RESONANCE AND FILTERS

1422-1 RESONANCE AND FILTERS Experiment 4, Resonant Frequency and Impedance of a Parallel Circuit, For more courses visit www.cie-wc.edu

OBJECTIVES: 1. To demonstrate the resonant frequency of a parallel LC circuit can be determined either experimentally (from a working circuit) or theoretically (using circuit component values). 2. To verify by experimental means that the impedance of a parallel resonant circuit is maximum at resonance.

3. To show the impedance of a parallel LC circuit at resonance (Z O ) is much greater than either the inductive or capacitance reactance of the branch circuits,

INTRODUCTION Parallel Resonance is not as straight forward as series resonance. When the Q is below 10, the circuit resistance makes most circuit calculation inaccurate. When the Q is above 10, the formulas in this experiment are reasonably accurate.

At resonance, I L has the same magnitude as X C, and the f O (resonant frequency) is still as shown below:

The impedance of a parallel L C circuit at resonance (Z O ) is much greater than the reactance of either branch circuit. Below is the formulas for the impedance at resonance:

LC PARALLEL RESONANT PRACTICE CKT

LC PARALLEL RESONANT PRACTICE CKT MATH

The practical solution in predicting or finding f O in a working circuit is dependent upon the impedance of a parallel circuit at the resonant frequency. Z O is maximum in the previous circuit, so I O will be at its minimum level The following circuit is a good test circuit for determining resonant frequency

TEST CIRCUIT / RESONANT FREQUENCY

CIRCUIT / RESONANT FREQUENCY PICTORIAL

PARTS REQUIRED 1 107 mh ferrite coil 1 0.01 µf disc capacitor (103) 1 100 kω potentiometer (use the one on the trainer) 1 1000 µf electrolytic capacitor

PROCEDURE Note: During this experiment, you will be asked to make both resistance and voltage measurements. Take your time in making the measurements Remember to zero your ohmmeter before taking the resistance measurements

1. Construct the circuit shown on the following slide. (previous circuit shown) The component values are as follows: a) C = 0.01 µf b) L = 107 mh c) R 1 = 100 kω (use terminals 1 and 3 of the 100 k potentiometer on the trainer) 2. Turn the trainer on. a) Set the range switch to x 10 b) Set FREQ knob to maximum CCW position

3. Set your meter on the 10 VAC scale, and connect it across R 1 4. Rotate the FREQ knob until a dip or null is shown on the multimeter. a) Be very careful to get the exact null point! b) A little variation will cause a large difference in your readings

c) Mark this point with a soft lead pencil for future reference. (This is the f O of the circuit) d) Estimate the value of the resonant frequency, and record the data in the Experiment 4 data table e) Shut off the trainer 5. Use the following equation to calculate f O

a) Record this value in the data table for experiment 4 b) Compare the theoretical value for f O with the experimental value of f O, obtained in step 4. (The values should be close.) (Steps 6 through 12 will provide the data to determine the impedance of the circuit at resonance.)

6. Use the previous circuit except modify it by moving the wire from terminal 3 of the 100 kω potentiometer to pin 2 of 100 kω the potentiometer NOTE: Remember if the voltage drop is the same across two components in a series circuit, the impedances will be equal. Also note the components connected between points A and B are in series with R 1.

Therefore, if the voltage drop across points A and B is the same as the voltage drop across R 1, then the resistance of R 1 is the same as the impedance across terminals A and B.

7. Turn on the trainer a) Make sure the FREQ knob hasn t moved from the resonant frequency calibration point in step 4. b) The purpose of this procedure is to adjust the variable resistor (potentiometer) so that the voltage drop across the resistor (E R ) and the voltage drop across terminals A and B are equal c) Record their value in the Exp. 4, data table.

8. Shut off the trainer. a) Disconnect the variable resistor, and measure the resistance between terminals 1 and 2. b) Record the value in the Exp. 4, data table 9. Repeat steps 7 & 8, except set the FREQ knob to the nearest frequency calibration to the left of the resonant frequency

9. Continued a) The data will provide the impedance value at a frequency that is less than the resonant frequency 8. Repeat steps 7 & 8, except set the FREQ knob to the nearest frequency calibration to the right of the resonant frequency a) The data will provide the impedance value at a frequency that is greater than the resonant frequency

11. Zero the ohmmeter on the x 1 scale. Disconnect the ferrite coil and measure its resistance. a) Record the value in the Exp. 4, data table 12. Calculate the values of X L and Q of the coil using coil 107mH at the resonant frequency of 4867 Hz. a) Record the value in the Exp. 4, data table

13. Calculate the impedance of the circuit using either of the below equations. a) Record the value in the Exp. 4, data table NOTE: Under the best of laboratory conditions, the impedance at resonance is difficult to measure. A realistic ratio between the calculated impedance and the impedance measured above is approximately 10:1. In other words, if the calculated impedance is 500,000W, then a measured impedance of 50,000W is acceptable.

14. Compare the data obtained in step 8 (impedance at resonant frequency) to the calculated impedance value. Were your results as expected? If not, why not?

CIE RESULTS The data obtained when CIE performed this experiment is listed in the Experiment 4 data table. If you coil resistance is not 120W, your data may be considerably different. Note: The estimated resonant frequency of 5000 Hz compares favorably with the theoretical value of 4867 Hz.

1422-1, EXPERIMENT 4, DATA TABLE

The impedance of the circuit reaches the maximum at resonance. The data clearly shows that at some frequency below resonance, Z= 6740 W; at resonance, Z O = 65,400 W; and at some frequency greater than resonance, Z = 1640 W.

Initially, when one compares the calculated Z O (89 KW) to the measured value of 65.4 KW, it would seem the results are unacceptable. However, when circuit conditions, test equipment, and technique are taken into consideration, the calculated value is quite good.

FINAL DISCUSSION Using laboratory techniques, we were able to predict the resonant frequency of a parallel circuit to within 3% of the theoretical value. This prediction was based on the circuit operation. (Z of the circuit is maximum at resonance.)

The rise of impedance values to a maximum level was verified by the following data: at some frequency below resonance, Z= 6740 W; at resonance, Z O = 65,400 W; and at some frequency greater than resonance, Z = 1640 W

The major discrepancy is the comparison between the calculated impedance and the measured value. This is where certain circuit conditions can sharply reduce the actual circuit impedance. These conditions deal with the value of Q, and with the circuit loading of the meter.

QUESTIONS?

RESOURCES Rubenstein, C.F. (2001, January). Resonance and Filters. Lesson 1422-1: Experiment 1, Resonant Frequency and Circuit Impedance. Cleveland: Cleveland Institute of Electronics.