Name Massachusetts Institute of Technology Department of Nuclear Science and Engineering Department of Electrical Engineering and Computer Science 22 071 6 071 Introduction to Electronics Signals and Measurement Spring 2006 Quiz 2 Please write your name on each page of the exam in the space provided Please verify that there are 11 pages in your exam To the extent possible do your work for each question within the boundaries of the question or on the back side of the page preceding the question Extra pages are also provided for computation Note that the total number of points is 100 Closed book No Calculators Partial credit adds up so make sure that you show your work 22 071 6 071 Spring 2006 Quiz 2 Page 1 Name Problem 1 15 points What is the gain Vo for the following circuit Vs R2 R1 Vs Vi 22 071 6 071 Spring 2006 Quiz 2 A Vi Vo Page 2 Name Problem 2 15 points The circuit below operates in steady state driven by the sinusoidal source Vs R Vs L C Vo A Calculate the transfer function H Vo Vs B Graph H as a function of frequency and indicate how an increase in R will affect your graph Vo Vs 22 071 6 071 Spring 2006 Quiz 2 Page 3 Name Problem 3 15 points For the following circuit the capacitor C is known The circuit operates under sinusoidal steady state conditions Determine the value of resistors R so that the phase difference between Vo and Vs is Vo Vs 2 2 R R Vs 22 071 6 071 Spring 2006 Quiz 2 C C Vo Page 4 Name Problem 4 10 points Tau finds a black box with 3 terminals labeled Tau who took 6 071 last year decides to make resistance measurements across the terminals at DC 0 Hz and at high frequency large She observes the following results Resistance at Measure resistance across DC 0 High Freq 40 Which of the following equivalent circuits is inside Tau s black box x C R x y R L y L C z z Circuit A x Circuit B R y x C y L L C R z Circuit C 22 071 6 071 Spring 2006 Quiz 2 z Circuit D Page 5 Name Problem 5 15 points Find the impedance Zin across terminals a b as indicated in the following circuit R a v L Av Zin C b 22 071 6 071 Spring 2006 Quiz 2 Page 6 Name Problem 6 15 points R1 R3 Is R2 C v For the circuit above the current Is has the form I Is t 0 0 t 0 t 0 Where I 0 constant A Determine the voltage v at t 0 and at t B Determine the equivalent resistance seen by the capacitor 22 071 6 071 Spring 2006 Quiz 2 Page 7 Name Problem 7 15 points The signal Vs t is applied to the circuit as indicated in the schematic below C 50nF Vs R Y t 1k The Fourier transform of the input signal Vs t is shown below The output signal Y t is taken across the resistor Draw the Fourier transform of the signal Y t on the following graph 22 071 6 071 Spring 2006 Quiz 2 Page 8 Name Blank page For computation 22 071 6 071 Spring 2006 Quiz 2 Page 9 Name Blank page For computation 22 071 6 071 Spring 2006 Quiz 2 Page 10 Name Problem Points 1 2 3 4 5 6 7 Total 22 071 6 071 Spring 2006 Quiz 2 Page 11
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