Question

3, 35%) Given the following circuit: ) Redraw the eircuit as a funetion of the complex frequency, including the component values and the physical wnits, bat with no initial conditions: b) Obtain the transfer funetion H) c) Calculate ..)for )-12uit) V using the Laplace Transform technique. Notice that this problem was also solved in the Practice Exam 1 (Probliem 4) using the time domain technique 1) Caloulste vt) for v.) tr)

Answer 1

(a) convert into frequency domain (b) z = (1) Vertical-bar Vertical-bar (1/s)H = (1)(1/s)/1 + 1/s + 1 = 1/s + 1 + 1 z = 1/s + 1 + 1 = s + 2/s + 1 Apply nodal analysis at node (1) V(s) - V_1(s)/1 + V(s)/1/s + V(s)/(s + 2)/s + 1 = 0 V(s)[1 + s + s + 1/s + 2] = V_i(s) V(s)[(s + 1) + (s + 1)/s + 2] = V_i(s) V(s)[(s + 1)[s + 3/s + 2] = V_i(s) V(s) = [(s + 2)/(s + 1)(s + 2)]V_i(s) equation (1) output voltage V_0(s) = [1/s + 1/1/s + 1 + 1] V(s) [voltage division rule] V_0(s) = [1/s + 2] V(s) equation (2) \r\n from (1) & (2) V_0(s) = 1/s + 2 [s + 2/(s + 1)(s + 3)]V_i(s) V_0(s) = [1/(s + 3)(s + 1)] V_i(s) Transfer function H(s) = V_0(s)/V_i(s) = 1/(s + 3)(s + 1) (c) for i/p