Objectives:

The objectives of this experiment are:
1. To understand all primary controls of the oscilloscope and be able to measure all types of AC and DC signals using the oscilloscope.

2. To be able to determine when to use DC-Coupling or AC-Coupling when observing signals on an oscilloscope.

3. To understand the frequency response characteristics of the digital multimeter (BK Precision 2880A) for AC voltage measurement.

Parts and Equipment:

Resistors: 10 K, 15 K 
Capacitor: 0.01 µF
Oscilloscope
Digital Multimeter
Oscillator
DC Power Supply
Breadboard and wire

Textbook Reference:

"Engineering Circuit Analysis" by Hayt & Kemmerly, pp. 295-296.
or "Electric Circuits" by Nilsson & Riedel, 6th Ed., pp. 409-461.

Material Review:

For the oscilloscope, see the attached Oscilloscope Reference Guide.

For the multimeter, see the specification sheet for the BK Precision Model 2880A Multimeter. Note the AC voltage frequency tolerance.

RMS values for voltage and current:
In d.c. circuits the power delivered to a circuit element is given by the product of the voltage across the element and the current through the element. This is also true of the instantaneous power to a resistor in an a.c. circuit. For many applications the instantaneous power is of only minimal interest and the average power delivered over time is of primary interest. This is particularly true in power systems. In order to have an easy way of measuring power the effective or rms method of measuring voltage and current was developed. The effective value is defined as the value of the equivalent d.c. quantity that would deliver the same average power to the same resistor. Since power is given by p(t) = v(t)i(t) = v(t)²/R = i(t)²R, it is necessary to integrate to find the average value of the power. For a periodic function the average is found by integrating over one period and dividing by the period. For d.c. power the average and the instantaneous values are the same since it is a constant. Therefore by setting the equivalent d.c. power equal to the average a.c. power and solving for the equivalent d.c. voltage or current a relationship can be found for the effective voltage or current. The following equations demonstrate this.

If v(t) = V_msin(t) then

The same is true for current, since power is proportional to the square of the current as well as to the square of the voltage. RMS stands for 'root mean square' since the effective value of the voltage or current is found by taking the square ROOT of the MEAN value of the SQUARE of the time varying quantity.

Procedure 1:
Construct the following circuit

1. Set the signal generator, connected to node 1 at 2 kHz, 1.8 V_RMS. Set the DC power supply to 9 V_DC (Node 3).

2. Connect CH1 of the oscilloscope to node 1 and CH2 to node 2. Set the vertical position of both channels so the zero reference is at the center of the screen. Set the time scale to display one or two complete cycles.  There must be at least one complete cycle of a waveform on the screen in order for the oscilloscope or Wavestar to calculate some of the measurements.

3. Set both channels of the oscilloscope for AC coupling and the voltage scales set for the largest on screen display with the same scale for both channels.  Then print the waveforms and record the peak to peak and rms voltages of each waveform and the oscilloscope scale settings.

4. Change both input channels to DC coupling.  Then increase the voltage scales to bring the waveform back on screen while still keeping the same scale for both channels.  Print the waveforms and the measurements from Wavestar.  Record the maximum and minimum voltage of each waveform (use the cursor mode for these measurements).

5. Switch back to ac coupling on both channels and set the Scope to x-y mode and determine the phase shift between the ac waveforms at node 1 and 2, using the elliptical pattern.

6. Switch back to voltage - time (Y-T) display and determine the phase shift using the period and time delay.  Use the measure mode to measure the period.  Use the cursor mode to measure the time difference between the positive slope zero crossings of the two waveforms to get the delay time.  To make this measurement as accurately as possible you must expand the time scale to maximize the on screen distance between the two zero crossings.  You may have to use the horizontal position control to center the space between the zero crossings of the two waveforms on the screen.  You should also increase the vertical gain so the slope of the lines is higher to make it easier to see exactly where the zero crossing is.  This will put the peaks of the waveform off the screen, but they are not needed for this Dt measurement. Check to make sure that both channels are set for zero at the center of the screen before switching to cursor mode.

Procedure 2:
1. Connect the digital multi-meter to the signal generator output.

2. Connect one channel of the oscilloscope to the signal generator output.

3. Set the signal generator at 1 kHz and the voltage level at 1.0 V_RMS.

4. Adjust the settings on the oscilloscope for the largest possible on screen display with two or three cycles of the waveform and verify the voltage by measuring the rms voltage using the measure mode and comparing to the meter results.  Also measure the peak to peak voltage.

V_RMS = V_p-p/(2*sqrt(2))  for a sinusoidal waveform given by:
 v(t) = V_max cos(omega t + theta)
 
5. Record  V_RMS from DMM and both V_RMS and  V_p-p from the oscilloscope at 1 kHz.  Then without changing the amplitude setting repeat the measurements at each of the following frequencies of (2, 5, 10, 20, 50, 100, 500) kHz. Always keep about two or three cycles of the waveform on the screen.
 
6. Using the oscilloscope measurements as reference, calculate the percent error of the multi-meter readings.
 
7. Using a computer spreadsheet program, graph the percent error vs. frequency. (Note: plot the frequency (horizontal axis) on a log scale; error (vertical axis) on a linear scale

8. Compare the error tolerance on the DMM spec sheet with your results.
 

Questions:
1. What is the difference between the AC coupling and DC coupling on the oscilloscope? When should AC coupling be used? When should DC coupling be used?

2. Calculate the Thévenin equivalent resistance of the circuit to the right of the capacitor.  This Thévenin equivalent is what is seen by the ac voltage between node 2 and ground, since the DC supply looks like a short circuit to the ac signal. Use this value to calculate the theoretical phase angle between the ac voltage at node 2 and the voltage at node 1 using steady state ac analysis. Compare this calculated angle with the measured angle.  

3. What is the difference between peak-to-peak voltage and RMS voltage?
 
4. How should the Oscilloscope settings be adjusted when measuring AC voltages of unknown magnitude and frequency?

5. For a sinusoidal signal, V_rms = V_max/sqrt(2).  Derive the value of  V_rms for the following waveform.

What can you say about these measuring instruments based on your experimental observations?

This page last updated 08/21/2007