Question

Design a second-order high-pass filter for each case below and state its transfer function H(s):

a) k=1, ω0= 1300 rad/s and Q=0.707
b) k=1, ω0= 950 rad/s and Q=0.8
Assume L=1H
Table: Second order RLC filters

Answer 1

To design a second-order high-pass filter, you can use the general form of the transfer function for this type of filter. For (a), the transfer function is (s^2) / ((s^2) + (0.707s) + (1300^2)). For (b), the transfer function is (s^2) / ((s^2) + (0.8s) + (950^2)).

Step-by-step explanation:

To design a second-order high-pass filter, we can use the general form of the transfer function for this type of filter:

H(s) = k * (s^2) / ((s^2) + (s/Q) + (ω0^2))

where k is the gain, ω0 is the resonant angular frequency, and Q is the quality factor.

(a) For case a, with k=1, ω0=1300 rad/s, and Q=0.707, the transfer function is:

H(s) = (s^2) / ((s^2) + (0.707s) + (1300^2))

(b) For case b, with k=1, ω0=950 rad/s, and Q=0.8, the transfer function is:

H(s) = (s^2) / ((s^2) + (0.8s) + (950^2))