Question

Extra Credit: 10 points (a) Find the overall transfer function of the following operational amplifier circuit. Show all the calculations R, 100 kO R2 200 kn C,= 1pf C2=0.1pt R 2.5 ka R-10 ko C RA R Vo

Answer 1

R_1 = 100 k ohm, R_2 = 200 k ohm, c_1 = 1 mu f, c_2 = 0.1 mu F r_3 = 2.5 k ohm R_4 = 10 k ohm Applying Laplace By visual ground concept v^+ = v^- so v^+ = 0 so v^- = 0 Applying nodal at inverting terminal of op-amp 1 0 - v_i(s)/r_1 + 0 - v_i(s)/c_1 s + 0 - v_1(s)/R_2 + 1/c_2 s = 0 -v_i(s)/R_1 - c_1 s (s) - v_1(s) c_s s/1 + R_2 c_2 s = 0 -v_i(s) [1/r_1 + c_1 s] = v_1(s) c_2s/1 + r_2 c_2 s v_1(s) = -v_i(s) [1 + R_1 c_1 s/R_1] times [1 + R_2 c_2 s/c_2 s] rightarrow (1) \r\n Applying nodal analysis at inverting terminal of op-amp (2) 0 - v_1(x)/r_3 + 0 - v_0(s)/R_4 = 0 -v_1(s)/r_3 = v_0s(s)/R_4 rightarrow (2) Replace v_1(s) in equation (2) with equation (1) -1/R_3 [-v_i(s) [1 + R_1 c_1 s/r_1 times 1 + r_2 c_2 s/c_2 s] = v_0(s)/R_4 v_i(s) = [(1 + R_1 c_1 s) (1 + r_2 c_2 s)/R_1 R_2 c_2 s] = v_0(s)/R_4