MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE 6 002 Circuits and Electronics Quiz 2 November 15 2005 YOUR NAME SOLUTIONS Recitation Instructor TA General Instructions 1 Please verify that there are 15 pages in your exam booklet 2 Please do all of your work in the spaces provided in this examination booklet 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 the booklet Place the answer to each question within the appropriate answer box 3 You may use two double sided pages of notes and a calculator while taking this exam For examiner s use only Problem Points Score Grader 1 30 2 30 3 40 Total 100 Problem 1 30 Points For the circuits below please find expressions for the specified voltage or current over the indicated time ranges in terms of the circuit parameters Plot the waveform on the provided axes and clearly identify the key parameters in your graph A Consider the circuit of Fig 1 The switch is closed for t 0 open for 0 t t and closed for t t where t 3L R Find and plot the current i t 1 I DD V 1mA GG 1 3 B 10 2 5V V 1V R 5k L 1mS T L Figure 1 Plot i t over all time indicating important waveform parameters L iL t t 0 0 t I 1 iL t 0 t t1 1 e 2 iL t t t1 t I 1 e 6 e 2 2 1 iL I 1 e 6 2 2 L R 1 L 2R t 3 t 1 R B Consider the circuit of Figure 2 in which 0 The switch is open for t 0 and closed for t 0 v 0 V Find and plot the voltage v t C 0 Figure 2 1 Plot v t over all time indicating important waveform parameters 1 Find the Thevenin equivalent as seen by the capacitor when the switch closes Apply VT IT By KVL around the loop VT R1 1 IT R2 IT VT IT R1 1 R2 REQ R1 1 R2 1 Find the time constant REQC R1 1 R2 C 2 Find V1 at t 0 At t 0 3 Find V1 at t 0 At t 0 V1 0 V1 R1 1 V0 R1 1 R 2 4 Find V1 at t At t V1 0 V1 t t 0 0 V1 t t 0 t Vo R1 1 e R1 1 R2 C R1 1 R2 V1 V0 R1 1 R1 1 R2 t Problem 2 30 Points Searching through your 6 002 lab kit you discover a curious purple two terminal device that you affectionately decide to name Device Q Taken by the moment you set out to find the large signal I V response of this device By applying voltage v between the two Q device terminals you measure the current i flowing through Device Q to be Q i A v Q 4 2 Q 2 for v 0 where A 1 x 10 A V Q a What is the small signal current i of Device Q if you operate it at a DC operating q point V with a small signal voltage excitation v Please write the general expression Q q for i in terms of A V v q Q q Answer iq 2 AVQ v q b You insert the Device Q into the circuit below From previous experience you know that the MOSFET in the circuit has a threshold voltage V 1V and has an output drainsource characteristic that looks like a resistor R voltage v MOSFET GS T 500 when the gate source 15V and it is operating in its linear triode region What is the value of v OUT when v 0 7V IN vOUT V s The MOSFET is off since v 0 7V VT and is 0 v OUT IN 15V What is the value of v OUT when v 15V IN V is o R i s A Vs Vo 2 Vo R A Vs Vo 2 Vo A R Vs2 2 A R Vs Vo A R Vo2 0 A R Vo2 2 A R Vs 1 Vo A R Vs2 Vo 2 A R Vs 1 2 A R 2 A R V 1 2 2 A R V 2 s s 2 A R 2 A R V 1 2 2 A R V 2 s s 1 2 AR 4 25 20 Vo 15 10 1 10 Vo 5V Vo V s v OUT 2 AR 5 c Ripple in the power supply causes the value of v to fluctuate by a few percent S around the intended 15V Write the expression for v of the fluctuation v when v 15V s out the fluctuation in v in terms OUT IN From part a you know that iq 2 AVq v q iq vq 1 v q rq 500 iq 500 vs Rq 500 vout RMOSFET 500 v out rq rq RMOSFET vs 1 vs 2 Problem 3 40 Points You are given a LINFET transistor whose drain current in saturation is given by i B v D While this transistor has a linear i v D GS GS V T relation all other characteristics are as usual i 0 and operation in saturation requires G v GS V T and v GS V v The transistor is used in the amplifier circuit below T DS vI A Assume the transistor is biased to operate in saturation Draw the equivalent network for this circuit where the transistor is replaced by its large signal equivalent circuit Draw the large signal circuit model for the amplifier Vout B VGG VI VT RL Vi IDD B For the LINFET to operate in saturation X v Y I Derive expressions for X and Y and give numerical answers 1 For the MOSFET to turn on VGS VT VGG v I VT v I VGG VT v I 1 5V For the MOSFET to be in saturation v V v GS T DS Vo VI VGG VI VT I DD I DS RL VGG VT I DD RL B VGG VI VT RL VGG VT R L BVI VGG 1 BRL 1 BRL VT I DD RL V 1 BRL 1 BRL VT I DD R L V I GG BRL V I 3 1 2 1 V I 0 8 X 0 8 Y 1 5 0 8 v 1 5 I C Still under the saturation operation assumption draw the small signal equivalent network for the circuit Assume that v V v where V is a constant voltage and v I I i I is a small signal excitation Label all circuit elements Make sure all controlling and controlled values are clearly shown i vout Bvi RL vi D Assuming that v V v derive an expression for the small signal gain I v v out out i v BRL 5 i I …
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