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hw 1 - equivalent circuit c Draw a phasor diagram showing...

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1 EPOW/ECSE-4080 Semiconductor Power Electronics Homework #1 Due Date: Thursday, 9/06/07 1. (30%) The figure below shows a linear RLC circuit supplied by a dc source. The 0.1 Ω series resistor represents the internal resistance of the source. The switch is closed at t = 0, prior to which the inductor and capacitor are completely discharged. Assume the open-circuit voltage of the source is 10 V. a) Calculate the output voltage v 0 in steady state, that is, after S is closed for sufficiently long time. b) Determine transient response of v 0 (starting from t = 0) when the capacitor is removed. c) Determine transient response of v 0 when the inductor is removed. d) Give the s-domain expression for the output voltage when both inductor and capacitor are present. 2. (30%) Consider again the RLC circuit shown above. The source is now a sinusoidal voltage: t v s π 10000 cos 100 = , and the switch is always closed. a) Draw the equivalent impedance network of the circuit. b) Calculate the periodical response of the inductor current and the capacitor voltage based on the ac
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Unformatted text preview: equivalent circuit. c) Draw a phasor diagram showing the inductor current, the capacitor voltage, and the source voltage. d) Convert the inductor current and capacitor voltage phasor into time-domain expressions as given above for the source voltage. 3. (20%) Use the inductor current and the capacitor voltage as state variable and develop a state-space description for the RLC circuit shown above (assume the switch is closed). Convert the model into s-domain and use it to derive the transfer function from the source voltage to the capacitor voltage. Compare the result with your answer to Problem 1d) 4. (20%) Consider a periodic rectangular voltage shown below. Determine a) The fundamental amplitude and frequency of the voltage, b) The amplitude and rms value of the 3 rd and 5 th harmonic, and c) The total rms value of the voltage. 1 Ω + − S 100 μ F + v − 1 mH 0.1 Ω 10 0.05 0.03 0.1 0.08 t...
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