Switch-Mode Regulators Buck Regulator Boost Regulator Buck-Boost Regulator Cúk Regulator Buck Regulator vgvg vovo RoRo C L VsVs isis iLiL icic i0i0 iDiD

vgvg t KT 0 TT+KT 2T KT 0 TT+KT 2T iLiL t i Lmax i Lmin KT 0 T T+KT 2T t ioio icic t KT 0 TT+KT 2T vovo ∆v o For 0 ≤ t ≤ KT v s – v o = L ∆ i L / (KT) assuming that v o ≈ constant then, ∆ i L = K (v s – v o ) / (f L) …..(1) where ∆ i L = i Lmax - i Lmin For KT ≤ t ≤ T -v o = L ( - ∆ i L /(T-KT) ∆ i L = v o (1-K) / (f L) …..(2) equating (1) and (2), then, K (v s – v o ) / (f L) = v o (1-K) / (f L) then, V o = K V s where V o is the average value of v o Another method; Noting that i s = i L in the interval 0 ≤ t ≤ KT KT 0 T T+KT 2T isis i Lmax i Lmin ioio (exaggerated!) then, I s = K i o noting that Vs Is = Vo Io and, V o = K V s VoVo K 0 1 VsVs

I c is the average rectified value of i c I c = ½ T/2 ∆I L /2 = ⅛ ∆I L /f ∆ V o = 1/C. I c = ∆I L / (8fC) = v o (1-K) / (8f 2 LC) Boost Regulator vgvg vovo RoRo C L VsVs isis iDiD icic i0i0 For 0 ≤ t ≤ KT mode 1 vgvg t KT 0 TT+KT 2T vgvg VsVs isis vovo RoRo icic i0i0

KT 0 TT+KT 2T isis t i smax i smin IsIs KT 0 T T+KT 2T t iCiC mode (2) For KT ≤ t ≤ T vovo RoRo C VsVs isis iDiD icic i0i0 IoIo isis KT 0 TT+KT 2T t vovo ∆v o For 0 ≤ t ≤ KT V s = L ∆ i s / (KT) ∆ i s = KV s /(fL) …(1) For KT ≤ t ≤ T V s – V o = - L ∆ i s /(T-KT) ∆ i s = (1 – K) (V o – V s ) / (fL) …(2) then, K V s = (1 – K) (V o – V s ) Vo = Vs / (1 – K) I o. K T = (I s –I o ). ( T – KT) then, I s = I o / (1-K) ∆ V o = 1/C. (I o. KT) ∆ V o = K I o / f C K VoVo 01 VsVs 0.5 2V s !

Buck-Boost Regulator vgvg vovo RoRo C L VsVs isis iDiD icic i0i0 iLiL for 0 ≤ t ≤ KT L VsVs isis iLiL vovo RoRo i0i0 C icic Mode 1 V s = L ∆ i L / KT ∆ i L = K Vs / (f L) t KT 0 TT+KT 2T vgvg KT 0 TT+KT 2T iLiL t i Lmax i Lmin ioio KT 0 T T+KT 2T t i Lmax i Lmin KT 0 T T+KT 2T t i Lmax i Lmin ioio I s K = I o (1 – K) I s = K / (1-K). I o

vovo RoRo C L iDiD icic i0i0 iLiL For KT ≤ t ≤ T mode 2 KT 0 T+KT t iCiC T 2T KT 0 T+KT t T 2T vCvC VoVo K VsVs !

Ćuk Regulator vovo RoRo C1C1 L2L2 VsVs isis i L2 icic i0i0 iDiD vgvg L1L1 2C2C vgvg t KT 0 TT+KT 2T vovo RoRo C1C1 L2L2 VsVs i L1 icic i0i0 L1L1 2C2C Mode 1 For 0 ≤ t < KT + _ i L2

vovo RoRo C1C1 L2L2 VsVs i L1 icic i0i0 L1L1 2C2C + _ i L2 Mode 2 For KT ≤ t < T For 0 ≤ t < KT V s = L 1 ∆ I L1 /(KT) (1) ∆ I L1 = K Vs /(fL 1 ) For KT≤ t < T V s – V C1 = - L 1 ∆ I L1 /(1-K)T (2) Substituting from (1) into (2), V s – V C1 = - K /(1-K) V s V C1 =[(1 + K/(1-K) ] V s V C1 = V s /(1-K) For 0 ≤ t < KT V C1 – V o = L 2 ∆ I L2 /(KT) (3) For KT≤ t < T -V o = - L 2 ∆ I L2 /(1-K)T (4) Substituting from (3) into (4), – V o = - K ( V C1 – V o ) / (1-K) V o = K V C1 V o = K/(1-K) V s

for 0 < t ≤ KT V c1 – V o = L 2 ∆I L2 / (KT) ∆I L2 = K ( V C1 – V o ) / (fL 2 ) ∆I L2 = K [ Vs /(1-K) – KVs /(1-K) ] / (fL 2 ) ∆I L2 = K V s / fL 2 t i L1 i L1max i L1min t i L2 i L2max i L2min KT T T v c1 t i C1 i L2max i L2min KT T -i L1max -i L1min IoIo IoIo t KT T ∆v C1 (exaggerated!)

V s I s = V o I o V s I s = K V s /(1-K). I o I s = K/(1-K). I o ∆ v C1 = 1/C 1. ∫ i C1 dt = I o T K/C 1 ∆ v C1 = K I o /(fC 1 ) ∆ v o = 1/C 2. ∫ i C2 dt = 1/C 2. ½. T/2. ½ ∆I L2 ∆ v o = K V s / (8f 2 C 2 L 2 ) i C2 t KT T T+KT 2T t vovo ∆V o (exaggerated!)