The transfer function H(s) = 1/(s + 1)²of a filter is to be implemented by cascading two first order filters H_i(s) = 1/(s + 1), i = 1, 2.

(a) Implement Hi(s) as a series RC circuit with input v_i(t) and output v_{i +1}(t), i = 1, 2. Cascade two of these circuits and find the overall transfer function V₃(s)/V₁(s). Carefully draw the circuit.

(b) Use a voltage follower to connect the two circuits when cascaded and find the overall transfer function V₃(s)/V₁

(s). Carefully draw the circuit.

(c) Using the voltage follower circuit implement a new transfer function

Carefully draw your circuit.

G(s) (s + 1000)(s + 1)