(Solved): Design a Low Pass Filter (LPF) Butterworth filter with the following parameters: =0.3;=4; Cuto ...

Design a Low Pass Filter (LPF) Butterworth filter with the following parameters: $$?=0.3;?=4$$; Cutoff frequency $$f_c=4\mathrm{GHz}\left({?}_c=2?f_c\right)$$; and Ripple frequency at stop band $$f_r=8\mathrm{GHz}({?}_r=$$ $$2?f_r$$ ); for the load/source impedances of $$50\mathrm{Ohm}$$. (Please attached your code and the screenshots of your results at the end if you try the bonus part) 1. Calculate all poles and scale them to the $$f_c=4\mathrm{GHz}\left({?}_c=2?f_c\right)$$; then draw/mark them on a graph; 2. Obtain the expression of transfer function $$\mathrm{H}(\mathrm{s})$$ and plot it in Matlab/Python vs. $$\mathrm{s}=\mathrm{j}?$$ for both amplitude and phase (10 pts bonus); 3. Obtain the lump elements' values for load/source impedances of $$50\mathrm{Ohm}$$; then draw them on a diagram. 4. Obtain the corresponding distributed LPF and its corresponding transmission line implementation; then draw diagram and make down parameters of the distributed LPF.