What is the order of the filter, when the gain decreases at the r

| What is the order of the filter, when the gain decreases at the rate of 60 dB/decade?

A. Second order low pass filter

B. Third order high pass filter

C. Third order low pass filter

D. None of the above

Please scroll down to see the correct answer and solution guide.

Right Answer is: C

SOLUTION

Concept:

The roll off of a filter is defined as the slope of the filter's response in the transition region between the pass-band and stop-band.
Roll-off is given in dB/decade(ten times the frequency) or in dB/octave (doubling of frequency).
If the response changes rapidly with frequency, the roll-off is said to be steep.

The roll-off for a general first-order low pass filter is - 20 dB/decade, i.e. the gain decreases by 20 dB for a decade (10 times) change in frequency.

For an n^th order filter, the roll-off is given by:

Roll-off (n^th order) = n × 20 dB/decade

Application:

Given, Roll-off = - 60 dB/decade (negative sign indicates that the gain is decreasing with an increase in frequency)

The order will be:

60 dB/decade = n × 20 dB/decade

n = 3

Conclusion:

So the given filter is a third-order filter.
Since the gain is decreasing with an increasing frequency, it is a low pass filter.