Design the simplest bandpass filter (based on a Butterworth prototype) satisfying the following requirements (mask)
Passband from 100 KHz to 150KHz
Stopband extending outwards from 160 KHz and inwards from 90 KHz
Gain in the passband between -0.1 dB to 0 dB
Gain in the stopband at most -40 dB
(a) Specify a bandpass mask with parameters G1, G2, δε, ως, ως, ως, ως
(b) Starting form the Butterworth prototype filter make the lowpass to bandpass transformation, resulting in a BPF with parameters G, w₁, W2, and N.
(c) Fit the above BPF into the mask derived above, by selecting the above parameters. Hint: You can design a "tight" filter by making sure the passband constraints are satisfied with equality, while the stopband constraints are satisfied as inequalities. Based on the former equalities you can get two equations: one for the product of w₁w2 and one for their difference w2 - w₁ that will determine w₁ and w₂ (as a function of N). Based on the latter inequalities you will find the correct value for N.
(d) Indicate the order of the filter, the FRF magnitude, and provide its Bode plot (amplitude only). You are not asked to find the overall (complex) FRF, neither are you asked to implement this filter using R, C and opamps.