Final Exam Solutions 10 - Final EE42\/100 Summer 2010 Solutions 1(10 points Consider the 2 RLC circuits below For each circuit assume that V IN is an AC

Final Exam Solutions 10 - Final EE42/100 Summer 2010...

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Final - EE42/100, Summer 2010 - Solutions August 23, 2010
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1. (10 points) Consider the 2 RLC circuits below. For each circuit, assume thatVINis an AC signal withangular frequencyω(i.e.VIN=cos(ωt)), and sinusoidal steady-state has been achieved. Computethe transfer function of each circuit. Which one resembles a low-pass filter, and which one a high-passfilter? Be sure to mathematically justify your answers.For RLC circuit 1:
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2. (15 points) Consider the 2 diode and ideal op-amp circuits below. For each circuit, assume that V IN is an AC signal ranging from -3 to 3. Assume also that the initial voltage across the capacitor is 0, and C is large such that it doesn’t discharge appreciably across one input cycle. What are the minimum and maximum values of V OUT for each circuit? For Op-amp configuration 1: Suppose first that we disregard all circuit components to the right of V A . The minimum voltage for V A is 2 V , since if V A tries to go below 2 V , the diode connecting V A is forward-biased and shorts. The short forces V A to become 2 V . When V A is at its minimum of - 3 V , the maximum voltage of 5 V is stored across capacitor C . When V A increases to 3 V , the 5 V across capacitor C causes V A to increase to 8 V . Meanwhile, the voltage V OUT = - 100 k Ω 1 k Ω V A , and without the diode connecting V OUT , the V OUT would range from - 200 V to - 800 V . The diode connecting V OUT with the 2 V source only ensures that V OUT does not exceed - 2 V , so V OUT is free to go from - 200 V to - 800 V . 4
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Maximum V OUT : - 200 V Minimum V OUT : - 800 V For Op-amp configuration 2: As in Op-amp configuration 1, if we first disregard all circuit components to the right of V A , the minimum and maximum voltages for V A would be 2 V and 8 V respectively. Meanwhile, V OUT would like to range from - 200 V to - 800 V . However, the diode and 2 V source connected to V OUT ensures that if V OUT were to ever go below - 2 V , the diode shorts, and V OUT becomes - 2 V . Hence, where as V OUT would go from - 200 V to - 800 V without the diode and voltage source connected to it, V OUT is held at - 2 V with the diode and voltage source.
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