1. Phasors and Kirchhoff’s Current Law
Week 3: Experiment 23

2. Measurement Issues Thevenin Equivalent Circuit
Amplitude vs. Voltage Peak-to-Peak
True RMS

3. Thevenin Equivalent Circuit
The arbitrary function generator can be modeled as a 50mV-5V source with an internal resistance of 40 W.
Consider this when trying to deliver power to your circuit (Rload)
Function
Generator

4. Thevenin Equivalent Circuit
The oscilloscope can be modeled as a 1MW load resistor in parallel with your circuit.
Your Circuit

5. Amplitude and Peak-to-Peak Voltage
Vpp VM

6. RMS – Root Mean Square

7. RMS vs. True RMS RMS of a sinusoid is 0.707 VM
Some instruments assume that the voltage measured is always a sinusoid
Output RMS values are wrong for all other waveshapes
This is what your digital multimeter does.
True RMS, which is what the Velleman outputs, is calculated using the equation on the previous slide.

8. Changes to Experiment Frequency of operation: 40 kHz
You will have to use the arbitrary function generator on the Velleman scope
Amplitude of voltage supply: 5 V
Inductor: 10 mH
Capacitor: 2.2 nF
R1: 4 kW
R3: 2 kW
Pick R2 and R4 (shunt resistors) appropriately.
Be aware that the stored energy in the inductor could send amount of current out of phase with the voltage back into the scope if incorrect components are used (XC appraches -j ∞ W).
Reference all phase measurements to the phase of the voltage supply.

9. New Circuit

10. Transient Analysis Source: Vsin
Instructions state that you need to wait a few cycles before making any measurements from the plot.
This is because the capacitor has an initial condition of 0V (no charge stored on the electrodes).
This can be changed as IC (initial condition) is an attribute in the capacitor model.
In certain circuits, the capacitor and inductor in a circuit can store energy extremely efficiently (i.e., the time constant of the circuit is much shorter than 1/f).

11. Transient Plot
Automatically generated when current markers are placed in the schematic.

12. To Obtain Smooth Curve
Set the Step Ceiling to a small fraction of T, the period of one cycle.

13. Bode Plots Phase angles can be determined from PSpice by:
Measuring the difference in the zero crossing of the voltage from the arbitrary function generator and the DUT using the transient analysis
Displaying the phase angle on a plot generated during an AC Sweep.
Note that the voltage source must be changed from Vsin to Vac.
P() marco will display the phase angle of the parameter inserted [e.g., V(R2:2)]

14. Schematics
PSpice Schematics uses superposition when performing the AC Sweep. So, both voltage sources may be put into the same circuit.
You select which plot is generated during the simulation run.

15. To Plot Phasor Information

16. Add a Trace to the New Plot

17. Select P() in the List of Functions or Macros

18. Select Voltage or Current from the List of Simulation Output Variables
It will appear within the paraphrases as the argument of the phase function. You can add multiple traces at once by putting a comma between each on the list at the bottom of the pop-up window. Then, click OK.

19. To Change the x axis to Log(f)

20. Phase Angle in Degrees Vs. Frequency
The angle in phasor notation should be between -180o to +180o.

21. Phase Angle Measurement
Two techniques using the Velleman scope
Waveform Parameters
Measurement of relative phase to internal reference at the operating frequency of the arbitrary function generator.
Bode Plot
Measurement of the phase of the signal on Channel 1 with respect to the signal on Channel 2 over a frequency range specified by the user.

22. Waveform Parameters

23. Bode Plot
Select Phase Plot from View menu after having set the Frequency Range, Frequency Start, and other measurement parameters and then click Start to obtain the phase measurement.

24. Natural Frequency of Circuit
The specified frequency of operation of the voltage source is close to the natural frequency of the RLC network.
If a sharp square wave was obtained from the arbitrary voltage source, you would be able to see the ringing associated with the energy transfer between the inductor and capacitor before the system reached steady-state.

25. Transient Response
If you wanted to, you could look at the transient response to a square wave input (i.e., see the ringing associated with the natural and forced response of this RLC circuit), by adding Vpulse to the circuit.
Set the amplitude of Vsin to 0V. Then set the amplitude of Vpulse to 5V and the PW to 100us and PER to 200us. The plot of the response for a similar circuit is shown on the following slide.

26. Transient Response: Square Wave Input
Voltage at the node after the inductor.
Currents (in mA) through the inductor, capacitor, and R1.