Question

Design a filter that has infinite DC gain, a gain of one from 1Hz to 100 Hz and filters (1storder) any signals above 100 Hz.a) Sketch the bode plotb) Sketch the s-planec) write the transfer function of the filterd) write the differential equatione) write out the unforced transient responsef) write out the frequency response

Answer 1

Answer:

Attached below are the  sketches

answer :

c) G(s) = 100 / ( s + 100 )

d) y'(t)  + 100Y(s) = 100 X(s)

e) g(t) = e^-100t  u(t)

Explanation:

a) Sketch the bode plot

The filter here is a low pass filter

b) Sketch the s-plane

attached below.     pole ( s ) is at 100

c) write the transfer function of the filter

Transfer function ; G(s) = 100 / ( s + 100 )

d) write the differential equation

Y(s) / X(s) = 100 / s + 100

Y(s) [ s + 100 ] = 100 X(s)

= sY(s) + 100Y = 100 X(s)

∴ differential equation = y'(t)  + 100Y(s) = 100 X(s)

e) write out the unforced transient response

g(t) = e^-100t  u(t)

f) write out the frequency response

attached below