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ELC131_LAB_6_AC.docxELC 131 Lab 6: Alternating Current
Introduction: Prior to this lab, you have dealt only with DC voltages and currents. This lab will introduce the fundamentals of alternating current (AC). AC electricity changes both its magnitude and its direction, or polarity, as a function of time. Most of the electrical energy used in the world is generated and supplied as alternating current. A great deal of your future work in electronics will be dealing with AC voltages and currents, such as audio-frequency (AF) information and radio-frequency (RF) carriers.
Objectives: Upon completion of this lab exercise the student will be able to:
1. Calculate the peak and peak-to-peak values of a sinusoidal AC voltage given the effective or RMS voltage.
2. Calculate the cycle time of a sinusoidal AC voltage given the frequency.
3. Calculate the instantaneous value of a sinusoidal AC voltage given the voltage and frequency of the waveform.
4. Use a function generator to output AC waveforms of a specified voltage and frequency.
5. Use the oscilloscope to display an AC waveform and measure the peak and peaktopeak voltage, instantaneous voltage, and the frequency of the AC waveform.
Parts and Equipment: DMM and meter leads
B&K 4011A function generator
coax cable with BNC-type connector
Tektronix model 1002 oscilloscope
Tektronix P2220 oscilloscope voltage probe
Prelab: Complete Section 3, Step 1.
Complete Section 4, Step 1.
Complete Section 5, Step 1.
Section 1: The Sine Wave and Alternating Current
The most common AC voltage encountered in electronics is a sinusoidal waveform, which is commonly referred to as a sine wave. A sinusoidal waveform can be generated by rotating a conductor through a magnetic field. A sinusoidal waveform can also be created by electronic circuits called oscillators.
The independent variable, or X-axis value, of an AC waveform can be defined in terms of either radians or degrees. In math and physics, a sinusoidal function is typically described in radians. One cycle of an AC waveform is always 2π radians or 360°. One cycle is defined as the period where the waveform repeats. One cycle of a sine wave is shown in Figure 1.
Figure 1: One Cycle of a Sine Wave
The independent variable, or X-axis value, of an AC waveform can be defined as a function of time. The unit of time used to measure AC waveforms is the second. A sine wave described as a function of time is shown in Figure 2.
Figure 2: One Cycle of a 60Hz Sine Wave
An AC waveform is commonly discussed in terms of frequency instead of the time of one cycle. Frequency, f, is measured in Hertz. Frequency is the reciprocal of the period, T, as shown in equation Eq. 1.
For example, the frequency of the sine wave of Figure 2 with T = 16.67 ms is calculated in equation Eq. 2.
The dependent variable, or Y-axis value, of an AC waveform is defined in terms of voltage. The maximum value is called VPK, and the minimum is called -VPK. The instantaneous voltage of a sinusoidal waveform as a function of the angle through the cycle is shown in equation Eq. 3.
For example, at 34° into the cycle, the instantaneous voltage of the sine wave of Figure 1 would be calculated as follows:
The instantaneous voltage of a sinusoidal waveform as a function of time is calculated as shown in equation Eq 4.
For example, the instantaneous voltage of the sine wave of Figure 2, 5 ms into the cycle would be calculated as follows: (switch to radians in your calculator)
AC waveforms can be expressed in terms of the peak value, the peak-to-peak value, or the rootmeansquare, or effective value. The rootmeansquare (RMS) value of an AC voltage is the value that yields the average power of the waveform. The terms VRMS and VAC are used interchangeably to express the effective value of an AC waveform. The relationship between the effective value and the peak value of a sinusoidal waveform is shown in equation Eq 5.
The same relationship holds true for AC current as shown in equation Eq. 6.
The peak-to-peak value of a waveform is calculated as shown in equation Eq. 7.
For example, by rearranging equation Eq.5, the effective value of the sine wave of Figure 2 would be calculated as shown in equation Eq. 8.
Section 2: Oscilloscope Measurements
The horizontal axis of the oscilloscope display is time. The vertical axis of the oscilloscope display is voltage. The amount of time represented by each division on the scope's display is determined by the SEC/DIV control. The amount of voltage represented by each division on the scope's display is determined by the VOLTS/DIV control.
Figure 3: Sine Wave Displayed on an Oscilloscope
Figure 3 shows a sine wave as it might be displayed on the screen of an oscilloscope. Assume that for Figure 3 the oscilloscope used to obtain the waveform is set as follows:
The peak voltage of the waveform shown in Figure 3 would be determined as follows:
The peak-to-peak voltage for Figure 3 would be determined as follows:
The voltage 2 ms after the start of the sine wave shown in Figure 3 would be determined as follows:
The time of one cycle for Figure 3 would be determined as follows:
Section 3: Peak and Peak-to-Peak Voltage Measurements
VOMs and DMMs make RMS measurements of voltage and current. However, it is often desirable to obtain measurements of voltage in real time. Oscilloscopes are used to view and measure voltage in respect to time. With an oscilloscope, characteristics such as the peak value, the peak-to-peak value, the voltage at a specified time, and the time of one cycle can be measured.
Step 1: Use equations Eq. 5 and Eq. 7 to calculate the values of VPK, and VPK-PK for the sinusoidal voltages listed in Table 1. Record these values in Table 1.
Step 2: Apply power to the oscilloscope. Set up the oscilloscope as follows:
CH 1 VOLTS/DIV – 1.00 V
SEC/DIV – 100 µs
CH 1 MENU TRIG MENU
Coupling – AC Type – Edge
BW Limit – 20 MHZ Source – CH 1
Volts/Div – Coarse Slope – Falling
Probe – 10X Mode – Auto
Invert – OFF Coupling – DC
Adjust the TRIGGER LEVEL control to set the trigger level at the center of the graticule, 0 V. (The trigger level is denoted by an arrow head at the right side of the graticule.)
Adjust the VERTICAL POSITION control to position the trace at the center of the graticule, 0 V. (The vertical position is denoted by an arrow head at the left side of the graticule.)
Connect the probe to the CH 1 input of the oscilloscope. Insure that the attenuation switch on the probe is set to the 10X position.
Step 3: Set up the function generator as follows:
FUNCTION – Sine waveform RANGE (Hz) – 5k
Step 4: Connect the coax cable with the BNC type connector to the OUTPUT (50 ) of the function generator. Connect the DMM meter leads to the coax cable connected to the function generator. The polarity of the DMM leads does not matter. Connect the oscilloscope voltage probe to the output of the function generator as illustrated in Figure 4.
Be absolutely certain that the ground lead of the coax cable is connected to the ground lead of the oscilloscope probe. Failure to do this may damage the function generator.
Figure 4: Connection of DMM and Oscilloscope to Function Generator
Step 5: Apply power to the function generator. Adjust the FREQUENCY (COARSE and FINE) controls of the function generator for an output of 1000 Hz.
Step 6: Adjust the OUTPUT LEVEL control of the function generator for an output of 1.00 VRMS as indicated on the DMM.
Step 7: Count the number of divisions from the center of the oscilloscope display to the positive peak of the sine wave. Record this value in Table 2. Record the VOLTS/DIV setting in Table 2. Determine and record the measured value of VPK in Table 2.
Step 8: Count the number of divisions from the positive peak of the sine wave to the negative peak. Record this value in Table 2. Record the VOLTS/DIV setting in Table 2. Determine and record the measured value of VPK-PK in Table 2.
Step 9: Repeat Step 6, Step 7, and Step 8 for the remaining voltages in Table 2. Adjust the CH1 VOLTS/DIV selection as needed to make the measurements.
|
VRMS |
VPK |
VPK-PK |
|
1.00 V |
1.41 |
2.82 |
|
2.50 V |
3.53 |
7.07 |
|
5.00 V |
7.07 |
14.14 |
Table 1: Calculated Values of VPK and VPK-PK
|
VRMS |
# of DIV VPK |
V/DIV |
VPK |
# of DIV VPK-PK |
V/DIV |
VPK-PK |
|
1.00 V |
0.7V |
2V |
1.4V |
1.2V |
2V |
2.4V |
|
2.50 V |
1.8 |
2 |
3.6 |
3.2 |
2 |
6.4V |
|
5.00 V |
3.5 |
2V |
7 |
7 |
2 |
14V |
Table 2: Measured Values of VPK and VPK-PK
Step 9: Calculate the percent error between the calculated and measured values for VPK and VPKPK from Table 1 and Table 2. Record this data in Table 3.
|
VRMS |
% error in VPK |
% error in VPK-PK |
|
1.00 V |
0.70% |
14.9% |
|
2.50 V |
1.98% |
9.47% |
|
5.00 V |
1% |
0.42% |
Table 3: Error Calculations for Data from Tables 1 and 2
Section 4: Instantaneous Voltage Measurements
Step 1: Use equation Eq. 4 to calculate the instantaneous voltage of a 2.50 VPK, 1 kHz sine wave at the times listed in Table 4. Record the calculated values in Table 4.
Step 2: Set the CH 1 VOLTS/DIV switch of the oscilloscope to 1 V. Adjust the OUTPUT CONTROL of the function generator of Figure 4 for an output of 2.50 VPK. Make sure that the frequency is still 1 kHz.
Step 3: Use the oscilloscope to measure the instantaneous voltage of the 2.50 VPK, 1 kHz sine wave at the times listed in Table 4. Record the measured values in Table 4.
Step 4: Calculate and record the percent error between the calculated and measured values in Table 4.
|
time |
v calculated |
v measured |
% error |
|
200 μs |
2.37V |
2.4V |
1.26% |
|
400 μs |
1.47V |
1.45V |
1.36% |
|
600 μs |
-1.47V |
-1.45V |
1.36% |
|
800 μs |
-2.37V |
-2.4V |
1.26% |
Table 4: Instantaneous Voltage Calculations and Measurements
Section 5: Time Measurements
Step 1: Use equation Eq. 1 to calculate the time of one cycle for each of the frequencies listed in Table 5. Record these calculated values in Table 5.
Step 2: Set the CH 1 VOLTS/DIV switch of the oscilloscope to 500 mV. Adjust the OUTPUT CONTROL of the function generator of Figure 4 for an output of 1.00 VRMS.
Step 3: Depress the appropriate RANGE selector and adjust the FREQUENCY (COARSE and FINE) controls for an output of 250 Hz. Adjust the SEC/DIV control so that at least one cycle of the sine wave is displayed on the oscilloscope.
Step 4: Measure the time of one cycle. Record the measured value in Table 5.
Step 5: Repeat Step 3 and Step 4 for the remaining frequencies listed in Table 5.
Step 6: Calculate and record the percent error between the calculated and measured values in Table 5.
|
frequency |
time calculated |
time measured |
% error |
|
250 Hz |
4ms |
4ms |
0% |
|
1.8 kHz |
555us |
560u |
0.9% |
|
45 kHz |
22us |
21u |
4.5% |
|
160 kHz |
6.25us |
6.1u |
Table 5: Cycle Time Calculations and Measurements
Questions:
1. Calculate the RMS value of a 17.8 VPK sine wave.
2. Calculate the peak value of a 28 VRMS sine wave.
3. What is the time of one cycle of a 500 Hz sine wave?
4. What is the frequency of a sine wave when the time of one cycle is 1 ms?
5. What is instantaneous voltage of a 120 VPK sine wave 30° after the start of the cycle?
6. What is instantaneous voltage of a 20 VPK, 15 kHz sine wave 20 μs after the start of the cycle?
7. How much time has elapsed at 45° of a 2 kHz AC waveform?
Figure 5: Oscilloscope Display for Questions 8, 9, and 10
8. If the VOLTS/DIV control is set to 5 and the SEC/DIV control is set to 200μ. What is the peak voltage and period time of the waveform displayed in Figure 5?
VPK = T =
9. If the VOLTS/DIV control is set to 500m and the SEC/DIV control is set to 1m. What is the peak-to-peak voltage and frequency of the waveform displayed in Figure 5?
VPK-PK = f =
10. If the VOLTS/DIV control is set to 2 and the SEC/DIV control is set to 5m. What is the RMS voltage and frequency of the waveform displayed in Figure 5?
VRMS = f =
9
