03selfexmdiafall - the left The current through the device...

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6.012 - Electronic Devices and Circuits - Take Home Diagnostic Exercise Your name: Today’s date: The four problems in this exercise deal with material you will use in 6.012 from the prerequisite courses. Give yourself one hour to work it. Solutions will be distributed at the next recitation and you can then judge for yourself which material you need to review. Problem 1 - Basic linear circuit analysis Consider the circuit illustrated below: + - + - 1 k W v A 1 k W 10 k W 10 k W v IN + - v OUT A v A A = 1 mS 1 2 (a) What is the voltage v OUT when the input voltage, v IN , is 2 Volts? v OUT = (b) What is the Thevenin equivalent resistance of the circuit to the right of Nodes 1 and 2? R T = Problem 2 - Linear differential equations Consider a parameter c P (t), which varies temporally according to the equation: dc P (t)/dt + A c P (t) = B where A and B are positive constants. What is c P (t) for t > 0 if c P (0) = 0 and c P (t) is finite? c P (t) =
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Problem 3 - Linearization about an operating point Consider the non-linear two-terminal electronic device, D, illustrated below on
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Unformatted text preview: the left. The current through the device, i D (t), is related to the voltage across its terminals, v AB (t), by the equation, i D (t) = I C (v AB + 4 v AB 3 ), where I C = 10-3 A. There is no charge or flux storage associated with this device. i D Non-linear two-terminal device, D R i d A B -a b + +-v ab v AB A linear equivalent circuit for the device D valid for small signal operation about a bias point, v AB = V AB , is shown to the right. What is R for the bias point V AB = 2V? R = Problem 4 -Simple electrostatics In a certain sample of material the electric field, E(x,y,z), varies only in the x-direction, i.e., E(x,y,z) = E(x), where E(x) is shown below. The dielectric constant, e , is uniform throughout the sample with a value of 10-10 coul/V-cm. E(x) [V/cm] 2 10 -3-2 -1 1 2 3 x [µm] 2-10 On the axes provided below, sketch and dimension the net charge distribution in this sample. -3 -2 -1 1 2 3 x [µm] End of diagnosis; you may get up from the couch....
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This note was uploaded on 07/20/2009 for the course CSAIL 6.012 taught by Professor Prof.cliftonfonstadjr. during the Fall '03 term at MIT.

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03selfexmdiafall - the left The current through the device...

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