Question

Calculate transfer functions for BOTH of the circuits below. Choose values such that w1 100 and w2 100000 rad/s respectively. I encourage you to use mesh or nodal analysis to check your methods if you try to solve it by grouping components as I did for the RC RC circuit in class. Vout Vio Vut Vin How are the bode plots different? Apply the shortcut of simply multiplying the two filters together to have a 3rd option. Why do these differences exist within the three bode plots? www www

Answer 1

In this domain. Apply KCL v_a - v_i (s)/R_2 + v_a/(1/sc_2) + v_a/(1/sc_2) + v_a/1/sc_1 + R_1 = 0 v_a [1/R_2 + sc_2 + sc_1/R_1 sc_1 + 1] = v_i/R_2 v_a = v_i/R_2 [1/R_2 + sc_2 + sc_1/R_1 sc_1 + 1] v_0 = v_a [R_1/R_1 + sc_1] [By applying voltage division principle] Therefore v_0 = v_i R_1/(R_1 + 1/sc_1) (1 + R_2 sc_2 + R_2 c_1 s/R_1 sc_1 + 1) \r\n v_0/v_i = R_1 sc_1/(1 + R_1 ds_1) (1 + R_2 sc_2 + R_2 c_1 s/1 + R_1 sc_1) = R_1 sc_1/1 + R_1 sc_1 + R_2 sc_2 + s^2 R_1 R_2 c_1 c_2 + R_2 c_1 s v_0/v_i = R_1 sc_1/1 + s (R_1 c_1 + R_2 c_1 + R_2 c_2) + s^r R_1 R_2 c_1 c_2 ---(1) Bode plot zero at origin and two poles at 5 = 1/R_1 R_2 c_1 c_2 Apply KCL we get \r\n v_a - v_i/(1/sc_1) + v_a/R_1 + v_a/(R_2 + 1/sc_2) = 0 v_a sc_1 + v_a sc_2/R_2 sc_2 + 1 = v_i (sc_1)