Laboratory 3. Oscilloscopes 2
Equipment: Bench equipment, decade capacitor, 10k decade resistor, box of leads, bncbnc cable, bnc T connector, 2-bnc-banana cables.
Reading: Review circuit theory of sinusoidal steady state analysis, impedance and
admittance, and Kirchhoff’s Law’s Using Phasor Analysis (Dorf and Svoboda, Sections
10.8 and 10.9)
Review the posted material on Lissajous figures.
Prelab assignment:
1. Review the Figure 1 RC circuit, and determine the relationship between Vout and
Vs in terms of RL and CL (ignore Rs as Rs<<RL). Conduct this analysis in the
steady state using phasors.
2. Look up the definition of capacitive reactance Xc of the capacitor.
3. When the frequency of the source is 1.2 khertz, determine the value of
capacitance that will give a capacitive reactance Xc of 10kohm.
4. The gain of a circuit is defined as the ratio of the output voltage to the input
voltage. Develop an expression for the gain of this circuit in terms of RL and Xc
(note that Rs is small enough to neglect.).
5. From this gain, determine the expression for the magnitude of this gain.
6. Also, determine the expression for the phase angle of this gain.
7. When Vin=1/0o volts, RL=10kohm, and capacitive reactance Xc=10kohm,
determine the magnitude and angle of Vout.
8. For this same value of capacitance, determine capacitive reactance Xc for
frequencies of 12khertz and 1.2 khertz.
9. Determine the magnitude and phase angle of Vout for the two capacitive
reactances of Step 8.
10. Review the material on Lissajous figures.
11. Review the laboratory procedure and prepare to complete the steps of the
procedure.
12. Complete and pass the Lab 3 Quiz before coming to lab.
Laboratory Procedure
1. Set up the function generator to put out a 1.2 kilohertz, 1v peak sine wave, and
display this wave on Channel 1 of the oscilloscope. Measure the period of this
wave__________________. Is it correct?_________________
2. This circuit uses a decade resistor and capacitor. Note that both devices connect
their components between the “H” and “L” studs. The other stud(s) are connected
to the case—these should be connected to ground when you are using these
devices in medium or high voltage situations, or with high frequencies.
Familiarize yourself with the decade resistor by connecting it to your ohmmeter,
and make sure that you understand the knob settings of this device. Set the
decade resistor to 10 kohms. Determine the capacitance value needed for a value
of capacitive reactance of 10kohms at 1.2 khertz. CL=_________. Set the decade
capacitor to this value.
3. Use the decade resistor and capacitor to connect the circuit shown in Figure 1.
Connect Vout to Channel 2 of the oscilloscope. Make sure that Channel 2 is on,
and both channels have probe setting of 1x and DC coupling.___________
4. The function generator has an internal resistance Rs of 50 ohms. This is small
enough that it can be neglected in this lab. Given that Vin = 1/0o (peak volts),
with the R and C values of steps 2 and 3, predict the value of
Vout__________(magnitude and angle). Will Vout lead or lag Vin?
Also, predict the value of the voltage across the resistor RL:_____________
5. Set the vertical and horizontal knobs on the scope to get a reasonable display.
You should see two sinusoidal traces of the same frequency, but differing
amplitudes and phase angles. It will be most convenient to have zero offset in
both waves.
a. Adjust the horizontal position to put the Channel 2 peak on the center
scale of the display. Measure the level from this display: __________
b. Turn on the cursor button, and set the cursor source to Ch. 2. Adjust CurA
to the positive peak of the Ch. 2 voltage, and CurB to the negative peak of
this voltage. Record these two values:
CurA__________ CurB________
c. Compare the values of steps 5a and 5b with the prediction of Step 4:
What is the per cent error?
6. Now, push the “Measure” button, and turn “Display All” on, with Ch2 as the
source. Record the peak-peak, peak, and rms voltages for this wave. Are these
measurements consistent?
7. Turn “Display All” and the cursors off. The phase angle between Vin and Vout
can be measured by the horizontal displacement between the two signals. Adjust
the traces to display the positive going zero crossings of the two waves. Change
the horizontal sensitivity so that you get at least three divisions between the zero
crossings of these two waves. Record:
a. the number of divisions between these waves:___________
b. the horizontal scale:_____________
c. the time difference between the two waves (a*b)__________
d. the period of the wave:______________
e. the angle of Vout relative to Vin, in degrees (360*(c/d)__________
How does this compare with the angle prediction of Step 4 (note that the
per cent error of an angle doesn’t make much sense):
8. Now, turn the cursors on. Select type “Time” Set the horizontal sensitivity to
20usec/div.
a. Place Cu1 on the Vin zero crossing, and Cu2 on the Vout zero crossing.
Record the time difference_________
b. Repeat this measurement with 50usec/div__________
c. Repeat with 100usec/div_________
d. Repeat with 200usec/div__________
e. Which setting(s) is the best for making this measurement?
9. Select MeaureTimeDelay12(rising edge). Note that this value will appear
at the bottom of the screen. Record this delay:___________ How does it
compare with the previous values.
10. Many oscilloscopes, including the Agilent DSO3062A, measure voltages relative
to ground. This has worked well for measuring Vin and Vout in this experiment,
as both signals are referenced to ground. There are some cases where it is
necessary to measure a voltage difference which is not relative to ground,
however. The voltage across the resistance RL (call this VR) in this experiment is
a case in point. To measure VR, note that this voltage is the difference between
Vin and Vout.
a. Select “Math”
b. Set Source A to Ch1 and Source B to Ch2.
c. Select the operator A-B.
d. Look at the display, you should now see three traces. Note the vertical
sensitivity for the Math trace. Set the vertical gain for Ch1 and Ch2 so
that all three traces are the same.
e. What is the amplitude of VR?
f. What is the phase angle of VR?
g. Do these values agree with the expected values predicted in Step 4?
The effect of frequency on phase shift:
11. Leave the decade box resistance and capacitance settings the same. Increase the
frequency of the frequency generator to 12 kilohertz. What is the capacitive
reactance at this frequency? Xc=_______________
12. Measure the output voltage magnitude and angle (using the method of step 7).
Vo=____________ angle:_____________
13. Repeat 11-12 for a frequency of 120 hertz Xc=____________
Vo=_________ angle:__________
14. Comment on the effect of frequency on the output voltage for this circuit:
Lissajous method
15. Set the function generator back to 1.2khz. Use the Lissajous method to measure
the phase angle of Vout. In order to do this, you need to put the oscilloscope into
the x-y mode.
To do this, push the “Time/Delayed” button in the horizontal control section.
Select Time Base X-Y from the menu. You should now see an oval. The size of
the oval can be adjusted with the yellow and green amplitude knobs. Set the
position of both Ch1 and Ch2 to zero.
A Lissajous figure can be used to measure the phase angle between two sinusoidal
voltages of the same frequency.
Note that the vertical height “B” is the peak-peak amplitude of the Ch. 2 signal. The
height “A” is the amplitude of this same signal when the Ch. 1 signal is at zero
amplitude. Therefore, ratio of these two values is the sine of the angle between them:
A
sin( )  
B
A=__________________
B=__________________
Phase angle= __________________
How do your results compare with the previous measurement?
___________________________
Extra Credit- 2.5%—Lissajous figures of signals with different frequencies.
16. Lissajous figures can also be used to measure the difference in frequency
between two signals. Connect the sinusoidal frequency of the National
Instruments i/o box to Channel 1 of the oscilloscope, and the output of the HP
function generator to Ch. 2 of the scope. Set the NI function generator frequency
range switch to 100-10khz. Go back into the Y-T mode and set this signal to be
approximately150 hertz. Record the exact value of this frequency:________
17. Go back into the X-Y mode. Set the HP function generator frequency to 100
hertz, and increase it slowly until you get an oval. This indicates that the two
frequencies are the same. Record this frequency____________.
18. It may not be possible to get the two function generators to put out the exact same
frequency. What is the effect of having two slightly different frequencies on these
two signals?
19. Now increase the HP function generator frequency by a factor of 2, 3, and 4 in
turn. Observe the pattern that emerges at each of these frequencies, and comment
on the relationship between the Lissajous figure and the frequencies of the two
signals.
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Last modified:12/27/2006 tho