Biomathematical Analysis on Impedance Measurement During Covid-19 Pandemic

Bin Zhao1*, Xia Jiang2

1. School of Science, Hubei University of Technology, Wuhan, Hubei, China.

2. Hospital, Hubei University of Technology, Wuhan, Hubei, China.

Corresponding Author: Dr. Bin Zhao, School of Science, Hubei University of Technology, Wuhan, Hubei, China.

Copy Right: © 2022 Dr. Bin Zhao, This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Received Date: October 27, 2022

Published Date: November 10, 2022

Abstract

The coating impedance size can reflect the aging degree of the coating to a certain extent, therefore, the measurement of the coating impedance size can monitor the aging degree of the coating in real time. Since the coating is traditionally considered as an insulating medium, its impedance value before aging is as high as 10^8 Ω or more, it is difficult to achieve accurate impedance measurement, and the current generated by loading by voltammetry at low voltage is very weak and easily affected by external electromagnetic interference noise, and the measurement accuracy is low. In this paper, by pluralizing the high impedance, establishing the mathematical model of differential amplification circuit, and then using sinusoidal fitting in which processing, so that the obtained signal is more accurate during COVID-19 pandemic.

Keywords: High impedance measurements, Differential circuits, Sine fitting

Introduction

In the industrial field, impedance is an important parameter, and the measurement and analysis of impedance helps us to understand the changes of morphological characteristics of the object under test[1]. For example, in the oil and gas pipeline transmission system, the impedance of the pipeline corrosion protection layer needs to be measured to grasp its service life[2];in the field of biomedicine, the clinical application of bioimpedance technology has a great front[3]; in the field of corrosion monitoring, the monitoring of aircraft coatings, which is an effective means to prevent corrosion of the base metal[4], these belong to the category of high impedance measurement, with an impedance of up to 108 Ω. Therefore, in the processing of these weak signals processing, the idea of sinusoidal fitting is used to process to obtain more information during COVID-19 pandemic.

Differential amplifier circuit mathematical model

The excitation signal is formed by bucking the sine signal generated by filtering, assuming that the bucking scale factor is ????1 and the amplitude of the sine signal before bucking is ????, the excitation signal is expressed as:

????_????(????) = ????₁????????????????(????????)?1?

If the differential amplification is ????2, the output ???????? of the differential amplifier circuit and the input ????????satisfy the following vector relationship;

????? = ^{????2????????} ????? ?2?

Translated into a specific functional form of time it can be expressed as:

???? (????) = ^{????1????2|???????? |} ????????????(???????? + ????)?3?

????0: Reference impedance, standard resistance is generally used in measurement circuits.

????: Difference between ???????? and the impedance angle of ???????? + ????????.

If the presence of the input capacitance ????0 of the amplified input system is not considered,???????? is the measured coating complex impedance ????????, and if the presence of the input capacitance is considered, it is the combined impedance of the coating complex impedance in parallel with the capacitance, satisfying the following relationship

 ????   =      ^????????       ?4?

1+???????? ????0 ????????

The complex impedance of the coating under test is:

????   =      ^????????      ?5?

1−???????? ????0 ????????

Understanding of sine fitting

Simple moving average method

First, we use the simple moving average method to feel the meaning of "moving".

There is a sequence as follows

If a moving average with a window of 5 is used, the element with a sequence of 11 and a value of 2 should be replaced with

????11 = (8 + 5 + 2 + 1 + 3)/5?6?

Then the element with a sequence of 12 and a value of 1 should be replaced with

????12 = (5 + 2 + 1 + 3 + 6)/5?7?

For fast calculation, the following formula can be used for recursion

????12 = (5 ∗ ????11 + 6 − 8)/5?8?

Simple   moving   average   is   defined as: Simple   moving   average of data ????1, ????2, . . ., ???????? with window ????:

The iteration form is:

In MATLAB, there is a corresponding smooth function available. We can use ???????????????????????? to verify smooth (y, span). The following figure shows the result of data 2= smooth (data1,5)

Results

In large impedance measurements, the signal is extremely weak, so a differential circuit is introduced to change it into complex impedance form, and the simplicity of sine fitting in amplitude and phase calculation is used to assist in calculating the impedance magnitude, which plays an important role in subsequent large impedance measurements

Reference

1.ZHANG Chaoquan, GUO Benqing, LI Ke, LI Lei, ZHOU Wanting. A CMOS low-noise active down-conversion mixer[J]. Microelectronics & Computer, 2022, 39(1): 101-106. doi: 10.19304/J.ISSN1000-7180.2021.0661

2.DONG Zhen-zhen, GAN Ye-bing, LUO Yan-bin. Design of GaAs RF front-end LNA[J]. Microelectronics & Computer, 2020, 37(7): 16-20.

3.PEI Bing-xi, LI Zhen-tao, HUANG Dong-chang, GUO Yang. Physical Design of 2 133 Mb/s DDR3 Memory Interface[J]. Microelectronics & Computer, 2017, 34(7): 79-83.

4.LIU Jian-ming, GU Kai, XU Xiang-yu. Two-Side Drecommendation Algorithm on G-S Model[J]. Microelectronics & Computer, 2016, 33(4): 117-120.

5.SHEN Chao-peng, LI Shu-guo. Design and Implementation of Snow3G on FPGA Supporting f8?f9 Algorithm[J]. Microelectronics & Computer, 2015, 32(9): 90-94. doi: 10.19304/j.cnki.issn1000-7180.2015.09.018

6.MAO Fang-yu, MA Jian-ping, MENG Fan-zhen, RUAN Ai-wu, TIAN Tong. A High PAE RF COMS Power Amplifier for IOT Applications[J]. Microelectronics & Computer, 2015, 32(7): 29-32,37. doi: 10.19304/j.cnki.issn1000-7180.2015.07.007

7. WU Li-wei, HAO Ming-li, DAI Zhi-wei, ZHENG Xin-nian, WANG Ming-hua, YIN Jun-jian. 50 MHz-2 GHz Wide Band Low Noise Amplifier Module[J]. Microelectronics & Computer, 2015, 32(10): 50-53,57. doi: 10.19304/j.cnki.issn1000-7180.2015.10.011

8.YOU Yun-xia, CHEN Lan, WANG Hai-yong, LU: Zhi-qiang. Radio Frequency Power Amplifier Based on SiGe HBT[J]. Microelectronics & Computer, 2014, 31(4): 144-147.

9. MA Xuan, WANG Zi-qiang. Circuit Design for Transmitter System of 10 Gb/s SerDes[J]. Microelectronics & Computer, 2014, 31(2): 14-17,22.

10.ZHENG Yu, DUAN Ji-hai, XU Shi-chao. Design of a 3~5 GHz LNA with the Function of Both a Single-end Input and Differential Output is Achieved[J]. Microelectronics & Computer, 2014, 31(6): 103-106.

11.DUAN Ji-hai, LEI Yao-yong, XU Wei-lin. Design of 5.25 GHz Gilbert Mixer with High Gain and Low Noise[J]. Microelectronics & Computer, 2013, 30(9): 133-136,140.

12.CHEN Zheng, DUAN Ji-hai, HUANG Sheng. Design of a Variable Gain LNA Applied in CMMB[J]. Microelectronics & Computer, 2013, 30(12): 160-163.

13.PEI Shi-feng, NAN Jing-chang, MAO Lu-hong. Design and Simulation of RFID Dual-band LNA Based on CMOS Process[J]. Microelectronics & Computer, 2012, 29(6): 23-27.

14. ZHANG Hong, LIANG Yuan. 0.13μm CMOS Dual-Channel UWB LNA Design[J]. Microelectronics & Computer, 2012, 29(10): 37-41,46.

15. WANG Wei, GONG Zhao-ying, YANG Keng, MA Xiao-ying, TANG Zheng-wei, WANG Yue-sheng. Design of Inductorless CMOS Low Noise Amplifier for 3~5 GHz UWB Receiver[J]. Microelectronics & Computer, 2012, 29(6): 130-133,137.

16.PAN Ke, HE Shu-zhuan, LI Li, PAN Hong-bing, LI Wei. An Adaptive Termination Resistors Control Circuit[J]. Microelectronics & Computer, 2011, 28(2): 82-85,90.

17.XIA Wen-dong. Research of Internet of Things Based on 3G-WLAN Interactive System[J]. Microelectronics & Computer, 2011, 28(7): 139-142.

18. DAI Peng, YE Zhao-hua, ZHANG Zhe, WANG Xin-an, ZHANG Xing. Implementation of Security System for 3G USIM Card[J]. Microelectronics & Computer, 2011, 28(1): 165-168,172.

19. ZHUANG Hai-xiao, MA Cheng-yan, YE Tian-chun, HUANG Wei, PAN Wen-guang, YU Yun-feng, WU Zhen-yu. Dual-Band CMOS LNA for Multimode GNSS Receiver[J]. Microelectronics & Computer, 2011, 28(1): 69-73.

20. HUANG Wei, ZHUANG Hai-xiao, MA Cheng-yan, YE Tian-chun. Design of CMOS LNA in Dual-Band GPS Receiver[J]. Microelectronics & Computer, 2010, 27(12): 153-156.