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Frequency response: Resonance, Bandwidth, Q factor

Frequency response: Resonance, Bandwidth, Q factor Resonance. Let s continue the exploration of the Frequency response of RLC circuits by investigating the series RLC circuit shown on Figure 1. RRCVR+-VsI Figure 1 The magnitude of the transfer function when the output is taken across the resistor is ()()222()1 VRRCHVsLCRC = + ( ) At the Frequency for which the term 21LC 0 = the magnitude becomes ()1H = ( ) The dependence of ()H on Frequency is shown on Figure 2 for which L=47mH and C=47 F and for various values of R. Spring 2006, Chaniotakis and Cory 1 Figure 2. The Frequency 01LC = is called the resonance Frequency of the RLC network.

The frequency 0 1 LC ω= is called the resonance frequency of the RLC network. The impedance seen by the source Vs is 1 1 ZRjL jC RjL C ω ω ω ω =++ ⎛⎞ =+⎜⎟− ⎝⎠ (1.3) Which at 0 1 LC ωω== becomes equal toR. • Therefore at the resonant frequency the impedance seen by the source is purely resistive.

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