Transcription of Frequency response: Resonance, Bandwidth, Q factor
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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.
The bandwidth is the difference between the half power frequencies Bandwidth =B =ω2−ω1 (1.11) By multiplying Equation (1.9) with Equation (1.10) we can show that ω0 is the geometric mean of ω1 and ω2. ω0= ωω12 (1.12) As we see from the plot on Figure 2 the bandwidth increases with increasing R. Equivalently the sharpness of the resonance increases with decreasing R.
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