HW2_Soln - January 30, 2008 ECE315 Homework # 2 Solutions...

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January 30, 2008 ECE315 Homework # 2 Solutions (Rev. 0) Spring 2008 1. Textbook Chapter 4, Problem 4. As given in equation (4.8) in your text, the collector current in the npn BJT is (ignoring the Early eﬀect) I c = AqD n n 2 i N B B W B ± exp( qV BE kT ) - 1 ² , where N B is the acceptor doping in the base region, and W B is the dimension of the undepleted base. So if the base width thickness is increased by a factor of two, then the collector current will decrease by more than a factor of two for the same bias conditions as a portion of the thinner base region was partially depleted depending on the magnitude of the collector bias. Otherwise stated, doubling its thickness causes the undepleted base dimension to increase by more than a factor of two. 2. Textbook Chapter 4, Problem 7. Consider this DC circuit. (a) Examining the circuit diagram V BE 1 = V BE 2 V B , I X = I C 1 + I C 2 = I S 1 exp( qV BE 1 kT ) + I S 1 exp( qV BE 1 kT ) = 3 I S 2 exp( qV B kT ) . Solving for V B yields V B = kT q ln( I x 3 I S 2 ) = 25 . 86(10 - 3 ) ln ± 1 . 2(10 - 3 ) (3)2 . 5(10 - 16 ) ² = 0 . 7267 volts . (b) Maximum value of R c to remain in forward active mode. .. V CE = V CC - I x R C > V sat CE . Solving for R c gives R C < ( V CC - V sat CE I X ) . Assuming V sat CE 0 . 2 volts, then R C < 2 . 3 / 1 . 2 or 1.92 kΩ. 3. Textbook Chapter 4, Problem 11. Consider another DC circuit.

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ECE315 January 30, 2008 Page 2 Examining the circuit diagram, we can write V X = V E = I E R , I C = I S exp h q kT (1 . 5 - V X ) i . Assuming a large β in forward active mode then I C I E . Note that V CE = 2 - V X , so V X can not exceed roughly 1.8 volts or transistor will be in saturation. These equations must be solved simultaneously. A graphical solution appears below.
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This note was uploaded on 09/28/2008 for the course ECE 3150 taught by Professor Spencer during the Spring '07 term at Cornell University (Engineering School).

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HW2_Soln - January 30, 2008 ECE315 Homework # 2 Solutions...

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