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Resonant frequency:

ωr

2 = 1/LC = 1000000/ (0.02 x 0.015)

ωr = 57735 rad/s

fr= ωr /2π = 31622.77 / 2π = 9189 [Hz]

Q-factor:

Qr = (ωr L) / R = 1/ (ωr CR) = (1/R) √(L/C) = 11.55

Bandwidth:

Qr = fr / BW BW = 9189 / 11.55 = 795.6 Hz

Lower and upper -3 dB frequencies are determined with

BW = 795.6 = f1 - f2

Lower and upper cut-off frequencies are, assuming equal spacing, 8791.2 and 9586.8

Hz (exact values, obtained using exact expressions, are 8800 Hz and 9595 Hz.

Q3. Cutoff frequency

ω = 1/RC

f = 1 / (2π RC) = 1.59 kHz

Magnitude of output voltage is

VOUT = 1 / √[(1 + (ωRC)2] x VIN

at 500 Hz: VOUT = 9.54 V

at 1 kHz: VOUT = 8.47 V

at 2 kHz: VOUT = 6.22 V

at 4 kHz: VOUT = 3.7 V

Q4. Cut-off frequency

ω = 1/RC

f = 1 / (2π RC) = 7.96 kHz

Magnitude of output voltage is

VOUT = ωRC/ √[(1 + (ωRC)2] x VIN

at 2 kHz: VOUT = 4.87 V

at 15 kHz: VOUT = 17.67 V

at 40 kHz: VOUT = 19.62 V

at 100 kHz VOUT = 19.94 V