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A tank circuit uses a 0.09 uH inductor and a 0.4-uF capacitor. The resistance of the...
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The quality factor Q of a component is by DEFINITION the rapport between the power stored and the power loss in that particular component at resonance. Higher the quality factor is, higher the amplitude of oscillations are.
Q = Energy Stored/Energy Loss = Power Stored/Power Loss =Ps/Pl
at the resonant frequency of
`F_r = 1/(2*pi*sqrt(L*C)) =1/(2*pi*sqrt(9*10^(-8)*4*10^(-7)))=`
If we write the quality factor as
`Q = F_r/(Delta(F))`
we can find the bandwidth of the circuit as
`Delta(F) = F_r/Q`
For a SERIES circuit (which is the case here because the inductor resistance is always considered in series with the inductance) the current I through all components is the same and the stored an loss power are
`Ps = I^2*X(L) = I^2*omega*L`
`Pl = I^2*R`
`Q = (omega_r*L)/R = (2*pi*Fr*L)/R = (2*pi*838820*9*10^(-8))/0.3= 1.5811`
The bandwidth of the circuit is
`Delta(F) = F_r/Q =838820/1.5811=530516 Hz = 530.5 KHz`
For the circuit to have a quality factor Q =150 the values of the components need to be
L =0.09 miliH (not microH)
C =0.4 microF
but in this case the bandwidth will be `Delta(F) = 53 Hz`
Posted by valentin68 on September 8, 2013 at 6:36 AM (Answer #1)
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