The circuit below is a resonant bandpass filter. It blocks low and high frequenc

Question

The circuit below is a resonant bandpass filter. It blocks low and high frequencies and passes a narrow band of frequencies. Find the transfer function for this circuit. omega0 is the center frequency, defined as the frequency at which the magnitude of the transfer function is maximum. Show that omega 0 = 1 / omega and omega Ht are the lower and upper cutoff frequencies, where the magnitude of the transfer function is 3dB below is maximum value. The bandwidth is the distance between these two frequencies. i.e. BW = omega H - omega LO. Show that BW = omega0/Q. For C = 1mu F, find the values of L and R so that the filter has a center frequency of 1000 Hz and a bandwidth of 100 Hz. Sketch Bode plots of the magnitude and phase of the frequency response, indicating all important values.

Explanation / Answer

you can find the transfer function by finding the ratio of the laplace transform of the output is to input signal

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