Presentation on theme: "CHAPTER 4 RESONANCE CIRCUITS"— Presentation transcript:
1 CHAPTER 4 RESONANCE CIRCUITS Tunku Muhammad Nizar Bin Tunku MansurPegawai Latihan VokasionalPusat Pengajian Kejuruteraan Sistem Elektrik
2 Content Series Resonance Parallel Resonance Important Parameters Resonance Frequency, oHalf-power frequencies, 1 and 2Bandwidth, Quality Factor, QApplication
3 IntroductionResonance 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.
5 At ResonanceAt 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 toThe current at resonance
7 Resonance FrequencyResonance frequency is the frequency where the condition of resonance occur.Also known as center frequency.Resonance frequency
8 Half-power FrequencyHalf-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.
12 Quality Factor (Q-Factor) The ratio of resonance frequency to the bandwidthThe “sharpness” of response curve could be measured by the quality factor, Q.
13 Q-Factor Vs BandwidthHigher value of Q, smaller the bandwidth. (Higher the selectivity)Lower value of Q larger the bandwidth. (Lower the selectivity)
14 High-QIt 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 isThe maximum power dissipated at resonance whereThus 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 powerHence, 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, ωoHalf power frequencies, ω1 and ω2Bandwidth, Amplitude of current at ωo, ω1 and ω2.
19 SolutionSince Q 10 , we can regard this as high-Q circuit. Hence
20 SolutionCurrent, I at = oCurrent, I at = 1 , 2
21 Practice Problem 14.7A series connected circuit has R=4Ω and L=25mH. CalculateValue 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 SolutionValue of C that will produce Q = 50Bandwidth
23 SolutionSince Q 10 , we can regard this as high-Q circuit. Hence
24 SolutionPower dissipated at = oPower dissipated at = 1 , 2
38 PASSIVE FILTERSA filter is a circuit that is designed to pass signals with desired frequencies and reject or attenuates othersA filter is a Passive Filters if it consists only passive elements which is R, L and C.Filters that used resonant circuitBandpass FilterBandstop Filter
39 BANDPASS FILTERA bandpass filter is designed to pass all frequencies withinω1 ωo ω2