Band Width and Q-Factor:
Angular frequency variation of power in LCR series circuit.
`P = P_(max) sqrt(R^2/[R^2+(L omega - 1/(C omega))^2])`
Graph between `P & omega` as shown in the figure.
`omega_1 = +R/(2L) + (omega_r^2 +R^2/(4L^2))^(1/2)` and `omega_2 = - R/(2L) + ((omega_r^2)+ R^2/(4L^2))^(1/2)`
Now, `omega_1 -omega_2 = R/L`
or `(omega_r +Delta omega) - (omega_r -Delta omega) =R/L`
The frequency interval between half maximum power points is known as band width.
The ratio of resonance frequency and band width is known as quality factor (Q).
`Q = omega_r/(2 Delta omega) = (omega_r L)/R`
Q factor is a measure of the sharpness of resonance. Resonance will be sharp if the value of bandwidth
`(2 Delta omega)` is small. This is of course possible only when the power-frequency curve fa ll steeply around
`omega = omega_r`
`P = P_(max) sqrt(R^2/[R^2+(L omega - 1/(C omega))^2])`
Graph between `P & omega` as shown in the figure.
`omega_1 = +R/(2L) + (omega_r^2 +R^2/(4L^2))^(1/2)` and `omega_2 = - R/(2L) + ((omega_r^2)+ R^2/(4L^2))^(1/2)`
Now, `omega_1 -omega_2 = R/L`
or `(omega_r +Delta omega) - (omega_r -Delta omega) =R/L`
The frequency interval between half maximum power points is known as band width.
The ratio of resonance frequency and band width is known as quality factor (Q).
`Q = omega_r/(2 Delta omega) = (omega_r L)/R`
Q factor is a measure of the sharpness of resonance. Resonance will be sharp if the value of bandwidth
`(2 Delta omega)` is small. This is of course possible only when the power-frequency curve fa ll steeply around
`omega = omega_r`