WO2020150933A1 - 一种开端同轴探头的电极极化校正方法及处理终端 - Google Patents

一种开端同轴探头的电极极化校正方法及处理终端 Download PDF

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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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resistance
formula
capacitance
open
coaxial probe
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余学飞
辛学刚
孙颖
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South China University of Technology SCUT
Southern Medical University
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South China University of Technology SCUT
Southern Medical University
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    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R35/00—Testing or calibrating of apparatus covered by the other groups of this subclass

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  • 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

本发明涉及一种开端同轴探头的电极极化校正方法及处理终端，所述方法包括如下步骤：步骤1：预设开端同轴探头的等效电路模型，等效电路模型的电极极化串联阻抗；步骤2：接收用户输入的净负载阻抗的一组实测数据，计算出电阻Rp、电阻Rs和电容Cs的值；步骤3：将净负载阻抗的一组实测数据减去对应Zs的值，得到去极化后的阻抗，完成极化校正。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。

Description

一种开端同轴探头的电极极化校正方法及处理终端 技术领域
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。
背景技术
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。
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。
发明内容
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；
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。
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：
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：
Figure PCTCN2019072857-appb-000001
并定义
Figure PCTCN2019072857-appb-000002
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
Figure PCTCN2019072857-appb-000003
Figure PCTCN2019072857-appb-000004
式中A,n,B,m,C,I均为常数；
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
Figure PCTCN2019072857-appb-000005
从而分别得到一组
Figure PCTCN2019072857-appb-000006
和
Figure PCTCN2019072857-appb-000007
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：
Figure PCTCN2019072857-appb-000008
Figure PCTCN2019072857-appb-000009
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；
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：
Figure PCTCN2019072857-appb-000010
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。
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，
存储器，用于存储程序指令；
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。
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。
附图说明
图1为本发明开端同轴探头的等效电路模型；
图2为本发明较佳实施例的流程图；
图3为本发明一种处理终端的结构示意图。
具体实施方式
下面，结合附图以及具体实施方式，对本发明做进一步描述：
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：
Figure PCTCN2019072857-appb-000011
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。
定义
Figure PCTCN2019072857-appb-000012
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。
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：
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：
R p＝f(ω,A,n)
C s＝g 1(ω,B,m)
R s＝g 2(ω,C,I)
其中，A,n,B,m,C,I均为常数，
因此，可以将公式③进一步写成关于ω的函数，即公式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
Figure PCTCN2019072857-appb-000013
从而可以将公式①转换成公式⑤：
Figure PCTCN2019072857-appb-000014
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：
Figure PCTCN2019072857-appb-000015
Figure PCTCN2019072857-appb-000016
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，
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：
Figure PCTCN2019072857-appb-000017
Figure PCTCN2019072857-appb-000018
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
Figure PCTCN2019072857-appb-000019
从而分别得到一组
Figure PCTCN2019072857-appb-000020
和
Figure PCTCN2019072857-appb-000021
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。
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。
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。
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，
存储器101，用于存储程序指令；
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。
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。

Claims (2)

  1. 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：
    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：
    Figure PCTCN2019072857-appb-100001
    并定义
    Figure PCTCN2019072857-appb-100002
    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
    Figure PCTCN2019072857-appb-100003
    Figure PCTCN2019072857-appb-100004
    式中A,n,B,m,C,I均为常数；
    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
    Figure PCTCN2019072857-appb-100005
    从而分别得到一组
    Figure PCTCN2019072857-appb-100006
    和
    Figure PCTCN2019072857-appb-100007
    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：
    Figure PCTCN2019072857-appb-100008
    Figure PCTCN2019072857-appb-100009
    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；
    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：
    Figure PCTCN2019072857-appb-100010
    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。
  2. 一种处理终端，其包括，
    存储器，用于存储程序指令；
    处理器，用于运行所述程序指令，以执行如下步骤：
    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：
    Figure PCTCN2019072857-appb-100011
    并定义
    Figure PCTCN2019072857-appb-100012
    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
    Figure PCTCN2019072857-appb-100013
    Figure PCTCN2019072857-appb-100014
    式中A,n,B,m,C,I均为常数；
    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
    Figure PCTCN2019072857-appb-100015
    从而分别得到一组
    Figure PCTCN2019072857-appb-100016
    和
    Figure PCTCN2019072857-appb-100017
    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：
    Figure PCTCN2019072857-appb-100018
    Figure PCTCN2019072857-appb-100019
    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；
    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：
    Figure PCTCN2019072857-appb-100020
    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。
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