Electrical Engineering ⇒ Topic : Bandwidth of a Series Resonant Circuit

David
 
Bandwidth of a Series Resonant Circuit Consider the current versus frequency graph of a RLC series circuit shown in Fig. (a). It is clear from the graph that the current reaches maximum value (= I_{r}) 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 f_{1} below fr and frequency f_{2 }above fr such that at f_{1} and f_{2}, the circuit current = 0.707 I_{r} where Ir is the circuit current at resonance as shown in Fig. (a) Then,
figure (a) Bandwidth of the series resonant circuit is Bandwidth, BW = Δf = f_{2} f_{1} 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., I_{r}). Note that f_{1} and f_{2} are the limiting frequencies at which current is exactly equal to 70.7% of the maximum value. The frequency f_{1} (i.e., on the lower side) is called the lower cut off frequency and the frequency f_{2} (i.e., on the higher side) is called the upper cut off frequency. The frequencies f_{1}and f_{2} are also called halfpower frequencies (or halfpower points) or 3dB frequencies. (i) The frequencies f_{1 }and f_{2} are called halfpower frequencies as explained hereafter. At series resonance, the circuit current is maximum (= I_{r}) and circuit impedance is R. Also power delivered at resonance is maximum (P_{max}) and is given by ;  
 
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