ECE 213 Electrical Circuits II Lab
LAB #4
Spring 2015
Name ___________________
Section ______________
Root Mean Square Values
Introductive
Waveforms of voltage and current that vary periodically with time may be characterized by their
average value or their root-mean-square (RMS) value. The latter is used to determine the power
supplied, dissipated, or stored by a circuit element. Some of the measuring instruments you will
use respond to average values of voltage or current, while others respond to RMS values.
Objective:
(l) Leam how to determine the values of RMS voltage for three types of waveforms: a sinusoid, a
square wave, and a triangular wave.
(2) Understand the difference between a true—RMS and a conventional multimeter.
Equipment Needed:



Function Generator
Oscilloscope
Digital Multimeter (true RMS)
Background Information
Figure 1 - AC signal
Amplitude is a nonnegative scalar measure of a wave‘s magnitude of oscillation. In electrical
engineering it may be thought of as the maximum absolute value reached by a voltage or current
waveform. An amplitude measurement may be reported as peak, peak-to-peak, average, or RMS.
ECE 213 Electrical Circuits II Lab
LAB #4
Spring 2015
Peak amplitude is the height of an AC waveform as measured from the zero mark to the highest
positive or lowest negative point on a graph. This can also be known as the crest amplitude of a
wave.
Peak-to-peak amplitude is the total height of an AC waveform as measured from maximum
positive to maximum negative peaks on a graph. Often abbreviated as “P-P”
Average amplitude is the mathematical mean of the waveform over a period. Technically, the
average amplitude of any waveform with equal-area portions above and below the x-axis is zero.
However, as a practical measure of amplitude, an average value of a waveform is often
calculated as the mathematical mean of the absolute value of the waveform.
RMS stands for Root-Mean-Square and is a way of expressing an AC quantity of voltage or
current in terms functionally equivalent to DC. For example, l0 volts AC RMS is the amount of
voltage that would produce the same amount of heat dissipation across a resistor of given value
as a l0 volt DC power supply. RMS is also known as the "equivalent" or “DC equivalent" value
of an AC voltage or current. The RMS values for sinusoidal, square and Triangular waveforms
can be seen below.
RMS Value
Sinusoidal Voltage:
Square Wave Voltage:
Triangular Wave Voltage:
True RMS vs Non-True RMS
In this laboratory "true RMS" voltage meters are used. The relationship between the magnitude
of the waveform and the measured value would be given by the appropriate equation shown
above. However, many meters available are not "true RMS" meters, or “Non-True RMS”. As a
result they are only designed for measurements in circuits with either DC voltages or sinusoidal
AC voltages. For obtaining the AC voltage most digital meters effectively perform a full-wave
rectification of the waveform and then compute the average value. A constant factor is then
applied to compute a RMS value. In practice you will not get the exact results predicted by the
equations, due to a number of errors. There errors could be inability to set the peak voltage to the
ECE 213 Electrical Circuits II Lab
LAB #4
Spring 2015
exact value, slight errors in the meter reading, and inaccuracies in the shape of the waveform
produced by the function generator. Also, it is assumed that the duty cycle of the square wave is
exactly 50% in these calculations, which might not actually be the case for your waveform
generator.
Procedure
1. Connect the output terminals of the Function Generator to a 1kΩ Resistance.
2. Turn on the Function Generator and use the oscilloscope to observe the voltage drop
across the 1kΩ resistance.
3. Select the sine wave output option of the Function Generator
a. Set the frequency to l kHz in the function generator.
b. Adjust the DC offset control in the Function Generator to obtain a zero DC level
in the output.
c. Use the output level control in the Function Generator to obtain a 3 Volt peak
value on the sine wave. (Observe the peak value in the oscilloscope and adjust the
output level control knob of the Function Generator to obtain 3V).
d. With the oscilloscope measure the RMS value of the generated waveform.
e. Next use a true RMS multimeter to measure the AC RMS voltage.
4. Repeat the steps from 3.a to 3.d using a triangular wave.
5. Repeat the steps from 3.a to 3.d using a square wave with a 50% duty factor.
6. Adjust the DC offset control to add a 3 Volt DC offset to the original 1 kHz sine wave. In
order to see the DC offset in the screen. Make sure to use the DC coupling on the
oscilloscope. Now the waveform should vary from 0 to 6 Volts. Record both peak-topeak voltage and RMS voltage. Sketch this waveform.
7. Use the multimeter to measure AC RMS voltage and the DC voltage across the
resistance. Repeat the same step 6 for the triangular wave and the square wave.
ECE 213 Electrical Circuits II Lab
LAB #4
Spring 2015
Data Sheet:
Make sure all units are presented in the data sheet.
Instruments Used:
___________________________________________________________
___________________________________________________________
___________________________________________________________
___________________________________________________________
Procedure 1. (Steps 3 through 5)
Table D1: RMS and Peak-to-Peak Values for Waveforms
Waveform
Calculated
RMS
value
(1)
Sine Wave
Square
Wave
Triangular
Wave
RMS
Percent
Peak-to-Peak
Voltage
Error (%)
Voltage
Measured
measured
with DMM 100%*(2with an
1)/(1)
oscilloscope
(2)
(4)
RMS value
from
Oscilloscope
(5)
Percent
Error (%)
100%*(51)/(1)
ECE 213 Electrical Circuits II Lab
LAB #4
Spring 2015
Procedure 2 (Step 6 through 7)
For sinusoidal waveform:
Oscilloscope Digital Readings
Peak-to-Peak voltage of the sinusoid: _________________________
DC offset of the sinusoid: _________________________
AC RMS Measurement: _________________________
DMM Readings
AC Potential Measurements: _________________________
DC Potential Measurements: _________________________
For square waveform:
Oscilloscope Digital Readings
Peak-to-Peak voltage of the sinusoid: _________________________
DC offset of the sinusoid: _________________________
AC RMS Measurement: _________________________
DMM Readings
AC Potential Measurements: _________________________
DC Potential Measurements: _________________________
For triangular waveform:
Oscilloscope Digital Readings
Peak-to-Peak voltage of the sinusoid: _________________________
DC offset of the sinusoid: _________________________
AC RMS Measurement: _________________________
DMM Readings
AC Potential Measurements: _________________________
DC Potential Measurements: _________________________
ECE 213 Electrical Circuits II Lab
LAB #4
Spring 2015
Problem Further:
1. Does a change in the duty cycle of the square wave with no offset voltage cause a change
in the RMS Voltage value? What about power value?
2. Do your measured values agree with the calculated values in all cases in procedure 1? If
not, why?
3. Determine the theoretical RMS voltage value and DC voltage value you should have
measured in Step 7 of the procedure and compare this to what you actually measured.
Hints: True RMS ac + dc =SQRT( ac^2 + dc^2) . AC signals are different.
4. Draw a table comparing the calculated values and the RMS voltage measured from Step 7
including the percent error. Remember: Percent Error = [(Measured –
Calculated)/Calculated]*100%