1422-1 RESONANCE AND FILTERS
Experiment 4, Resonant
Frequency and Impedance of a
Parallel Circuit,
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OBJECTIVES:
1.
2.
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).
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 (ZO) 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, IL has the same magnitude
as XC, and the fO (resonant frequency) is
still as shown below:
 The
impedance of a parallel LC circuit at
resonance (ZO) 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 fO in a working circuit is dependent
upon the impedance of a parallel circuit at
the resonant frequency.
 ZO is maximum in the previous circuit, so
IO 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
Construct the circuit shown on the
following slide. (previous circuit shown)
The component values are as follows:
1.
a)
b)
c)
C = 0.01 µF
L = 107 mH
R1 = 100 kΩ (use terminals 1 and 3 of the
100 k potentiometer on the trainer)
Turn the trainer on.
2.
a)
b)
Set the range switch to “x 10”
Set FREQ knob to maximum CCW position
Set your meter on the 10 VAC scale, and
connect it across R1
Rotate the FREQ knob until a dip or null
is shown on the multimeter.
3.
4.
a)
b)
Be very careful to get the exact null point!
A little variation will cause a large difference
in your readings
c)
d)
e)
5.
Mark this point with a soft lead pencil for future
reference. (This is the fO of the circuit)
Estimate the value of the resonant frequency, and
record the data in the Experiment 4 data table
Shut off the trainer
Use the following equation to calculate fO
a)
b)
Record this value in the data table for
experiment 4
Compare the theoretical value for fO with
the experimental value of fO, 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.)
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 R1.
6.
Therefore, if the voltage drop across points
“A” and “B” is the same as the voltage drop
across R1 , then the resistance of R1 is the
same as the impedance across terminals
“A” and “B”.
Turn on the trainer
7.
a)
b)
c)
Make sure the FREQ knob hasn’t moved
from the resonant frequency calibration
point in step 4.
The purpose of this procedure is to adjust
the variable resistor (potentiometer) so that
the voltage drop across the resistor (ER) and
the voltage drop across terminals A and B
are equal
Record their value in the Exp. 4, data table .
Shut off the trainer.
8.
a)
b)
9.
Disconnect the variable resistor, and
measure the resistance between terminals 1
and 2.
Record the value in the Exp. 4, data table
Repeat steps 7 & 8, except set the FREQ
knob to the nearest frequency calibration
to the left of the resonant frequency
Continued
9.
a)
8.
The data will provide the impedance value at
a frequency that is less than the resonant
frequency
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.
Record the value in the Exp. 4, data table
12. Calculate the values of XL 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
a)
13.
Calculate the impedance of the circuit using
either of the below equations.
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.
a)
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, ZO =
65,400 W; and at some frequency greater
than resonance, Z = 1640 W.
 Initially,
when one compares the calculated
ZO (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, ZO =
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.
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