ENGR225 Circuit Analysis                                                Name_________________________

Lab #8 - Sinusoidal AC Measurements in RLC Circuits    Date__________________________

Objectives:

To verify some of the basic ideas involved in ac circuit analysis by experimental observations.

To gain experience with phasor calculations.

To gain experience using the oscilloscope to make waveform measurements.

Procedures:

1.         Measure the 18mH inductor and the 0.68μF capacitor on the HP LCR meter to determine their actual values and to determine if there is appreciable resistance (use Rs and Ls or Cs on the meter) in their equivalent circuits that will need to be added in the circuit below.

2.                  Build the circuit shown below.  The general procedure is to set the Wavetek Function Generator output for a 10V peak (20Vpp) 1kHz sine wave, and then connect it up to your circuit.  Then measure the voltage across each of the components L, C, and R2.  Start with the voltage across R2 and then swap R2 with C and R2 with L+RL to get the other measurements.   Record and label these waveforms.  The details on how to make these measurements are in the next paragraph.  Follow the directions closely.

Connect channel 2 with coaxial cable to the LO output of the Wavetek.  Set the channel 2 input for a 10X probe.  Connect channel 1 to a second cable from the HI output of the Wavetek and be sure that it channel 1 is set for a 10X probe.  Set your volts/div to 5V/div on both channels. Adjust the sec/div control so that you see about 2 cycles of the 1kHz waveform.   Measure the peak-to-peak voltage for channel 1 and channel 2 using the Vamp function, and adjust the amplitude to 20V (note that it should read the close to the same on both channels).  Now we will use the waveform on channel 2 as our reference (Vs) waveform, and we will connect the HI output signal to the circuit.  Use a probe on channel 1 to measure VR2, VL, and VC.  Adjust the volts/div control of the channel 1 waveform so that it appears about the same size as the channel 2 Vs waveform, and add the phase 1–>2 (phase of channel 1 with respect to channel 2) measurement to the two amplitude measurements already on the screen.  Make all of your measurements like this.

·        Determine the current I in the circuit using VR2/R2.

·        What is the phase angle difference between Vs and I in this circuit?  Note that VR2 is in phase with the current I.  What does this indicate about the nature of this circuit at this frequency (ie. Does it look inductive or capacitve?)?

·        What is the phase angle difference between VC and I in this circuit?  Is VC ahead or behind I?  Explain why this is or is not what you expected.

·        What is the phase angle difference between VL and I in this circuit?  Is VL ahead or behind I?  Explain why this is or is not what you expected.

·        Draw the phasor diagram for the current I and the voltages VR2, VL, and VC.  There is one additional voltage VR across the internal 50 ohm resistance of the Wavetek that we did not measure, but we can note that it should be nearly the same as VR2.  Add VR to your phasor diagram.

·        Does Kirchhoff’s voltage law work as you sum the voltages around this circuit?  Explain what you find when you consider this.  The phasor diagram should help you.

4.         Monitor the voltage across R2 while slowly increasing the frequency above 1kHz.  Choose a frequency that will give you a maximum amplitude on channel 2 (and a minimum phase angle).  Record this frequency and the waveforms that you obtain while repeating the measurements of part 2.

5.                  Answer the questions of part 3 again with reference to the measurements taken in part 4.

6.                  Increase the frequency of the Wavetek to 2.5kHz and again obtain the waveforms while repeating the measurements of part2.

7.                  Answer the questions of part 3 again with reference to the most recent measurements taken in part 6.

Note: This lab shows how an L and a C can be used to tune a circuit to respond best (highest output) to a particular band of frequencies.  This is an insight into how radios are able to pick out an individual station from all of the radio waves that are present.

Note: I have included on my website a printout of a Mathcad document that shows the approximate results that you should expect as you do the experiment.  It is approximate because I did not measure the specific values of the C or L, but only used their apparent values and an estimated value for RL.