1. Introduction to Phasors Week 2: Experiment 22

2. 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.

3. Modifications to Experiment 22 Frequency of the voltage source: 50 kHz Amplitude of voltage source: 4V Capacitor: 1 nF Inductor: 10 mH Shunt Resistors: – Use 10  with 1 k  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.

4. 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, January 30, 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, February 3, at 8:00pm. You should make sure that the upload happened.

5. 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.

6. 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.

7. Test Circuit Channel 1: Voltage Measurement Channel 2: 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.

8. Phase Delays Lagging and Leading

9. 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.

10. Time (seconds) Voltage (V)

11. 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:  t = 40 second – 0 seconds Signal 3 and Signal 1:  t = 480 seconds – 0 seconds

12. Steps The sinusoidal function that describes Signal 1, the reference voltage, is V(t) = 5V sin (  t) where f =  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 (  t +  ) where  T and  2  t/T  is called the phase shift

13. Lagging and Leading Don’t get fooled by the positions of the curves on the graph! Signal 2: V(t) = 5V sin (  rad/ s -1 )t –   ) –  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 (  rad/ s -1 )t +   ) –  is 0.251 radians or 14.4 degrees – Signal 3 leads Signal 1 as it reaches zero at an earlier time than Signal 1

14. Cursors: Velleman Oscilloscope

15. 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.

16. Phase Measurement: Velleman Oscilloscope

17. 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.

18. Percent Difference