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 Final Exam Please write your name on each page of the exam in the space provided Please verify that there are 26 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 Problem Points 1 2 3 4 5 6 7 8 9 10 Total 22 071 6 071 Spring 2006 Final Exam Page 1 Name General Useful Information Diodes Id Ideal diode model Anode Id Cathode Reverse Bias Region Forward Bias Region Vd Vd Id 0 7 Volt offset model Vg 0 7 Volts 0 7 V Vd Vg Id Vd Vd Full diode model Id Is exp 1 V T VT 25 mV Id Vd Id Vz Zener Diode Vz Vd Ideal model Id Reverse bias region Vz Reactive Elements Capacitor dVc dt j ZC C C I c C Ic Vc Inductor dI L dt Z L j L VL L 22 071 6 071 Spring 2006 Final Exam L IL VL Page 2 Name General Useful Information Op Amps Vc Ideal Op amp model negative feedback I I I 0 V V V Vo IVVc Ideal 3 state op amp model open loop and positive feedback Vc I I 0 Vc Vo A V V Vc BJTs I V Vo I for A V V Vc non linear for Vc A V V Vc linear VVc for A V V Vc non linear collector Ie Ic Ib Ic Ib For operation in the active region Ic Ib Vbe 0 7 V Vbe base Ie emitter c b b b c Ib e 0 7 V e Boolean Identities A 0 A A 1 A A B B A AB BA A B C A B C A BC AB C A BC A B A C A B C AB AC A A A A A 0 A 1 1 A A A A 0 0 A A 1 A AB A A A B A A B A C A B C A A B A B AB A B 22 071 6 071 Spring 2006 Final Exam A B A B Page 3 Name Problem 1 10 points The op amp in the following circuit outputs a current of 5 mA Io 5 mA The transistor has 100 Calculate the value of the resistor R 24 Volts 10 Volts Io R 22 071 6 071 Spring 2006 Final Exam Page 4 Name Problem 2 10 points In this circuit the op amp may be considered to be ideal and it is not saturated It drives a load of unspecified resistance Vs R1 V V iL Load R2 A Approximately what is the voltage V B What is the voltage V C Therefore what is the current iL and what is the purpose of this circuit D If R1 is increased by a factor exp 1 what is the expected change in iL Hint use the I V characteristic relationship for a diode 22 071 6 071 Spring 2006 Final Exam Page 5 Name Problem 3 10 points In this circuit R1 100k R2 25k Rc 25k Re 5k C 1 F and the of the transistor at its DC operating point is 100 Vcc 10V Rc R1 Vi C Vc Ib Vb Ve R2 Re A If Ib is negligible what is the steady state DC value of Vb B In that case using a standard simplified model of the transistor determine the DC values of Vc and Ve 22 071 6 071 Spring 2006 Final Exam Page 6 Name C Estimate the DC value of Ib in that case D If this value of Ib is accounted for in calculating Vb then how much does it change from your answer in A E Approximately what is the time constant of the high pass filter made up by C and the rest of the circuit F For AC signal frequencies well above the high pass cut off what are the small signal voltage gains of the circuit at the outputs i e vc vi and ve vi 22 071 6 071 Spring 2006 Final Exam Page 7 Name Problem 4 10 points Here you will analyze the following circuit VDD VDD R NOR 0 Vi NOT C V1 Vout V2 This circuit combines two logic gates NOR and NOT and an RC network Assume that the logic gates are ideal no delay time between the output and the input and the output swings between 0 and VDD Furthermore the voltage transfer characteristic of the inverter gate NOT is V2 Vout Vout V2 V DD 2 V DD 2 Vout VDD 0 VDD 0 VDD 2 V2 VDD Also assume that the diode is ideal with the following Id Vd characteristic curve Id Anode Id Cathode Reverse Bias Region Vd Forward Bias Region Vd We will apply a trigger pulse Vi and arrange our circuit parameters so that the output Vout is a pulse of specified duration 22 071 6 071 Spring 2006 Final Exam Page 8 Name We will solve this problem by breaking it down into small parts analyze each part and then put it all together for the final answer A Fill in the truth table for the NOR gate A B A 0 0 VDD VDD Y B 0 VDD 0 VDD Y B Now let s independently consider the RC network in order to explore its general characteristics The voltage V1 has the form shown on the graph below It has been at VDD Volts for a very long time and then at time 0 goes to zero Volts returning to VDD at time t1 VDD V1 VDD R C V1 V2 0 0 t1 time What is the voltage V2 at time 0 What is the voltage V2 at time 0 Give an expression for the voltage V2 for time 0 22 071 6 071 Spring 2006 Final Exam Page 9 Name Assuming that t1 RC ln 2 what is the voltage V2 at time t1 Hint the voltage across the capacitor is V2 V1 C Draw the complete evolution for V2 V1 VDD VDD time V2 R C V1 V2 VDD 0 22 071 6 071 Spring 2006 Final Exam t1 time Page 10 Name D Now let s connect a diode to the RC circuit as shown below Draw the evolution of V2 in this case V1 VDD VDD time V2 R C V1 V2 VDD 0 time t1 E Now connect the NOT gate as shown below With the given voltage transfer characteristic for the inverter gate and for t1 RC ln 2 draw the evolution of the output voltage Vout Indicate relevant transition times and values V1 VDD VDD 0 R C …