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: 1Name:__________________________________________ General Useful Information Diodes: Ideal diode model AnodeCathode+-VdId IdVdRevers e-BiasRegionForward-BiasRegion 0.7 Volt offset model Vg = 0.7 Volts +-VdId0.7 V IdVdVg Full diode model exp 1TVdId IsV⎡⎤⎛⎞=−⎢⎥⎜⎟⎝⎠⎣⎦ 25TVm V +-VdId Zener Diode Vz Ideal model Id Vz IdVdVzReverse biasregion Reactive Elements: Capacitor ccdVI=Cdt CjZCω=− CVcIc+- Inductor LLdI=LdtV LZjLω= VLIL+-L 22.071/6.071 Spring 2006 Final Exam Page: 2Name:__________________________________________ General Useful Information Op-Amps Ideal Op-amp model (negative feedback) I+ = I- = 0 V+ = V- V+V-I+I-Vc+Vc-Vo Ideal 3 state op-amp model (open loop and positive feedback) I+ = I- = 0 Vc+, for A(V+ - V-) > Vc+ ; non-linearVo = A(V+ - V-), for Vc- < A(V+ - V-) < Vc+ ; linearVc-, for A(V+ - V-) < Vc, ; non-linear ⎧⎪⎨⎪⎩V+V-I+I-Vc+Vc-Vo BJTs Ie = Ic + Ib For operation in the active region Ic = Ibβ Vbe=0.7 V IbIccollectorbaseemitterVbe+_Ie 0.7 V bce=bceIb βΙb Boolean Identities A + 0 = A A1=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 AA = A• A + A 1= A0=0• A + AB = A A(A +B)=A A + A B A+B= (A + B) (A + C) = A + B C AB A B=+ A+B A B=• 22.071/6.071 Spring 2006 Final Exam Page: 3Name:__________________________________________ Problem 1 - (10 points) The op-amp in the following circuit outputs a current of 5 mA. (=5 mA). The transistor has β=100. Calculate the value of the resistor R. Io +24 VoltsR+10 VoltsoI 22.071/6.071 Spring 2006 Final Exam Page: 4Name:__________________________________________ 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. iLoadR1R2VV+-LVs 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 , what is the expected change in iexp(1)L ? (Hint: use the I-V characteristic relationship for a diode) 22.071/6.071 Spring 2006 Final Exam Page: 5Name:__________________________________________ Problem 3 - (10 points) In this circuit R1=100kΩ, R2=25kΩ, Rc=25kΩ, Re=5kΩ, C=1µF and the β of the transistor at its DC operating point is 100. RcReR1R2Vcc=10VViIbVbVcVeC 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: 6Name:__________________________________________ 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: 7Name:__________________________________________ Problem 4 - (10 points) Here you will analyze the following circuit. VDDCV1V2ViVoutR+VDD0NOTNOR 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: VoutV2 V2Vout2DDV> 0 2DDV<DDV V2VoutVDDVDD0VDD2 Also assume that the diode is ideal with the following Id-Vd characteristic curve. AnodeCathode+-VdId IdVdRevers e-BiasRegionForward-BiasRegion We will apply a trigger pulse and arrange our circuit parameters so that the output is a pulse of specified duration. iVoutV22.071/6.071 Spring 2006 Final Exam Page: 8Name:__________________________________________ 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 ABY A B Y 0 0 0 VDD VDD0 VDDVDD 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. VDDCV1V2R timeV1VDDt100 What is the voltage V2 at time=0-? What is the voltage V2 at time=0+? Give an expression for the voltage V2 for 0time ≥22.071/6.071 Spring 2006 Final Exam Page: 9Name:__________________________________________ Assuming that, what is the voltage V1ln(2)tRC=2 at time=t1+? (Hint: the voltage across the capacitor is V2- V1) C. Draw the complete evolution for V2. VDDCV1V2R timetimeV1V2t1VDD0VDD 22.071/6.071 Spring 2006 Final Exam Page: 10Name:__________________________________________ D. Now let’s connect a diode to the RC circuit as shown below. Draw the evolution of V2 in this case. VDDCV1V2R timetimeV1V2t1VDD0VDD E. Now connect the NOT gate as shown below. With the given voltage transfer characteristic for the inverter gate and for 1ln(2)tRC= draw the evolution of the output voltage Vout. Indicate relevant transition times and values. VDDCV1V2RVout timetimeV1t1VDD0VDDVout00 22.071/6.071 Spring 2006 Final Exam Page: