Question

PPöblem 2 (30 points You are given the control system shown below where the excitation is the voltage source vst(0) and the response is the voltage vc(0). Assume that the opamps are ideal R1 L R Ri Ri VE t) R1 F(t) 2 C2 R3 a. Given that R 10k2, determine find VE(s) as a function of voltages Vs(s) and Vr (8). Given that R-1 Ω, L-100m H and C-100mF, determine the transfer function Vc(s)Vi() b, 100μF, determine the transfer c, Given that R2-10kS2, R3-1 kΩ and C2 function Ve (s)/Ve(s). Construct a block diagram for the overall system showing voltages Vs(s), VE(s), Ve(s) and Vr (s). d. e. Determine the transfer function Ve(s/Vs(s).

Answer 1

Apply Laplace transform to the given circuit, we get The voltage at node 'c' is v_c = V_E (s) for ideal op - amp, the voltage at inverting & non - inverting terminal is same so V_A = V_B: V_D = V_G At node A, by K C L V_A (s) - V_s (s)/R_1 + V_A (s) - 0 /R_1 = 0 rightarrow (1) = > 2 V_A (s)/R_1 = V_s (s)/R_1 \r\n = > V_A (s) = V_s (s)/2 rightarrow (2) At node B, by KCL - V_F (s) + V_B (s)/R_1 + V_B (s) - V_E (s)/R_1 = 0 - V_F (s) + 2 V_B (s) = V_E (s) = > V_E (s) = -V_F (s) + 2 V_A (s) { because V_A (s) = V_B (s) } = > V_E (s) = -V_F (s) + 2 V_s(s)/2 Therefore V_E (s) = V_s (s) - V_F (s) rightarrow (3) At node ' c' apply KC L V_E (s)/R_1 + V_E (s) - V_D (s)/S L + R = 0 V_E (s) - V_s (s)/2/R_1 + V_E (s) - V_c (s)/S L + R = 0 = < V_E (s) [1/R_1 + 1