Lab Report 6

Circuit Analysis-II
Spring-2022
Grading
CLO1 CLO2 CLO3 Total
Comments:
Lab Report:
Experiment No: 06 Date of Submission:
March-06-2022
Experiment Title: Measuring the Phase Deference
Between Two Waveforms
Students’ Names:
1.Shadad khan
2.Muhammad Sheharyar Shahid
Batch: Teacher:
BSEE 2020-24 Dr. Ghulam Mustafa
Semester Lab Engineer:
4th Engr. Hasnain Ahmad
M.S. Paghunda Ali
Department of Electrical Engineering

LAB REPORT 6: Measuring the Phase Deference Between Two Waveforms
6.1: Abstract
In this experiment the phase difference of passive low pass and passive high pass filters were
analyzed using oscilloscope. There are many different methods of finding phase difference, but in
this experiment, Lissajous curve method and the time difference method was used. While
performing this experiment one probe of oscilloscope was attached to the input and the second
probe was attached to the output. This gives us two curves and time difference were calculated
accordingly.
6.2: Objectives
The objectives of this lab are:
 To gain familiarity with the lab equipment, oscilloscope.
 To measure the phase difference between two voltage waveforms using an oscilloscope.
6.3: Background
In this lab experiment, we found the phase difference by time difference method and Lissajous
curve. In time difference method we find the time difference (td) between two waveforms and by
using the formula below, the phase difference is calculated.
𝑡𝑑
𝜃2- 𝜃1 = 360. ……………………………(i)
𝑇
By Lissajous curve method, first we find out the value of C and A from oscilloscope and by using
the formula given we calculate the phase difference for two wave forms.
𝐶
= ±𝑠𝑖𝑛−1 (𝐴) 𝑖𝑓 𝑡𝑜𝑝 𝑜𝑓 𝑒𝑙𝑙𝑖𝑝𝑠𝑒 𝑖𝑛 𝑄𝑢𝑎𝑑𝑟𝑎𝑛𝑡 1
𝜃2- 𝜃1 = { 𝐶
= ± [180 − 𝑠𝑖𝑛−1 (𝐴)] 𝑖𝑓 𝑡𝑜𝑝 𝑜𝑓 𝑒𝑙𝑙𝑖𝑝𝑠𝑒 𝑖𝑛 𝑄𝑢𝑎𝑑𝑟𝑎𝑛𝑡 2
6.4: Equipment
 Function generator
 Oscilloscope
 Resistor 2.2k
 Capacitors 0.33uF
6.5: Procedure
6.5.1: The Time Difference Method:
Figure 6.1
The steps for time difference method are as follows:

 Display both channels as a function of time as shown in Figure 6.1.
 Scale each voltage channel so that each waveform fits in the display.
 Ground or zero each channel separately and adjust the line to the center axis of the display.
 Return to AC coupling.
 (Optional) If you can continuously adjust the voltage per division, scale your waveforms
to an even number of divisions. You can then set the zero crossing more accurately by
positioning the waveform between gridlines on the display.
 Pick a feature (e.g., peak or zero crossing for sinusoids, rising, or falling transition for
square waves) to base your time measurements on. The peak of a sinusoid is not affected
by DC offsets but is harder to pinpoint than the zero crossing.
 Measure the period T between repeats. Digital oscilloscopes often measure f = 1/T
automatically.
 Measure td, the smallest time difference between occurrences of the feature on the two
waveforms.
 The phase difference is then
𝑡𝑑
𝜃2- 𝜃1 = 360. 𝑇 ………………………………(İ)
 The sign of 𝜃2- 𝜃1 is determined by which channel is leading the other.

6.5.2: Lissajous Curve Method
The steps of the Lissajous curve method are:
Figure 6.2: Lissajous curve

 Set the oscilloscope to xy mode.
 Scale each voltage channel so that the ellipse fits in the display. (This may be a line if the
phase difference is near 0 or 180.)
 Ground or zero each channel separately and adjust the line to the center (vertical or
horizontal) axis of the display. (On analog scopes, you can ground both simultaneously and
center the resulting dot.)
 Return to AC coupling to display the ellipse.
 (Optional) If you can continuously adjust the voltage per division, scale your waveforms
to an even number of divisions. You can then center the ellipse more accurately by
positioning the waveform between gridlines on the display.
 Measure the horizontal width A and zero crossing width C as shown in Figure 6.2.
 The magnitude of the phase difference is then given by
𝐶
= ±𝑠𝑖𝑛−1 (𝐴) 𝑖𝑓 𝑡𝑜𝑝 𝑜𝑓 𝑒𝑙𝑙𝑖𝑝𝑠𝑒 𝑖𝑛 𝑄𝑢𝑎𝑑𝑟𝑎𝑛𝑡 1
𝜃2- 𝜃1 = { 𝐶
= ± [180 − 𝑠𝑖𝑛−1 (𝐴)] 𝑖𝑓 𝑡𝑜𝑝 𝑜𝑓 𝑒𝑙𝑙𝑖𝑝𝑠𝑒 𝑖𝑛 𝑄𝑢𝑎𝑑𝑟𝑎𝑛𝑡 2
 The sign of 𝜃2- 𝜃1 must be determined by inspection of the dual channel trace.
6.6: Results and Discussion:
F (Hz) td (ms) T (ms) 𝜽2- 𝜽1 𝜽2- 𝜽1

(Calculated) (Theoretical)
20 0.8 50 -5.76 -5.21
50 0.627 20 -11.3 -12.85
100 0.620 10 -22.3 -24.52
200 0.581 5 -41.18 -42.37
500 0.32 2 -57.6 -66.33
1000 0.20 1 -72 -77.64
2000 0.118 0.5 -84.2 -83.74
5000 0.048 0.2 -86.4 -87.49
20000 0.011 0.05 -79.2 -89.37
Table 6.1: Phase difference using the time difference method
F (Hz) C A 𝜽2- 𝜽1 𝜽2- 𝜽1

(Calculated) (Theoretical)
20 - - - -
50 - - - -
100 390 440 62.4 65.48
200 416 680 37.1 47.63
500 390 980 23.45 23.67
1000 200 1060 10.88 12.36
2000 112 984 6.54 6.26
5000 56 1030 3.12 2.51
20000 20 1280 0.67 0.63
Table 6.2: Phase difference using the Lissajous curve method
The Time Difference Method
Figure 1, Curve at 20 Hz Figure 2, Curve at 100Hz
Figure 3, Curve at 20KHz
Lissajous Curve Method

Figure 4, shows Curve at 200Hz Figure 5, shows Curve at 2KHz
Figure 6, shows Curve at 1KHz Figure 6, shows Curve at 5KHz
In the experiment we find the phase difference using two methods as explained above. For time
difference method the trend we observe in phase difference of Low pass is that with increasing
frequency phase difference will increase in negative. For phase difference of High Pass filter, we
used Lissajous curve method and the trend we observed is that increasing frequency decreases the
phase difference. This is due to low pass filters lower frequencies are allowed but higher
frequencies will be blocked, and inverse case in high pass filter. So, if we see the trend, we notice
that at initial frequencies of low pass phase difference is small because output curve is
approximately in phase to the input curve. But when saw the trend for High pass we notice that at
initial frequencies phase difference is higher because it does not allow smaller frequencies so when
we increase our frequency of signal phase difference decreases and at very high frequency it nearly
became in phase with input curve.
Overall, there was little deviation in the readings, the highest error for low pass was 12.06% which
is due to the tolerance of the components and parallax error in taking readings. On the other hand,
the high pass filter gives very distorted results on 20 and 50 Hz. At low frequency the high pass
filter will block the signal. The value of C and A were not clear from the graph so first two values
for high pass were skipped.
6.7: Conclusion
The low pass filter passes the lower frequencies while block the higher one. And for high pass
filter the higher frequencies are allowed to pass while rejects the lower. We observed this
practically. We calculated the phase difference using oscilloscope which enhance our knowledge
of using oscilloscope.
6.8: Reference:
EE-226 Circuit Analysis-II Laboratory Manual, Spring 2021, pp.27-28 (formulae given).
Performance Table:
Shadad Sheharyar
1) Title 7) Results
2) Abstract 8) Conclusion
3) Introduction 9) Discussion
4) Equipment 10) Performance table
5) Procedure 11) Table
6) Pre lab calculation
Grading Table:
Criterion Evaluation
Title, Abstract & Introduction (5
Points)
Experiment Procedure (5
Points)
Results & Discussion (10
Points)
Report Format (5
Points)

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Circuit Analysis-II

Department of Electrical Engineering

The steps for time difference method are as follows:

 The sign of 𝜃2- 𝜃1 is determined by which channel is leading the other.

Figure 6.2: Lissajous curve

6.6: Results and Discussion:

F (Hz) td (ms) T (ms) 𝜽2- 𝜽1 𝜽2- 𝜽1

F (Hz) C A 𝜽2- 𝜽1 𝜽2- 𝜽1

The Time Difference Method

Figure 1, Curve at 20 Hz Figure 2, Curve at 100Hz

Figure 3, Curve at 20KHz

Lissajous Curve Method

Figure 6, shows Curve at 1KHz Figure 6, shows Curve at 5KHz

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