Discussion
The roll-off of a first order low pass filter is :
Answer: B
The roll-off is -20 dB/decade.
A first-order low pass filter has the response \(H(f) = 1/(1 + jf/f_{c})\). Well above the cut-off frequency its magnitude is about fc/f, so each tenfold increase in frequency divides the gain by 10, a fall of 20 dB, equal to -6 dB per octave.
The positive slopes belong to high pass behaviour below cut-off, and -40 dB/decade is the roll-off of a second-order filter, which has two poles. Each additional pole adds a further -20 dB/decade.
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