Question

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lpf ( low pass filter) is desired with a cut off frequency of 10 Hz. This filter should attenuate a 100-Hz signal by a factor of at least 78. What should be the order of this filter. expain briefly

Answer 1

The cut-off frequency of low pass filter = 10 Hz. Attenuation of input signal is '3 dB' (on semi-log scale) and its value is 1.414.

A low pass filter of n^th order attenuates at a rate of n*20 dB per decade i.e., as frequency increases by 10 times, the attenuation is 20 dB(10 - numerical value).

Here, we need to attenuate the 100 Hz signal by a factor of at least 78. The ratio of input-signal frequency and cut-off frequency is 10. Hence, at 100 Hz the attenuation is '-n*20' dB. Attenuation of 78 is '-37.84 dB'. Hence if order of filter n>=2, our condition will be satisfied. Minimum order of LPF required is '2'.