Question

Consider the design of a low-pass filter meeting the following requirements:

i) The pass-band attenuation is less than 0.1 dB for frequencies less than 5 k rad./sec. and is less than 0,5 dB for frequencies less than 20 k rad./ sec.
ii) The stop-band loss is at least 50 dB for frequencies greater than 100k rad/sec.
iii) The 3 dB cutoff frequency is less or equal 30krad. /sec.
a) Find the order of a Butterworth filter to meet these requirements.
b) Find the transfer function of the corresponding Butterworth filter.

Answer 1

To design a low-pass filter meeting the given requirements, we can use a 2nd order Butterworth filter with a specific transfer function.

Step-by-step explanation:

To design a low-pass filter that meets the given requirements, we can use a Butterworth filter. The order of a Butterworth filter determines its roll-off rate, which controls how quickly the filter attenuates frequencies beyond the cutoff frequency. To find the order of the filter, we need to consider the requirements for pass-band attenuation and stop-band loss. Based on these requirements, a 2nd order Butterworth filter is sufficient.

The transfer function of a Butterworth filter can be represented as:

H(s) = K / (s^2 + 1.4142s + 1)

where K is a constant. This transfer function satisfies the given requirements and provides the desired attenuation characteristics.