Download ECE225L Spring 2009 Practical Exam 2 - Op-amp and Filter Problems and more Exams Electrical Circuit Analysis in PDF only on Docsity! ECE225L PRACTICAL EXAM #2 SPRING 2009 Instructions: 1. Closed-book, closed-notes, open-mind exam. 2. Work each problem on the exam booklet in the space provided. 3. Write neatly and clearly for partial credit. Cross out any material you do not want graded. Name: Problem 1: /15 Problem 2: /15 Problem 3: /20 Problem 4: /15 Problem 5: /15 Problem 6: /20 Total: /100 1 Problem 1 (15 Points) − + 2 3 6 v 1 v 2 4 3 1 v o R 2 + R R R + − − + − The output of the above op-amp subtractor is vo = ( 1 + R2 R1 ) ( R4 R3 + R4 ) v2 − R2 R1 v1 Assuming that you have only one uA741 op-amp available and plenty of 10k resistors, implement the function vo = v2 − 3v1 using a minimal number of 10k resistors. 2 Problem 4 (15 Points) 20 −20 H (dB) 10 100 1000 11 10 100 1000 θ (deg) 90 45 0 −45 −90 f (Hz) f (Hz) 0 The above plots represent straight-line approximations of the Bode magnitude (dB) and phase (deg) of a certain transfer function in a linear circuit. (a) Find the sinusoidal steady-state output vo(t) if the input is vi(t) = 10 cos(2πt) V. (b) Find the sinusoidal steady-state output vo(t) if the input is vi(t) = 10 cos(2π √ 1000t) V. (c) Find the sinusoidal steady-state output vo(t) if the input is vi(t) = 10 cos(200πt) V. 5 Problem 5 (15 Points) sL 2 R 1 R o V (s) i V (s) − + − + (a) Derive the transfer function of the above circuit in the form: H(s) = Vo(s) Vi(s) = K(1 + s/z) (1 + s/p) and identify K, z, and p in terms of R1, R2 and L. (b) Choose the correct Bode magnitude plot and filter type below. pz 20 dB/dec10 10 20log K (b) High−Pass Filter 20log K ωω H (dB) (a) Low−Pass Filter H (dB) −20 dB/dec zp 6 Problem 6 (20 Points) R o V (s) 1 sC sL − + i V (s) − + (a) Derive the transfer function for this second-order filter as: H(s) = ω2n s2 + 2ζωns + ω2n and specify ζ and ωn in terms of R, L, and C. (b) If vi(t) = cosωnt and ζ = 1/2, find vo(t) in steady state. (c) If vi(t) = cosωnt and ζ = 1, find vo(t) in steady state. 7
