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W09 314 HW03 solution - EECS 314 Winter 2009 Homework set...

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EECS 314 Winter 2009 Homework set ___ Student’s name ___________________________ Discussion section # _______ (Last, First, write legibly, use ink) (use ink) Instructor is not responsible for grading and entering scores for HW papers lacking clear information in the required fields above Scores for the HW set: Problem 1 2 3 4 5 6 7 Total Score Problem 1 The “Golden Rules” applied to a basic Op Amp circuit For the circuit shown on the diagram, do the following: Part 1 (10 points) Write the node voltage equation for V + , first without using the GR and then after applying the GR, in the space below. Part 1 2 3 4 Total Without using Golden Rules, apply KCL at the V + node. Summing currents leaving the node: 10mA + (V + - 0) / 200 + I+ = 0 => 10mA + V + / 200 + I+ = 0 Now, apply Golden Rule (zero current entering input nodes of op-amps). 10mA + V + / 200 + 0 = 0 => 10mA + V + / 200 = 0 From the latter equation, calculate the voltage V + in volts and write your answer: V + = __-2___ V V + / 200 = -10 mA => V + = -10 mA * 200 = -2V © 2008 Alexander Ganago Page 1 of 1
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EECS 314 Winter 2009 Homework set ___ Student’s name ___________________________ Discussion section # _______ (Last, First, write legibly, use ink) (use ink) Instructor is not responsible for grading and entering scores for HW papers lacking clear information in the required fields above Problem 1, continued The ckt diagram is repeated here for your convenience. Part 2 (10 points) Write the node voltage equation for V , first without using the GR and then after applying the GR, in the space below. Without using Golden Rules, apply KCL at the V - node. Summing currents leaving the node: I 10 + I 50 + I- = 0 => (V - - (-4))/10k + (V - - V OUT )/50k + I- = 0 Now, apply Golden Rules (zero current entering input nodes of op-amps, V + = V - ). (-2 + 4)/10k + (-2 - V OUT )/50k + 0 = 0 => 2/10k + (-2 - V OUT )/50k = 0 From the latter equation, calculate the voltage V OUT in volts and write your answer: V OUT = __8____ V 2 /10k - 2/50k = V OUT /50k => V OUT = 10 - 2 = 8 V © 2008 Alexander Ganago Page 2 of 2
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EECS 314 Winter 2009 Homework set ___ Student’s name ___________________________ Discussion section # _______ (Last, First, write legibly, use ink) (use ink) Instructor is not responsible for grading and entering scores for HW papers lacking clear information in the required fields above © 2008 Alexander Ganago Page 3 of 3 Part 3 (10 points) From the the node voltages, calculate the currents I 10 , I 50 , and I 91 in mA and write your answers: I 10 = __.2____ mA I 50 = __-.2____ mA I 91 = __87.9 mA Part 4 (10 points) From KCL, calculate the Op Amp's output current I OUT in mA and write your answer: I OUT = ___88.1___ mA I OUT = I 91 + (-I 50 ) = 87.9 mA + .2mA = 88.1 mA Verify whether KCL is valid at the ground node. Write your conclusion: Yes / No (circle one) Do not be surprised by the possible “violation” of KCL: your calculation is incomplete, because the circuit diagram is incomplete, lacking the power supplies (such as – 12 V and +12 V), which can carry large currents! Show your work.
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