Transcript Introduction to Phasors

Introduction to Phasors
Week 2:
Experiment 22
Experimental Procedures
• Do not do the steps labeled “Extra Credit” in
the Procedure. No extra credit will be given.
• The procedures will be modified during the
semester to increase the frequency of
operation.
• 10X probes will be rarely needed when using
the oscilloscope. Do not use the 10X probe
that came with your oscilloscope except when
it is explicitly mentioned in the lab lecture.
Modifications to Experiment 22
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Frequency of the voltage source: 50 kHz
Amplitude of voltage source: 4V
Capacitor: 1 nF
Inductor: 10 mH
Shunt Resistors:
– Use 10 W with 1 kW resistor.
– For the inductor and capacitor, select value that is
no more than 5% of the magnitude of the
impedance of the element under test.
Analysis
• The calculations may be performed by hand or
you may modify the MatLAB program that you
wrote for Week 1 to perform the calculations.
Reports
• A report template is posted on the Scholar site.
– Pre-lab report
• Complete the Analysis section of the template
• Convert to a .pdf
• Upload using the Week 2 Pre-Lab Report link on the Assignments
section of Scholar by Monday, Sept. 5 at 1:00pm.
– Post-validation report
• Complete the entire report template including the Analysis section
• Convert to a .pdf
• Upload using the Week 2 Post-Validation Report link on the
Assignments section of Scholar by Friday, Sept. 9 at 8:00pm.
You should make sure that the upload happened.
Experiment
• Use the Velleman Oscilloscope
– Function generator option to create a sinusoidal
voltage signal
– Measure the time-varying voltage using one
channel of the oscilloscope
– Measure the time-varying current using the other
channel of the oscilloscope
• You may need to use the trigger function on the
oscilloscope.
Function Generator:
Velleman Oscilloscope
• The parameter Amplitude
on the function generator
is actually the peak-to-peak
voltage of the signal
outputted.
– Use an amplitude of 8V
rather than 4V.
– Use a frequency of 50 kHz.
Test Circuit
Channel 1:
Channel 2:
Voltage
Measurement
Current
Measurement
Reminder: The current
flowing through the
device under test (DUT)
is equal to the voltage
measured on Channel 2
divided by the shunt
resistor.
Phase Delays
Lagging and Leading
Calculation of Phase
• Suppose you have three signals that you have
measured with your oscilloscope
– One signal is your reference
• I have chosen the reference to be the signal in Blue on
the following slide
– The phase of the other two signals will be
calculated with respect to the reference signal.
• The period of each signal should be the same, which
means that all signals have the same frequency.
6
4
Voltage (V)
2
Signal 1
Signal 2
0
0
100
200
300
400
500
600
700
Time (seconds)
-2
-4
-6
Signal 3
Steps
• Calculate the period, T, for the reference
signal
– This is the time for a full cycle to be completed.
• T= 500 second for Signal 1
– Calculate the difference in time between zero
crossings of
• Signal 2 and Signal 1: Dt = 40 second – 0 seconds
• Signal 3 and Signal 1: Dt = 480 seconds – 0 seconds
Steps
• The sinusoidal function that describes Signal
1, the reference voltage, is
V(t) = 5V sin (wt) where f = w/2p = 1/T = 0.002 s-1
• To write the sinusoidal function that describes
Signals 2 and 3, we need to address the fact
that there is a shift in the zero crossings
V(t) = A sin (wt + f) where w = 1/T and f = -2p Dt/T
• f is called the phase shift
Lagging and Leading
• Don’t get fooled by the positions of the curves on the graph!
• Signal 2: V(t) = 5V sin ((12.6 rad/s-1)t – 28.8o)
– f is 0.5 radians or 28.8 degrees
– Signal 2 lags Signal 1 as it reaches zero at a later time than Signal 1
• Signal 3: V(t) = 5V sin ((12.6 rad/s-1)t + 14.4o)
– f is 0.251 radians or 14.4 degrees
– Signal 3 leads Signal 1 as it reaches zero at an earlier time than Signal 1
Cursors:
Velleman Oscilloscope
A cursor is moved by left clicking
and dragging it to the appropriate
location.
The display at the bottom of the
scope screen is the difference in
voltage between the two
horizontal cursors and the
difference in time between the
two vertical cursors. Note that
the sign convention of the display
is the absolute value of the
difference between the cursors.
The values in parentheses for the
voltage measurements are the
actual voltages at the two
cursors.
Phase Measurement:
Velleman Oscilloscope
Waveform Parameters
The displayed phase is an angle in
degrees, but is measured relative to
an internal reference to the
oscilloscope.
Check the values listed in the table
before using them as the answers for
the measurements requested in the
experiments.
Percent Difference
Expected - Actual
%difference =
 100%
Expected