1 Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6 002 Electronic Circuits Fall 2003 Quiz 2 Please write your name on each page of the exam in the space provided and circle the name of your recitation instructor and the time of your recitation at the bottom of this page Please verify that there are 16 pages in your exam To the extent possible do all of your work on the pages contained within this exam In particular try to 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 available at the end of your exam You may use one double sided page of notes and a calculator while taking this exam Good luck Problem Points Score Grader 1 25 2 25 3 25 4 25 Total 100 Name Instructor Time Perreault 10 11 Antoniadis 11 Chaniotakis 11 12 Umans 12 1 Kolodziejski 2 3 Name Problem 1 2 25 Points Yikes Inc has manufactured a large batch of identical MOSFETs which unfortunately do not display squarelaw characteristics Instead they are characterized by the following equation when operated in saturation The MOSFETs operate in saturation when and Yikes begins to experiment with these devices and builds the following circuit containing a single MOSFET The supply voltage is Assume for this problem that both and are greater than 0 VSU R D M1 iG 0 G vS S I0 A Calculate the node voltage at the source assuming saturation Note that the gate terminal MOSFET is connected to ground 8 points of the Name 3 B What is the maximum value of for which satisfies the saturation discipline 5 points Maximum value of C For a given value of 5 points Minimum value of what are the constraints on for which satisfies the saturation discipline Maximum value of Name 4 D Draw a small signal model for the two terminal device constructed by connecting the gate and drain of the Yikes MOSFET as shown in the figure below Derive an expression for the relationship between the 0 0 small signal current and the small signal voltage 7 points iDS M1 vDS 0 versus 1 0 32 Name Problem 2 5 25 Points After years of research Yehaa Inc has invented a new MOSFET which is shown below along with its small signal model under the saturation discipline D D iDS iG 0 ig 0 vDS i ds g m v gs G G vgs vGS S S This new MOSFET has an extremely high transconductance 465 for reasonable bias values The only catch is that 4 5 is highly sensitive to temperature As a result the traditional amplifiers designed using the MOSFET have unpredictable gains Yehaa researchers work on this problem and after a few more months announce they have discovered the breakthrough amplifier circuit shown below They claim that under certain conditions the small signal gain of the new amplifier is insensitive to 465 In this problem you will verify their claim VSU RL iDS G vI vO D S RS Assume for this problem that the MOSFET always operates under the saturation discipline and that it is biased such that its transconductance is 4 5 A Draw the small signal equivalent circuit for the amplifier Clearly mark the small signal input 8 small signal output in your circuit 4 points 7 and the over Name B Determine the small signal transfer function 6 8 9 7 for the circuit 8 points Name 7 C Determine one or more constraints that are required in order for the claims made by the Yehaa researchers to be true In other words what are the constraints under which the small signal gain is indepen dent of 465 Express these constraints in terms of one or more of the following parameters 465 BA and 5 points D Emboldened by their recent success the Yehaa researchers make a second claim that the small signal output resistance of the amplifier is independent of If true this property would make the new amplifiers C even more appealing to existing customers using the older amplifier model for which Determine an expression for the small signal output resistance of the amplifier and use it to confirm or disprove the second claim Recall that the small signal output resistance is the Thevenin resistance seen between the output node and ground 8 points Small signal output resistance Name Problem 3 8 25 Points DFEG EIHJC KLC6 M A Sketch by inspection in the figure below for given Give expressions for initial and final values in your sketch 8 points i R1 L R2 What is the time constant N v v O 0 t Name 9 DFEP EQHRC in the figure below for given that the switch is moved from 1 to 2 at B Sketch by inspection C What is the time constant N Give expressions for initial and final values in your sketch 8 points ES 1 2 V0 R2 C2 R1 v C1 v O 0 t Name 10 DFEG E H C TUC6 V DLC6 V C and in the figure below for given that C Sketch by inspection 8 value of W Give an expression for the maximum value of in your sketch 9 points v C L i v 0 X 8Y Maximum value of t What is the Name Problem 4 11 25 Points Minnie Delay is interested in designing a light in her dorm room that turns brighter gradually when switched ON and dims gradually when switched off Having just learned RC circuits in 6 002 she comes up with the following design VS A A bulb R C B switch S R ON B vB The bulb can be modeled as a resistance of value Similarly when turned ON the switch can be modeled as a resistor of value BZ Assume that is a positive DC voltage The following questions 6 is NOT the voltage across the bulb concern the node voltage at note that A When the switch is in the ON state what is the steady state value of the node voltage Steady state value of 5 points Name 12 starting at B After being ON for a long time the switch is turned OFF at time Sketch the form of D Clearly indicate the initial values final values in the steady state and the time constant Na 6 points vB t O T0 Name 13 starting at C After being OFF for a long time the switch is turned ON at time cb Sketch the form of b Clearly indicate the initial value final value in the steady state and the time constant N b Also write E an expression for as a function of starting at time b Remember that the switch has a resistance BZ when turned ON 9 points vB t O T1 b Name 14 to reach half its initial value i e D For the situation in Part C how long does it take the voltage Rd its value at b from the instant the switch is turned ON Assume that BZ …
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