1. The experiment of the series
resonant circuit
s1210196 Yoichi Saito

2. Abstract
Based on the basic knowledge, I’ll
understand the series resonant
circuit with an inductor, a capacitor
and a resister, and learn it by
experimenting.

3. What is resonance?
Resonance is to transmit energy among
three elements: inductor, capacitor,
resister.

4. Circuit diagram

5. Explanation of the words
• OSC: The device that receives the
electrical signals from the circuit.
• FG: The device that outputs the
electrical signals into the circuit.
• V0: The whole voltage in the circuit.
• VR: The voltage of the resistance.

6. The rate of the expanding the voltage
• This parameter is expressed as Q.
• The value of Q can be calculated by the
formula as follows:
• Q = f0/(2Δf)
• f0 is the frequency.
• Δf is the amount of change of the
frequency.

7. The measurement of the series
resonant circuit:
what should I measure?
Purpose

8. Measurement
1. Make sure the value of L and C.
2. Calculate the resonance frequency.
3. Use two resistances that the value of Q
is 10 and 100.
4. Calculate the values of 2Δf and Q by
using the L, C and R.
Next>>

9. Measurement
5. Using the FG and OSC, make the table
and calculate the value of 2Δf and Q.

10. Theoretical values(Q = 100)
• R = 10Ω
• C = 10000pF
• L = 10mH
• f0 = 1/2π√LC = 16kHz
• 2Δf = 0.08kHz

11. Theoretical values(Q = 10)
• R = 100Ω
• C = 10000pF
• L = 10mH
• f0 = 1/2π√LC = 16kHz
• 2Δf = 0.8kHz

12. Result Q = 100
f0 Voltage1 Voltage2 phase V1*5/V2 normalized value
15.7 2.44 0.6 0° 1.23 1
16 3.08 0.54 45°delay 0.88 0.72
16.5 4.12 0.4 65°delay 0.49 0.4
17 4.64 0.3 70°delay 0.32 0.26
17.5 4.84 0.25 78°delay 0.29 0.24
18 5 0.2 78°delay 0.2 0.16
15.5 2.64 0.56 26°lead 1.06 0.86
15 4.04 0.42 66°lead 0.52 0.42
14.5 4.64 0.3 79°lead 0.32 0.26
14 4.92 0.24 87°lead 0.24 0.2

13. Result Q = 10
f0 Voltage1 Voltage2 phase V1*5/V2 normalized value
15.7 3.92 2.96 0° 3.78 1
16 4 2.96 15°delay 3.7 0.98
16.5 4.24 2.64 34°delay 3.11 0.82
17 4.56 2.32 45°delay 2.54 0.67
17.5 4.8 2 50°delay 2.88 0.55
18 4.88 1.76 60°delay 1.8 0.48
15.5 3.92 2.96 14°lead 3.78 1
15 4.16 2.84 40°lead 3.17 0.84
14.5 4.64 2.24 55°lead 2.41 0.64
14 4.88 1.84 65°lead 1.89 0.5

14. Result
• Q = 100 (Theoretical value)
・ Q = 26.2 (Measured value)
・2Δf = 0.6kHz (Measured value)
• Q = 10 (Theoretical value)
・ Q = 7.9 (Measured value)
・2Δf = 2kHz (Measured value)

15. Consideration and Conclusion
• There is a difference between the theoretical
value and measured value of f0 and Q because
the parameter of L and C has an error(About
f0, slide 11 & 12).
• The value of Q and is calculated by the
formula as follows:
Q = √LC/CR
Next>>

16. Consideration and Conclusion
In fact, an inductor has resistance(r).
Therefore, exact formula is as follows:
Q = L/(R + r)√LC
It is clear that the theoretical value and
the measured value about f0 and Q.