MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 6 002 Electronic Circuits Fall 2002 Final Exam Name Recitation Section Recitation Instructor Teaching Assistant Enter all your work and your answers directly in the spaces provided on the printed pages Make sure that your name is on all sheets Use the backs of the printed pages as scratch paper but we will only give full credit to answers that you neatly transfer to the spaces on the printed pages Answers must be derived or explained not just simply written down The quiz is closed book but calculators and both sides of one 8 12 11 page of notes are allowed This quiz contains 16 pages including the cover sheet Make sure that your quiz contains all 16 pages and that you hand in all pages except the last page Problem Points Grade Grader 1 20 2 20 3 16 4 20 5 24 Total 100 Name 2 Problem 1 20 points The circuit below shows a single stage ampli er designed around a MOXFET a hypothetical transistor similar to a MOSFET except that iD K vGS VT 3 3 For the purposes of this problem assume that the MOXFET gain parameter K 0 625mA V 3 and that its threshold voltage is VT 2 2V In the circuit above VS 10V R1 30k R2 70k RD 37 5k and C 0 15 F The saturation region models for the MOXFET are shown below where a is the large signal bias model and b is the small signal incremental model A The ampli er output voltage will be of the form vOU T VOU T vout t Determine VOU T a numerical value is required VOU T V Name 3 B Find an expression for the transconductance gm in terms of the symbolic MOXFET parameters VT and K and the operating point VGS Do not evaluate your answer numerically gm C For an input signal of the form vi t VI cos t the complex amplitude of the output signal vout t will be of the form j VI V out G0 1 j In terms of the transconductance gm and the circuit parameters nd expressions for the highfrequency gain G0 and the time constant Do not evaluate your answers numerically G0 Name 4 D The small input signal is now given by vi t Va cos t Vb u t The resulting output signal has the form vout t Vc cos t Vd Ve e t u t Determine Vc Vd Ve and in terms of Va Vb and G0 where and G0 are de ned in part C Vc Vd Ve Name 5 Problem 2 20 points Consider the RLC circuit shown below A The voltage source is a unit step at time t 0 Three circuit variables vC vL and iL are presented plotted against time as shown in the three gures on the next page Time is measured in milliseconds on the horizontal axes The vertical axes may represent voltage measured in Volts or current measured in Amperes as appropriate The traces are labeled 1 2 and 3 The label is in the upper right corner of each trace You are to identify the traces which trace is which circuit variable Circle the circuit variable that corresponds to the indicated trace below Trace 1 vC vL iL Trace 2 vC vL iL Trace 3 vC vL iL Name 6 Note Time is measured in milliseconds on the horizontal axes The vertical axes may represent voltage measured in Volts or current measured in Amperes as appropriate The arrows represent the slope of the curve at t 0 Name 7 B Assume the inductance L is 75 H i What is the approximate numerical value of the capacitance C ii What is the approximate numerical value of the resistance R iii Estimate the Q of the circuit Circle the best answer Q 1 1 Q 10 10 Q Name 8 C For each question circle the correct completion i If the resistance R is increased the Q increases decreases remains the same ii If the capacitance C is increased the Q increases decreases remains the same iii If the inductance L is increased the oscillatory period increases decreases remains the same iv If the capacitance C is increased the oscillatory period increases decreases remains the same D After a long time T vs returns to zero and the stored energy decays i If the capacitance C is increased the time at which the stored energy falls to half its value at time T increases decreases remains the same ii If the inductance L is increased the time at which the stored energy falls to half its value at time T increases decreases remains the same iii If the resistance R is increased the time at which the stored energy falls to half its value at time T increases decreases remains the same Name 9 Problem 3 16 points The source vs t has the waveform shown in the graph on the next page The nonlinear element N has the i v relation sketched below Assume that the op amps are ideal i e in nite gain no input current zero output resistance no saturation On the axes provided sketch the waveforms of va t vb t and vo t Follow the time divisions indicated in the graph and label the amplitude of your waveforms If any of your graphs contains impulses be sure to indicate their area Name 10 Name 11 Problem 4 20 points A simple MOSFET inverter is shown above The input output relationship is also shown above NOT to scale where the MOSFET has been modeled using the familiar square law relationship iDS K vGS VT 2 2 in the saturation region and the triode region is compressed onto the single curve iDS K 2 v 2 DS The MOSFET parameters are VT 1V and K 1mA V 2 A Determine the voltages V1 and V2 in the input output graph for this inverter V1 V V2 V Name Two identical inverters from part A are cascaded to form the bu er circuit shown below The input output relationship is qualitatively sketched below NOT to scale B Determine the voltages VA VB VC and VD VA V VB V VC V VD V 12 Name 13 C For a given input voltage each transistor in the bu er circuit will be in one of three regions of operation cuto CO saturation SAT and triode region TR As the input voltage vIN is increased from 0 to 4V the bu er passes through four states In the following table indicate the four states by circling the region of operation of the transistors for each range of input voltage Input Voltage M1 M2 0V vIN VT CO SAT TR CO SAT TR VT vIN VC CO SAT TR CO SAT TR VC vIN VD CO SAT TR CO SAT TR VD vIN 4V CO SAT TR CO SAT TR Name 14 Problem 5 24 points Match the indicated variable to the form of its response for t 0 by circling the appropriate letter corresponding to the …
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