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

[9] User's guide for the EDUX1052G

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:
  
  • Clamps, cables, breadboard
  • Resistors/potentiometers
  • Inductances
  • Multimeter
  • Oscilloscope
  • Function-generator

CAUTION!

Be careful with the polarisation of the capacitor and the inductor, usually the terminals are marked with +/- or one pin is longer than the other, in this case the longer pin is the positive terminal.

Ceramic Capacitor	Foil Capacitor	Inductance	Resistor

Always make sure to unload your capacitor, before you connect it. Make sure that the capacitor is not loaded by connecting a resistor to the terminals and short-circuiting it across it.

6.     Resetting the Oscilloscope

7.      Experiment Procedure

To practice measuring capacitance, use each method to measure one ceramic capacitance:

5.1 Start measuring the capacitance of the ceramic capacitor 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.

5.1.1 Note the value of the capacitor. (Matlab)

5.2 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.

5.2.1 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.

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

5.2.3 (Homework) Calculate the capacitance from the measured time difference and note the values for the ceramic capacitor.

Fig. 1: measurement of capacitance by using tau

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

5.3.1 Use the breadboard to build the circuit.

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

5.3.3 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. Take in mind that the amplitude shown on the oscilloscope is peak to peak (pp). We define the amplitude as usual from the middle to peak. So the half pp value. Make sure not to confuse the values with one another when entering them to Matlab to guarantee a successful evaluation later on. (Matlab)

5.3.4 (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 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

5.4 Measure the capacitance of the capacitors (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.

5.4.1 Connect the Voltmeter/Oscilloscope in parallel to LC.

5.4.2 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.

5.4.3 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 5.4.2. What do you see and what do you measure for the resonance frequency?(Matlab)

5.4.4 What condition is satisfied when reaching resonance frequency?

5.4.5 (Homework) Calculate the capacitance for the capacitor using the value observed through the Bode plot.

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

8.      Evaluation of Experiment Results

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 in F for task 5.2.3, 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: 5.2.3
3.  Please type your value in F for task 5.3.4, 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!
   unit: F
   relevant section: 5.3.4
4.  Please type your value in F for task 5.4.5, 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: 5.4.5