Bandwidth and Q factorAt resonance, the voltages across the capacitor and the pure inductance cancel out, so the series impedance takes its minimum value: Zo = R. Thus, if we keep the voltage constant, the current is a maximum at resonance. The current goes to zero at low frequency, because XC becomes infinite (the capacitor is open circuit for DC). The current also goes to zero at high frequency because XL increases with ω (the inductor opposes rapid changes in the current). The graph shows I(ω) for circuit with a large resistor (lower curve) and for one with a small resistor (upper curve). A circuit with low R, for a given L and C, has a sharp resonance. Increasing the resistance makes the resonance less sharp. The former circuit is more selective: it produces high currents only for a narrow bandwidth, ie a small range of ω or f. The circuit with higher R responds to a wider range of frequencies and so has a larger bandwidth. The bandwidth Δω (indicated by the horiztontal bars on the curves) is defined as the difference between the two frequencies ω+ and ω- at which the circuit converts power at half the maximum rate.Now the electrical power converted to heat in this circuit is I2R, so the maximum power is converted at resonance, ω = ωo. The circuit converts power at half this rate when the current is Io/√2. The Q value is defined as the ratio
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