Test: Frequency Filters

fC = 4.6 kHz.

Phase shift = -tan^-1f/fC = -tan^-12 = -63°.

The given circuit is a bandpass filter. The upper and lower cut-off frequencies depend on the RC constant. However, since R1C1 = R2C2, this means that both the cut-off frequencies are equal. Thus they meet at the same point and form the response as above.

Phase shift = 180° – tan-1f/fC
Phase shift = 180-45 = 135°.

The cut-off frequency for the above filter is fc = 1/2πR2C1
fC = 1000000/2π25×10 = 636 Hz.

Roll-off rate is the rate at which the gain of a filter decreases outside the pass-band. Roll of rate is increased as the order increases. For an nth order filter, roll-off rate is 20xn dB/decade.

The above circuit is a low pass filter of the non-inverting type, where the input is at the non-inverting end. The gain is A = 1+R3/R2 / 1+jωR1C1
Thus maximum gain is A = 1+R3/R2.

Net phase shift is 180 + tan^-1fC/f
f_c = 1/2πR1C1 = 1000000/2π20×2 = 3.978 kHz
Phase shift = 180 + tan^-13.987/3 = 233.04°.

The maximum gain is at low frequencies and at low frequencies, the capacitance reactance is infinite and thus the total feedback impedance Z_F = R_F = R2
Thus gain = -Z_F/Z = -R₂/R₁
Amplitude = 5.5 = R2/R1 = R2/10k
R2 = 55kΩ.

A passive filter can consist of all R, L and C elements. An op-amp is used in an active filter, and it also provides amplification along with filtering. There are no inductors used in active filters because they are bigger in size and bulky. Active filters are used at audio frequency and passive filter at radio frequency.