haper 4 D converer and D swich
4.1 Applicaion - Assumpion Applicaion: D swich: Replace mechanic swiches D converer: in racion drives Assumions: Ideal D sources Ideal Power emiconducor Devices
4.2 D swich o ON/OFF D curren Principle scheme using GO ON i G OFF a) V R i V i V i V i V V R i G R
sing hyrisor: ON ON OFF ommuaion ircui () OFF O P V O P
4.3 D converer classificaion 4.3.1 Based on he mehod of implemenaion Direc Pulse converer Indirec Inverer onrolled recifier 4.3.2 Based on he funcion Volage decreasing serial circui D firs quadran chopper Volage increasing parallel circui D second quadran chopper Pulse onrol he value of resisor ep-down (Buck) converer ep p (Boos) converer Buck Boos converer úk - converer 4.3.3 Based on he mehod of conrol Pulse frequency Pulse wih wo values of curren
4.4 Operaion principles of D - D converer 4.4.1 D firs quadran chopper Operaion principles I : = = i : exponenially increases o he value ( - E ư )/R i Energy from he source i V E ư is parly sored in he inducance, almos is V R used o charge E ư, and he res is wased on resisor R i i V I I las in duraion 1. I finishes when OFF signal is sen o swich. uc V V 1 2 Δ MIN i M
I V: = = i V : exponenially decreases o he value -E ư /R Energy (sored in ) is free, almos is used o charge E ư, he res is wased on resisor R i i V V uc R E ư V V 1 2 i i V I Δ MIN i M I V las in duraion 2. I finishes when ON signal is sen o he swich.
Average value of he volage on he load i = 1 = z uc V V z: duy raio z 1 i i V E ư 1 2 Δ i zi V R i i V I MIN M I z R E i =
4.4.2 D second quadran chopper Operaion principles I : uc V V = = i ; exponenially increases o he value E ư /R i V V E ư 1 2 i Energy from he source E ư is almos sored in he inducance, he res is wased on he resisor R i R i iv imin M I las in duraion 1. I finishes when he OFF signal is sen o he swich
I V: = uc V V = i V ; exponenially decreases o he value (E ư )/R < Energy from he source E ư and from (sored by previous I), is wased parly on he resisor R, almos is reurned o he source. i V V i R E ư 1 2 i i iv imin M I V las in duraion 2. I finishes when he ON signal is sen o he swich.
Average value of he volage on he load i 2 = = 1 = = = z ( 1 ) i V V i R E ư uc V V 1 2 i i iv imin M I z E = R i
4.4.3 Pulse resisor converer i uc i R R p uc RP =i +i R 1 2 i i R i M MIN Operaion principles I : = i : increases wih he linear facor / I las in duraion 1. I finishes when he ON signal is sen o he swich.
i i R R p uc =i +i R 1 2 i i R i M MIN I = i R ; Exponenially decrease o he value /R p. I las in duraion 2. I finishes when he OFF signal is sen o he swich
Equivalen value of resisor R ei i i R R p uc =i +i R 1 2 i i R i M MIN 2 I = RpI 2 I = = 2 R Rei p 2 Rei = Rp = ( 1 z) R R p ei Rp
4.4.4 ep Down Buck converer Assumpion: he inducor curren is always posiive oninuous onducion Mode (M): ( ) z = (1 z) O O D volage ransfer funcion: M O = = z
Deermine and : he value of he filer inducance ha deermines he boundary beween M and DM: b = (1 zr ) 2 f For > b, he converer operaes in he M he filer inducor curren i in he M consiss of a dc componen IO wih a superimposed riangular ac componen. Almos all of his ac componen flows hrough he filer capacior as a curren i c. urren i c causes a small volage ripple across he dc oupu volage O. o limi he peak-opeak value of he ripple volage below a cerain value r, he filer capaciance mus be greaer han: (1 z ) O min = 2 8f r
4.4.5 ep p Boos converer Assumpion: oninuous onducion Mode z = ( )(1 z) O D volage ransfer funcion: M O 1 = = 1 z
Deermine and : he value of he filer inducance ha deermines he boundary beween M and DM: b = (1 z) 2 f 2 zr For > b, he converer operaes in he M A larger filer capacior is required in comparison o ha in he buck-derived converers o limi he oupu volage ripple. he filer capacior mus provide he oupu dc curren o he load when he diode D is off. he minimum value of he filer capaciance ha resuls in he volage ripple r is given by: min = zo Rf r
4.4.6 Buck Boos converer he condiion of a zero vol-second produc for he inducor in seady sae yields: z = O (1 z ) D volage ransfer funcion: M O z = = 1 z
Deermine and : he value of he filer inducance ha deermines he boundary beween M and DM: b = (1 z) 2 f 2 R For > b, he converer operaes in he M he srucure of he oupu par of he converer is similar o ha of he boos converer (reversed polariies are he only difference): min = zo Rf r
4.4.7 úk converer apacior 1 is in seady sae if: I 2z = I 1 (1 z ) For a lossless converer P = I = I = P 1 O 2 O D volage ransfer funcion: M O z = = 1 z
Deermine and : he value of he filer inducance ha deermines he boundary beween M and DM: (1 zr ) (1 zr ) = ; = 2zf 2f b1 b2 he oupu par of he úk converer is similar o ha of he buck converer. Hence, he expression for he filer capacior is: (1 z ) O min = 2 8f r he peak-o-peak ripple volage in he capacior 1 can be esimaed as: r1 = zo Rf 1
4.5 ommuaion circui 4.5.1 circui V i V u ()= = u i u () u i = i u O u i 2 1 di u () + id + = d ω v: angular frequency of circui u i = () sin ωv+ i ()cos ωv 1 ω v =
1 u = u() + id = = + [ u () ] cos ωv+ i()sinωv
4.5.2 Analysis he commuaion circui of he D chopper uc i V1 i V1 u i u V1 V2 i i V V R E ư 1 V3 V
i V1 i V1 u i u V1 V2 V V1 V3 2 1 2 V1 V2 V K 1 Q K 1 V3 V 1 3 4 5 6 7 u i I V (, 1 ) -K 1 = i V, u V =, = V1 uppose ha u = i V1 I u V2 = ; u V1 = u V1 u V2 i V2 V2 i = i V1 = i V2 = K 1 i V2 i V I
i V1 i V1 u i u V1 V2 1 V3 V V V1 V3 2 1 2 V1 V2 V K 1 Q K 1 3 4 5 6 7 I V1, V3 ( 1, 3 ) u i -K 1 A 1 send he ON conrol signal o V1 = ; u V = - = - V is OFF V1 urren = I z runs hrough V1 i V1 I u = cos ω ( ) v 1 u V1 u V2 i V2 V2 i = sin ωv( 1) I K 1 i V2 i V
i V1 i V1 u i u V1 V2 V V1 V3 2 1 2 V1 V2 V K 1 Q K 1 V3 V 1 3 4 5 6 7 u i -K 1 u V1 = i V1 = I -i u V2 = -u i V2 = i V1 I V1 A = 3, he curren i = ; V3 is OFF u ( 3 ) = -K 1 ; K 1 =.7.9 u V1 V2 u V2 i V2 K 1 i V2 i V I
i V1 i V1 u i u V1 V2 V V1 V3 1 2 V1 V2 V K 1 Q K 1 V3 V 2 1 3 4 5 6 7 u i I V1 ( 3, 4 ) -K 1 All curren, volage values are preserved as he ime = 3 V1 i V1 I u V1 u V2 i V2 V2 K 1 i V2 i V I
i V1 i V1 u i u V1 V2 1 V3 V V V1 V3 2 1 2 V1 V2 V K 1 Q K 1 3 4 5 6 7 u i I V2 ( 4, 6 ) -K 1 A = 4 he ON conrol signal is sen o V2 u V2 = V1 he negaive volage of pus on V1 V1 is OFF 1 i = I u = u ( ) + I d 4 I = ( 4) K 1 4 I i V1 I u V1 u V2 K 1 V2 i V
i V1 i V1 u i u V1 V2 1 V3 V V V1 V3 2 1 2 V1 V2 V K 1 Q K 1 3 4 5 6 7 u i I V2 ( 4, 6 ) -K 1 i V2 = I u V1 = u i V1 = = u = -u V i V1 I A = 6, = V is ON, V2 is OFF he I V begins ( 6 ) = u = u V1 V1 V2 u V2 i V2 K 1 i V2 i V I
harging o a he very sar of operaion ON he valve V2 firs onnec capacior direcly o source by a resisor for curren resricion Deermine he values and V1 uses he duraion ( 4, 5 ) o recover he blocking abiliy ( 5 4 ) MIN = offv1 K 1 ( 5 4) = = I I M offv1 K 1 V2 uses he duraion ( 1, 2 ) o recover he blocking abiliy ( 2 1 ) MIN = offv2 2 4 v π offv 2 2 1 = = = 2 ( ) 4 2 π
4.6 Principles o conrol volage pulse converer Pulse widh change 1 Pulse frequency change wo values of curren 4.6.1 Pulse widh conrol Keep f = 1/, change 1 1 2 u cm u P uc Đ ON OFF
4.6.2 Pulse frequency conrol Keep 1, change f = 1/ Pulse generaor ONM Delay 1 OFF Đ
4.6.3 wo values of curren conrol ON Ð uc u i1 Δ M OFF u i2 M MIN u i1 u i2 uc I' =I u i1 u i2 u i1 u i2 uc ommuaion BM ircui ON M uc > OFF uc < Ð V Pulse generaor plays he role of he curren conrol
4.7 Muli quadran pulse converer II I III IV I
4.7.1 wo quadran converer wih reversed curren V 1 2 V
4.7.2 wo quadran converer wih reversed volage 12 V2 V1 12 V2 V1 1 V1 V2 2 i 1 2 = = (2z 1) z >.5 zi > z <.5 zi < 1 2
4.7.3 Four quadran converer 12 V4 V3 12 V2 V1 34 V2 V1 34 V1 1 3 V3 V4 4 2 V2 12 V3 1 12 V1 V1 3 34 3 34