PWM-Scheme and Current ripple of Switching Power Amplifiers

Transcription

1 axon oor PWM-Sch and Currn rippl of Swiching Powr Aplifir Abrac In hi work currn rippl caud by wiching powr aplifir i analyd for h convnional PWM (pulwidh odulaion) ch and hr-lvl PWM-ch. Siplifid odl for iaion ar inroducd for h lcion of h wiching frquncy and h inducanc in ri for a crain oor. Inroducion p o now rvo oor ar widly applid in all powr driv bcau of hir ipl conrol ragy and high prforanc. In ordr o kp all powr lo in h powr circui, wiching powr aplifir bad on powr MOSFET ar ofn ud in uch a y. Howvr, wiching aplifir produc currn rippl, which i rongly aociad wih h PWM-ch ud in h powr aplifir, h wiching frquncy and h inducanc in h circui. Thi currn rippl will cau powr lo in h winding and ddy currn lo in h iron cor. A larg currn rippl ay cau couaion probl and vn horn h lif i of a oor. For h raon h apliud of h currn rippl u b liid in a oor o an accpabl valu (ypically < % I n ). In gnral, h apliud of currn rippl i rducd by incraing h induanc in h ain circui or by incraing h wiching frquncy of h powr aplifir. I i alo poibl o adop a propr PWM-ch. In hi work h currn rippl will b dicud for wo ainly ud PWM ch: convnional bipolar PWM and hr-lvl PWM. Powr circui Th wiching powr aplifir ofn ud i a choppr a hown in Fig.. In h circui h load of a oor i ribd wih -L-E, in which E i h inducd volag of h roor winding, proporional o h pd of roaion. and L ar h rianc and inducanc of h roor winding, rpcivly. According o h flow pah of h currn in h circui, hr ar igh diffrn working a, which ar hown in Fig. 2 (a)-(h). I D S Fig. DC choppr of driv 29.8./9Pw.doc/ZJ /9

2 axon oor I I D S D S I (a) I (b) D S D S I (c) I (d) D S D S I () I (f) D S D S (g) (h) Fig. 2 Opraing a of a choppr for rvo-driv 29.8./9Pw.doc/ZJ 2/9

3 axon oor Pulwidh Modulaion Th baic philoophy of wiching aplifir i ha of pul conrol in which h duraion of poiiv, ngaiv and zro pul ar conrolld o obain h dird avrag oupu. Thr ar vral baic principl: pulwidh odulaion (PWM), pul frquncy odulaion (PFM) and currn hyri conrol (CHC). For h rvo driv, h fir principl i ainly ud. According o h wavfor of h oupu volag, hr ar wo-lvl PWMch and hr-lvl PWM-ch. A convnional ch i a wo-lvl PWM. In hi ch h wo powr wich S, S 4 in Fig. ar conrolld wih h a wiching ignal S and h ohr wo wich, S 3 ar conrolld invrly wih /S, a hown in Fig. 3. Th wiching ignal i producd by h croing poin bwn h rquird volag r and h riangl rfrnc volag. Th wiching frquncy of h powr wich i conan, and qual h frquncy of h riangl volag ignal. Th oupu volag i ihr or -. Th powr circui work in h four diffrn a a hown in Fig. 2 (a), (b), (c), and (d). Wih a hr-lvl PWM-ch, h oupu volag i wichd aong,, and -. A coonly ud hr-lvl PWM-ch i h coplnary PWM-ch. A hown in Fig. 4, wo riangl rfrnc ignal, 2 in invr pha ar ud o gnra wiching ignal S /3 and S 4/2. In h powr circui, S i conrolld wih S /3 and S 3 i conrolld invrly wih S /3. S 4 i conrolld wih S 4/2 and i invrly conrolld. Wih hi PWM-ch, h igh a of h powr circui in Fig. 2 ar fully ud o conrol h currn. In Fig. 4, h conducion a of h circui ar indicad wih a...h, corrponding o h a in Fig. 2 (a)...(h). Th oupu volag appar a hr lvl, +,, and -. Th pulwidh of or - i proporional o h rquird volag r, and in h r of h priod, h oupu volag i zro. Th advanag of hi PWM-ch ar: h apliud of currn rippl i vry all whn h inducd volag nar zro (h oor work a a low pd), and h wiching frquncy i only half h frquncy of h oupu volag pul. Wih h applicaion of h coplnary PWM-ch, hrfor, h wiching frquncy a wll a h apliud of currn rippl in h oor can b rducd copard o h convnional PWM dicud abov. Thr ar alo ohr hr-lvl PWM-ch for h choppr. For inanc h PWMch ud in MINIPOS i alo a hr-lvl PWM, in which h wich and S 4 ar conrolld according o h polariy of h rquird volag, and S and S 3 ar wichd by a PWM ignal producd by a icroconrollr. Th wiching frquncy of S and S 3, howvr, i h a a h frquncy of h oupu volag pul. S r /S E - Fig. 3 /f i Wavfor of convnional wo-lvl PWM-ch S /3 S 4/2 + d - d r f d g d f 2 i a h a a h h b h b b h g Fig. 4 Wavfor of coplnary PWM-ch c f 29.8./9Pw.doc/ZJ 3/9

4 axon oor Currn rippl of a choppr Diffrn fro an linar powr aplifir, h wiching powr aplifir i a diconinuou ln. Th oupu volag i a pul ri producing currn diorion or currn rippl in an induciv load. Th currn haronic ar ponibl for xra powr lo in h powr circui and h roor winding, and ddy currn lo in h iron cor of h oor. A larg currn rippl ay vn cau couaion difficuli in h oor and ovrcurrn faul in h powr aplifir alhough h currn coponn i blow h raing valu. In hi cion h rlaion bwn h apliud and wiching frquncy a wll a h working poin of a oor will b udid and forula will b givn for h calculaion of currn rippl in h convnional PWM-ch and h coplnary PWM-ch. A dicud abov, h oupu volag i only wo-lvl whn h convnional PWMch i ud o conrol h powr aplifir. Th currn wavfor in h roor winding i hown in Fig. 5. Whn h volag drop acro powr ln i nglcd, h currn quaion ar givn a follow, I M = I τ + E ( τ ) () I = I τ M T + T E ( τ ) (2) whr T i h wiching priod T = /f, E i h inducd volag,, L ar h rianc and inducanc of h roor coil, rpcivly. τ i h lcrical i conan τ=l/. i h pulwidh of h poiiv volag I M I E i = T I E ( ) - /f Fig. 5 Currn wavfor wih h convnional PWM-ch and I = IM + I 2 ( ) i h coponn of h currn. Fro Eq. () and (2), h pak-pak valu of h currn rippl i givn a, = I I pp M = T T T E + I + ( 2 τ τ ) ( τ τ ) ( τ τ ) T +. 5( τ + τ ) (3) In h ady ca, h axiu currn rippl appar a 5% duy cycl ( =T /2, E=, I=), and Eq. (3) rduc o, 2 = + T T (4) 29.8./9Pw.doc/ZJ 4/9

5 axon oor In h a way, h quaion of h currn rippl (Fig. 6) can b givn for a hr-lvl PWM-ch. Whn h volag drop acro h powr ln i nglcd, h currn rippl i, = I I pp M = T T E + I + ( τ ) ( τ τ ) ( τ τ ) T +. 5( τ + τ ) (5) whr T i h pul priod of h oupu volag. In h coplnary PWM-ch, T=/(2f ), i.. only half h valu of T, and T I + E = I M I E - T Fig. 6 Currn wavfor wih a hr-lvl PWM-ch In h ady ca, h axiu currn rippl appar alo a 5% duy cycl ( =T/2, E= /2, I=), and Eq. (5) rduc o, = + T T (6) In Fig. 7 a coparion of currn rippl a a funcion of h inducd volag of h roor coil bwn convnional PWM and hr-lvl PWM i givn a h a pul frquncy of h oupu volag. I how ha h axiu currn rippl in h convnional PWMch i a E= and wic a high a in h hr-lvl PWM-ch whr h axiu.9.8 ippl currn rlaing o inducd volag E25 I~pp/*T/2L Convnional PWM-ch Thr-lvl PWM-ch E/ Fig. 7 Coparion of currn rippl bwn h convnional PWM-ch and a hr-lvl PWMch 29.8./9Pw.doc/ZJ 5/9

6 axon oor li a E= /2. A a rul, for a givn apliud of currn rippl, h wiching frquncy of h coplnary PWM-ch i only on fourh of ha of h convnional PWMch. Furhror, inc h currn rippl of a hr-lvl PWM-ch i vry all a low pd, i i paricularly appropria for h poiionning ak of a oor rvo driv. Pracical iaion of h axiu currn rippl In h nginring dign of rvo driv, i i rquird o drin h wiching frquncy and h inducanc in ordr o rduc h axiu currn rippl blow an accpabl lii. For hi purpo, i i poibl o u a ipl quaion o approxia h currn rippl. Hr, wo approxia quaion ar givn for h convnional PWM-ch and h hr-lvl PWM-ch, rpcivly. In h convnional PWM-ch, h axiu currn rippl i givn by Eq. (4). Whn h pul priod T of h oupu volag i uch allr han h lcrical i conan (T <<τ), Eq. (4) can b iplifid o, T = = 2L 2Lf (7) Th rror of h iaion i aociad wih h raio T /. An rror iulaion i givn in Fig. 8. Th rror of h iaion will b allr han 2% whn T < τ. To a hr-lvl PWM-ch, h axiu 8 currn rippl can alo iad wih a iplifid 6 ε quaion fro Eq. (6), whn T i all nough. i % T = (8) 4 L T Th rul of h rror analyi abov i valid alo for Eq. (8). Fig. 8 laiv rror of h iaion Fro Eq. (7) and (8), h axiu currn rippl i ainly dpndn on h -link volag, h wiching frquncy, and h inducanc of h circui. 4 2 Pracical applicaion of iaion forula In pracical applicaion, w can u h wo approxia forula o ia h currn rippl in a rvo oor. On anohr hand, w can alo u h o calcula h inducanc rquird in h circui in ordr o lii h apliud of currn rippl. Th condiion o u Eq. (7) and (8) i ha h pul priod u b allr han h lcrical i conan of h roor coil. For MAXON oor, h lcrical i conan rang fro.8 o.25, corrponding o a wiching frquncy rang fro 4 o 2.5 khz. ually, h wiching frquncy of h aplifir ud for h MAXON oor i highr han 2 khz. Thrfor, h iaion of h apliud of currn rippl wih h quaion Eq. (7) and (8) i rliabl. Two calculaion xapl and a pracical aurn o h calculad rul ar givn in appndix /9Pw.doc/ZJ 6/9

7 axon oor Concluion In hi work, h currn rippl producd by wiching aplifir for DC MAXON oor ar udid in dail. For pracical purpo wo ipl forula can b ud o ia h axiu currn rippl and drin h inducanc rquird o lii h currn rippl. Appndix Exapl : Th calculaion of h currn rippl in a DC oor upplid wih a wiching powr aplifir, convnional PWM-ch Moor Moor parar: n = 24 V, I n =3.3 A, L = 56 µh, =.35 Ω Powr aplifir: 4-Q Srvo aplifir, MMC-Q658-5PDA, Sri Nr. 633, =48 V, f =26.7 khz Addiional xrnal inducanc: L =6 µh L + L Elcrical i conan: τ = =. 86 Th axiu currn rippl i givn by Eq. (4), 2 = + 2 f τ 2 f τ 2 V = Ω kHz kHz. 86 =. 775A or h axiu currn rippl can b iad wih Eq. (7) 48V = = = 775. A 2Lf 2 6. H 26. 7kHz Th rul fro Eq. (4) and Eq. (7) ar h a. If h currn rippl i o b liid o blow % of I n, h oal inducanc in h circui according o Eq. (7) hould b, 48V L = = = H 2 I f 2 % 3. 3A 26. 7kHz Hnc, h xra inducanc in ri wih h roor coil i now (inad of.6 H), L = L L = H. 56H = 2. 64H Or h wiching frquncy hould b incrad wihou any ohr inducanc in ri, according o Eq. (7), f 48V = = = 3kHz 2 I L 2 % 3. 3A. 56H 29.8./9Pw.doc/ZJ 7/9

8 axon oor Exapl 2: Th calculaion of h currn rippl in a DC oor upplid wih a wiching powr aplifir, hr-lvl PWM-ch Moor E EBA2A Moor parar: n = 24 V, I n =.22 A, L = 24 µh, =2.34 Ω Powr aplifir: MINIPOS, =24 V, f =6 khz Addiional xrnal inducanc: L =4 µh L + L Elcrical i conan: τ = =. 274 Th axiu currn rippl i givn by Eq. (6), = + 2 f τ 2 f τ 24V = 2. 34Ω + 2 6kHz kHz. 274 =. 56 A or h axiu currn rippl can b iad wih Eq. (8) 24V = = =. 56 A 4Lf 4. 64H 6kHz If h currn rippl i o b liid blow % of I n, h oal inducanc in h circui according o Eq. (8) hould b, 24V L = = =. 82H 4 I f 4 % 22. A 6kHz Thn, h inducanc in ri i now (inad of.4 H), L = L L =. 82H. 24H =. 58H Or h wiching frquncy hould b incrad wihou any ohr inducanc in ri, according o Eq. (7), f 24V = = = 25kHz 4 I L 4 % 22. A. 24H No: in hi xapl, h -link volag qual h raing volag of h oor n. In ordr o kp h dynaical prforanc of h oor nar h raing opraing poin, h link volag hould b abou wic h raing volag. Howvr, DS (drain-ourc)of h MOSFET in MINIPOS i 5 V, and hrfor, h -link volag hould b kp blow 25 V. For hi raon, MINIPOS powr ag i no appropria for oor wih a raing volag highr han 6 V /9Pw.doc/ZJ 8/9

9 axon oor Pracical aurn of currn rippl Moor: , Powr aplifir: 4-Q Srvo aplifir, MMC-Q658-5PDA, Sri Nr. 633 f = 26.7 khz, = 48 V, L = 6 µh In h following, wo currn wavfor of an ocillocop ar hown. ni of currn aurn: 2.2 A/V ) noll = V, zro pd 2) noll = 9V, high pd 29.8./9Pw.doc/ZJ 9/9