Question

Design a Butterworth band-reject filter with the following specifications:

i) Center frequency of ω₀ = 1M rad./sec.
ii) A3 dB bandwidth of 200krad/sec.
iii) The pass band attenuation is less than 0.1 dB for frequencies greater than 1.25Mrad. /sec.
iv) The stop band attenuation is at least 40 dB for frequencies between 1Mrad. /sec. and 1.01Mrad. /sec.
Give an RLC realization of this Butterworth filter using 10k Ohm resistors.

Answer 1

To design a Butterworth band-reject filter, determine the transfer function using the given specifications and then substitute the values to get the RLC realization of the filter.

Step-by-step explanation:

To design a Butterworth band-reject filter with the given specifications, we can start by determining the transfer function of the filter. The transfer function for a Butterworth filter is given by:

H(s) = K / [s^2 + (ω₀/Q)s + ω₀^2]

Where ω₀ is the center frequency, Q is the quality factor, and K is a normalization constant. The first step is to determine the values of Q and K using the given specifications, and then substitute those values into the transfer function to get the desired RLC realization of the filter.