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EEE 302 Electrical Networks II

EEE 302 Electrical Networks II. Dr. Keith E. Holbert Summer 2001. Resonant Circuits. Resonant frequency : the frequency at which the impedance of a series RLC circuit or the admittance of a parallel RLC circuit is purely real, i.e., the imaginary term is zero (ωL=1/ωC)

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EEE 302 Electrical Networks II

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  1. EEE 302Electrical Networks II Dr. Keith E. Holbert Summer 2001 Lecture 22

  2. Resonant Circuits • Resonant frequency: the frequency at which the impedance of a series RLC circuit or the admittance of a parallel RLC circuit is purely real, i.e., the imaginary term is zero (ωL=1/ωC) • For both series and parallel RLC circuits, the resonance frequency is • At resonance the voltage and current are in phase, (i.e., zero phase angle) and the power factor is unity Lecture 22

  3. Quality Factor (Q) • An energy analysis of a RLC circuit provides a basic definition of the quality factor (Q) that is used across engineering disciplines, specifically: • The quality factor is a measure of the sharpness of the resonance peak; the larger the Q value, the sharper the peak where BW=bandwidth Lecture 22

  4. Bandwidth (BW) • The bandwidth (BW) is the difference between the two half-power frequencies BW = ωHI – ωLO = 0 / Q • Hence, a high-Q circuit has a small bandwidth • Note that: 02 = ωLO ωHI • See Figs. 12.23 and 12.24 in textbook (p. 692 & 694) Lecture 22

  5. Series RLC Circuit • For a series RLC circuit the quality factor is Lecture 22

  6. Class Examples • Extension Exercise E12.8 • Extension Exercise E12.9 • Extension Exercise E12.10 • Extension Exercise E12.11 • Extension Exercise E12.12 Lecture 22

  7. Parallel RLC Circuit • For a parallel RLC circuit, the quality factor is Lecture 22

  8. Class Example • Extension Exercise E12.13 Lecture 22

  9. Scaling • Two methods of scaling: 1) Magnitude (or impedance) scaling multiplies the impedance by a scalar, KM • resonant frequency, bandwidth, quality factor are unaffected 2) Frequency scaling multiplies the frequency by a scalar, ω'=KFω • resonant frequency, bandwidth, quality factor are affected Lecture 22

  10. Magnitude Scaling • Magnitude scaling multiplies the impedance by a scalar, that is, Znew = Zold KM • Resistor:ZR’ = KMZR = KMR R’ = KM R • Inductor: ZL’ = KMZL = KMjL L’ = KM L • Capacitor:ZC’ = KMZC = KM / (jC) C’ = C / KM Lecture 22

  11. Frequency Scaling • Frequency scaling multiplies the frequency by a scalar, that is, ωnew = ωold KF but Znew=Zold • Resistor:R” = ZR = R R” = R • Inductor: j(KF)L = ZL = jL L” = L / KF • Capacitor: 1 / [j (KF) C] = ZC = 1 / (jC) C” = C / KF Lecture 22

  12. Class Example • Extension Exercise E12.15 Lecture 22

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