1. CHAPTER 4 RESONANCE CIRCUITS
Tunku Muhammad Nizar Bin Tunku Mansur
Pegawai Latihan Vokasional
Pusat Pengajian Kejuruteraan Sistem Elektrik

2. Content Series Resonance Parallel Resonance Important Parameters
Resonance Frequency, o
Half-power frequencies, 1 and 2
Bandwidth, 
Quality Factor, Q
Application

3. Introduction
Resonance is a condition in an RLC circuit in which the capacitive and reactive reactance are equal in magnitude, thereby resulting in a purely resistive impedance.
Resonance circuits are useful for constructing filters and used in many application.

4. Series Resonance Circuit

5. At Resonance
At resonance, the impedance consists only resistive component R.
The value of current will be maximum since the total impedance is minimum.
The voltage and current are in phase.
Maximum power occurs at resonance since the power factor is unity.

6. Series Resonance Total impedance of series RLC Circuit is At resonance
The impedance now reduce to
The current at resonance

7. Resonance Frequency
Resonance frequency is the frequency where the condition of resonance occur.
Also known as center frequency.
Resonance frequency

8. Half-power Frequency
Half-power frequencies is the frequency when the magnitude of the output voltage or current is decrease by the factor of 1 / 2 from its maximum value.
Also known as cutoff frequencies.

9. Bandwidth, 
Bandwidth,  is define as the difference between the two half power frequencies.
The width of the response curve is determine by the bandwidth.

10. Current Response Curve

11. Voltage Response Curve

12. Quality Factor (Q-Factor)
The ratio of resonance frequency to the bandwidth
The “sharpness” of response curve could be measured by the quality factor, Q.

13. Q-Factor Vs Bandwidth
Higher value of Q, smaller the bandwidth. (Higher the selectivity)
Lower value of Q larger the bandwidth. (Lower the selectivity)

14. High-Q
It is to be a high-Q circuit when its quality factor is equal or greater than 10.
For a high-Q circuit (Q  10), the half-power frequencies are, for all practical purposes, symmetrical around the resonant frequency and can be approximated as

15. Maximum Power Dissipated
The average power dissipated by the RLC circuit is
The maximum power dissipated at resonance where
Thus maximum power dissipated is

16. Power Dissipated at 1 and 2
At certain frequencies, where ω = ω1 and ω2, the dissipated power is half of maximum power
Hence, ω1 and ω2 are called half-power frequencies.

17. Example 14.7 If R=2Ω, L=1mH and C=0.4 F, calculate
Resonant frequency, ωo
Half power frequencies, ω1 and ω2
Bandwidth, 
Amplitude of current at ωo, ω1 and ω2.

18. Solution
Resonant frequency
Bandwidth
Quality Factor

19. Solution
Since Q 10 , we can regard this as high-Q circuit. Hence

20. Solution
Current, I at  = o
Current, I at  = 1 , 2

21. Practice Problem 14.7
A series connected circuit has R=4Ω and L=25mH. Calculate
Value of C that will produce a quality factor of 50.
Find 1 , 2 and .
Determine average power dissipated at
 = o , 1 and 2. Take Vm = 100V

22. Solution
Value of C that will produce Q = 50
Bandwidth

23. Solution
Since Q 10 , we can regard this as high-Q circuit. Hence

24. Solution
Power dissipated at  = o
Power dissipated at  = 1 , 2

25. Parallel Resonance

26. Parallel Resonance
The total admittance
Resonance occur when

27. At Resonance At resonance, the impedance consists only conductance G.
The value of current will be minimum since the total admittance is minimum.
The voltage and current are in phase.

28. Parameters in Parallel Circuit
Parallel resonant circuit has same parameters as the series resonant circuit.
Resonance frequency
Half-power frequencies

29. Parameters in Parallel Circuit
Bandwidth
Quality Factor

30. Example 14.8 If R=8kΩ, L=0.2mH and C=8F, calculateωo
Q and 
ω1 and ω2
Power dissipated at ωo, ω1 and ω2.

31. Solution
Resonant frequency
Bandwidth
Quality Factor

32. Solution
Since Q 10 , we can regard this as high-Q circuit. Hence

33. Solution
Power dissipated at  = o
Power dissipated at  = 1 , 2

34. Practice Problem 14.8
A parallel resonant circuit has R=100kΩ, L=25mH and C=5nF. Calculate o
1 and 2 Q 

35. Solution
Resonant frequency
Bandwidth
Quality Factor

36. Solution
Since Q 10 , we can regard this as high-Q circuit. Hence

37. APPLICATION

38. PASSIVE FILTERS
A filter is a circuit that is designed to pass signals with desired frequencies and reject or attenuates others
A filter is a Passive Filters if it consists only passive elements which is R, L and C.
Filters that used resonant circuit
Bandpass Filter
Bandstop Filter

39. BANDPASS FILTER
A bandpass filter is designed to pass all frequencies within
ω1  ωo  ω2

40. BANDPASS FILTER
SERIES RLC CIRCUIT

41. BANDPASS FILTER
PARALLEL RLC CIRCUIT

42. BANDSTOP FILTER
A bandstop or bandreject filter is designed to stop or reject all frequencies within
ω1  ωo  ω2

43. BANDSTOP FILTER
SERIES RLC CIRCUIT

44. BANDSTOP FILTER
PARALLEL RLC CIRCUIT

45. EXERCISE

46. Problem
A series bandpass filter has f1 and f2 equal to 10kHz and 11 kHz. Determine
fo and Q
R and L if C = 1nF
Im if Vin = 24V
Value of maximum power dissipated