How to calculate capacitance by EC methods

Capacitive Sensor Operation Part 1: The BasicsPart 1 of this two-part article reviews the concepts and theory of capacitive sensing to help to optimize capacitive sensor performance. Part 2 of this article will discuss how to put these concepts to work.Noncontact capacitive sensors measure the changes in an electrical property called capacitance. Capacitance describes how two conductive objects with a space between them respond to a voltage difference applied to them. A voltage applied to the conductors creates an electric field between them, causing positive and negative charges to collect on each objectCapacitive sensors use an alternating voltage that causes the charges to continually reverse their positions. The movement of the charges creates an alternating electric current that is detected by the sensor. The amount of current flow is determined by the capacitance, and the capacitance is determined by the surface area and proximity of the conductive objects. Larger and closer objects cause greater current than smaller and more distant objects. Capacitance is also affected by the type of nonconductive material in the gap between the objects. Technically speaking, the capacitance is directly proportional to the surface area of the objects and the dielectric constant of the material between them, and inversely proportional to the distance between them as shown.:In typical capacitive sensing applications, the probe or sensor is one of the conductive objects and the target object is the other. (Using capacitive sensors to sense plastics and other insulators will be discussed in the second part of this article.) The sizes of the sensor and the target are assumed to be constant, as is the material between them. Therefore, any change in capacitance is a result of a change in the distance between the probe and the target. The electronics are calibrated to generate specific voltage changes for corresponding changes in capacitance. These voltages are scaled to represent specific changes in distance. The amount of voltage change for a given amount of distance change is called the sensitivity. A common sensitivity setting is 1.0 V/100 µm. That means that for every 100 µm change in distance, the output voltage changes exactly 1.0 V. With this calibration, a 2 V change in the output means that the target has moved 200 µm relative to the probe.Focusing the Electric FieldWhen a voltage is applied to a conductor, the electric field emanates from every surface. In a capacitive sensor, the sensing voltage is applied to the sensing area of the probe. For accuratemeasurements, the electric field from the sensing area needs to be contained within the space between the probe and the target. If the electric field is allowed to spread to other items—or other areas on the target—then a change in the position of the other item will be measured as a change in the position of the target. A technique called "guarding" is used to prevent this from happening. To create a guard, the back and sides of the sensing area are surrounded by another conductor that is kept at the same voltage as the sensing area itself. When the voltage is applied to the sensing area, a separate circuit applies the exact same voltage to the guard. Because there is no difference in voltage between the sensing area and the guard, there is no electric field between them. Any other conductors beside or behind the probe form an electric field with the guard instead of with the sensing area. Only the unguarded front of the sensing area is allowed to form an electric field with the target.DefinitionsSensitivity indicates how much the output voltage changes as a result of a change in the gap between the target and the probe. A common sensitivity is 1 V/0.1 mm. This means that for every 0.1 mm of change in the gap, the output voltage will change 1 V. When the output voltage is plotted against the gap size, the slope of the line is the sensitivity.A system's sensitivity is set during calibration. When sensitivity deviates from the ideal value this is called sensitivity error, gain error, or scaling error. Since sensitivity is the slope of a line, sensitivity error is usually presented as a percentage of slope, a comparison of the ideal slope with the actual slope.Offset error occurs when a constant value is added to the output voltage of the system. Capacitive gauging systems are usually "zeroed" during setup, eliminating any offset deviations from the original calibration. However, should the offset error change after the system is zeroed, error will be introduced into the measurement. Temperature change is the primary factor in offset error.Sensitivity can vary slightly between any two points of data. The accumulated effect of this variation is called linearity erro. The linearity specification is the measurement of how far the output varies from a straight line.To calculate the linearity error, calibration data are compared to the straight line that would best fit the points. This straight reference line is calculated from the calibration data using least squares fitting. The amount of error at the point on the calibration line furthest away from this ideal line is the linearity error. Linearity error is usually expressed in terms of percent of full scale (%/F.S.). If the error at the worst point is 0.001 mm and the full scale range of the calibration is 1 mm, the linearity error will be 0.1%.Note that linearity error does not account for errors in sensitivity. It is only a measure of the straightness of the line rather than the slope of the line. A system with gross sensitivity errors can still be very linear.Error band accounts for the combination of linearity and sensitivity errors. It is the measurement of the worst-case absolute error in the calibrated range. The error band is calculated by comparing the output voltages at specific gaps to their expected value. The worst-case error from this comparison is listed as the system's error band. In Figure 7, the worst-case error occurs for a 0.50 mm gap and the error band (in bold) is –0.010.Figure 7. Error valuesBandwidth is defined as the frequency at which the output falls to –3 dB, a frequency that is also called the cutoff frequency. A –3 dB drop in the signal level is an approximately 30% decrease. With a 15 kHz bandwidth, a change of ±1 V at low frequency will only produce a ±0.7 V change at 15 kHz. Wide-bandwidth sensors can sense high-frequency motion and provide fast-responding outputs to maximize the phase margin when used in servo-control feedback systems; however, lower-bandwidth sensors will have reduced output noise which means higher resolution. Some sensors provide selectable bandwidth to maximize either resolution or response time.Resolution is defined as the smallest reliable measurement that a system can make. The resolution of a measurement system must be better than the final accuracy the measurement requires. If you need to know a measurement within 0.02 µm, then the resolution of the measurement system must be better than 0.02 µm.The primary determining factor of resolution is electrical noise. Electrical noise appears in the output voltage causing small instantaneous errors in the output. Even when theprobe/target gap is perfectly constant, the output voltage of the driver has some small but measurable amount of noise that would seem to indicate that the gap is changing. This noise is inherent in electronic components and can be minimized, but never eliminated.If a driver has an output noise of 0.002 V with a sensitivity of 10 V/1 mm, then it has an output noise of 0.000,2 mm (0.2 µm). This means that at any instant in time, the output could have an error of 0.2 µm.The amount of noise in the output is directly related to bandwidth. Generally speaking, noise is distributed over a wide range of frequencies. If the higher frequencies are filtered before the output, the result is less noise and better resolution (Figures 8, 9). When examining resolution specifications, it is critical to know at what bandwidth the specifications apply.Capacitive Sensor Operation Part 2: System OptimizationPart 2 of this two-part article focuses on how to optimize the performance of your capacitive sensor, and to understand how target material, shape, and size will affect the sensor's response.Effects of Target SizeThe target size is a primary consideration when selecting a probe for a specific application. When the sensing electric field is focused by guarding, it creates a slightly conical field that is a projection of the sensing area. The minimum target diameter is usually 130% of the diameter of the sensing area. The further the probe is from the target, the larger the minimum target size.Range of MeasurementThe range in which a probe is useful is a function of the size of the sensing area. The greater the area, the larger the range. Because the driver electronics are designed for a certain amount of capacitance at the probe, a smaller probe must be considerably closer to the target to achieve the desired amount of capacitance. In general, the maximum gap at which a probe is useful is approximately 40% of the sensing area diameter. Typical calibrations usually keep the gap to a value considerably less than this. Although the electronics are adjustable during calibration, there is a limit to the range of adjustment.Multiple Channel SensingFrequently, a target is measured simultaneously by multiple probes. Because the system measures a changing electric field, the excitation voltagefor each probe must be synchronized or the probes will interfere with each other. If they were not synchronized, one probe would be trying to increase the electric field while another was trying to decrease it; the result would be a false reading. Driver electronics can be configured as masters or slaves; the master sets the synchronization for the slaves in multichannel systems.Effects of Target MaterialThe sensing electric field is seeking a conductive surface. Provided that the target is a conductor, capacitive sensors are not affected by the specific target material; they will measure all conductors—brass, steel, aluminum, or salt water—as the same. Because the sensing electric field stops at the surface of the conductor, target thickness does not affect the measurement中文翻译电容式传感器操作第一部分：基础 这篇文章的第一部分回顾了电容式传感器的概念和理论来帮助我们优化电容式传感器的性能。

Oscilloscope Measurement LabMeasuring Impedance and Capacitance with an Oscilloscope and Function GeneratorA circuit made up of a resistor and capacitor causes a phase shift between the current and voltage. In this lab, you will be able to observe this effect and use it to measure the magnitude and angle of impedance, equivalent series resistance, and capacitance.TheoryImpedance is the total opposition to current flow in an alternating current circuit. It is made up of resistance (real) and reactance (imaginary) and is usually represented in complex notation as Z = R + jX, where R is the resistance and X is the reactance.Real-world components are made up of wires, connections,conductors and dielectric materials. These elements combine to make up the impedance characteristics of the component, and this impedance changes based on the test signal frequency and voltage level, the presence of a DC bias voltage or current andenvironmental factors such as operating temperatures or altitude. Of these potential influences the test signal frequency is often the most significant factor.Unlike ideal components, real components are not purely inductive or capacitive. All components have a series resistance, which is the R parameter in its impedance. But they also have multiple contributors to their reactance. For example, a capacitor has a series inductance that becomes more apparent at high frequencies. When we measure a real capacitor, the series inductance (ESL) will impact the capacitance reading, but we won't be able to measure it as a separate, distinct component.The impedance measuring technique used in this lab uses two voltage waveforms at different points to calculate the unknown impedance, Zx. as shown in Figure 1. Equation 1 shows how the circuit can be used to find Zx.Equation 1:Figure 1. Circuit for measuring impedance of a device by measuring two voltage dropsEquipment List▪Tektronix AFG2021 arbitrary/function generator▪DPO4104 oscilloscope▪ A 1 kΩ precision resistor▪Two Tektronix TPP1000 voltage probes▪ A 10 uF ceramic capacitor▪An unknown capacitorProcedure1. Set up the test circuit as shown in Figure2. Note that RESR and C are both associated with the ceramic capacitor under test,and that Rfg is the 50 Ω output impedance of the function generator.2. Set the function generator to output a 1.9 V amplitude, 100 Hz sine wave.3. Adjust the vertical scale setting of the oscilloscope to use as much of the display as possible – by using as much of the rangeas possible, you will improve the accuracy of your voltage measurements.4. Use the oscilloscope to probe at nodes A1 and A2. Figure 4 shows an example of the resulting waveform.5. Select the oscilloscope’s average acquisition mode and set the number of averages to 128. This will reduce the effects ofrandom noise on your measurements.6. Set the oscilloscope to measure the four parameters listed below. (An example is given in Figure 4.)a. Channel 1 frequencyb. Phase between channel 2 and channel 1c. Channel 1 amplituded. Channel 2 amplitude, as shown in Figure 4.7. Carefully record both the four measurements.8. Replace the 10 µF capacitor with the unknown capacitor.9. Repeat steps 3 through 6 for the unknown capacitor.Figure 2. Impedance test circuit with a capacitor as the device under test (DUT). Figure 3. Measurement example on a 10 µF capacitor.Sample CalculationFrom the measurement setup, we know:Stimulus frequency, f = 100 HzPrecision Resistor, R1 = 1 kΩFrom the measurements taken on the oscilloscope and shown in Figure 3:Voltage amplitude measured at A1, V A1 = 1.929 VVoltage amplitude measured at A2, V A2 = 0.310 VPhase difference between voltage measured at A2 relative to A1, θ = -79.95°Note that at node A1, the voltage has a phase angle of 0°, that is it is in phase with the function generator output. At A2 the voltage is shifted ahead by the phase angle θ.The impedance of the capacitor under test can be found using Equation 1, given above.The impedance can be expressed in polar form, where the magnitude is given by:Equation 2: Z=V A2R ref�V A12−2V A1V A2cosθ+V A22The angle of the impedance is given by subtracting the two angles:Equation 3: α=θ−tan−1−V A2sinθV A1−V A2cosθFor the test in our example, we can use Equation 2 and Equation 3 to find the magnitude and angle of the impedance of the capacitor under test:Z=(0.310)(1x103)�22Z = 163.193Ωα=−79.95°−tan−1�−0.310sin (−79.95°)()�α= -89.197°Now we can convert to the rectangular form of the impedance to find the resistance and capacitance.Z=R ESR−jZ=Zcos∝+jZsin∝Using the equations above, we can solve for the ESR and Capacitance of the DUT:Equation 4: R ESR=Zcos∝Equation 5: C=−12πfZsinαUsing Equation 4 and Equation 5 we can calculate the equivalent series resistance (ESR) and capacitance for the capacitor under test:R ESR=163.193cos(−89.197)R ESR = 2.29 ΩC=−1()()C = 9.75 µFAnalysisCalculate the magnitude of the impedance, angle of the impedance, series resistance, and capacitance of the 10 uF capacitor. How do your results compare to the ones in the example calculations above. Show your calculation.Calculate the magnitude of the impedance, angle of the impedance, series resistance, and capacitance of the unknown capacitor.Compare the magnitude of the impedance, angle of the impedance, series resistance, and capacitance of the two capacitors. Explain why each parameter changed the way it did.Post-Lab AssessmentAnswer the following:1. List the concepts you have learned doing this exercise._ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _2. List 8 curriculum-prescribed experiments where you can leverage the measurement concepts learntfrom this experiment? What parameters would you measure in those experiments?Measured parameter S. No. Title of curriculum-prescribedexperiments12345678Copyright © 2013, Tektronix. All rights reserved. Tektronix products are covered by U.S. and foreign patents, issuedand pending. Information in this publication supersedes that in all previously published material. Specification andprice change privileges reserved. TEKTRONIX and TEK are registered trademarks of Tektronix, Inc .All other tradenames referenced are the service marks, trademarks or registered trademarks of their respective companies.04/2013 48W-29165-0。

超级电容测试方法超级电容：采用物理、化学或者混合方式实现超大容量双层电容器。

主要用来“削峰填谷”，比如：主电源和备用电源切换时的续电（基站及服务器，网络机房，通讯等行业）；快速充放电短时储存环境（比如动车的启动与刹车时充放电时省电，并且减小对启动电源的要求，地铁车辆，电动车，太阳能发电等）；在快充快放环境是替代一些蓄电池和动力电池（电动工具行业，电动大巴等）。

超级电容特点：快充快放、循环寿命长、放电电流大、功率密度较高、安全、稳定及温度特性好、单节电压较低。

费思负载在测试超级电容时的特点，精确度：负载就有0.05%的电压回读精确度，保证测试的精确度集成功能：集成了超级电容的内阻和容量测试功能。

测试方法简单。

完善的接口：RS232,USB,GPIB口并且配备相应软件，数据，图像报告，循环测试一键完成。

配件及软件：可监控电容组的每分电容的电压一致性和电压值，同时监控温度，测试内容：内阻、容量、单节一致性、充放电曲线。

测试仪器：电源（电压高于电容组的最高开路电压，电流适当）、电容器、负载仪（功率及电压适当）、示波器（长存储最好）、万用表（选用，使用费思负载，可不使用本仪器）。

充电方式：恒流转恒压充电。

接线方式，测试之前请确认电容的正负极。

请确认连接电路。

超级电容充电测试负载设置：远端采样打开，电池（电容）恒压功能打开，Shift+0打开电容测试功能。

设定截止电压，电容计算电压的上下限。

设定充电电流。

按on/off键，开始测试，屏幕显示测试结果。

一键完成测试。

本测量测试，充电时间，充电内阻，充电电量，电容容量。

充电曲线，漏电流等测试。

充电曲线，请链接上位机软件。

以上设置，请参看相关说明书。

放电方式：接线方式：请确定电容正负极及确定连接方式。

超级电容放电测试负载设置：远端采样打开，电池（电容）恒压功能打开，Shift+0打开电容测试功能。

设定截止电压，电容计算电压的上下限。

设定放电电流。

按on/off键，开始测试，屏幕显示测试结果。