Question

1 2 + – i(t) C R L iT i(t) iD + – L C R 1. Analysis and design of a buck-boost converter: A buck-boost converter is illustrated in Fig. 1(a), and a practical implementation using a transistor and diode is shown in Fig. 1(b). + (a) Vg v Figure 1 Buck–boost converter of Problem 1: (a) ideal converter circuit, (b) implementation using MOSFET and diode. – Q1 D1 (b) + Vg v Page 2 iL (t) + vL (t) – i (t) + – Q1 C + – C R DTs Ts (a) Find the dependence of the equilibrium output voltage V and inductor current I on the duty ratio D, input voltage Vg, and load resistance R. You may assume that the inductor current ripple and capacitor voltage ripple are small. (b) Plot your results of part (a) over the range 0 ≤ D ≤ 1. (c) Dc design: for the specifications Vg = 20 V V = −10 R = 6Ω fs = 100 kHz (i) Find D and I (ii) Calculate the value of L that will make the peak inductor current ripple ∆i equal to ten percent of the average inductor current I. (iii) Choose C such that the peak output voltage ripple ∆v is 0.1 V. (d) Sketch the transistor drain current waveform iT (t) for your design of part (c). Include the effects of inductor current ripple, and label numerical values and axes. What is the peak value of iT ? Also sketch iT (t) for the case when L is decreased such that ∆i is 50% of I. What happens to the peak value of iT in this case? (e) Sketch the diode current waveform iD(t) for the two cases of part d. 2. The boost converter illustrated in Fig. 2 operates with the following conditions: Input voltage Vg = 5.2. V Output voltage V = 7 V Switching frequency fs = 600 kHz All elements are ideal, and the converter operates in steady state with small inductor current ripple and small capacitor voltage ripple. L D1 + Vg v – Figure 2 Boost converter of Problem 2. (a) What is the duty cycle? (b) Sketch the waveform of the MOSFET drain-to-source voltage. Label the numerical values of all relevant times and voltages. (c) Find the dc component of the voltage waveform of Part b. Page 3 L1 iT Q1 L2 i1 + i 2 + – C1 vC1 D1 C2 R – 3. To reduce the switching harmonics present in the input current of a certain buck converter, an input filter consisting of inductor L1 and capacitor C1 is added as shown in Fig. 3. Such filters are commonly used to meet regulations limiting conducted electromagnetic interference (EMI). For this problem, you may assume that all inductance and capacitance values are sufficiently large, such that all ripple magnitudes are small. + Vg v – Figure 3 Addition of L − C input filter to buck converter, Problem 3. (a) Sketch the transistor current waveform iT (t). (b) Derive analytical expressions for the dc components of the capacitor voltages and inductor currents. (c) Derive analytical expressions for the peak ripple magnitudes of the input filter inductor current and capacitor voltage. (d) Given the following values: Input voltage Vg = 12 V Output voltage V = 5 V Switching frequency fs = 400 kHz Load resistance R = 1.25 Ω Select values for L1 and C1 such that (i) the peak voltage ripple on C1, ∆vC1, is two percent of the dc component VC1, and (ii) the input peak current ripple ∆i1 is 10 mA.