RLC Resonance



ECEN 2612 RLC Resonance (10.0 points) Lab #6

Name:

Partner:

Objectives:

• To be able to measure resonant frequency, quality factor, and phase relationships in a series RLC circuit, and to compare experimental results with theory.

• To be able to display the frequency response of a circuit on the oscilloscope using the signal generator frequency-sweep capability.

Procedure:

1. Use both the LCR meter and the DMM to measure and record the component values used in the circuit. Nominal values are L = 20 mH, C = 0.003 µF, and R = 1kΩ. Put nominal and measured values in a useful table. (1.0 point)

2. (a) Set up the circuit with a sine wave input. Display vS on CH1 and vR on CH2 using 1 V/div and 10 µs/div. Use measured element values and verify theoretically the resonant frequency which should be about 20 kHz. Use the scope to set the amplitude of vS to 3 V (6 Vpp), and adjust the function generator frequency for resonance. The vR should be a maximum at resonance. Show that vR and vS are in phase at resonance by triggering the scope with the CH1 (vS) signal.

(b) Measure the peak-to-peak value of vR, and then calculate its peak (amplitude) value. Put the data and results for this step (2) in a table with two rows, one for vS and one for vR, and two columns (amplitude in Vp, and phase angle in deg). Assume the phase angle of vS is 0 deg.

(c) Measure the function generator frequency from its scope display and record this value. Compare it with the function generator display. This is the circuit’s resonant frequency, f0. Describe how you obtained f0. Compare this measured value of f0 from the scope with the theoretical value, f0 =(1/(2(((LC)), using the LCR meter values of L and C. Put the data and results for this step in a table.

(d) Vary f above and below f0 and describe scope amplitude and phase changes. (1.0 point)

3. (a) Rearrange the circuit so the capacitor is grounded in common with the generator. Display vS on CH1 and vC on CH2. Draw the circuit diagram and show the scope connections. Following the procedure in step 2(b), determine the peak-to-peak and peak amplitudes of vC. Put data and results in a one-row table. Determine the phase shift of vC with respect to vS. Draw/print the scope display. Indicate on it where the horizontal shift measurement was taken, and calculate the phase shift (a leading phase angle is positive and a lagging one is negative).

(b) Repeat step 3(a) for the inductor voltage, vL. Rewire the circuit, follow the same procedure, and include the same sketches, data, and results.

(c) From what you have observed, predict what the voltage across the series combination of the capacitor and inductor (vL + vC) should be. Then check out your prediction by direct measurement and describe how you make this measurement. Were you correct? (2.0 points)

***Note: Since this is a two-session lab, this is a good break point for the first session.

- First session: Steps 1 thru 3 completed.

- Second session: Steps 4 thru 6 completed.

Note: In the following sections, you will set up the digital function generator and scope to display vR vs. frequency. To accomplish this display, the oscilloscope is set to a low-frequency time sweep and the function generator is set to a corresponding sweep of its vS sine frequency.

4. Rearrange the circuit as in step 2 to display vR on CH2 using 1 V/div. But use CH1 to display the Sync output from the function generator. You must also set the scope horizontal sweep to trigger on this CH1 signal.

Set the function generator to produce a Sweep output. Use its menus to set the sweep values as follows: Start Freq = 10 kHz; Stop Freq = 30 kHz; Sweep Time = 10 msec; Sweep Mode = Linear. You may need to experiment with these settings, and you may need instructor help.

Set the scope so that it displays the CH1 sync output waveform with start and stop sweep points covering 10 DIV. (Note that the number of divisions between successive start points may be more than 10 DIV.) It is suggested that you start with scope trigger settings of: Edge; CH1; Normal; and DC Coupling.

Note that the sync pulses from the generator are supplied at the beginning of each sweep, and so we are using them to lock the 10 kHz to 30 kHz sweep between the 10 scope divisions.

Leave CH1 on to give you markers at the beginning of each sweep, and now turn on CH2. If your trigger has been set correctly to view the sync signal, you should now be able also to observe the frequency response of your circuit with a properly set CH2. It is suggested that for both CH1 and CH2, Coupling be set to DC and BW Limit be set to On.

Describe and print/sketch what you see. (1.0 point)

Note: If desired, you can take a picture of the graphs using a cell phone camera and print them for your lab report. ALL printed figures must be clear, focused, and neatly labeled, as required in lab instructions. Non-black background is best for scope prints so you can write on them.

5. The upper half of the envelope seen in the scope display in step 4 should have the same shape as the magnitude response of the transfer function H(s) = VR(s)/VS(s). This response is called a bandpass response. In a bandpass response, the output signal, vR(t), is relatively large over a band of frequencies around the resonant frequency, f0, but relatively small outside that band. The horizontal axis in the sketch from step 4 can be calibrated as a frequency axis by identifying the start and stop points which are supposed to be 10 DIV apart.

(a) The center frequency for this circuit is the resonant frequency f0. Note this on your display.

(b) The half-power points are where the magnitude has decreased to 70.7% (which is the maximum magnitude divided by (2). Find those points on your display. These are the lower half-power point, f1, and the upper half-power point, f2.

(c) Sketch a plot of the magnitude response of the resistor voltage versus frequency based on the scope display from step 4. The horizontal axis should be labeled with the three frequency values just determined. The band of frequencies between the two half-power points is called the “half-power bandwidth.” Compute the half-power bandwidth, B = f2 - f1, and compare to the theoretical value B = R/(2(L) Hz, using the value of L from the LCR meter. (1.0 point)

6. This circuit, with the output taken as the resistor voltage, vR, can be used to select (or “pass”) frequency components of a signal near the resonant frequency and to reject (or “stop”) other frequencies. A measure of the "selectivity" of a circuit is given by a quantity called the quality factor, Q. The larger the value of Q, the better the frequency selectivity. (Note: Q is unit-less.)

In this circuit, the quality factor is

related to voltage magnitudes by [pic] or [pic], calculated at resonance;

and related to frequencies by [pic];

and related to component values by [pic].

Compare the values of these four equations for Q using data and results from step 3, from step 5, and from step 1, respectively. Show ALL of your calculations. (2.0 points)

REPORT: Keep a complete record of all data, results, observations, and answers to questions, written neatly and legibly on the unlined side of standard engineering paper. Attach the lab sheet as a cover.

Remember: DO NOT write terms like “very close” or “almost” for comparisons. Instead, calculate percent difference (include plus/minus signs), and state measured and theory values. (2.0 points)

You have two lab sessions for this experiment, and it is due at the beginning of the following lab session!

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