Electrical Engineering ⇒ Topic : Bandwidth of Parallel Resonant Circuit

Seema
 
Bandwidth of Parallel Resonant Circuit Just as the bandwidth of a series resonant circuit is defined from currentfrequency curve, similarly the bandwidth of a parallel resonant circuit is defined from impedancefrequency curve as shown in Fig.(a) The bandwidth of a parallel resonant circuit is defined as the range of frequencies over which the circuit impedance is equal to or greater than 70.7% of maximum circuit impedance (i.e. Z_{r}, the impedance at resonance). The circuit impedance is maximum (i.e. Z_{r}) at fr while halfpower points (i.e. f_{1 }and f_{2}) occur at 0.707 Z_{r}. Using the same procedure as was used for series resonant circuit, it can be shown that
figure (a) The points on the curve in Fig. (a) where the upper and lower cutoff frequencies intersect the curve (at 70.7% of Z_{r}) are called the halfpower points. Thus the bandwidth (BW) of a parallel resonant circuit is often refened to as the band of frequencies between the halfpoints on the impedancefrequency curve. At halfpower frequencies (i.e. f_{1} and f_{2}), the power dissipated in the circuit is onehalf of that dissipated at resonant frequency (J,). A signal at a frequency outside the bandwidth is transmitted with less than 1/2 the output power of a signal of similar strength at the resonant frequency. Note. The power at cut off frequencies is half that at the resonant frequency and are known as half power frequencies. They are also called 3 dB frequencies because power decreases by 1/2 and in decibels it is  
 
Seema
 
Bandwidth of Parallel Resonant Circuit Just as the bandwidth of a series resonant circuit is defined from currentfrequency curve, similarly the bandwidth of a parallel resonant circuit is defined from impedancefrequency curve as shown in Fig.(a) The bandwidth of a parallel resonant circuit is defined as the range of frequencies over which the circuit impedance is equal to or greater than 70.7% of maximum circuit impedance (i.e. Z_{r}, the impedance at resonance). The circuit impedance is maximum (i.e. Z_{r}) at fr while halfpower points (i.e. f_{1 }and f_{2}) occur at 0.707 Z_{r}. Using the same procedure as was used for series resonant circuit, it can be shown that
figure (a) The points on the curve in Fig. (a) where the upper and lower cutoff frequencies intersect the curve (at 70.7% of Z_{r}) are called the halfpower points. Thus the bandwidth (BW) of a parallel resonant circuit is often refened to as the band of frequencies between the halfpoints on the impedancefrequency curve. At halfpower frequencies (i.e. f_{1} and f_{2}), the power dissipated in the circuit is onehalf of that dissipated at resonant frequency (J,). A signal at a frequency outside the bandwidth is transmitted with less than 1/2 the output power of a signal of similar strength at the resonant frequency. Note. The power at cut off frequencies is half that at the resonant frequency and are known as half power frequencies. They are also called 3 dB frequencies because power decreases by 1/2 and in decibels it is  
 
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