1422-1 RESONANCE AND FILTERS
Experiment 1, Resonant
Frequency and Circuit
Impedance
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OBJECTIVES
1.
2.
To verify experimentally our theoretical
predictions concerning the resonant
frequency of a series circuit
To show experimentally, that at series
resonance, the current in a circuit is
maximum and the impedance is at
minimum
INTRODUCTION
 The
impedance of any series RLC circuit
depends on the signal frequency. The
following formula illustrates the formula
for the impedance at any given
frequency.
 At
resonance XT is equal to zero. This is
because XC and XL cancel each other out.
 XC
will decrease with frequency
 XL will increase with Frequency
 There is one frequency where XL = XC

It is at this frequency where XT = 0, which is
called the resonant frequency (f0) and the
circuit condition is called resonance
 At
resonance (XT = 0), and the previous
equation for total impedance can be
rewritten as Z0 = R. XT is sometimes
written as X.
Z0 is the total impedance at resonance
The subscript “O” is often used to designate
the resonate circuit condition
 Use
the formula below to calculate
Resonant Frequency
SEVERAL IMPORTANT FACTS
 When
the signal frequency is below
resonant frequency (fO), the circuit is
capacitive (that is XC is greater than XL).
 When the signal frequency is above
resonant frequency (fO), the circuit is
inductive (that is XL is greater than XC).
 At resonance, the circuit is resistive
(XC = XL).
 The
greater the LC product, the lower the
resonant frequency of the circuit
A practical approach to finding the fO of a
series RLC circuit is outlined in the
following steps
1. Apply a signal voltage to the circuit
2. Vary the signal frequency
While the frequency is varied, measure
the voltage drop across the resistance
3.
a.
When the voltage drop reaches its maximum
value, the circuit is at resonance.
The signal frequency that produces the maximum
or peak voltage drop is the resonant
frequency
SEVERAL PRECAUTIONS MUST BE TAKEN
 The
output voltage of the signal source
must be kept fairly constant
 The voltmeter should have a high
sensitivity rating, (that is a high ohms/volt
rating)
 Take your time!
 Make
sure the resistance scale is zeroed,
on the Analog Multimeter, before making
resistance measurements
 Use
the voltage doubler circuit when making
voltage measurements

The voltage doubler circuit may not be
necessary when using a Digital Meter
PARTS REQUIRED
1
1
1
1
1
107mH ferrite core inductor
0.01µF Mylar capacitor (103)
0.033µF Mylar capacitor (333)
2700Ω ½ W resistor (red-violet-red-gold)
1000µF Electrolytic capacitor
PROCEDURE
 Caution:
Take your time! When using the
Analog Meter: Make sure the resistance
scale is zeroed before making resistance
measurements; and use the AC voltage
doubler circuit when making voltage
measurements. The voltage doubler is
optional when using a Digital Meter
PROCEDURE
1.
2.
Measure and record the value of the
2700W resistor
Mark your frequency generator knob as
shown in the series RLC response
characteristics graph, which is shown on
the next slide
SERIES RLC RESPONSE CHARACTERISTICS GRAPH
3.
Construct the circuit using the following
schematic diagram
VOLTAGE DOUBLER SCHEMATIC CKT
VOLTAGE DOUBLER PICTORIAL DIAGRAM
1422, EXP 1, SERIES RLC CKT PICTORIAL
Make sure to use the correct components!
b. L = 107mH, C = 0.01µF and R = 2700Ω
Turn on the trainer, set the generator to the
X10 range and turn the FREQ knob to its
maximum counterclockwise (CCW) position
Set your meter on the 10V scale and connect
it across the 2700Ω resistor
a.
4.
5.
a.
b.
When using an Analog meter, connect a 1000µF
capacitor in series with the sine-wave frequency
generator output to block the d-c, as seen in the
schematic and pictorial diagram.
The majority of digital meters have a capacitor
built in the meter to accomplish this
Your results may vary compared to our results,
depending on your trainers’ signal generator.
Our results varied by meter used, trainer, and
the rated value of the components, so do not
be overly concerned if this occurs.
DATA TABLE FOR EXPERIMENT 1
Rotate the FREQ knob slowly until the
voltage drop (ER) across the resistor
reaches a maximum value. Using a soft
lead pencil, mark the position on the
frequency knob on the frequency scale.
6.
a.
b.
This mark indicates the resonant frequency
of the circuit
Estimate the frequency and record it in the
data table
c.
d.
7.
Also record the values of ER and the applied
voltage E at the resonant condition
Then turn off the trainer
Use the fO equation and calculate the
resonant frequency where L = .0107 H
and C = 0.01 x 10-6 F and record the
value in the data table
8.
Compare the estimated resonant
frequency to the calculated resonant
frequency. Remember: The frequency
calibration of the generator is not exact.
If your answer is close, you have
demonstrated the ability to predict the
resonant frequency
Using the calibration marks of the
generator as a guide, set the FREQ knob
indicator to the first calibration mark.
9.
a.
b.
c.
Note: the knob should be rotated to the
fullest CCW position
Record the voltage drop across the resistor
(ER) and applied voltage E in the data table
Continue this procedure at each calibration
mark and then shut off the trainer
10.
a.
b.
Plot the readings, using the Response
Characteristics graph of a Series RLC
circuit
Plot the voltage drop across the resistor (ER)
for each frequency mark obtained in step 9
Also plot the value of the voltage drop (ER)
obtained at the resonant frequency in step 6.
RESPONSE CHARACTERISTICS GRAPH
11.
a.
b.
c.
Now determine the impedance at each
of the frequency calibration marks,
which is a two step process.
Calculate the current flowing in the circuit at each
calibration mark by applying Ohm’s Law, I = E/R.
Then determine the impedance (Z = E/I) at each
calibration mark.
Record these values in the following table
DATA TABLE FOR STEP 11
12. Erase
the pencil marks on your trainer
13. Repeat steps 2 through 5, but replace the
capacitor with a 0.033µF capacitor
14. Calculate the resonant frequency and
record the new resonant frequency in step
1
15. Calculate the LC product; multiply the
value of L by the value of C for steps 6
and 12 and record the data in table 1
16.
Record the value of fO obtained in steps
6 and 13, as well as the LC product in
the following table. Note the fO
decreases as the LC product increases
STEP
6
13
LC Product
Resonant
Frequency
RESULTS
 The
following data shows it is possible to
predict the resonant frequency of a series
RLC circuit, and then to confirm the
theoretical results with experimental data
 In the 1st circuit we used the following
components (L = 0.107H and C = 1 x 10-8 F)
 We
predicted fO = 4868 Hz which compared
favorably to the experimental estimate of
4600 Hz
 In
the 2nd circuit we used the following
components (L = 0.107H and C = 3.3 x
10-8 F)
 We
predicted fO = 2679 Hz which compared
favorably to the experimental estimate of
2400 Hz
 The
data table for step 11 illustrates that
the impedance of the circuit will have its
minimum value at the resonant frequency
 The data table for steps 15 and 16
illustrates that the LC product increases
as the resonant frequency decreases.
RESULTS - DATA TABLE FOR EXPERIMENT 1
DATA TABLE FOR STEP 11
LC PRODUCT AND fO TABLE RESULTS
STEP
LC Product
Resonant
Frequency
6
1.07 x 10-9
4868 Hz
13
3.53 x 10-9
2679 Hz
FINAL DISCUSSION
 The
problem of determining resonant
frequency can be determined in two ways
1.
Use the resonant frequency formula
2.

We also used the practical approach when
the circuit was constructed. We made use
of the principle that the voltage drop
across the resistor will reach its maximum
value only at resonance
We were able to see both methods were
affective as demonstrated in the
results. An exact reading of the
practical fO is not possible due to the
imperfect calibration of the signal
generator
RESPONSE RESULTS GRAPH OF SERIES RLC CKT
 We
were also able to see another
characteristic of the Series RLC circuit in
the Response Results Graph of Series
RLC Circuit
 As
the frequency was increased, we were
able to see the voltage drop across the
resistor increase reaching a maximum value
at resonance
 At
the same time, we were able to view the
impedance of the circuit decrease to a minimum
value at resonance and is equal to the resistance of
the circuit.
VOLTAGE DOUBLER CONVERSION GRAPH
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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