Download Practical Exam 2 for ECE225L: Electrical Circuits, Fall 2008 and more Exams Electrical Circuit Analysis in PDF only on Docsity! ECE225L PRACTICAL EXAM #2 FALL 2008 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: /10 Problem 6: /25 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 = 2v2 − 3v1 using a minimal number of 10k resistors. 2 Problem 3 (15 Points) 0.01 0.1 1 10 100 H ( d B ) ω(rad/s) 1000 0.01 0.1 1 10 100 ω(rad/s) 1000 θ ( d e g ) (a) Write the following transfer function in Bode form: H(s) = 100 (s + 1)(s + 10) (b) Draw the (straight-line) Bode magnitude and phase plots and label all slopes for the frequency response H̄(jω) = H(ω) 6 θ(ω). 5 Problem 5 (10 Points) Step−Down Full−Wave Transformer C−Filter Variable Load Resistor + − + − + − + T 2 v (t) C V r V dc V m Figure 2: Output of Full−Wave Rectifier with Ripple Voltage from a C−Filter R =1k 10:1 p ωv (t)=160sin t 1 − V L I L L v (t) v (t) s r C 1 Bridge Rectifier Figure 1: Full−Wave Rectifier Circuit with C−Filter and Variable Load Resistor t T T Hint: The average voltage of a full-wave rectified sinusoid vr(t) = Vm| sinωt| is Vavg = 2Vm/π. (a) Assuming that the capacitor C1 is not present in the above full-wave rectifier circuit, find the average (DC) voltage VL and average (DC) current IL flowing in the 1k-resistor. (Assume that the diodes are ideal with no voltage drop across them.) (b) After inserting a very large capacitor C1 after the diode bridge, find the average (DC) voltage VL and average (DC) current IL flowing in the 1k-resistor. (Assume that the diodes are ideal with no voltage drop across them.) 6 Problem 6 (25 Points) A second-order filter is represented by the following transfer function H(s) = s2 + 400 (s + 20)2 (a) Compute H̄(j2) (magnitude and angle). (b) Compute H̄(j20) (magnitude and angle). (c) Compute H̄(j200) (magnitude and angle). (d) What type of filter is represented by H(s)? Underline the correct answer below: (i) Low-pass (ii) High-pass (iii) Band-pass (iv) Notch or Band-stop (e) Using Parts (a)-(c), find the steady-state output voltage vo(t) of this filter when the input voltage is vi(t) = 100 cos 2t + 100 cos 20t + 100 cos 200t V 7
