1 WO 2020150933A1
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Definitions
- the invention relates to the technical field of electrode polarization correction, in particular to an electrode polarization correction method of an open-ended coaxial probe and a processing terminal.
- the existing electrode polarization correction method is to plate a layer of platinum on the surface of the metal electrode.
- the platinum coating is not easy to react with the electrolyte solution, thereby reducing the surface charge obtained by the electrode, thereby reducing the electrode polarization resistance, and achieving the purpose of electrode polarization correction.
- it is necessary to clean the tip of the open-ended coaxial probe, and alternate measurements between the calibration sample and the sample to be tested. As a result, mechanical cleaning or ultrasonic scrubbing of the open-ended coaxial probe will cause platinum coating. The layer is degraded so that the electrode polarization cannot be corrected accurately.
- one of the objectives of the present invention provides an electrode polarization correction method of an open-ended coaxial probe, which can solve the problem of electrode polarization correction of an open-ended coaxial probe;
- the second object of the present invention is to provide a processing terminal, which can solve the problem of electrode polarization correction of the open-ended coaxial probe.
- an electrode polarization correction method of an open-ended coaxial probe which includes the following steps:
- Step 1 Preset the equivalent circuit model of the open-ended coaxial probe.
- the equivalent circuit model includes resistance R p , resistance R s , resistance R f , capacitance C s and capacitance C f , and resistance R s and capacitance C s are connected in parallel
- a first parallel branch is formed, the resistance R f and the capacitor C f are connected in parallel to form a second parallel branch, the resistance R p , the first parallel branch and the second parallel branch are connected in sequence;
- the net load impedance of the equivalent circuit model Z( ⁇ ) is calculated by formula 1:
- ⁇ represents the angular frequency
- j represents the imaginary unit of the complex number
- Z s represents the electrode polarization series impedance
- Z s H 1 ( ⁇ ,A,n,B,m,C,I)+jH 2 ( ⁇ ,B,m,C,I)
- H 1 ( ⁇ ,A,n,B,m,C,I) is the real part of Z s
- H 2 ( ⁇ ,B,m,C,I) is Z s
- A, n, B, m, C, I are all constants;
- Step 2 Receive a set of measured data of the net load impedance of the open-ended coaxial probe input by the user, and respectively interpolate and derive the real and imaginary parts of a set of measured data of the net load impedance to obtain a set of discrete derivative values J ( ⁇ ), let To get a set of with Value, by the formula 2 and 3 respectively H 1 ( ⁇ , A, n , B, m, C, I) derivative H '1 ( ⁇ , A, n, B, m, C, I) , and H 2 ( ⁇ ,B,m,C,I) derivative H′ 2 ( ⁇ ,B,m,C,I) each set of discrete values, and A,n,B is obtained by fitting each set of discrete values ,m,C,I value, thus get the value of resistance R p , resistance R s and capacitance C s :
- Re[Z( ⁇ )] represents the real part of Z( ⁇ )
- Im[Z( ⁇ )] represents the imaginary part of Z( ⁇ )
- ReJ( ⁇ ) represents the real part of J( ⁇ )
- ImJ( ⁇ ) means to take the imaginary part of J( ⁇ )
- H′ 1 ( ⁇ ,A,n,B,m,C,I) means to H 1 ( ⁇ ,A,n,B,m,C, I)
- H′ 2 ( ⁇ ,B,m,C,I) means to derive H 2 ( ⁇ ,B,m,C,I);
- Step 3 Substitute the values of resistance R p , resistance R s and capacitance C s into formula 4 for calculation to obtain the value of Z s :
- the second technical solution for achieving the objective of the present invention is: a processing terminal, which includes:
- Memory used to store program instructions
- the processor is configured to run the program instructions to execute the steps of the electrode polarization correction method of the open-ended coaxial probe.
- the present invention does not need to change the physical structure of the open-ended coaxial probe, and through the method of data processing, it effectively reduces the electrode polarization error of the coaxial probe measurement system, achieves the purpose of electrode polarization correction, and is easy to calculate. , And easy to expand and use.
- Figure 1 is an equivalent circuit model of the open-ended coaxial probe of the present invention
- FIG. 2 is a flowchart of a preferred embodiment of the present invention.
- FIG. 3 is a schematic structural diagram of a processing terminal of the present invention.
- the open-ended coaxial probe When using the open-ended coaxial probe to measure the dielectric properties of the sample to be tested, the open-ended coaxial probe needs to be immersed in the electrolyte. The charged particles in the electrolyte are forced to move to the oppositely charged electrode plate due to electrostatic force in the electrostatic field. The probe shows that an electric double layer is formed, and the charged particles are adsorbed and temporarily stored in the electric double layer, resulting in a double-layer electrode polarization effect, which can be simulated as a capacitor connected in series with the probe and the effective impedance of the sample under test Specifically, the open-ended coaxial probe can be equivalent to a resistance-capacitance series-parallel circuit, and defined as an equivalent circuit model, as shown in Figure 1.
- the equivalent circuit model includes resistance R p , resistance R s , resistance R f , The capacitor C s and the capacitor C f , the resistor R s and the capacitor C s are connected in parallel to form a first parallel branch, the resistor R f and the capacitor C f are connected in parallel to form a second parallel branch, the resistor R p , the first parallel branch and the first parallel branch The two parallel branches are connected in sequence to form a series.
- the net load impedance Z( ⁇ ) of the equivalent circuit model is calculated as formula 1:
- f represents the frequency
- j represents the imaginary unit in the complex number
- Z s is the electrode polarization series impedance of the left half of the equivalent circuit model (the circuit part composed of resistor R p , resistor R s and capacitor C s ).
- H 1 ( ⁇ ) is the real part of Z s and H 2 ( ⁇ ) is the imaginary part of Z s .
- the resistance R p , the resistance R s and the capacitance C s are all functions of ⁇ .
- A, n, B, m, C, and I are all constants
- formula 3 can be further written as a function of ⁇ , namely formula 4:
- H 1 ( ⁇ ,A,n,B,m,C,I) is the real part of Z s
- H 2 ( ⁇ ,B,m,C,I) is the imaginary part of Z s
- Re[Z( ⁇ )] represents the real part of Z( ⁇ )
- Im[Z( ⁇ )] represents the imaginary part of Z( ⁇ )
- H′ 1 ( ⁇ ,A,n,B,m ,C,I) represents the derivative of H 1 ( ⁇ ,A,n,B,m,C,I)
- H′ 2 ( ⁇ ,B,m,C,I) represents the derivative of H 2 ( ⁇ ,B, m,C,I) Derivation
- a set of measured data of net load impedance is obtained through multiple measurements, and the real and imaginary parts of a set of measured data of net load impedance are respectively interpolated and derivated.
- the real part and the imaginary part obtained after the derivative together form a corresponding set of discrete derivative values J( ⁇ ), that is, still J( ⁇ ) is a complex number, let To get a set of with
- the value of is equivalent to obtaining a set of discrete values of H′ 1 ( ⁇ ,A,n,B,m,C,I) and H′ 2 ( ⁇ ,B,m,C,I), so you can Fit a set of discrete values of to obtain the parameters A,n, in H′ 1 ( ⁇ ,A,n,B,m,C,I) and H′ 2 ( ⁇ ,B,m,C,I) B, m, C, I, so that the values of the resistance R p , the resistance R s and the capacitance C s can be further obtained, that is
- H′ 1 ( ⁇ ,A,n,B,m,C,I) and H′ 2 ( ⁇ ,B,m,C,I) corresponding to the polarization effect of each angular frequency ⁇ are also known .
- subtract a set of measured data of net load impedance from the value corresponding to Z s that is, subtract a set of measured data of each net load impedance at different ⁇ from Z s at the corresponding ⁇ , so in this subtraction ,
- the subtract and the subtract are a set of measured data (subtract) and Z s (subtract) corresponding to the net load impedance at the same ⁇ respectively, to get the impedance after depolarization, that is, in the equivalent circuit model
- the electrode polarization series impedance of the left half (the circuit part composed of the resistor R p , the resistor R s and the capacitor C s ) is removed to achieve the depolarization effect, that is, to achieve the purpose of electrode polarization correction.
- the electrode polarization correction method of the open-ended coaxial probe can be realized through the processing of the above steps.
- the present invention also relates to a processing terminal 100 of a physical device implementing the above method, which includes:
- the memory 101 is used to store program instructions
- the processor 102 is configured to run the program instructions to execute the steps in the electrode polarization correction method of the open-ended coaxial probe.
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Abstract
The present invention relates to an electrode polarization correction method for an open-ended coaxial probe and a processing terminal. The method comprises the following steps: step 1, presetting an equivalent circuit model of an open-ended coaxial probe and electrode polarization series impedance of the equivalent circuit model; step 2, receiving one group of actually measured data of net load impedance inputted by a user, and calculating values of a resistor Rp, a resistor Rs and a capacitor Cs; and step 3, subtracting the value of corresponding Zs from the group of actually measured data of net load impedance to obtain de-polarized impedance so as to complete polarization correction. The present invention effectively reduces the electrode polarization error of a coaxial probe measurement system by means of data processing, without changing the physical structure of an open-ended coaxial probe, thereby achieving electrode polarization correction, simplifying the calculation, and facilitating promotion and use.
Description
本发明涉及电极极化校正技术领域，具体是一种开端同轴探头的电极极化校正方法及处理终端。The invention relates to the technical field of electrode polarization correction, in particular to an electrode polarization correction method of an open-ended coaxial probe and a processing terminal.
当金属电极浸入到电解质中，会因为电极表面分子的离解或从溶液中吸收离子而获得表面电荷，从而使来自电解质的带相反电荷的离子的浓度在金属电极区域增加。这些带相反电荷的离子被有效地束缚并在电极-电解质界面处形成所谓的双电层，也即存在电极极化效应。由于电极极化效应，在使用开端同轴探头测量具有明显直流电导率的样品的介电特性(包括介电常数和电导率)时需要进行电极极化校正。When a metal electrode is immersed in an electrolyte, surface charges are obtained due to the dissociation of molecules on the electrode surface or the absorption of ions from the solution, so that the concentration of oppositely charged ions from the electrolyte increases in the area of the metal electrode. These oppositely charged ions are effectively bound and form a so-called electric double layer at the electrode-electrolyte interface, that is, there is an electrode polarization effect. Due to the electrode polarization effect, electrode polarization correction is required when using an open-ended coaxial probe to measure the dielectric properties (including permittivity and conductivity) of samples with obvious direct current conductivity.
现有的电极极化校正方法是将金属电极表面镀上一层铂。由于铂涂层不容易与电解质溶液反应，从而降低由电极获得的表面电荷，从而降低电极极化阻抗，达到电极极化校正的目的。但是在确定待测样本的介电特性时，要清洁开端同轴探头的尖端，同时在校准样品和待测样品之间交替进行测量，导致开端同轴探头的机械清洁或超声波擦洗会导致铂涂层降解，从而不能准确的使电极极化校正。The existing electrode polarization correction method is to plate a layer of platinum on the surface of the metal electrode. The platinum coating is not easy to react with the electrolyte solution, thereby reducing the surface charge obtained by the electrode, thereby reducing the electrode polarization resistance, and achieving the purpose of electrode polarization correction. However, when determining the dielectric properties of the sample to be tested, it is necessary to clean the tip of the open-ended coaxial probe, and alternate measurements between the calibration sample and the sample to be tested. As a result, mechanical cleaning or ultrasonic scrubbing of the open-ended coaxial probe will cause platinum coating. The layer is degraded so that the electrode polarization cannot be corrected accurately.
发明内容Summary of the invention
针对现有技术的不足，本发明的目的之一提供一种开端同轴探头的电极极化校正方法，其能够解决开端同轴探头电极极化校正的问题；In view of the shortcomings of the prior art, one of the objectives of the present invention provides an electrode polarization correction method of an open-ended coaxial probe, which can solve the problem of electrode polarization correction of an open-ended coaxial probe;
本发明的目的之二提供一种处理终端，其能够解决开端同轴探头电极极化校正的问题。The second object of the present invention is to provide a processing terminal, which can solve the problem of electrode polarization correction of the open-ended coaxial probe.
实现本发明的目的之一的技术方案为：一种开端同轴探头的电极极化校正方法，包括如下步骤：The technical solution for achieving one of the objectives of the present invention is: an electrode polarization correction method of an open-ended coaxial probe, which includes the following steps:
步骤1：预设开端同轴探头的等效电路模型，所述等效电路模型包括电阻R
p、电阻R
s、电阻R
f、电容C
s和电容C
f，电阻R
s和电容C
s并联形成第一并联支路，电阻R
f和电容C
f并联形成第二并联支路，电阻R
p、第一并联支路与第二并联支路依次连接；所述等效电路模型的净负载阻抗Z(ω)采用公式①进行计算：
Step 1: Preset the equivalent circuit model of the open-ended coaxial probe. The equivalent circuit model includes resistance R p , resistance R s , resistance R f , capacitance C s and capacitance C f , and resistance R s and capacitance C s are connected in parallel A first parallel branch is formed, the resistance R f and the capacitor C f are connected in parallel to form a second parallel branch, the resistance R p , the first parallel branch and the second parallel branch are connected in sequence; the net load impedance of the equivalent circuit model Z(ω) is calculated by formula ①:
并定义
And define
式中，ω表示角频率，j表示复数的虚数单位，Z
s表示电极极化串联阻抗，且Z
s＝H
1(ω,A,n,B,m,C,I)+jH
2(ω,B,m,C,I)，H
1(ω,A,n,B,m,C,I)为Z
s的实部，H
2(ω,B,m,C,I)为Z
s的虚部，即
式中A,n,B,m,C,I均为常数；
In the formula, ω represents the angular frequency, j represents the imaginary unit of the complex number, Z s represents the electrode polarization series impedance, and Z s = H 1 (ω,A,n,B,m,C,I)+jH 2 (ω ,B,m,C,I), H 1 (ω,A,n,B,m,C,I) is the real part of Z s , H 2 (ω,B,m,C,I) is Z s The imaginary part of In the formula, A, n, B, m, C, I are all constants;
步骤2：接收用户输入的开端同轴探头的净负载阻抗的一组实测数据，分别将净负载阻抗的一组实测数据的实部和虚部进行插值求导，得到一组离散的导数值J(ω),令
从而分别得到一组
和
的值，由公式②和③分别得到H
1(ω,A,n,B,m,C,I)的导数H′
1(ω,A,n,B,m,C,I)和H
2(ω,B,m,C,I)的导数H′
2(ω,B,m,C,I)的各一组离散值，根据所述各一组离散值拟合获得A,n,B,m,C,I的值，从而得到电阻R
p、电阻R
s和电容C
s 的值：
Step 2: Receive a set of measured data of the net load impedance of the open-ended coaxial probe input by the user, and respectively interpolate and derive the real and imaginary parts of a set of measured data of the net load impedance to obtain a set of discrete derivative values J (ω), let To get a set of with Value, by the formula ② and ③ respectively H 1 (ω, A, n , B, m, C, I) derivative H '1 (ω, A, n, B, m, C, I) , and H 2 (ω,B,m,C,I) derivative H′ 2 (ω,B,m,C,I) each set of discrete values, and A,n,B is obtained by fitting each set of discrete values ,m,C,I value, thus get the value of resistance R p , resistance R s and capacitance C s :
式中，Re[Z(ω)]表示取Z(ω)的实部，Im[Z(ω)]表示取Z(ω)的虚部，ReJ(ω)表示取J(ω)的实部，ImJ(ω)表示取J(ω)的虚部，H′
1(ω,A,n,B,m,C,I)表示对H
1(ω,A,n,B,m,C,I)求导，H′
2(ω,B,m,C,I)表示对H
2(ω,B,m,C,I)求导；
In the formula, Re[Z(ω)] represents the real part of Z(ω), Im[Z(ω)] represents the imaginary part of Z(ω), and ReJ(ω) represents the real part of J(ω) , ImJ(ω) means to take the imaginary part of J(ω), H′ 1 (ω,A,n,B,m,C,I) means to H 1 (ω,A,n,B,m,C, I) Derivation, H′ 2 (ω,B,m,C,I) means to derive H 2 (ω,B,m,C,I);
步骤3：将电阻R
p、电阻R
s和电容C
s的值代入公式④进行计算，得到Z
s的值：
Step 3: Substitute the values of resistance R p , resistance R s and capacitance C s into formula ④ for calculation to obtain the value of Z s :
按相同角频率ω将步骤2中的净负载阻抗的一组实测数据减去对应Z
s的值，得到去极化后的阻抗，完成极化校正。
According to the same angular frequency ω, subtract the corresponding Z s from a set of measured data of the net load impedance in step 2 to obtain the impedance after depolarization, and complete the polarization correction.
实现本发明的目的之二的技术方案为：一种处理终端，其包括，The second technical solution for achieving the objective of the present invention is: a processing terminal, which includes:
存储器，用于存储程序指令；Memory, used to store program instructions;
处理器，用于运行所述程序指令，以执行所述开端同轴探头的电极极化校正方法的步骤。The processor is configured to run the program instructions to execute the steps of the electrode polarization correction method of the open-ended coaxial probe.
本发明的有益效果为：本发明无需改变开端同轴探头的物理结构，通过数据处理的方法，有效减小了同轴探头测量系统的电极极化误差，达到电极极化校正的目的，计算简便，且方便扩展和使用。The beneficial effects of the present invention are: the present invention does not need to change the physical structure of the open-ended coaxial probe, and through the method of data processing, it effectively reduces the electrode polarization error of the coaxial probe measurement system, achieves the purpose of electrode polarization correction, and is easy to calculate. , And easy to expand and use.
图1为本发明开端同轴探头的等效电路模型；Figure 1 is an equivalent circuit model of the open-ended coaxial probe of the present invention;
图2为本发明较佳实施例的流程图；Figure 2 is a flowchart of a preferred embodiment of the present invention;
图3为本发明一种处理终端的结构示意图。Figure 3 is a schematic structural diagram of a processing terminal of the present invention.
下面，结合附图以及具体实施方式，对本发明做进一步描述：Hereinafter, the present invention will be further described with reference to the drawings and specific implementations:
在使用开端同轴探头测量待测样本的介电特性时，需要将开端同轴探头浸入至电解质中，电解质中带电粒子在静电场中受到静电力而被迫向带相反电荷的电极板移动，在探头表明形成双电层，带电粒子被吸附并暂时储存在双电层中，产生双层电极极化效应，该双层电极极化效应可以模拟为与探头-待测样本有效阻抗串联的电容器，具体地，可以将开端同轴探头等效成电阻电容串并联电路，并定义为等效电路模型，如图1所示，该等效电路模型包括电阻R
p、电阻R
s、电阻R
f、电容C
s和电容C
f，电阻R
s和电容C
s并联形成第一并联支路，电阻R
f和电容C
f并联形成第二并联支路，电阻R
p、第一并联支路和第二并联支路依次连接构成串联。该等效电路模型的净负载阻抗Z(ω)计算如公式①：
When using the open-ended coaxial probe to measure the dielectric properties of the sample to be tested, the open-ended coaxial probe needs to be immersed in the electrolyte. The charged particles in the electrolyte are forced to move to the oppositely charged electrode plate due to electrostatic force in the electrostatic field. The probe shows that an electric double layer is formed, and the charged particles are adsorbed and temporarily stored in the electric double layer, resulting in a double-layer electrode polarization effect, which can be simulated as a capacitor connected in series with the probe and the effective impedance of the sample under test Specifically, the open-ended coaxial probe can be equivalent to a resistance-capacitance series-parallel circuit, and defined as an equivalent circuit model, as shown in Figure 1. The equivalent circuit model includes resistance R p , resistance R s , resistance R f , The capacitor C s and the capacitor C f , the resistor R s and the capacitor C s are connected in parallel to form a first parallel branch, the resistor R f and the capacitor C f are connected in parallel to form a second parallel branch, the resistor R p , the first parallel branch and the first parallel branch The two parallel branches are connected in sequence to form a series. The net load impedance Z(ω) of the equivalent circuit model is calculated as formula ①:
式中，ω表示角频率，即ω＝2πf，f表示频率，j表示复数中的虚数单位。In the formula, ω represents the angular frequency, that is, ω=2πf, f represents the frequency, and j represents the imaginary unit in the complex number.
定义
definition
即Z
s为等效电路模型中左半部分(由电阻R
p、电阻R
s和电容C
s构成的电路部分)的电极极化串联阻抗。
That is, Z s is the electrode polarization series impedance of the left half of the equivalent circuit model (the circuit part composed of resistor R p , resistor R s and capacitor C s ).
根据电化学理论可知，若满足Bode四个条件，即因果性、线性、稳定性及阻抗谱在全部频率范围内为有限，电极极化阻抗的实部和虚部满足以因果律为基础的色散关系(也称为Kramers-Kronig关系)，根据Kramers-Kronig关系，可将公式②写成公式③：According to electrochemical theory, if the four conditions of Bode are met, namely, causality, linearity, stability and impedance spectrum are limited in all frequency ranges, the real and imaginary parts of the electrode polarization impedance satisfy the dispersion relationship based on the law of causality. (Also known as Kramers-Kronig relationship), according to the Kramers-Kronig relationship, formula ② can be written as formula ③:
Z
s＝Z′
s(ω)+jZ″
s(ω)＝H
1(ω)+jH
2(ω)------③
Z s ＝Z′ s (ω)+jZ″ s (ω)=H 1 (ω)+jH 2 (ω)------③
即H
1(ω)为Z
s的实部，H
2(ω)为Z
s的虚部，根据Kramers-Kronig关系，可知，电阻R
p、电阻R
s和电容C
s均为关于ω的函数，即可分别采用如下函数表达式：
That is, H 1 (ω) is the real part of Z s and H 2 (ω) is the imaginary part of Z s . According to the Kramers-Kronig relationship, it can be seen that the resistance R p , the resistance R s and the capacitance C s are all functions of ω , You can use the following function expressions respectively:
R
p＝f(ω,A,n)
R p ＝f(ω,A,n)
C
s＝g
1(ω,B,m)
C s ＝g 1 (ω,B,m)
R
s＝g
2(ω,C,I)
R s ＝g 2 (ω,C,I)
其中，A,n,B,m,C,I均为常数，Among them, A, n, B, m, C, and I are all constants,
因此，可以将公式③进一步写成关于ω的函数，即公式④：Therefore, formula ③ can be further written as a function of ω, namely formula ④:
Z
s＝H
1(ω,A,n,B,m,C,I)+jH
2(ω,B,m,C,I)------④
Z s ＝H 1 (ω,A,n,B,m,C,I)+jH 2 (ω,B,m,C,I)------④
即H
1(ω,A,n,B,m,C,I)为Z
s的实部，H
2(ω,B,m,C,I)为Z
s的虚部，也即
That is, H 1 (ω,A,n,B,m,C,I) is the real part of Z s , H 2 (ω,B,m,C,I) is the imaginary part of Z s , that is
从而可以将公式①转换成公式⑤：Thus, formula ① can be converted into formula ⑤:
如果对公式⑤的实部和虚部分别进行求导运算，分别得到公式⑥和⑦：If the real part and imaginary part of formula ⑤ are differentiated, formula ⑥ and ⑦ are obtained respectively:
式中，Re[Z(ω)]表示取Z(ω)的实部，Im[Z(ω)]表示取Z(ω)的虚部，H′
1(ω,A,n,B,m,C,I)表示对H
1(ω,A,n,B,m,C,I)求导，H′
2(ω,B,m,C,I)表示对H
2(ω,B,m,C,I)求导，
In the formula, Re[Z(ω)] represents the real part of Z(ω), Im[Z(ω)] represents the imaginary part of Z(ω), H′ 1 (ω,A,n,B,m ,C,I) represents the derivative of H 1 (ω,A,n,B,m,C,I), H′ 2 (ω,B,m,C,I) represents the derivative of H 2 (ω,B, m,C,I) Derivation,
在频率足够低时，例如频率低于100KHz，公式⑥和⑦的第二项均可以忽略不计，因此得到公式⑧和⑨：When the frequency is low enough, for example, the frequency is lower than 100KHz, the second term of formula ⑥ and ⑦ can be ignored, so formula ⑧ and ⑨ are obtained:
由于Z(ω)的值可以进行实际测量获得，通过多次测量得到净负载阻抗的一组实测数据，并对净负载阻抗的一组实测数据的实部和虚部分别进行插值求导，求导后得到的实部和虚部共同构成对应的一组离散的导数值J(ω),即仍然J(ω)为复数，令
从而分别得到一组
和
的值，相当于得到H′
1(ω,A,n,B,m,C,I)和H′
2(ω,B,m,C,I)的一组离散值，因此可以根据这各自的一组离散值进行拟合，得到H′
1(ω,A,n,B,m,C,I)和H′
2(ω,B,m,C,I)中的参数A,n,B,m,C,I，从而进一步可以得到电阻R
p、电阻R
s和电容C
s的值，即得到Z
s的值。
Since the value of Z(ω) can be obtained by actual measurement, a set of measured data of net load impedance is obtained through multiple measurements, and the real and imaginary parts of a set of measured data of net load impedance are respectively interpolated and derivated. The real part and the imaginary part obtained after the derivative together form a corresponding set of discrete derivative values J(ω), that is, still J(ω) is a complex number, let To get a set of with The value of is equivalent to obtaining a set of discrete values of H′ 1 (ω,A,n,B,m,C,I) and H′ 2 (ω,B,m,C,I), so you can Fit a set of discrete values of to obtain the parameters A,n, in H′ 1 (ω,A,n,B,m,C,I) and H′ 2 (ω,B,m,C,I) B, m, C, I, so that the values of the resistance R p , the resistance R s and the capacitance C s can be further obtained, that is, the value of Z s can be obtained.
由于H′
1(ω,A,n,B,m,C,I)和H′
2(ω,B,m,C,I)相应的每个角频率ω的极化效应的值也是知道的，按相同角频率ω将净负载阻抗的一组实测数据减去对应Z
s的值，即将不同ω处的各净负载阻抗的一组实测数据减去对应ω处的Z
s，因此该减法中，减数和被减数为相同ω处分别对应的净负载阻抗的一组实测数据(被减数)和Z
s(减数)，得到去极化后的阻抗，也即将等效电路模型中左半部分(由电阻R
p、电阻R
s和电容C
s构成的电路部分)的电极极化串联阻抗去除， 达到去极化效果，也即实现电极极化校正的目的。
Since H′ 1 (ω,A,n,B,m,C,I) and H′ 2 (ω,B,m,C,I) corresponding to the polarization effect of each angular frequency ω are also known , At the same angular frequency ω, subtract a set of measured data of net load impedance from the value corresponding to Z s , that is, subtract a set of measured data of each net load impedance at different ω from Z s at the corresponding ω, so in this subtraction , The subtract and the subtract are a set of measured data (subtract) and Z s (subtract) corresponding to the net load impedance at the same ω respectively, to get the impedance after depolarization, that is, in the equivalent circuit model The electrode polarization series impedance of the left half (the circuit part composed of the resistor R p , the resistor R s and the capacitor C s ) is removed to achieve the depolarization effect, that is, to achieve the purpose of electrode polarization correction.
因此，如图2所示，通过以上步骤的处理，即可实现开端同轴探头的电极极化校正方法。Therefore, as shown in Figure 2, the electrode polarization correction method of the open-ended coaxial probe can be realized through the processing of the above steps.
如图3所示，本发明还涉及一种实现以上方法的实体装置的处理终端100，其包括，As shown in FIG. 3, the present invention also relates to a processing terminal 100 of a physical device implementing the above method, which includes:
存储器101，用于存储程序指令；The memory 101 is used to store program instructions;
处理器102，用于运行所述程序指令，以执行所述开端同轴探头的电极极化校正方法中的步骤。The processor 102 is configured to run the program instructions to execute the steps in the electrode polarization correction method of the open-ended coaxial probe.
对于本领域的技术人员来说，可根据以上描述的技术方案以及构思，做出其它各种相应的改变以及变形，而所有的这些改变以及变形都应该属于本发明权利要求的保护范围之内。For those skilled in the art, various other corresponding changes and modifications can be made based on the technical solutions and concepts described above, and all these changes and modifications should fall within the protection scope of the claims of the present invention.
Claims (2)
- 一种开端同轴探头的电极极化校正方法，其特征在于：包括如下步骤：A method for correcting electrode polarization of an open-ended coaxial probe is characterized in that it comprises the following steps:步骤1：预设开端同轴探头的等效电路模型，所述等效电路模型包括电阻R p、电阻R s、电阻R f、电容C s和电容C f，电阻R s和电容R s并联形成第一并联支路，电阻R f和电容C f并联形成第二并联支路，电阻R p、第一并联支路与第二并联支路依次连接；所述等效电路模型的净负载阻抗Z(ω)采用公式①进行计算： Step 1: Preset the equivalent circuit model of the open-ended coaxial probe. The equivalent circuit model includes resistance R p , resistance R s , resistance R f , capacitance C s and capacitance C f , and resistance R s and capacitance R s are connected in parallel A first parallel branch is formed, the resistance R f and the capacitor C f are connected in parallel to form a second parallel branch, the resistance R p , the first parallel branch and the second parallel branch are connected in sequence; the net load impedance of the equivalent circuit model Z(ω) is calculated by formula ①:
并定义And define
式中，ω表示角频率，j表示复数的虚数单位，Z s表示电极极化串联阻抗，且Z s＝H 1(ω,A,n,B,m,C,I)+jH 2(ω,B,m,C,I)，H 1(ω,A,n,B,m,C,I)为Z s的实部，H 2(ω,B,m,C,I)为Z s的虚部，即
式中A,n,B,m,C,I均为常数； In the formula, ω represents the angular frequency, j represents the imaginary unit of the complex number, Z s represents the electrode polarization series impedance, and Z s = H 1 (ω,A,n,B,m,C,I)+jH 2 (ω ,B,m,C,I), H 1 (ω,A,n,B,m,C,I) is the real part of Z s , H 2 (ω,B,m,C,I) is Z s The imaginary part of
In the formula, A, n, B, m, C, I are all constants;步骤2：接收用户输入的开端同轴探头的净负载阻抗的一组实测数据，分别将净负载阻抗的一组实测数据的实部和虚部进行插值求导，得到一组离散的导数值J(ω),令从而分别得到一组
和
的值，由公式②和③分别得到H 1(ω,A,n,B,m,C,I)的导数H′ 1(ω,A,n,B,m,C,I)和H 2(ω,B,m,C,I)的导数H′ 2(ω,B,m,C,I)的各一组离散值，根据所述各一组离散值拟合获得A,n,B,m,C,I的值，从而得到电阻R p、电阻R s和电容R s 的值： Step 2: Receive a set of measured data of the net load impedance of the open-ended coaxial probe input by the user, and respectively interpolate and derive the real and imaginary parts of a set of measured data of the net load impedance to obtain a set of discrete derivative values J (ω), let
To get a set ofwithValue, by the formula ② and ③ respectively H 1 (ω, A, n , B, m, C, I) derivative H '1 (ω, A, n, B, m, C, I) , and H 2 (ω,B,m,C,I) derivative H′ 2 (ω,B,m,C,I) each set of discrete values, and A,n,B is obtained by fitting each set of discrete values ,m,C,I value, thus get the value of resistance R p , resistance R s and capacitance R s :
式中，Re[Z(ω)]表示取Z(ω)的实部，Im[Z(ω)]表示取Z(ω)的虚部，ReJ(ω)表示取J(ω)的实部，ImJ(ω)表示取J(ω)的虚部，H′ 1(ω,A,n,B,m,C,I)表示对H 1(ω,A,n,B,m,C,I)求导，H′ 2(ω,B,m,C,I)表示对H 2(ω,B,m,C,I)求导； In the formula, Re[Z(ω)] represents the real part of Z(ω), Im[Z(ω)] represents the imaginary part of Z(ω), and ReJ(ω) represents the real part of J(ω) , ImJ(ω) means to take the imaginary part of J(ω), H′ 1 (ω,A,n,B,m,C,I) means to H 1 (ω,A,n,B,m,C, I) Derivation, H′ 2 (ω,B,m,C,I) means to derive H 2 (ω,B,m,C,I);步骤3：将电阻R p、电阻R s和电容R s的值代入公式④进行计算，得到Z s的值： Step 3: Substitute the values of resistance R p , resistance R s and capacitance R s into formula ④ for calculation to obtain the value of Z s :
按相同角频率ω将步骤2中的负载阻抗的一组实测数据减去对应Z s的值，得到去极化后的阻抗，完成极化校正。 According to the same angular frequency ω, subtract the corresponding Z s from a set of measured data of the load impedance in step 2 to obtain the impedance after depolarization, and complete the polarization correction. - 一种处理终端，其包括，A processing terminal, which includes,存储器，用于存储程序指令；Memory, used to store program instructions;处理器，用于运行所述程序指令，以执行如下步骤：The processor is used to run the program instructions to execute the following steps:步骤1：预设开端同轴探头的等效电路模型，所述等效电路模型包括电阻R p、电阻R s、电阻R f、电容R s和电容C f，电阻R s和电容C s并联形成第一并联支路，电阻R f和电容C f并联形成第二并联支路，电阻R p、第一并联支路与第二并联支路依次连接；所述等效电路模型的净负载阻抗Z(ω)采用公式①进行计算： Step 1: Preset the equivalent circuit model of the open-ended coaxial probe. The equivalent circuit model includes resistance R p , resistance R s , resistance R f , capacitance R s and capacitance C f , and resistance R s and capacitance C s are connected in parallel A first parallel branch is formed, the resistance R f and the capacitor C f are connected in parallel to form a second parallel branch, the resistance R p , the first parallel branch and the second parallel branch are connected in sequence; the net load impedance of the equivalent circuit model Z(ω) is calculated by formula ①:
并定义And define
式中，ω表示角频率，j表示复数的虚数单位，Z s表示电极极化串联阻抗，且Z s＝H 1(ω,A,n,B,m,C,I)+jH 2(ω,B,m,C,I)，H 1(ω,A,n,B,m,C,I)为C s的实部，H 2(ω,B,m,C,I)为C s的虚部，即
式中A,n,B,m,C,I均为常数； In the formula, ω represents the angular frequency, j represents the imaginary unit of the complex number, Z s represents the electrode polarization series impedance, and Z s = H 1 (ω,A,n,B,m,C,I)+jH 2 (ω ,B,m,C,I), H 1 (ω,A,n,B,m,C,I) is the real part of C s , H 2 (ω,B,m,C,I) is C s The imaginary part of
In the formula, A, n, B, m, C, I are all constants;步骤2：接收用户输入的开端同轴探头的净负载阻抗的一组实测数据，分别将净负载阻抗的一组实测数据的实部和虚部进行插值求导，得到一组离散的导数值J(ω),令从而分别得到一组
和
的值，由公式②和③分别得到H 1(ω,A,n,B,m,C,I)的导数H′ 1(ω,A,n,B,m,C,I)和H 2(ω,B,m,C,I)的导数H′ 2(ω,B,m,C,I)的各一组离散值，根据所述各一组离散值拟合获得A,n,B,m,C,I的值，从而得到电阻R p、电阻R s和电容C s的值： Step 2: Receive a set of measured data of the net load impedance of the open-ended coaxial probe input by the user, and respectively interpolate and derive the real and imaginary parts of a set of measured data of the net load impedance to obtain a set of discrete derivative values J (ω), let
To get a set ofwithValue, by the formula ② and ③ respectively H 1 (ω, A, n , B, m, C, I) derivative H '1 (ω, A, n, B, m, C, I) , and H 2 (ω,B,m,C,I) derivative H′ 2 (ω,B,m,C,I) each set of discrete values, and A,n,B is obtained by fitting each set of discrete values ,m,C,I value, thus get the value of resistance R p , resistance R s and capacitance C s :
式中，Re[Z(ω)]表示取Z(ω)的实部，Im[Z(ω)]表示取Z(ω)的虚部，ReJ(ω)表示取J(ω)的实部，ImJ(ω)表示取J(ω)的虚部，H′ 1(ω,A,n,B,m,C,I)表示对H 1(ω,A,n,B,m,C,I)求导，H′ 2(ω,B,m,C,I)表示对H 2(ω,B,m,C,I)求导； In the formula, Re[Z(ω)] represents the real part of Z(ω), Im[Z(ω)] represents the imaginary part of Z(ω), and ReJ(ω) represents the real part of J(ω) , ImJ(ω) means to take the imaginary part of J(ω), H′ 1 (ω,A,n,B,m,C,I) means to H 1 (ω,A,n,B,m,C, I) Derivation, H′ 2 (ω,B,m,C,I) means to derive H 2 (ω,B,m,C,I);步骤3：将电阻R p、电阻R s和电容C s的值代入公式④进行计算，得到Z s的值： Step 3: Substitute the values of resistance R p , resistance R s and capacitance C s into formula ④ for calculation to obtain the value of Z s :
按相同角频率ω将步骤2中的净负载阻抗的一组实测数据减去对应Z s的值，得到去极化后的阻抗，完成极化校正。 According to the same angular frequency ω, subtract the corresponding Z s from a set of measured data of the net load impedance in step 2 to obtain the impedance after depolarization, and complete the polarization correction.
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