Question

Transient Response in 1st and 2nd Order Circuits RI 220Ω , R2-470 Ω , C1 100 nF , C,-22 uF , C,- 220 uF a.) Draw the wiring diagram for a switched LC parallel circuit (with a series resistance R) powered by a 5V battery. Find an RLC combination that is nearly critically- damped

Answer 1

Wiring diagram Taking Laplace of above circuit writing KCL at node A I = I_1 + I_2 rightarrow 5/s - V_out (s)/R = V_out/Ls + V_out/1/cs implies V_in (s) - V_out (s)/R = V_out/Ls + Cs V_out (s) \r\n V_in (s)/R = V_out[1/R + 1/Ls + Cs] V_in (s)/R = V_out [Ls + R + CLRS^2/LRS] implies V_out/V_in = LS/LCRS^2 + LS + R H(s) V_out/V_in = LS/LRC/S^2 + S/RC + 1/LC on comparing denominator of H(s) with S^2 + 2 epsilon omega_n S + omega^2_n = 0 implies S^2 + S/RC + 1/LC = 0 omega^2_n = 1/LC omega_n = squareroot 1/LC 2 epsilon omega_n = 1/RC \r\n for heavily critically damped response epsilon almostequalto 1 2 times 1 times omega_n = 1/RC omega_n = 1/2RC so: 1/2RC = squareroot 1/LC implies 1/4R^2C^2 = 1/LC implies LC/R^2 C^2 = 4 implies L = 4R^2C from data if R = 220 C_1 = 100nF \r\n L = 4R^2 C = 4 times