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Experiment 2: Capacitors

Objectives of the experiment

Preparation for the lab

Function generator

A function generator provides a variable voltage source. In general, these signals can be generated with different waveform shapes, frequencies, and amplitudes. These values can be adjusted on real function generators. In contrast to an ideal function generator, the output current of a real system is limited. As with a real voltage source, an output impedance is specified here.

In Abbildung 1 the function generator used in the lab is shown. It has an output impedance of $50~\rm \Omega$. In the following, the settings are briefly described:

1. The waveform can be selected using the FUNCTION button. Pressing the button selects the next waveform. At start-up, the sine waveform (∿) is selected; the following waveforms are: triangle and square or pulse. The waveforms can be seen in the simulation below; a sawtooth signal is not possible with this function generator.
2. The frequency can be changed via two inputs
   1. The potentiometer under FREQUENCY allows precise adjustment. Turning clockwise increases the frequency.
   2. Using the buttons under the potentiometer, the frequency can be changed by one decade—i.e., by a power of ten—down (button with arrow to the left) or up (button with arrow to the right). The limits are $50~\rm mHz$ and $5~\rm MHz$.
3. There are also several controls for the voltage
   1. The potentiometer OFFSET allows precise selection of the DC component. To enable a DC component, press the ON button.
   2. At the output jack, two attenuations of $-20~\rm dB$ can be switched on. This reduces the peak-to-peak voltage range from [$0~\rm V$, $10~\rm V$] to [$0~\rm V$ , $1~\rm V$ ] or [$0~\rm V$ , $0,1~\rm V$ ].
   3. The AMPLITUDE, i.e. the peak-to-peak voltage, can be finely adjusted using a potentiometer.

Oscilloscope used

Even before the digital multimeter, the oscilloscope is the most important measuring instrument in electrical engineering and electronics. It makes it possible to display a voltage waveform u(t) over time t, observe it in “real time,” and measure it. In many experiments and analyses, it is a central component because it can make electrical processes visible. In addition to quantitative statements (how high is the voltage and when?), it is also helpful for qualitative results (for example: Is there a fault in the circuit?).

Good knowledge of the oscilloscope is necessary for this experiment. In Abbildung 2 you can see the control panel of the DS1052E used, which is briefly described here.

Please use the buttons marked with „ “ to learn more about the individual functions

General operation

Signal display and input

Scaling

Trigger

On the left you will find a nice introductory video. Note that the specific operation often depends on the manufacturer and model. However, the concepts are the same for all devices.

Virtual oscilloscopes

A virtual oscilloscope can be found on the pages of Dublin University. Try there to “oscilloscope” various function generator settings, e.g.:

• $200~\rm Hz$, sine, offset $1~\rm V$, amplitude $5~\rm V$
• $200~\rm Hz$, square, offset -$1~\rm V$, amplitude $3~\rm V$

What happens if the trigger level is set too high?

further virtual oscilloscopes

Preparation for the oral short test

For this experiment you should

1. be able to apply and explain the following concepts:
   1. periodic signal
   2. characteristic quantities in the signal-time waveform
      1. peak value (amplitude)
      2. peak-to-peak value
      3. arithmetic mean value
      4. RMS value (quadratic mean)
      5. rectified mean value
      6. period duration
      7. frequency
   3. creating the time waveform of a periodic signal
   4. graphical determination of the above quantities from the time waveform of a signal
   5. capacitance $C$
   6. behavior of current $i$ and voltage $u$ across $R$ and $C$ with a rectangular input voltage for $t=[0; \infty]$
   7. $i_{C,stat}$ and $u_{C,\rm stat}$ in steady state
   8. time constant $\tau$
   9. determination of $R$, $C$, $\tau$, $i_{C,\rm stat}$ and $u_{C,\rm stat}$ from the time waveform