Solved ELCT 222 Signals and Systems Computer Assignment 5

Suppose you build the following circuit producing an output signal 𝑣𝑣o(𝑡𝑡) by filtering the input signal 𝑣𝑣i(𝑡𝑡) in the lab. 1. (50 pts) Express the transfer functions 𝐻𝐻(𝑠𝑠) = 𝑉𝑉o(𝑠𝑠) 𝑉𝑉i(𝑠𝑠) for each case (as a function of the circuit elements) 2. (25 pts) Express and (25 pts) plot the step response 𝑦𝑦step(𝑡𝑡) of each circuit (for 𝑡𝑡 ∈ [−1,10]) by using the corresponding step function for a. Case 1: 𝐶𝐶 = 1, 𝐿𝐿 = 1, 𝑅𝑅 = 1 2 b. Case 2: 𝐶𝐶 = 0, 𝐿𝐿 = 1, 𝑅𝑅 = 1 c. Case 3: 𝐶𝐶 = 1, 𝐿𝐿 = 0, 𝑅𝑅 = 1 d. Case 4: 𝐶𝐶 = 1, 𝐿𝐿 = 1, 𝑅𝑅 = ∞