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Unformatted text preview: EE 3005 Spring 2011 Midterm 2 Solution Q #1 (25 pts) First Order Circuits The voltage va rises momentarily whenever load 1 is switched off. This is problematic for load 2 which does not work properly above 150 volts. Calculate how long the voltage is out of range when load 1 is switched off. That is, how long is va above 150 volts? Hint: Derive va(t), assuming the switch opens at t = 0. +
126 VDC Load 1 (63 ohms) 18 mH va _ Load 2 (18 ohms) Solution: va = k1 + k2 exp(-t/τ) τ = (18 mH)/18ohm = 1.0 ms iL (0-) = iL (0+) = 126V/(63ohm||18ohm) = 126V/14ohm = 9A iL(final) = 126V/ 18ohm = 7A va (initial) = va (0+) = iL (0+)(18ohm) = (9A)(18ohm) = 162V va (final) = iL (final)(18ohm) = (7A)(18ohm) = 126V va(t) = 126 + 36 exp(-t/1.0ms) The voltage is out of range from t = 0 until time t1, where…. va(t1) = 150 = 126 + 36 exp(-t1/1.0ms) t1 = -(1.0ms)*ln((150-126)/36) t1 = 0.405 ms va is out of range for 0.405 ms each time the load 1 is switched off. Q #2 (25 pts) Phasors Use phasor techniques to solve for ig(t). ig 1 mH + 12 cos(1000t) V _ 2000 μF 10 Ω Solution: ) Q #3 (25 pts) Power a) Calculate the total real and reactive power, and the power factor of the combined load. b) Add a component to bring the power factor to unity. Specify the type, value, and location of the component. + 120 Vrms (377 r/s) _ Solution: Leg 1: 11.5 14.4 15.3 mH Leg 2: Total load: To get a pf of 1.0, add a capacitor across the 120V rails to reduce the total var load to zero. That is, let Qcap = -500 VAR. Q #4 (25 pts) Filters Design a low-pass filter with unity gain in its pass-band and a gain of 0.01 (as determined by straight line Bode approximations) at 10,000 radians/sec. Draw the schematic and specify component values. (Hint: the break frequency is NOT 10,000 radians/sec). (Hint: Draw a straight-line Bode plot of the filter gain). Solution: The gain of this filter should be -40 dB at 10,000 radians/sec (because 0.01 is -40 dB). If we use a 1st order low pass filter, with a gain that decreases at 20 dB/decade in the stop band, the gain will be 0 dB (unity gain) 2 decades below 10,000 radians/sec. That point is the filter’s break frequency. Use RC filter with Use, (note: other RC combinations are possible) ...
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