The ZCS Boost Converter
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1 EEL646 Pwer Elernis II Chaper 6 Leure Dr. Sam Abdel-Rahman The ZCS Bs Cnverer The bs-quasi-resnan nverer wih an M-ype swih as shwn Fig. 6.(a, wih is equivalen irui shwn Fig. 6.(b. (a (b Fig 6. (a ZCS bs nverer wih M-ype swih. (b Simplified equivalen irui.
2 EEL646 Pwer Elernis II Chaper 6 Leure Dr. Sam Abdel-Rahman ZCS Bs: Equivalen Cirui Mdes (a (b ( (d Fig 6.4 (a Equivalen irui fr mde I. (b Equivalen irui fr mde II. ( Equivalen irui fr mde III. (d Equivalen irui fr mde I.
3 EEL646 Pwer Elernis II Chaper 6 Leure Dr. Sam Abdel-Rahman Mde I [ < ]: ZCS Bs Cnverer: Seady-Sae Analysis Assume swih and he dide are bh ON The upu vlage is given by dil L d The iial dur urren and apair vlage, i l ( v ( Inegrag Eq. (6.4, he dur urren bemes, i ( + i ( L L L L When he resnan dur urren reahes he pu urren,, he dide urns OFF, L I wih given by, I L i A, he dide urns OFF se L, and he nverer eners Mde II. I I
4 EEL646 Pwer Elernis II Chaper 6 Leure Dr. Sam Abdel-Rahman Seady-Sae Analysis (n d Mde II [ < ]: The swih remas lsed, bu he dide is OFF a Mde II as shwn Fig. 6.4(b. This is a resnan mde durg whih he apair vlage sars dereasg resnanly frm is iial value f. When i L I, he apair reahes is negaive peak. A. i L equals zer, and he swih urns OFF, hene, swihg a zer-urren. The iial ndis, v ( i ( L I Frm Fig. 6.4(b, he firs derivaives fr i L and v are, di d L L dv C d I v i L Usg he same slu ehnique used he buk nverer slve he abve differenial equas, he express fr i L ( (6.7 il( I + s ω( Z v ( s ( ω where ω LC A, i L ( and he ime erval an be baed frm evaluag Eq. (6.7 a yield, IZ ( s ( [ s I ( Z π + ] (6.9 ω ω (6.8 4
5 EEL646 Pwer Elernis II Chaper 6 Leure Dr. Sam Abdel-Rahman Seady-Sae Analysis (n d Mde III [ < ]: Mde III sars a, and he swih and he dide are bh pen as shwn Fig. 6.4(. Se v is nsan, he apair sars hargg up by he pu urren sure. The apair vlage, v C I d I ( + C v ( (6.4 The dide begs ndug a when he apair vlage is equal he upu vlage, i.e. v (. I ( C + v ( Time erval his perid I [ C v ( ] (6.4 Mde I [ < 4 ]: A, he apair vlage is lamped he upu vlage, and he dide sars ndug aga. The yle f he mde will repea aga a he ime f T s when S is urned ON aga 5
6 EEL646 Pwer Elernis II Chaper 6 Leure Dr. Sam Abdel-Rahman ZCS Bs-Typial Seady-Sae Wavefrms Typial seady sae wavefrms are shwn Fig Fig 6.5 Seady-sae wavefrms f he bs nverer wih M-ype swih. 6
7 EEL646 Pwer Elernis II Chaper 6 Leure Dr. Sam Abdel-Rahman lage Ga Cnserva f energy per swihg yle express he vlage ga, M / The pu energy is, ZCS Bs Cnverer E I T s (6.4 The upu energy, T s E i d (6.4 The upu urren equals i I -i L and i I fr ervals and <T s,, E T s ( I il d + I d (6.44 The pu urren is baed frm he nserva f upu pwer as: I R 7
8 EEL646 Pwer Elernis II Chaper 6 Leure Dr. Sam Abdel-Rahman ZCS Bs-lage Ga Subsiug fr he pu urren and by evaluag Eq. (6.44, he upu energy bemes E ( I d + I ( Ts L ( I + I ( Ts L I L [ ] (6.45 wih and ( T, and use he equas fr. s Ts + ( + ( ( and ( frm Eqs. (6.9 and (6.4, Eq. (6.45 bemes, E α C I + [ ( s α L I Ts ] ω I The vlage ga express is given by, (6.46 M fns M Q + + M α ( s α π Q M (6.47 where, α, M, I and f ns are given as befre. 8
9 EEL646 Pwer Elernis II Chaper 6 Leure Dr. Sam Abdel-Rahman ZCS Bs-Cnrl Charaerisi Curve Fig 6.6 shws he haraerisi urve fr M vs. f ns as a fun f he nrmalized lad. Fig 6.6 Charaerisi urve fr M vs. ƒ ns fr he bs ZCS nverer. 9
10 EEL646 Pwer Elernis II Chaper 6 Leure Dr. Sam Abdel-Rahman Example 6. ZCS Bs Cnverer Design a bs ZCS nverer fr he fllwg parameers:, W, f s 5kHz. 4. P Slu: 4 The vlage ga is M Le us sele urve f Fig. 6.6, Q an be apprximaed 6. f ns. 8. Frm he haraerisi The haraerisi impedane is given by, Z R 8 Ω. Ω Q 6 (6.48 Resnan frequeny is, f f f f s ns 5 khz kHz.8 (6.49 Slve Eqs. (6.48 and (6.49 fr L and C Z L πf C Z ω (.( π Ω π H 8.4nF
11 EEL646 Pwer Elernis II Chaper 6 Leure Dr. Sam Abdel-Rahman Example 6. Design a bs nverer wih ZCS, wih he fllwg design parameers: 5, P W a I.5A, and f s khz. Assume he upu vlage ripple is. % Slu: P The lad resisane, R I M s 6 5.4, (.5 Ω Frm he haraerisi urve f Fig. 6.5, apprximae Q 6 when we assume f n.58. f 7.4 khz..58 Frm Q and R, he haraerisi impedane is baed frm, Q R 6, and Z Z Z L C ( ω Slvg fr C and L L C π / se 8.7 C 46.7ηF L 8.5µH rad ZCS Bs Cnverer
12 EEL646 Pwer Elernis II Chaper 6 Leure Dr. Sam Abdel-Rahman 4 The ime ervals are given by L I 8.5. r i.7µ s 6 Z I i s ω. s.9µ s ω Z I n 8.7.9µ s i ( sα T 6. ( ( ( s µ s Example 6. (n d
13 EEL646 Pwer Elernis II Chaper 6 Leure Dr. Sam Abdel-Rahman Oher ZCS Bs Cnverer Figure 6.7(a shws he quasi-resnan bs nverer by usg he L-ype resnan swih, and he simplified irui and is seady sae wavefrms are shwn Fig.6. 7(b and (, respeively. (a Reverse apair vlage plariy (b ( Fig 6.7 (a ZCS bs nverer wih L-ype swih. (b Simplified equivalen irui. ( Seady-sae wavefrms.
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