Question

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A DCM boost converter is to be designed to operate under the following conditions. 18 V V36 V 5 W Pout < 100 W Vo =48 V fs = 150 kHz You may assume that there is a mechanism which automatically varies the duty ratio to maintain the output voltage constant at 48 V. Design the converter subject to the following conditions The converter must operate in DCM for the entire operating range. To ensure adequate design margin, the inductance L must be chosen that K never exceeds 75% of Kerit at all operating points Given the above requirements, choose the element values to minimize the peak inductor current The output peak voltage ripple should be less than 1 V. Specify (a) The inductor value, L. (5) (b) The output capacitor value, C (5) (c) The worst-case peak and r.m.s inductor current iL (5+2) (d) Design the inductor. At this frequency, ferrites are suitable as core material. Use Bm of 0.2 T. Data sheets are attached (10)

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18 v lessthanorequalto v_g lessthanorequalto 36 v 5w lessthanorequalto p_out lessthanorequalto 100w v_0 = 48 v B_s = 150 khz the A_v range will be, A_v min = 48/36 = 4/3 A_v max = 48/18 = 8/3 4/3 lessthanorequalto A_v lessthanorequalto 8/3 4/3 lessthanorequalto A_v lessthanorequalto 8/3 we have to choose the value of D, such that the converter operates at discontinuous conduction mode always \r\n For, boost converter k_rpit (D) = D(1 - D)^2 A_v = 1 + squareroot 1 + 4D^2/k/ 2 = 1 + squareroot 1 + 4D^2/D(1 - D)^2/2 at k_enpt (D) = D(1 - D)^2 case 1: for A_v = 4/3 1 + squareroot 1 + 4D^2/D(1 - D)^2/2 = 4/3 implies squareroot 1 + 4D^2/D(1 - D)^2 = 8/3 - 1 = 5/3 implies 1 + 4D/(1- D)^2) = 25/ 9 implies 4D /(1 - D)^2 = 16/9 implies D/1 - 2D + D^2 = 4/9 implies 9D = 4 - 8D + 4D^2 implies 4D^2 - 17 D + 4 = 0 implies 4D^2 - 17 D + 4 = 0 implies D =

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