This experiment explores the functionalities of the oscilloscope. In part 1, the oscilloscope is used to display a DC signal and an AC signal, and to measure the frequency of an AC signal. In part 2, the oscilloscope is used to display the exponential response of an RC circuit, and to estimate the time constant τ using the displayed signal. The results of the experiment are presented in this laboratory report.
1. Oscilloscope
The oscilloscope is a device that measures electrical waveforms at any point in an electrical circuit. The waveforms are normally displayed graphically in a voltage versus time format, wherein the Y axis is for voltage and X axis is for time .
Two of the more classifications of electrical signals are DC and AC. DC, short for direct current, is a fixed value voltage and current waveform that moves in one direction . AC, short for alternating current, looks like a sinusoid because the voltage levels are changing over time and the current direction switches directions (positively or negatively) at every cycle .
This lab includes measuring DC and AC signals, which will be discussed in the succeeding sections. For the AC signal, the frequency of oscillations is also measured.
Part 1.a. DC Signal
A standard D-size battery is measured of its voltage using both an oscilloscope and a digital multi-meter (DMM). The measured values are as follows:
Vscope=1.615 V, VDMM=1.615 V
Switched Battery:Vscope=-1.615 V, VDMM=-1.615 V
The measured values for different instruments appear to be equal. Moreover, the reversed polarity readings yielded similar results (negative, but still equal values). These results enforce the consistency and accuracy of the measuring instruments.
Upon unplugging the scope, the measured voltage slightly oscillates. Upon unplugging the DMM, the measured voltage remained constant.
Part 1.b. AC Signal
A 1000 Hz sine wave with 1V RMS value is produced using the signal generator and is fed to the oscilloscope. Two controls were critical in order to obtain a stable display: the LEVEL control, and the SLOPE control. These two controls are adjusted accordingly.
For the LEVEL control, it was observed that increasing the LEVEL shifts the displayed waveform to the left. Conversely, decreasing the LEVEL shifts the displayed waveform to the right. For the SLOPE control, switching the SLOPE value flips the graph with respect to the X-axis.
Next, the DC offset control is studied. As the name suggests, this adds a fixed offset voltage to the signal. The oscilloscope is set to DC coupling such that the DC component of the signal is not removed . Turning the DC offset knob shifts the displayed waveform up and down. When the DC offset is adjusted such that the average of the sine wave is at 1.0 V, the DMM measured the following DC value:
VDMM=0.390 V
This measured value is slightly off from the DC offset value in the oscilloscope. This discrepancy may be due to the measuring method inherently used by the DMM itself.
When the oscilloscope was set to AC coupling, it is expected that the DC component will be removed in the display, making the sine wave be centered at 0 V . However, it is observed that the waveform shifted up to 2 V; the sine wave is now centered at 3 V. This happened because the DC offset was added to the signal inside the oscilloscope. The resulting signal is different from the one fed by the signal generator. Since the AC coupling operation’s real principle was to equate the average the value of the signal to 0 V , the oscilloscope must have computed it in such a way that there is still a DC offset of 3V but the running average of the waveform is 0.
The DC offset is then set to 0V, accurately adjusting with the DMM set to DC. When the DMM is shifted to AC, the measured value is:
VDMMAC=0.675 V
The measured peak-to-peak voltage in the oscilloscope is:
Vpk-pk=2 V
Thus, the peak voltage is:
V0=22=1 V
The RMS voltage is:
VRMS=V02=0.7071
This value has a very small discrepancy with the RMS value measured by the DMM. This difference may be due to compatibilities of the measuring instruments with the signal generator. However, the error of only around 5% can be considered accurate in this case.
Part 1.c. Frequency
At this point, the frequency of the AC signal is measured. The horizontal scale is adjusted such that the display would show one complete period of the waveform. The measured period T from the display is:
5 divs, 0.2×10-3sdiv
Therefore, the frequency f of the signal is:
f=1T=15×0.2×10-3=1000 Hz
The measured frequency at the signal generator is:
fsiggen=497 Hz
This frequency value is half that of the frequency measured using the oscilloscope.
2. RC Time Constant
The RC charging circuit is investigated of its time constant τ. A square waveform is generated to simulate the charging and the discharging phases of the RC charging circuit , noting the distinction between the two for each cycle. The initial values of the circuit parameters are as follows:
R=5.0 kΩ, C=0.1 μF, f=200 Hz
The RC charging circuit is studied of the effects of the values of R, C and f to the output waveforms. Here are the results obtained:
- Increasing R decreases the slope
- Decreasing R increases the slope
- Increasing C increases capacitance, increases the maximum charge (asymptotes)
- Decreasing C decreases the maximum charge (asymptotes)
- Increasing f decreases the period
- Decreasing f increases the period
The RC setup circuit is then reverted to the initial values. The displayed waveform is inspected to estimate the time constant charging and discharging times. The resulting waveform is shown in the following figures (first is a sketch from the scope eyeball method, second is snapshot of the GA display):
Figure 1. Scope Display Sketch
Figure 2. Graphical Analysis Display
The measured quantities from the graphs are tabulated in the following table:
The RC values are computed using equations 7 and 8:
Discharging: V0.003=-5.5=6--6e-0.003-0τ-6
0.5=12e-0.004τ→0.04166=e-0.004τ→τ=1.25 ms
Charging: V0.001=4.9=6--61-e-0.001-0τ-6
10.9=12-12e-0.001τ→0.09166=e-0.001τ→τ=0.418 ms
The calculated values are significantly far from the estimated values using scope eyeball and GA fit, especially the rising time constant. Nevertheless, the values are within the expected range of values.
3. References
Earley, Elizabeth. "What's the Difference Between AC and DC?" 17 September 2013. MIT School of Engineering. 15 October 2014 <http://engineering.mit.edu/ask/what%E2%80%99s-difference-between-ac-and-dc>.
Poole, Ian. "Understanding Oscilloscope Specifications / Specs." 2014. Radio-Electronics.com. 15 October 2014 <http://www.radio-electronics.com/info/t_and_m/oscilloscope/oscilloscope-specs-specifications.php>.
"RC Charging Circuit." 15 October 2014. Electronics-Tutorials. 15 October 2014 <http://www.electronics-tutorials.ws/rc/rc_1.html>.
Witte, Robert A. "AC and DC Coupling." 9 September 2013 . National Instruments. 15 October 2014 <http://www.ni.com/white-paper/14753/en/>.
