Question

a first order low pass filter is used to attenuate noise with frequencies higher than 26khz. what is the largest cutoff frequency (in khz) to achieve -20db attenuation? (1 decimal)

Answer 1

The largest cutoff frequency to achieve -20dB attenuation for a first-order low pass filter, with the noise occurring at frequencies higher than 26kHz, would theoretically be set at 2.6 kHz.

Step-by-step explanation:

To achieve a -20dB attenuation with a first-order low pass filter, we need to set the cutoff frequency at a point where the noise at 26kHz is attenuated by 20dB.

In the case of a first-order low pass filter, the gain drops off at -20dB/decade once the frequency exceeds the cutoff frequency. The logarithmic scale means that noise at 26kHz should be on the first decade line after the cutoff point for it to be attenuated by 20dB.

Therefore, to facilitate a -20dB attenuation at 26kHz, the cutoff frequency should be 2.6 kHz. It is worth noting that real-world results may vary due to the characteristics of the filter design, but this gives a theoretical starting point.