Q2 (Total 50 points) DCM mode boundary analysis of the Cuk converter of Fig.3. The capacitor...

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Q2 (Total 50 points) DCM mode boundary analysis of the Cuk converter of Fig.3. The capacitor voltage ripples are small. (a) (25 pt) Sketch the diode current waveform for CCM operation. Find its peak value, in terms of the ripple magnitudes AiL1, AiL2, and the de components I, and I₂, of the two inductor currents i(t) and i12(t), respectively. (b) (25 pt) Derive an expression for the conditions under which the Cuk converter operates in the discontinuous conduction mode. Express your result in the form K < Kerit (D), and give formulas for K and Kerit (D). VC₁ = A4, = D + Va 2₁ V₂DT, 241 HH Figure 3: Cuk converter for problem Q2. you CCM analysis of cuk converter is given as in Chapter 2. Some results that will need to use are below: D₁ v=-DV₁₁ 4₁=1 4 = (D) ² ½ / 42 = DR V.DT, Al₂ = 21₂ + R V Q2 (Total 50 points) DCM mode boundary analysis of the Cuk converter of Fig.3. The capacitor voltage ripples are small. (a) (25 pt) Sketch the diode current waveform for CCM operation. Find its peak value, in terms of the ripple magnitudes AiL1, AiL2, and the de components I, and I₂, of the two inductor currents i(t) and i12(t), respectively. (b) (25 pt) Derive an expression for the conditions under which the Cuk converter operates in the discontinuous conduction mode. Express your result in the form K < Kerit (D), and give formulas for K and Kerit (D). VC₁ = A4, = D + Va 2₁ V₂DT, 241 HH Figure 3: Cuk converter for problem Q2. you CCM analysis of cuk converter is given as in Chapter 2. Some results that will need to use are below: D₁ v=-DV₁₁ 4₁=1 4 = (D) ² ½ / 42 = DR V.DT, Al₂ = 21₂ + R V