hmwk 9 sol - EECS 314 Fall 2006 HW 09 Problem 1 Student's...

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Unformatted text preview: EECS 314 Fall 2006 HW 09 Problem 1 Student's name ___________________________ Discussion section # __________ (Last name, first name, IN INK) Alexander Ganago The big picture In HW 06 Problem 4, you analyzed the inductive kick in a DC motor circuit: on this diagram, the motor is shown as a series combination of the inductor L and resistor R M . When the switch is opened at t = 0+, the inductor current (which must be continuous!) causes a voltage drop in the shunt resistor R S which builds up the voltage V M across the motor. Notice that use of resistors (linear devices) leads to difficult choices: on the one hand, in order to minimize the voltage rise (when the motor is stopped), we need a very small shunt resistance; on the other hand, we also want to minimize the waste of power (when the motor is running) thus we need a very large shunt resistor. Tough choice … In this problem, you will see how we can use a semiconductor diode (non-linear device) to achieve both goals (small inductive kick and low power waste). In the circuit shown on the second diagram, the shunt resistor is replaced with a semiconductor diode, which is reverse-biased (not conducting) at DC steady state when the switch is closed and the motor is running. If the DC voltage V B is positive, then the current it pushes through the diode would be in the direction opposite to the arrow of the diode symbol: the diode does not conduct and thus does not absorb any power. When the switch is open and the DC source disconnected, the inductor pushes the current through the diode in the direction shown by the arrow of the diode symbol thus the diode is forward-biased: it conducts and the voltage drop across it does not exceed the offset voltage V D0 . Note that a forward-biased diode can burn out if the current through it exceeds the manufacturer’s specifications (safe limit). Problem Given: V B = 100 V, R B = 0.5 Ω , V D0 = 0.7 V, R M = 0.5 Ω . Determine the voltage V M across the motor and the inductor voltage V L at t = 0+ If needed, assume L = 1 H. Calculate the maximal current I MAX through the diode. Kevin Klein Homework 9 Problem 1 Solution Before the switch is closed, the diode is reverse biased, and the equivalent circuit looks like this: To find the voltage across the motor after t = 0, first find the initial current through the inductor before the switch is closed: ( ) 100 1 100 = = = MAX L I I A This is the maximal current through the diode. Once the switch is opened, the equivalent circuit looks like this: The current flowing through the inductor will be the same current that flows through the resistor by KCL. The voltage drop across the resistor is given by 50 5 . * 100 = = = IR V V. The voltage across the inductor can then be found by writing a KVL loop equation around the circuit: ( ) ( ) = + + + + R L D V V V Solution Page 1/2 Kevin Klein The diode will be forward biased in this case, and V R was just calculated above, so the above equation can be solved for V...
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This note was uploaded on 09/23/2009 for the course EECS EECS314 taught by Professor Ganago during the Fall '09 term at University of Michigan.

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hmwk 9 sol - EECS 314 Fall 2006 HW 09 Problem 1 Student's...

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