Experiment 5 - Capacitive I

1.      Context of the Experiment

This experiment concerns capacitive sensors. These can be found all around us. For using them, it is necessary to be able to measure a capacitance, which is this experiment’s main topic.

2.      Learning Goals of this Experiment

• Knowing: electrical measurement circuits, basics of electric circuits
• Abilities: understand physical concept of capacitive sensors, handling of oscilloscope and function generator
• Understand: possible measurement accuracy of measurement method

3.      Literature

[1] Lectures: Electrical Measurement Technology, Capacitive Sensors

[2] Oscilloscope Introduction Video (Video on EDUX1052G) → Please watch this video and make sure you understand how the oscilloscope is working before coming to the experiment!

[3] P. L. Regtien, Hg., Sensors for Mechatronics. Amsterdam: Elsevier, 2012.

[4] https://www.electronics-tutorials.ws/rc/time-constant.html

[5] how-to-measure-inductance-or-capacitance-using-oscilloscope

[6] https://www.tek.com/en/blog/what-is-an-oscilloscope-probe

[7] https://learn.sparkfun.com/tutorials/how-to-use-an-oscilloscope/all 

[8] https://learn.sparkfun.com/tutorials/how-to-use-a-multimeter/all

4.      Basics/Fundamentals

The most known capacitance is a plate capacitance, where two plate electrodes are being charged. For these it is possible to change the capacitance by changing the displacement of one plate, the dielectric, the effective area or deforming the plates as the capacitance depends on the permittivity ε due to the dielectric, the area A and the distance of the plates d: 

Capacitive sensors can be used for a lot of different applications, for example for measuring pressure, distance, proximity, acceleration, humidity, filling levels, gaps, angles, hygrometer applications and moisture. Advantages of capacitive sensors are their low costs, simple setup, their ability to withstand high temperature and pressure and their high reliability. One disadvantage is, that measuring materials with low dielectric constants can be challenging.

There are multiple ways to measure unknown capacitance, some of them are introduced in the following sections,

4.1 Tau-method (τ) 

Tau is the time constant of an RC circuit that takes to change from one steady state condition to another steady state condition when subjected to a step change input condition [4]. τ is the time taken for the capacitor from an initial charge voltage of zero to approximately 63.2% of the value of an applied DC voltage. The change of state from one stable condition to another generally occurs at a rate determined by the time constant of the circuit which itself will be an exponential value. The time constant of an RC circuit could be used to measure the value of the unknown capacitance, given that the resistance is known:

therefore:

4.2 AC signal phase shift

Another method is to use the phase shift of an applied AC voltage signal to an RC circuit.  The capacitance could be calculated from the reactance:

4.3 Resonance 

One way to measure unknown capacitance is done using the resonance frequency of a special circuit called the resonant circuit. This circuit is composed of an inductor and a capacitor connected in series. At resonance frequency, the effect of the capacitor is diminished by the effect of the inductor. Given the value of the inductance, one can calculate the value of the capacitance as follows:

Where  is the resonance frequency and  is the value of the inductance.

5.      Technical Basics & preparations

• have all measurement devices at hand and familiarize yourself with them: oscilloscope, internal function generator of the oscilloscope, multimeter.

5.1 Oscilloscope

One of the basic components of this experiment is the oscilloscope. The basics of how to use an oscilloscope is found in [7]. 

 5.2 Multimeter

Another basic component is the multimeter. Further details on how to use the multimeter are found in [8]                                                           

Preparations:

• Gather all the necessary measurement objects and instruments:
  • Aluminum foil two parts (150 mm x 10 mm, cut smaller lateron)
    
  • Paper
  • Clamps, cables, breadboard
  • Resistors/potentiometers
  • Inductances
  • Multimeter
  • Oscilloscope
  • Function-generator

6.      Experiment Procedure

5.1 Build your own capacitor using aluminum foil:

5.1.1 Build two electrodes out of the aluminum foil, approximately as big as your hand. The electrodes should be roughly of the same size and shape!

5.1.2 Attach the wires and clips to the multimeter and the electrodes

5.1.3 Use capacitance mode of multimeter and watch the display

5.1.4 Play around with overlapping area between electrodes and distance between electrodes (use sheet of paper as insulator between electrodes)

5.1.5 Use only one electrode. Take the clamp of the unused electrode in one hand and slowly place your hand onto the other active electrode (use sheet of paper as insulator between electrode and hand)

5.1.6 Attach the clamp in your hand to earth ground (e.g. at the earthing connection at your tables) → slowly place your hand onto the other active electrode (use sheet of paper as insulator between electrode and hand)

5.1.7 Place your hand on the electrode with a sheet of paper as insulator. Now compare the capacitance value on the multimeter with two situations (keep hand on electrode without moving)

i. Take off your shoes off and place your feet on the ground.

ii. Lift your feet from the ground.

5.1.8 Note the highest capacitance value your multimeter has shown during tasks 5.1.1 to 5.1.7.

5.2 Design a capacitive sensor to measure distances by using the following equipment: 2 sheets of aluminum foil (max. hand-size), one sheet of paper, cables and connectors, multimeter, oscilloscope. Your sensor will need to measure distances from 51 to 66 mm.

Hint: It might be useful to build a sensor that is folded to be able to cover a varying distance. Other types of sensors are of course also valid! If you decide to fold, we recommend to fold both electrodes at once.

To practice measuring capacitance, use each method to measure one off-the-shelf capacitance and your self-built capacitive sensor:

5.3 Start measuring the capacitance of the capacitors (self-built and ceramic) by using the multimeter. Before you connect the capacitor to the multimeter, make sure that the capacitor is not loaded by connecting the 1 kOhm resistance to the terminals.

5.3.1 Note the value of your capacitor and the off-the-shelf-capacitor. (Matlab)

5.4 Measure the capacitance of the capacitors (ceramic) by measuring TAU. Connect the capacitor according to fig. 1. Then connect the wave-gen of the oscilloscope set to 9V DC to the circuit. The oscilloscope should show the voltage across the capacitance rising until at full charge if used in single mode.

5.4.1 Calculate the value of 63.2% of the applied voltage and move one of the cursors to the point where the voltage reaches this value.

5.4.2 Move the other cursor to the beginning of the loading process. Measure the time difference between the two cursors. (Matlab)

5.4.3 (Homework) Calculate the capacitance from the measured time difference and note the values for the off-the-shelf-ceramic-capacitor.

Fig. 1: measurement of capacitance by using tau

5.5 Now measure the capacitance of the capacitors (ceramic) by using the setup shown in fig. 2 and the phase shift of a sine wave.

5.5.1 Use the breadboard to build the circuit.

5.5.2 Set the function generator to continuous sine wave with f=100Hz and an amplitude of 1.9V.

5.5.3 Connect CH1 of the oscilloscope to Point A and CH2 to point B. Also, connect mass appropriately. Then measure both voltages and the phase shift between the measurements at point A and B. (Matlab)

5.5.4 (Homework) Take a look at fig. 3 and use the following equations to calculate the impedance between A and B and the angle γ to find the value for the capacitance. Note the values for the off-the-shelf-ceramic-capacitor.

Fig. 2: measurement of capacitance by using the phase shift

    

Fig. 3: equivalent circuit (a) and vector diagram (b) for the measurement of capacitance by using the phase shift

5.6 Measure the capacitance of the capacitors (off-the-shelf foil (red)) by using the circuit from fig. 4. Connect the 560uH inductance and the capacitance to a resonator circuit and set the function generator to a sine wave with frequency 100Hz.

5.6.1 Connect the Voltmeter/Oscilloscope in parallel to LC.

5.6.2 Now change the frequency of the wave generator slowly (increase the frequency in the wave gen settings up to max. f=1MHz) and watch the voltmeter carefully. You will be able to see a sharp voltage drop, once you reach the resonance frequency.

5.6.3 After learning how to find the resonance frequency manually we want to use the full capabilities of the osciliscope in order to find the resonance frequency. To do so we generate a so-called Bode plot, which plots Gain and Phase against a varying range of frequencies. To use it press "Analyze" on the osciloscope and choose "Frequency Response Analysis", which you find under "Features" on the right side of the screen. Adjust the minimum and maximum frequency according to 5.6.2. What do you see and what do you measure for the resonance frequency?

5.6.4 What condition is satisfied when reaching resonance frequency?

5.6.5 (Homework) Calculate the capacitance for the off-the-shelf-foil-capacitor using the value observed through the Bode plot.

Fig. 4: measurement of capacitance by using the resonance frequency

5.7 Now you have sufficiently tested your measurement methods. Choose your preferred measurement method – keep in mind the necessary accuracy.

5.7.1 Create a table with five data points for your self-built sensor using the measurement method that was most accurate for your sensor.
Hint: the distance covered by the self-build sensor is not the value displayed on the position indicator of the test stand.

5.8 Now you have sufficient knowledge about your sensor, and you can start using it:

5.8.1 Connect your capacitive distance sensor to the position teststand, set the teststand to any valid position.

5.8.2 Measure the capacitance of your own self-built sensor at any position of the test stand. (Matlab)
Hint: you can use the Multimeter to measure the capacitance

Please remove your own sensor from the test stand only after you press the Save Data button in Matlab (reference sensor signals are measured in the background)

5.8.3 (Homework) Calculate the distance from the measured capacitance!

7.      Evaluation of Experiment Results

App

VIPS

The following values should be entered to vips in Stud.ip. Please note that only 30 minutes are available for entering values in vips, after which the vips entry is automatically terminated. The test is only to hand in the final values, so be prepared and have all values ready and at hand!

1. Matriculation number
2.  Please type your value for task 5.1.8, the highest capacitance value of the aluminum foil capacitance in F (use the scientific notation: 2e-3=2mF). Please use the decimal point and give only numerical values in scientific notation!
   unit:  F
   relevant section: 5.1.8
3.  Please type your value in F for task 5.4.3, measured by calculating C from τ. Use the scientific notation: 2e-3=2mF. Please use the decimal point and give only numerical values in scientific notation!
   unit: F
   relevant section: 5.4.3
4.  Please type your value in F for task 5.5.4, measured by using the phase shift. Use the scientific notation: 2e-3=2mF Please use the decimal point and give only numerical values in scientific notation!value for ceramic capacitor 5.5.4.
   unit: F
   relevant section: 5.5.4
5.  Please type your value in F for task 5.6.5, measured by using the resonance frequency. Use the scientific notation: 2e-3=2mF. Please use the decimal point and give only numerical values in scientific notation!
   unit: F
   relevant section: 5.6.5

6.  Please type your table values for task 5.7.1 as in Example 1 you will find below.
   unit: F
   relevant section: 5.7.1

7. Please type your measured distance value for task 5.8.3. Use the scientific notation: 2e-3=2mm. Please use the decimal point and give only numerical values in m!
   unit : m
   relevant section: 5.8.3

Example 1:

Enter the table shown below

in this format [3.5 4e-6; 5 6e-6].

Please use the decimal point and give only numerical values in mm, respectively F as in this example: [3.5 4e-6; 5 6e-6]