UNIVERSITY OF MASSACHUSETTS DARTMOUTH
DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING
ECE 201
CIRCUIT THEORY I
MEASUREMENT OF AC SIGNALS
INTRODUCTION
An AC (Alternating Current) signal is one whose value changes with time. The most
commonly encountered AC signals are the sinusoid (sin or cos), the square-wave, and the
triangular wave. These signals are easily obtained from a device known as a Function
Generator. AC signals are specified in several ways, usually depending upon the application.
For now, let’s consider the plot for 1.5 cycles of a 1 volt, 1 kHz sine wave shown below in
Figure 1.
1 kHz sine wave
1
0.8
0.6
voltage in volts
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
0
0.5
1
1.5
time in milliseconds
Figure 1. 1.5 cycles of a 1 volt, 1 kHz sine wave
This sinusoidal waveform can be described by the following definitions:
Amplitude or “peak” value, Vpeak
1 volt
“peak – to – peak” value, Vp-p
2 volts
Average value, Vdc ,Vave
0 volts
Period, T
1 millisecond
Frequency, f
1 kHz (1/period)
There is one additional definition that is used to describe the “equivalent” heating value of
the sine wave. This is the rms, or root-mean-square, value. It allows us to account for the energy
delivered by the sine wave even though the average value of its voltage is equal to 0. Without
doing the mathematics, (it’s in the Preliminary Work), the rms value of a sinusoidal voltage is
given by
Vrms = 0.707 Vpeak = (1/2) Vpeak
For the voltage shown in Figure 1, the rms value is 0.707 volts.
A plot of both the instantaneous and rms values of the voltage is shown here in Figure 2.
1 kHz sine wave
1
0.8
0.6
instantaneous value
rms value
voltage in volts
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
0
0.5
1
1.5
time in milliseconds
Figure 2. A plot of the instantaneous and rms values of a 1 volt sine wave.
As “hands-on” engineers, we need to be able measure the quantities that describe a
sinusoidal waveform just as easily as we write our own name. In most cases, these
measurements will be made with an oscilloscope. The exception is the measurement of the rms
value. It is usually easier to make this measurement using a properly calibrated multimeter.
PRELIMINARY WORK
1. Using the definition of the average value of a periodic function that you learned in
Calculus, determine the average value of a sinusoidal (sin or cos) waveform over one period.
2. The rms value of a waveform (in this case, voltage) is equal to the square root of the
average value of the function squared, or
1
 v (t )dt
T
T
2
0
Determine the rms value of a sinusoid and a square wave over one period.
LABORATORY PROCEDURE / RESULTS
1. Connect the function generator, oscilloscope, and 1 kΩ resistor as shown below in
Figure 3. Set the function generator to provide an output voltage of 2 volts peak-to-peak at 1 kHz
across the resistor.
Measure/calculate the peak and peak-to-peak values of the voltage, the period, and the
frequency using the Agilent oscilloscope. Record these values along with sketches of the
waveforms in your laboratory notebook. Use the floppy drive option to save a copy of your results
to use in your lab report.
Measure the rms value of the voltage across the resistor using your multimeter.
Calculate the rms voltage using the data obtained from your oscilloscope and compare the
values. Are they in agreement?
XSC1
G
XFG1
T
A
B
R1
1kOhm
Figure 3. Function Generator and Oscilloscope setup.
2. Change the function generator so that it provides a 2 volts peak-to-peak 1 kHz
triangular wave and repeat the measurements/calculations of step 1. The rms value of the
triangular wave should be
Vrms = (1/3) Vpeak
3. Change the function generator again, but this time provide a 2 volts peak-to-peak
1 kHz square wave and repeat the measurements/calculations of step 1. What do you obtain for
the rms value of the waveform? Does this make sense?