Problem 1: (30 points): The figure below shows a unipolar PWM converter with a switching frequency...

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Problem 1: (30 points): The figure below shows a unipolar PWM converter with a switching frequency of 50 kHz. Consider the following two cases: Case 1: Input current is controlled to be i, (t) = 20 sin (27×50t+30°) 4. Case 2: Input current is controlled to be i, (t) = -20 sin (27×50t) A. 155 sin (27 × 50t) V 5mH CH (i) VAR (t), (ii) VBM (t) and ide (t) An CH A + + An CH B CH n 200V For EACH of the two cases, (a) Calculate the required control voltages for the two legs, v. (t) and vc (t). Assume = 1V. (b) Draw (rough sketch) the following cycle-by-cycle averaged quantities for the time interval of 0 to 40 ms. Assume that the operation is in steady state from t = 0. An AB (c) Draw (rough sketch) the instantaneous VAN (1), VBR (1), and V₁B (t) in the time interval of 4.98 ms to 5.02 ms. Optional extra credit problem 1 (20 points): Simulate the above unipolar PWM converter of Problem 1 corresponding to Case 1 and show simulation plots of the instantaneous and CCA waveforms of the parameters required in Problem 2b and 2c. Problem 1: (30 points): The figure below shows a unipolar PWM converter with a switching frequency of 50 kHz. Consider the following two cases: Case 1: Input current is controlled to be i, (t) = 20 sin (27×50t+30°) 4. Case 2: Input current is controlled to be i, (t) = -20 sin (27×50t) A. 155 sin (27 × 50t) V 5mH CH (i) VAR (t), (ii) VBM (t) and ide (t) An CH A + + An CH B CH n 200V For EACH of the two cases, (a) Calculate the required control voltages for the two legs, v. (t) and vc (t). Assume = 1V. (b) Draw (rough sketch) the following cycle-by-cycle averaged quantities for the time interval of 0 to 40 ms. Assume that the operation is in steady state from t = 0. An AB (c) Draw (rough sketch) the instantaneous VAN (1), VBR (1), and V₁B (t) in the time interval of 4.98 ms to 5.02 ms. Optional extra credit problem 1 (20 points): Simulate the above unipolar PWM converter of Problem 1 corresponding to Case 1 and show simulation plots of the instantaneous and CCA waveforms of the parameters required in Problem 2b and 2c.