傳感器技術(shù)基礎(chǔ)：Chapter 4 Capacitive Sensor

1、Sensor Technology傳感器技術(shù)Chapter 4 Capacitive SensorAdvantages, Disadvantages, and Improvement for Capacitive Sensor1.2ContentSensing Principle, Structures & Characteristics4.14.2Signal Conditioning Circuit4.3Typical Applications 4.4Capacitive Sensor: A sensor who is a converter of non-electrical effec

2、ts into change of capacitance.Applications: Distance, area, volume, pressure, force, chemical composition, etc.Capacitive SensorSensing PrincipleTo a parallel-plate capacitor, if “fringing” effect of the lines at the edges of plates can be neglected, its capacitance can be found from:+Srd_r: Relativ

3、e permittivity/dielectric constant0: Permittivity in vacuum (8.8541012F/m)S: Area covered by two parallel-platesd: Distance between two parallel-platesAny phenomena or physical quantities producing a change of r ,S or d will result in change of capacitance C, thus can be in principle sensed by the d

4、eviceCapacitive Sensor (1)Capacitive Sensor Based on Distance Variation between two Parallel-platesSuppose initial capacitance is:If the distance d0 decreases d, then the capacitance will increaseC：Relative change of capacitance is：Fixed plateMoving plateCapacitive Sensor (1)When ,C/C0 can be expand

5、ed using Taylor series as：The relationship between relative change of capacitance C and the distance d0 is nonlinear. Under the condition of dd0, the above equation takes the linear form as:Sensitivity:Sensitivity increases with decrease of distance d0If the second-order nonlinear term is considered

6、 only while neglecting other high-order terms, the non-linear error can be obtained as:Conclusion: Linear relationship exists only when d/d0C2Attention: Change of distance in two opposite directions will cause change of different amount of capacitanceNonlinear error increases with decrease of distan

7、ce d0Capacitive Sensor (1)Capacitive Sensor (1)It should be noted that the distance d0 can not be too small, as it will break the dielectric. e.g., the minimal distance determined by dielectric breakdown is 30 kv/cm.The problem can be solved by adding an additional dielectric in a parallel-plate cap

8、acitive sensorThe total capacitance is:If d1 decreases d1, the capacitance will increase C:Moving plateSolidFixed plateAirCapacitive Sensor (1)The relative change of capacitance is:Approximately, To improve sensitivity, decrease non-linear error, and overcome the influence of external conditions, su

9、ch as supply voltage, temperature change, differential capacitor is often used:Capacitive Sensor (1)When ,C/C0 can be expanded using Taylor series as：Fixed plateFixed plateMoving plateIf high-order terms are neglected：Sensitivity K of differential capacitor is defined as:The nonlinear error L of dif

10、ferential capacitor is approximated as:Conclusion: For differential capacitor, the non-linear error decreases while at the same time, the sensitivity is doubled. Capacitive Sensor (1)Example (1)There is a capacitive sensor for displacement measurement, and the radius of the sensor is r=4 mm. Suppose

11、 initial gap between the plate and the work piece is d0=0.3 mm with air in the gap.Q1: If the gap between the plate and the work piece decreases d=10m, how much does the capacitance change?Q2: If the sensitivity of the signal conditioning circuit is Ku=100 mV/pF, what is the output voltage value whe

12、n d=1 m?Capacitive Sensor (2)Capacitive Sensor Based on Area Variation1. Fixed plate 2. Moving plate1. Fixed plate 2. Moving plate1. Fixed plate 2. Moving plate (1) Capacitor for Line Displacement MeasurementWhen the floating plate moves, the area covered by two plates changes, leading to change of

13、capacitance as:Sensitivity:Sensitivity is constantCapacitive Sensor (2)Fixed plateMoving plateThe parallel-plate structure is sensitive to distance variation, which affects the precision of measurement. In practical applications, coaxial-cylinder structure is often used Change of Capacitance with va

14、riation of xSensitivity： Linear relationship between input and output; Constant sensitivity; Low sensitivity as compared to parallel-plate structure; Large measurement rangeCapacitive Sensor (2)Fixed plateMoving plateAfter rotating ， When =0，Sensitivity:Linear output and constant sensitivityCapaciti

15、ve Sensor (2)(2) Capacitor for Angular Displacement MeasurementFixed plateMoving plate Initial capacitance with coaxial cylinder structureWhen measuring, one part of the dielectric is liquid, and the other part is air. Suppose C1 and C2 denote the capacitance generated from the liquid with height hx

16、, and the air with height (h-hx), respectively, we have：Capacitive Sensor (3)Capacitive Sensor Based on Dielectric VariationIt can be seen the relationship between the capacitance and the height of the liquid is linear. As a result, if we can measure the capacitance, we will know the height of the l

17、iquid. Capacitive Sensor (3)Since C1 and C2 are connected in parallel, we have the total capacitance as:Suppose the plate area is S，spacing distance is a; if there is a solid object with width d and dielectric constant r that goes across the two plates, then the capacitance is calculated as: Capacit

18、ive Sensor (3)(1) If the dielectric constant of the solid object as the relative change of capacitance will bewhere is the sensitivity factor, which increasesdenotes the non-linear factor, which decreases with increase of the spacing ratio d/(a-d).Capacitive Sensor (3)with increase of the spacing ra

19、tio d/(a-d).(2) The dielectric constant r keeps unchanged. If we change the width of the dielectric material, thenwhererepresents both the sensitivity and the non-linearity factor Capacitive Sensor (3)(3) If the dielectric fully occupies the space between two plates, i.e., d=a，then the initial capac

20、itance can be calculated asthenIfThereforewhich is proportional to r (linear relationship)Capacitive Sensor (3). We haveApplication: Measuring the rate of water content in crude oil(1)Good stability with temperatureCapacitance is determined by geometric size of the electrode plate.The material of th

21、e electrode plate does not affect its capacitance.(2)Simple structure and strong adaptabilityAfford to work under extreme temperature, strong radiation and high magnetic field.Afford to work under high pressure, high impact and overloading conditions .Advantages of Capacitive Sensor(3) Small electro

22、static attraction (10-5 N)Electrostatic field exists between two electrode plate, causing electrostatic attraction or electrostatic torque, which is related to the supply voltage, dielectric constant and spacing distance. (4) Good Dynamic response High natural frequencyShort dynamic response timeBe

23、able to work under several MHzBe suited for dynamic measurementAdvantages of Capacitive Sensor(5) Be able to perform non-contact measurement with average effectWhen its not allowed for contact-based measurement, capacitive sensor can be used to perform non-contact measurement.Average effect hold by

24、the sensor can decrease the effect of surface roughness on measurement results. Advantages of Capacitive SensorFurthermore, because of small electrostatic attraction between the two electrodes, the input energy needed is very small. Therefore, it is suited for measurement with low energy input. For

25、example, measuring small pressure, force, acceleration and displacement. The sensor can also be made with high sensitivity and resolution, thus can measure the displacement as small as 0.001m.Advantages of Capacitive Sensor(1) High output impedance, poor load capacityCapacitance is limited by the ge

26、ometric size of the electrode ( up to several hundred pF)，causing high output impedance, especially when the AC power is working within the audio range, the output impedance goes up to 106108, leading to poor load capacity.It can be easily affected by interference and causes unstable phenomenon. In

27、worst case, the sensor can not work properly, thus some shielding operations need to be performed to keep the interference way from the sensor. Disadvantages of Capacitive Sensor(2) High stray capacitance influence The initial capacitance of the sensor is small, but cable capacitance (12m cable can

28、have up to 800 pF), stray capacitance of the conditioning circuit, and the capacitance generated between the electrode and peripheral electric conductor are large.Reduce sensitivity of the sensorCause unstable work conditionAffect measurement precision.Disadvantages of Capacitive Sensor(3) Non-linea

29、r output characteristics Output of the capacitive sensor with distance variation is non-linear. Although it can be improved by using the differential capacitor, the nonlinear effect can not be totally removed.Other types of capacitive sensors show linear characteristics only neglecting the fringing

30、effect. Otherwise, the additional capacitance generated from the fringing effect will be added into the sensor, causing the output be nonlinear.Disadvantages of Capacitive SensorL: Summation of wire inductance and sensors inductance itself;r: Summation of wire resistance, electrode resistance, and m

31、etal support resistance ；Rg: Equivalent resistance between two electrodes;C0: Capacitance of the sensor itselfCp: Stray capacitance caused by wire, conditioning circuit, and generated between the electrode and peripheral electric conductor Sensor Design Consideration(1) Equivalent circuit of the sen

32、sorThe equivalent capacitance is:The relative change of capacitance is:Sensitivity:The sensor, whose capacitance is generally small, has high capacitive reactance and high working frequency. So the resistance can be neglected, and the equivalent impedance is calculated as: where，C=CP+C0Equivalent Ci

33、rcuit of Capacitor(1) Equivalent circuit of the sensor(2) Fringe effectFringe effect can cause distortion at the edge of electric field, thus making the sensor unstable and increasing non-linear error.To remove or reduce the fringe effect, some special structures can be designed as shown below.Capac

34、itive sensor with protection ringSensor Design ConsiderationStray capacitance is connected with the sensors capacitance in parallel, which affects the sensitivity.Several methods can be used to remove or reduce the stray capacitance: (3) Stray Capacitance Increase the initial capacitance of the sens

35、or; Be aware of grounding and shielding; Integration Use “actuated cable” (double shielding with allelic transmission ) technique Complete ShieldingSensor Design ConsiderationThe inner shielding layer has an equal-potential connection with core wire by an amplifier with unity gain, this will remove

36、the capacitance between inner shielding layer and core wireSensor Design Consideration“Actuated cable” (double shielding with allelic transmission ) techniqueSensor is connected with conditioning circuit by double shielding cable.1：1Conditioning circuitOuter shielding layerInner shielding layerCore

37、wireSensor“Actuated Cable” Technique1：1Conditioning circuitOuter shielding layerInner shielding layerCore wireSensor“Actuated Cable” TechniqueSensor Design ConsiderationThe outer shielding layer is connected to ground., which can prevent the interference from outside. The capacitance between two shi

38、elding layer is the input load of the amplifier. The amplifier should have high input impedance, capacitive load and unity gain(4) Temperature influence The change of environmental temperature will change the relationship between the measurement input and sensors output, causing temperature interfer

39、ence error.(a) The effect of temperature on geometric size Because of small spacing distance between two electrodes, the sensor is sensitive to the change of geometric size. Because each material has its own coefficient of linear expansion and a sensor is generally built with multiple types of mater

40、ials, temperature change will cause relative increase of the spacing distance, causing large temperature-related errorSensor Design Consideration(b) The effect of temperature on dielectric constant The effect of temperature on dielectric constant is dependent on medium itself. For example, the tempe

41、rature coefficient of dielectric constant for the air and mica is approximately equal to zero. On the other hand, some liquid medium whose temperature coefficient is pretty big, e.g., temperature coefficient of the dielectric constant for coil oil is 0.07%/. This means if the change of environmental temperature is 50，this will cause about 7%