Question

I been struggling with this problem and need some help. thanks!

Answer 1

Given R_1 = 1 k Ohm R_Load = 2 k Ohm C = 1 mu F L = 1 H convert the above network components to time domain to s - domain by replacing i_in (t) doubleheadarrow I_in (s) R_1 doubleheadarrow R_1 R_Load doubleheadarrow R_Load L doubleheadarrow s L C doubleheadarrow 1/s C Apply KVL at node v_1 (s) - I_in (s) + v_1 (s)/1/s 10^6 + v_1 (s) - v_out (s)/1 k = 0 \r\n - 10^6 + I_in (s) + 5 v_1 s9 + 10^3 v_1 (s) - 10^3 v_out (s) = 0 v_1 s9 [s + 10^3] = 10^3 v_out (s) + 10^6 I_in (s) v_1 (s) = 10^3 [v_out (s) + 10^3 I_in (s)]/s + 10^3 rightarrow (1) Apply KVL at node v_out (s) v_out (s) - v_1 (s)/1 k + v_out (s)/s + v_out (s)/2 k = 0 2 s v_out (s) - 2 v_1 (s) + 2 10^3 v_out (s) + s v_out (s) = 0