Electrical Engineering ⇒ Topic : Bandwidth of a Series Resonant Circuit
Bandwidth of a Series Resonant Circuit
Consider the current versus frequency graph of a R-L-C series circuit shown in Fig. (a). It is clear from the graph that the current reaches maximum value (= Ir) at resonance. It is also clear that at frequencies close to resonance, the current level is only a little below its maximum value. Thus the resonant circuit is said to select a band (i.e., range) of frequencies rather than just one frequency fr. We *arbitrarily select frequency f1 below fr and frequency f2 above fr such that at f1 and f2, the circuit current = 0.707 Ir where Ir is the circuit current at resonance as shown in Fig. (a) Then,
Bandwidth of the series resonant circuit is
Bandwidth, BW = Δf = f2 -f1
Hence bandwidth of a series resonant circuit is the range of frequencies for which the circuit current is equal to or **greater than 70.7% of the circuit current at resonance (i.e., Ir).
Note that f1 and f2 are the limiting frequencies at which current is exactly equal to 70.7% of the maximum value. The frequency f1 (i.e., on the lower side) is called the lower cut off frequency and the frequency f2 (i.e., on the higher side) is called the upper cut off frequency. The frequencies f1and f2 are also called half-power frequencies (or half-power points) or -3dB frequencies.
(i) The frequencies f1 and f2 are called half-power frequencies as explained hereafter. At series resonance, the circuit current is maximum (= Ir) and circuit impedance is R. Also power delivered at resonance is maximum (Pmax) and is given by ;
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