Signals Periodic in Time Domain Abstract: The purpose of this lab is to observe different AC signal waveforms. In this experiment we used a function generator and an oscilloscope. We learned how to read the graphs and determine important components like, the amplitude, the voltage, the frequency, and the period of the waves. We then connected the oscilloscope to the computer to send sound files and graph the waves. From the waves we could measure the period and ultimately calculate the frequency using the equation f=1/T. We then used a voltage divider to examine the behavior of a simple circuit. We determined that the resistance did not have an affect on the frequency of a wave. We also verified ohms law using the information in the graph. As the resistance increased, so did the voltage across it. Next we constructed a half wave rectifier and compared the graphs of the AC voltage in the circuit and the AC voltage across the diode. We were able to use the peak-to-peak voltages to determine the turn on voltage of the diode. We also verified the DC voltage using an equation and the multimeter. In the last part of the experiment we used a square wave voltage source on a simple RC circuit to observe the charging on the capacitor. When the voltage was at its peak, the capacitor would charge and when the voltage was at its low point the capacitor would discharge. Part 1: Function Generator and Oscilloscope In this part of the experiment we used a function generator to create the AC currents and we used the oscilloscope to display the graphs. Below in figures one through four you can see four different types of AC waves. Figure 1 shows a sine wave, figure 2 shows a square wave, figure 3 shows a triangular wave, and figure 4 shows a saw-tooth wave. In order to create these waves we connected the function generator to the input channel of the oscilloscope. After connecting the function generator to the oscilloscope we need to setup the function generator to produce the waveform we are looking to measure. To select the type of wave form you need to click the button with the picture of the waveform you want. Then you need to set up the values on the function generator. The oscilloscope will then display the graph for that AC function. You may have to then adjust the settings on the oscilloscope to display the waveform like you want. For the sine wave in figure 1, we measured the peak to peak voltage as 600mV, the period as 20ms, and the DC voltage as 1.2V. By taking the inverse of the period, we found the frequency as 50 hertz.
Figure 1: Sine Wave For the square wave in figure 2, the peak to peak voltage was 600mV, the frequency was 2k hertz, the duty cycle was 65%, and the DC voltage was 300mV. By taking the inverse of the frequency you can determine the period of the wave. The 65% duty cycle means that the upper voltage is there for 65% of the wave.
Figure 2: Square Wave For the triangular wave in figure 3, we set the minimum peak voltage to -0.25V. The peak to peak voltage was 600mV, the frequency was 25k hertz, and the DC voltage was 50mV.
Figure 3: Triangular Wave The saw tooth wave in figure 4 has a minimum peak voltage of 1.5V, a peak to peak voltage of 2.5V, a frequency of 14.6k hertz, and a DC voltage of 2.75V.
Figure 4: Saw tooth Wave
Part 2: Music Signals In this part of the experiment we connected our oscilloscope to the computer and then played music into it. We graphed the resulting waveforms in figures five through eight. Although none of the waveforms had a perfect period, some had a noticeable frequency. The drums in figure 5, flute in figure 6, and the guitar in figure 7 all seems relatively periodic. The guitar and drums in figure 8 did not seem to have a pattern to it.
Figure 5: Drums
Figure 6: Flute
Figure 7: Guitar
Figure 8: Guitar and Drum For the drums, flute and the guitar we estimated the periods and determined the approximate frequency it had by taking the inverse of the period. Table 1 below shows the measurements and calculations made.
Period Frequency Drums 1 sec 1 hertz Flute 1.25 msec 800 hertz Guitar 1sec 1 hertz
Table 1: Period and Frequency for Sounds
Part 3: Voltage Divider In this part of the experiment, we used the oscilloscope to graph the waveforms created by simple circuits. Figures nine through eleven show waves created by circuits with different resistances.
Resistance 100 ohms 100 ohms DC Value V 24.2m 24.2m V Peak-Peak Value 2V 50m V Frequency 200 hertz 200 hertz
Top Wave Bottom Wave
Table 2: Information on Figure 9
Figure 9: Resistor 100ohms
Resistance 1000 ohms 1000 ohms DC Value 0.220 V 0.220 V Peak-Peak Value 2V 0.5V Frequency 200 hertz 200 hertz
Top Wave Bottom Wave
Table 3: Information on Figure 10
Figure 10: Resistor 1000ohms
Resistance 3900 ohms 3900 ohms DC Value 0.485 V 0.486 V Peak-Peak Value 2V 1V Frequency 200 hertz 200 hertz
Top Wave Bottom Wave
Table 4: Information on Figure 11
Figure 11: Resistor 3900 ohms As you can see in figures 9-11, when R2 changed the frequency of the output signal did no change. You can also see that there is no phase difference between the two waves in
each graph. As the resistance increased, the peak to peak voltage increased as well. This can be verified using ohm's law, V=IR. As resistance increases, so does the voltage across that resistor. Tables 2-4 above each graph give details for the graph below it. It gives the resistance, DC value, peak-to-peak voltage, and the frequency for both the top and bottom sinusoid in each graph. The DC value is about half the peak to peak voltage value, or the same as the amplitude for each graph with about 97% accuracy. Table 2 below shows the resistance, the voltage measured, and the current measured for the bottom wave of each graph. As the resistance increases, the current decreases. This is because the resistors hinder the current flow. Ohm's law also verifies this, if the resistance increases in the equation, the current will decrease.
Resistance Figure 9 Figure 10 Figure 11 100 ohms 1000 ohms 3900 ohms Current 0.235 mA 0.192mA 0.125 mA
Table 2: Simple circuits
Part 4: Half-Wave Rectifier In this part of the experiment we created a half-wave rectifier circuit with a diode and a 2.2k ohm resistor like the one shown in figure 12.
Figure 12: Half-Wave Rectifier Circuit After creating the circuit we used the oscilloscope display to measure the peak-to-peak value of the waves created. Figure 13 below shows the results. The top wave is the AC voltage of the circuit and the bottom wave is the AC voltage across the diode. The peak to peak value for the circuit was 5V and the peak to peak voltage for the diode was
approximately 3V. From this information we can calculate the turn on voltage of the diode to be 2V.
Figure 13: Half-Wave Rectifier From the graph in figure 13 we can also see that the diode is on for 2ms while the period is 5ms. The measured time is less then half of the period. We then put the numbers we found into equation 1 below to find the DC value of the waveform and came up with 0.4V. When we measured the voltage with the multimeter we got 0.36 volts, which is close to the calculations.
Equation 1 We then increased the frequency to 1000 Hz and got a DC voltage of 0.26V and then increased the frequency to 5000 Hz and got a DC voltage of 0.26V. Graphing this would give us a straight line and will not show dependency. However, there should be a dependency between the two, the reason we could not show it was because of the range we used. In the next part of this experiment we switched the places of the diode and the resistor and the resulting waveform is in figure 14. The diode waveform is now flipped upside down, meaning that the diode is reverse biased from what we had before. It is still possible to find the diode voltage, we would just need a new KVL to reflect the switch in direction.
Figure 14: Half-Wave Rectifier
Part 5: RC Circuit with a Square Wave Input In this part of the experiment we applied a square wave to an RC circuit. When we were at the top of the square wave the capacitor was charging. When we were at the bottom of the square wave the capacitor was discharging. We connected the outputs to the oscilloscope, which created the graphs in figure 15. The top graph shows the AC voltage and the bottom graph shows the capacitor voltage. As you can see, the graph verifies the concept of the charging and discharging capacitor. While the AC voltage is high, the voltage of the capacitor gradually rises. Once the AC voltage decreases, the capacitor voltage gradually decreases. This also proves that although current through a capacitor can instantly change, the voltage cannot. We used the quick measurement feature on the oscilloscope to measure the peak-to-peak voltage and got 4.07V.
Figure 15: RC Circuit