電流控制型切換式直流穩壓器之迴路補償器分析與設計

ᔁॎ̚

̂රԫఙጯੰ࿪፟ր

ၡ! ࢋ

ώ͛ࢵАޙϲᘦᑅጡᄃपࣃ࿪߹ଠטඉர̝ᇴጯሀݭĄ҃ޢĂੵͽᖎٽ۞

៍هᄲځਫ਼ྮྃᐺጡ۞నࢍࣧநγĂ֭೩΍˘ྋژё̝पࣃ࿪߹ଠטݭਫ਼ྮྃ

ᐺጡనࢍ͞ڱĄٙ೩΍̝ਫ਼ྮྃᐺጡనࢍ͞ڱੵࠎుՎёγ֭ͷΞᅅٽгӀϡ т Excel 5.0 ̝࿪ཝइ྅హវ૟׎ր௚̼Ăซ಼҃̂೩੼׎నࢍड़தĄ౵ޢĂ 附上模擬與實驗結果以驗證所提ਫ਼ྮྃᐺጡనࢍ͞ڱ۞正確性與可行性。

ᙯᔣෟĈਫ਼ྮྃᐺጡనࢍăᘦᑅጡăपࣃ࿪߹Ą

LOOP COMPENSATOR ANALYSIS AND DESIGN FOR

CURRENT-MODE-CONTROLLED SWITCH-MODE REGULATORS

Jenn-Jong Shieh

Department of Electrical Engineering, Ta Hwa Institute of Technology

Hsinchu, Taiwan 307, R.O.C.

Key Words: loop compensator, regulators, peak current.

ABSTRACT

In this paper, the mathematical models of DC regulators for peak current-mode-controlled strategy are first derived. Then, a simple concept is adopted to illustrate the principle of the loop gain compensator design, and the closed form design method for the peak current-mode-controlled DC regulators is proposed. The proposed design method is designed step by step and can be used easily. In addition, conventional computer software programs, such as Excel 5.0, can be used to systematically increase the efficiency of the design process. Finally, a prototype hardware circuit is constructed and some simulation and experimental results are presented for illustration.

˘ă݈! ֏

ܕ˟˩ѐֽĂϹೱёۡ߹ᘦᑅጡ۞నࢍ៍ه̏ు႙ࠎ నࢍ۰ٙ˞ྋĂ׎͹ࢋ۞ࣧЯдٺΑத৺(power stage)̈ੈ

ཱིሀݭ̶ژԫఙ̝͟ᔌјሢĂЯѩ଀ͽᑕϡ˘ਠቢّଠט

நኢֽనࢍਫ਼ྮྃᐺጡ(loop compensator)Ąᔵ̏གྷѣޝк ጯ۰೩΍ྋՙϹೱёۡ߹ᘦᑅ̈ੈཱིሀݭ̼̝நኢᄃ͞ڱ [1-6]Ă൒Ϥٺېၗ۩มπӮ̼ԫఙ(state-space average technique)[1-3]ٙ଀ז۞ቢّ̼ሀݭ̝࿅඀౵ٽࠎˠٙந ྋĂͷ׎ੵΞᑕϡтگᇇဦ(Bode plot)ăॲ࢖ྫဦ(root locus) ᄃ؉̀ဦ(Nichols chart)ඈ͞ڱ̶ֽژᖼೱጡ۞পّ֭ͽࠎ

ဦ 1! पࣃ࿪߹ଠטր௚͞๴ဦ

ۡ߹ᘦᑅጡਫ਼ྮྃᐺጡనࢍ۞ૄᖂγĂТॡϺΞͽࢎؠт ᓏᐛୂຏޘ(audio susceptibility)ăᏮ΍ܡԩ(output impe- dance)ᄃ࠹၆ᘦؠޘඈࢦࢋ۞̈ੈཱིఢॾĂЯѩᇃࠎ࿪໚

నࢍ̍඀रٙܦ༚ĄΩ˘͞ࢬĂಶа଱͞ё̝̙ТĂۡ߹

ᘦᑅጡ̝ਫ਼ྮྃᐺጡనࢍΞડ̶ࠎ࿪ᑅଠטݭ(voltage mode control)ᄃ࿪߹ଠטݭ(current mode control)׌̂ᙷĄ

݈۰ᔵ൒ٺநኢ˯ޝटٽࠎ̍඀रٙநྋĂ൒҃׎д఍ந ѣΠΗπࢬ࿬ᕇ(right half plane zero)̝ᘦᑅ࿪ྮॡĂ൑ڱ

྿זޢ۰ٙ׍ѣ̝Αड़Ăѩࠎிٙ࠰ۢ۞ְ၁[1-3,8]ĄΩ

ଂགྷᑻ៍ᕇ֏̝Ă࿪߹ଠטݭώ֗ӈ׍ѣᒠม࿅߹᜕̝ܲ

Αਕͷϫ݈̏ѣкछᇄથϠய࿪߹ଠטݭ PWM ଠטϡ ICĂੵᆊॾ˩̶ܮآγ֭Ξͽ೩ֻ੼ᒠม࿪߹ͽӀۡତᜭ જт MOSFET ̝ΑதΗጱវฟᙯ̮ІĄЯѩĂ̷ೱёᘦᑅ ጡ̙ኢߏңݭၗĂͽ࿪߹ݭଠטࠎ˘υ൒̝ᔌ๕Ąᔵ൒࿪

߹ଠטݭ፟ט׍ѣ˯ࢗኜкᐹᕇĂ൒Я׎ࠎᗕਫ਼ྮଠטĂ

̙༊నࢍ̝ਫ਼ྮྃᐺጡໂٽֹ଀ᘦᑅጡ̙ᘦؠ[7-11]Ą ѩγĂಶ࿪߹а଱፟ט̝̙ТĂ࿪߹ଠטݭ˘ਠΞડ

̶ࠎπӮ࿪߹ଠט(average current mode control)ᄃपࣃ࿪

߹ଠט(peak current mode control)׌̂ᙷĄ൒҃Яޢ۰׍ѣ ҋજ݈㒝а଱ྃᐺ(automatic feed forward compensation)ᄃ Տ˘̷ೱฉഇӈү࿪߹ࢨט(pulse by pulse current limiting)

̝Αਕ[7-9]Ąᔵ൒̏ѣ࠹༊̝͛ᚥ೩΍׎ਫ਼ྮྃᐺጡ۞న

ࢍ͞ڱᄃඉரĂҭ׎̂ౌᅮགྷϤనࢍણᇴ̝ᖼೱ͞ਕ఍ந ਫ਼ྮྃᐺጡ̝నࢍ[8-12]ĄΩ˘͞ࢬĂྋژё(closed form)

̝నࢍ͞ڱΞ೩̷ֻೱ࿪ྮ۞ۡᛇ˯߽၅˧ᄃሀᑢ̶ژਕ

˧Ăҭϫ݈׎࠹ᙯ͛ᚥ̝ଣ੅̪̙к֍[13-16]ĄЯѩĂώ

͛੫၆पࣃ࿪߹ଠט፟ט̷̝ೱёᘦᑅጡĂ೩΍˘इᖎٽ ͷ၁ϡ̝ྋژёਫ਼ྮྃᐺጡనࢍڱ݋֭૟׎ր௚̼Ăͽ̂

಼೩੼ਫ਼ྮྃᐺጡనࢍ۞ܮӀّᄃΞҖّĄ

ဦ 2 पࣃ࿪߹ଠטր௚̝ॡԔဦ

˟ăपࣃ࿪߹ଠטሀݭ̝ޙϲ

̙ኢߏଳϡң჌ଠט፟טĂਫ਼ྮྃᐺጡనࢍ̝ࢵࢋ̍

үӈޙϲ׎࠹၆ᑕ̝ᇴጯሀݭĄဦ 1 ٙϯࠎपࣃ࿪߹ଠט ր௚͞๴ဦĂ׎࠹၆ᑕ̝ॡԔဦтဦ 2 ٙϯĄ׎̚R ă_s s_n ᄃs ̶Ҿܑࠎפᇹ࿪߹_f i ̝פᇹ࿪ܡă˯̿ᄃ˭ࢫ୆தć_L

s ࠎγొྃᐺ୆தćҌٺ׎΁̝࿪ྮ௑ཱིтဦٙ̚ϯĄϤe

ဦ 2 ӍˠΞ଀

min 2

, 1 1

s n s s s

s dT R i R i

R = + (1)

s e c s n s s

s Ri RsdT v sdT

R

i1,max = 1,min+ = − (2) Ϥё(1)ᄃё(2)Ξ଀т˭̝ᙯܼё

1 2

s s n s s e c s

R dT s dT R s v i

R = − − (3)

ॲፂᕘજநኢĂ૟ё(3)̝Чតณ̟ͽт˭̝ᕘજĈ d

D d= + ˆ

1 1

1 I ˆi

i = +

c c

c V v

v = +ˆ

n n

n S s

s = +ˆ

e e

e S s

s = +ˆ (4)

૟ё(4)΃ˢё(3)ͷ઄నγొྃᐺ୆த׽ؠ̙ត(sˆ_e =0)Ξ

଀т˭̝ᘦၗᄃ̈ੈཱིજၗሀݭĄ

ࢫ ᑅ ݭ 1 − Rs

Ls

2 2L_s

̿ ᑅ ݭ 1 − Rs

s s s

L DT R

2

−

0 ࢫ̿ᑅݭ 1 −Rs

s s s

L DT R

2

− 0

ᘦၗሀݭ

s e s n s c

s DT S DT

S R V I

R = − −

1 2 (5)

̈ੈཱིજၗሀݭ

+高階項 +

−

−

= R S S Td

DT s R v i

R_{s c s} ^s _n ^{s n} _e) _sˆ ( 2

2 ˆ ˆ ˆ

1 (6)

Я ࠎ ҂ ᇋ ̈ ੈ ཱི ̶ ژ ॡ Ădˆ<<D, iˆ₁<<I₁, vˆ_c<<V_c,

n

n S

sˆ << Ă߇ё(6)̝̚੼ลีΞنர̙ࢍĄЯѩĂё(6)Ξ ࢦາܑϯт˭Ĉ

ˆ ) 2 ˆ ˆ

ˆ (

1 s n

s s c

m DT s

R i R v F

d= − − (7)

׎̚

s e n s

m RS S T

F ( 2 )

2

= + (8)

૟̙Тݭё̝ᘦᑅጡ̝sˆ ΃ˢё(7)Ξ଀ _n ˆ ) ˆ ˆ

( ˆ

ˆ Fm H1vc H2i1 H3vg H4vo

d= + + + (9)

׎̚H₁~ H₄̝ણᇴࣃтܑ˘ٙϯĄ

Ϥё(9)Ξۢ dˆ ࠎ vˆ ă_c ˆi ă₁ vˆ ᄃg vˆ ̝ቢّ௡ЪͷᏮˢ_o

࿪ᑅ̝ត̼ณvˆ ΞͅߍٺయЇฉഇ̝ត̼ณ dˆ ̚Ąٽ֏̝Ă_g पࣃ࿪߹ଠטώ֗ӈ׍ѣҋજ݈㒝а଱ྃᐺ̝ΑਕĄტ˯

ٙࢗĂӍˠΞ଀тဦ 3 ٙϯ̝पࣃ࿪߹ଠט̈ܫཱིր௚

ဦĄ׎̚

g o

v F v

ˆ ˆ

1≡ ă

d F v^o ˆ ˆ

2 ≡ ă

g L

v F i

ˆ ˆ

3≡ ă

d F i^L ˆ

4≡ ᄃ

o o

o i

Z v ˆ

≡ ˆ

̝ଯጱ˜ૄٺېၗπӮሀݭ(state average model)[1-3]Ąࣃ

଀˘೩۞ߏ̙ኢߏपࣃ࿪߹ଠטٕߏπӮ࿪߹ଠטĂᔵ൒

༊యЇฉഇD>0.5ॡ૟ጱ࡭ᘦᑅጡ̙ᘦؠ̍үĂҭΞγΐ

୆தྃᐺ̝Ą[3,7-8]

ˬăਫ਼ྮྃᐺጡ̝నࢍࣧந

ࢵАᑕϡ୥഑ᆧৈ̳ё(Mason’s gain formula)ٺဦ 3

ဦ 3 पࣃ࿪߹ଠט̈ܫཱིր௚ဦ

̚ Ă Ӎ ˠ Ξ ଀ ౕ ਫ਼ ྮ (closed loop) ̝ ᓏ ᐛ ୂ ຏ ޘ (audio susceptibility) Gaud ,CLᄃᏮ΍ܡԩ(output impedance) Zo,CL

т˭Ĉ

v i i CL

aud T T

F F F F T F

G + +

− +

≡ 1

) (

4 3 2 1 1

, (10)

v i

o i o CL

o T T

F F Z F T Z

Z + +

− +

≡ 1

) (

4 5 2

, (11)

׎̚

2 2

4

1 )

(FH H F F FF F

T_v = _{m v} − ≅ _{m v} (12)

F4

F F

T_i = _{m i} (13)

Ϥ˯ࢗΞۢ࿪߹ଠטݭ̝ਫ਼ྮᆧৈ(loop gain)T ࠎ₁ T ᄃ_v T_i

̝࠹ณ׶(T₁=T_i+T_v)Ąࡶ࿪˧࿪ྮ̝ણᇴࠎ̏ۢĂ݋F ă_m F ᄃi F ΞึӀՐ଀Ăซ҃଀ۢ₄ T ̝گᇇဦĄဦ 4 ٙϯࠎ_i አតs ̂̈ॡ_e T ࠹၆ᑕ̝ត̼ĄϤဦ 4 Ξۢࡶ_i s ͉̂Ă_e

࿪߹ଠטݭ̝ᐹᕇ૟ঐεĂӈѩॡᘦᑅጡ̝ਫ਼ྮྃᐺጡ̝

үϡтТ࿪ᑅଠטݭਠĄѩγĂT ٺᕭگጡ Вॎᐛத _i ωzc(=

c r_c

1 rad/sec)ޢĂӈ׍ѣ-20db/dec ̝পّĄЯѩӍ ˠдઇਫ਼ྮྃᐺጡ̝నࢍॡĂΞ૟ր௚ਫ਼ྮᆧৈ̝Ϲ෸ᐛ த(crossover frequency)ጐณؠ੼Ăͽഇր௚ਫ਼ྮᆧৈд఼

࿅Ϲ෸ᐛதॡĂր௚ਫ਼ྮᆧৈ͹ࢋүϡࠎT Ąٽ֏̝Ăր_i

௚ਫ਼ྮᆧৈдω_zc̝ޢӈ׍ k/s ̝ݭၗ(type)ĄЯѩΞഇ୕

ᘦᑅጡ׍ 90°̝࠹Ҝዶྈ(phase margin)̈́ᕭੵ੼ѨᏘگ

ဦ 4 s ၆ᑕ_e T ̝ត̼ဦ _i

(harmonics) ̝ ّ ਕ Ą Ҍ ٺ ᘦ ᑅ ጡ ٙ ᅮ ̝ ׍ Ҳ ᘦ ၗ ᄱ म (steady state error)̝ΑਕĂӍˠӈΞӀϡ݈̝ࢗ࿪ᑅݭਫ਼଱

ྃᐺጡ̝నࢍ͞ڱϤT ֽనࢍ_v F Ăֹ଀ᘦᑅጡ̝ր௚ਫ਼_v

ྮᆧৈݭၗٺω_zc̝݈ࠎ k/sĂтѩ˘ֽᘦᑅጡӈΞ׍Ҳᘦ

ၗᄱम̝Αਕ[8,16]Ą

αăਫ਼ྮྃᐺጡ̝నࢍՎូ

ૄٺᆇጡన౯ϡ࿪ᅮࢋᄃщఢࢋՐĂܔ࿺ёᘦᑅጡ (flyback regulator)дፋ࣎ᘦᑅጡξಞҫѣᓝ֖ᅅࢦ۞г ҜĄЯѩĂώ͛ͽဦ 5 ٙϯ̝࿣ᗓݭ(isolated type)ܔ࿺ё ᘦᑅጡࠎనࢍ၆෪Ăֽᄲځ˯ࢗٙ೩̝ਫ਼ྮྃᐺጡనࢍ۞

ܮӀّᄃ၁ϡّĄ׎నࢍՎូЕࢗт˭Ĉ

Վូ 1 ֶయЇฉഇ̝ቑಛᏴϡዋ༊̝ PWM ଠט ICĄӈ

ࡶD>0.5ĂᑕᏴϡ׍ѣࠎγొ୆தྃᐺ̝ PWM ଠט IC ֭నࢍ࿪߹ຏീ࿪ܡR ̝ࣃĄ _s

Վូ 2 ޙ ϲ ᘦ ᑅ ጡ ̝ Ч ี ฟ ྮ ᖼ ொ ב ᇴ F₁~ F₅ᄃ Z [1-3]Ą o

) ( 1 ˆ

ˆ

1 s

s

N N D D v

F v ^zc

p s g

o

∆ +

= ′

≡ ω

(14)

) (

) 1 )(

1 ( ˆ

ˆ

2 2

s s s

N N D

V d

F v ^{zc za}

p g s o

∆

− +

= ′

≡ ω ω

(15)

) (

) 1 ( ˆ

ˆ

3 2

s s

R D

D v

F i ^zL

g L

∆ +

= ′

≡ ω

(16)

) (

) 1 ˆ (

4 2

s s

R D

V d

F i^{L g zL}

∆ +

= ′

≡ ω

(17)

ဦ 5! ࿣ᗓݭܔ࿺ёᘦᑅጡ

) (

) 1 1 ( ˆ ˆ

5 s

s

i D

F i ^zc

o L

∆ +

− ′

=

≡ ω

(18)

) (

) ( 1

ˆ ˆ

2 1 1 1

s s Q s R i

Z v _eq

o o

o ∆

+ +

=

≡ ω ω

(19)

׎̚

)2

( 1

) (

o o o

s Q s s

ω ω ⁺ +

=

∆ (20)

c D R D R R D

L Q D

Ls c

o s ( )

1

2

2 + ′

+ ′

′

= ′

ω ⁽²¹⁾

c R R D Q L

c eq

s +

′

=

2 1 1

1 1

ω ⁽²²⁾

D2

R R D

R_eq D _c ^Ls + ′

= ′ (23)

c R_c

zc

= 1

ω (24)

s

za DL

R D′²

ω = (25)

zL Rc

= 1

ω (26)

c L D

s o

= ′

ω (27)

c eq

o R

ω R

ω₁= (28)

Վូ 3 ॲፂϤצଠវ̶̝̄ᄃ̶ϓลᇴĂϤ࿪ᑅਫ਼ྮT_v ՙؠਫ਼ྮྮྃᐺጡ̝ݭၗĂͽֹր௚ਫ਼ྮᆧৈ̝

ݭၗࠎs k Ą

ဦ 6! ώ͛ଳϡ̝ਫ਼଱ྃᐺጡ׎၁ன࿪ྮဦ

ϤՎូ 2 ଀ۢצଠវF ̶̝ϓลᇴ̶ 2 ลĂ̶̄₂ ลᇴ̶ 2 ล(ӣѣ˘νΗπࢬ࿬ᕇω_zcᄃ˘ΠΗπ ࢬ࿬ᕇω_za)ĄЯѩਫ਼ྮྃᐺጡੵᅮ׍ 1 ࣎ٺࣧᕇ

̝ໂᕇγĂ౵͌إᅮ׍ 1 ࣎ໂᕇᄃ 1 ࣎࿬ᕇĄѩ γĂЯ˘ਠ̝ଠט᎕វ࿪ྮ̰࠰̏ѣ˘а଱ྃᐺ ϡ̝ྻზٸ̂ጡΞਬӀϡĂ҂ᇋјώᄃ၁ү̝ܮ ӀّĂӍˠଳϡтဦ 6 ٙϯ̝࿪ྮΞ႕֖ਫ਼ྮྃ

ᐺጡٙᅮՐ̝ݭၗĂ׎Ꮾ΍ˢᆧৈࠎ

















+ +

= +

≡

) 1 (

) 1 ( ) (

1 1 ) (

) ) ( (

3 2 1

cp cz c

c s

s

c c R s s E

s s V G

ω

ω (29)

׎̚

2 2

1 c

cz = R

ω ,

) //

( 1

3 2

2 c c

cp= R

ω (30)

Վូ 4 ՙؠ࿪߹ਫ਼ྮT ̝Ϲ෸ᐛத_i ω_ciͷ෸̂෸рĂҭ

̙Ξ̂ٺ̷ೱᐛத̝˘ΗĄአតs ̂̈࠹၆гΞ_e አតϹ෸ᐛதω_ciĂҭࡶs ͉̂Ă࿪߹ଠטݭ̝_e ᐹᕇ૟ঐεĄࣃ଀˘೩۞ߏࡶ൑γΐγొྃᐺ୆

தॡĂϹ෸ᐛதω_ciϤ࿪ྮણᇴՙؠ̝ͷࠎ˘ؠ ࣃĄ

Վូ 5 ՙ ؠ Ᏼ ؠ ࿪ ᑅ ᄃ ࿪ ߹ ਫ਼ ྮ ᆧ ৈ ̝ Ϲ ᕇ ᐛ த ωcivĂҭϹᕇᐛதᅮ̬ٺᕭگጡВॎᐛதω_zcᄃ

࿪߹ਫ਼ྮᆧৈ̝Ϲ෸ᐛதมω_icĄ˘ਠ҃֏Ă

<

∠

−

∠T_v,ωciv T_i,ωciv 130°ߏ˘̙᏾̝̍඀ᇾ۞Ą

Վូ 6 Ᏼؠዋ༊̝ω_cpăω_czͽ႕֖࿪ᑅਫ਼ྮᆧৈ̝ݭ

ၗࠎk ̝ࢋՐĄ s

ᔵ൒ۡᛇ˯Ӏϡᇴࣃ͞ڱΞՐ΍ω_cpᄃω_czĂ൒ͽ ϫෛڱ଀ۢω_cp=min{ω_zc,ω_za}ͷω_cz=ω_oӈΞ ႕֖ࢋՐĄ઄నω_zc<ω_zaĂӍˠΞ଀ۢ

c R c

c

R ^zc _c

1 )

//

( 1

3 2 2

=

=ω (31)

) (c₂ c₃ K_i K^v

= + (33)

׎̚

2 1

2 2

2

1 2

} ] ) ( 1 [

) ( 1 1 {

2 ) (

2

o civ

za civ

p g s s civ

s s

e n

v N

N D

V T R

R R S S K

ω ω

ω ω

ω ₊

+ + ′

=

(34)

2 1

2 2

2 2

2 }

) ( ] ) ( 1 [

) ( 1 { 2 )

( 2

o civ o

civ zL civ

s g

s s

e n i

Q D

R V R T S S K

ω ω ω

ω ω ω

+

− + + ′

=

(35)

s p g s p s s o

n R

L R V N N L

S =V = (36)

Վូ 8 ֶਫ਼ྮྃᐺϡྻზٸ̂ጡ̝Ꮾˢઐᑅ࿪߹(bias current)̂̈ᏴؠR ̝ࣃޢГ੨Ъё(31)~(33)ĂӍ₁ ˠֶԔΞ଀

) (

23 3

o zc

c K ω

= ω (37)

2 1 23

2=[ ( )−1]

o

K zc

c ω

ω (38)

2 2

1 R c

ωo

= (39)

׎̚

i v

K

K₂₃≡ K (40)

Վូ 9 ॲፂٙనࢍ̝ਫ਼ྮྃᐺጡĂ၆ࣧАనؠ۞ଠטវ ซҖሀᑢᄃّਕീྏĄ

Վូ 10 నࢍ˟ѨᏮ΍ᕭگ࿪ྮͽ႕֖Ꮾ΍ႛگ࿪ᑅࢋՐ ఢॾĄ[16,17]

ࣃ଀˘೩۞ߏ˯ࢗਫ਼ྮྃᐺጡ̝నࢍĂΞӀϡᅅٽг Ϥт Excel 5.0 ̝࿪ཝइ྅హវ૟׎ր௚̼Ąܑ˟ٙϯࠎώ

̝͛၁ּనࢍඕڍĄ

ܑ˟! पࣃ࿪߹ଠטݭ࿣ᗓݭܔ࿺ёᘦᑅጡ̝ਫ਼ྮྃᐺጡనࢍ

௑ཱི ࣃ ಏҜ ොྋ ௑ཱི ࣃ ಏҜ ොྋ

࿪˧࿪ྮણᇴ ࢍზਫ਼ྮ̝Ϲ෸ᐛத(ωic)[ᜈ]

Vg 48 V Wic2,1 444452551199

Vo 12 V Wic2,2 -2020.73 ̙Ъ Io 2.4 A Wic1,1 666673 rad/sec ୬Րࣃ(Wci1,1=ω_ci) Ls 22.5 µH Wic1,2 -666673 ̙Ъ Lp 90 µH fc 3 kHz

c 4400 µF ω_civ 18840 rad/sec ҋؠࣃ R 5 ohm ω_civ /ω_zl 414.48

R_l 0.005 ohm ωciv /ωza 0.06 R_c 0.012 ohm ω_civ /ω_o 8.89 Ns/Np 0.50 ωciv /ωzc 0.9948

Vg' 24.00 ω_civ /QW 3.92 fs 100.0 kHz ฟᙯ̷ೱᐛத G_Ti_Wciv 35.79 dB ω_s 628000 rad/sec ਫ਼ྮྃᐺጡనࢍ

Ts 0.00001 sec R1 7.60 kohm ҋؠ sn 320000 V/sec Kv 0.005 sf 80000 V/sec C2+C3 819.4 pF PWM 3 ਔگᆵޘአតଠטጡ C3 91.7 pF ୬Րࣃ

R_s 0.3 C2 728 pF ୬Րࣃ D 0.33 యЇฉഇ R2 648.6 kohm ୬Րࣃ D' 0.67 DC_Gain_Controller 104 dB ω_o 2119 rad/sec ਫ਼ྮྃᐺጡనࢍّ̝ਕෞҤᄃរᙋ

Q 2.27 ω_o /ω_zc 0.1119 Fm 2.08 ω_o /ω_zl 46.61 Fi 0.3 ωo /QW 0.44

H2 0.3 H2=Rs G_T_v /ω_civ 35.79 ᅮඈٺ G_T_i _ω_civ

H4 0.0222 G_T_v /ω_o 66 dB

ω_za 296296 G_Ti /ω_o 24 dB ω_zc 18939 DC_Gain_Tv 130 dB ω_zl 45.5 DC_Gain_Ti 16.59 dB

QW 4802.2 R2_new 648.56 kohm R2 ̝ͅរᙋࣃ Ki 6.75 WF 18939 rad/sec

ࢍზਫ਼ྮ̝Ϲ෸ᐛத(ω_ic) Deg_Ti /ω_civ -77.3 deg TiA 4.9618E-14 Deg_T_v /ω_civ -177.3 deg

TiB -0.022053 DegT_v(T_i -T_v)_ω_civ 99.9 deg υื႕֖≤130°

TiC -44.56

̣ăሀᑢᄃ၁រඕڍ

Ϥё(15)Ξۢܔ࿺ёᘦᑅጡ׎хдΠΗπࢬ࿬ᕇ(൑

ڱЪͼ౵̈࠹Ҝ۞୧І)ĂЯѩ׎ਫ਼ྮྃᐺጡ̝నࢍՀ׍߄ ጼّĄЯѩĂώ͛ͽဦ 5 ٙϯ၁ּ࿪ྮĂֽᄲځ֭រᙋٙ

೩ਫ਼ྮྃᐺጡనࢍԫఙ̝ΞҖّᄃ၁ϡّĄҌٺΑத࿪ྮ

̝నࢍĂϤٺቔ಼ѣࢨͷ࠹ᙯ͛ᚥ̏ѣ࠹༊̝ଣ੅Ăώ͛

̙Гᖴࢗ[3,8,18]Ą൒҃ࠎԆፋ੓֍Ӎˠ૟ᘦᑅጡ̝࠹ᙯ࿪

ྮણᇴЕࢗٺ˭Ĉ V 60

~

=36

Vg , VV_o=12 ,L_p=90µH,R_LP =105mΩ

5 .

=22

Ls µH,R_Ls =25mΩ,c=4000µF,R_c = m12 Ω kHz

=100

fs , R_s= 30. Ω, 630S_w:IRF

ЯࠎయЇฉഇٺፋ࣎̍үቑಛ࠰̈ٺ 0.5ĂЯѩᏴϡт UC 1842 ̝̙ᅮγొ୆தྃᐺ PWM ଠט IC[7]ĄѩγĂ ࣃ଀˘೩۞ߏϤٺ൑ᅮγొ୆தྃᐺ(ӈs_e=0)Ă࿪߹ਫ਼

ྮT ̝ Ϲ ෸ ᐛ த_i ω_ci Ϥ ࿪ ྮ ણ ᇴ ՙ ؠ ̝ ( ٺ ѩ ּ ̚ sec

/ rad 666673

ci=

ω )Ą

ЯѩĂࡶᏴؠω =_civ 2π(3k)rad/secĂR₁=7.6kΩͷ૟

˯ࢗඈ࿪ྮણᇴ΃ˢё(37)~(39)̚ĂӍˠΞ࠹༊टٽг૟

ਫ਼ྮྃᐺጡٙᅮ̝ણᇴՐ΍т˭Ĉ

C₃

R2 c2 7

2 1 3 45

8 6

UC1842

7.5k

10 20k

510

2.2n 1u R_S

R1

Sw

2k

ဦ 7 ᘦᑅጡ၁ᅫ࿪ྮဦ

100 50 0 -50

0 -100 -200

100 50 0 -50

0 -100 -200

T1 T1

Tv

T1 T1

Tv F2 F2

Tv

10⁰ 10² 10⁴ 10⁶ 10⁸

(rad/sec) (a)

10⁰ 10² 10⁴ 10⁶ 10⁸

(rad/sec) (b) Tv, Ti, F2

(deg) (dB) (deg) (dB)

Tv

Ti T1

ဦ 8! ᘦᑅጡᑕϡٙ೩ਫ਼ྮྃᐺጡޢ̝گᇇဦ Ω

=648.6k

R2 Ăc₂=728pFĂc₃=91.7pF

ᘦᑅጡ̝ፋវ၁ᅫ࿪ྮဦᄃ׎گᇇဦ̶Ҿтဦ 7 ᄃ 8 ٙ ϯĄϤဦ 8 ӍˠΞۢٙ೩నࢍ̝ਫ਼ྮྃᐺጡΞֹᘦᑅጡ׍

ѣܕ 80°̝࠹Ҝዶྈ(phase margin)γĂ࿪߹ਫ਼ྮT ̝Ϲ෸ _i

V0 12V

(I₀: 1A/div, lms/div; V₀: 100mV/div, lms/div) ဦ 9! ᘦᑅጡᏮ΍࿪ᑅ̝࢑ྶՎ৺ᜩᑕگԛဦ

ᐛதω_ciࣃቁ၁ᄃநኢ࠹௑Ąဦ 9 ٙϯࠎѩᘦᑅጡᏮ΍̝

ّਕপّဦĄϤဦ 9 ӍˠΞۢٙ೩̝ਫ਼ྮྃᐺጡ̙ኢٺՎ

৺ΐྶٕഴྶĂᘦᑅጡ࠰ѣ࠹༊։р̝ᇶၗᜩᑕγĂዋ༊

гΐˢ˟ѨᏮ΍ᕭ࿪ྮቁ၁Ξ႕֖Ꮾ΍ႛگ࿪ᑅ̝ࢋՐఢ ॾĄ

̱ăඕ ኢ

ώ͛ࢵАޙϲᘦᑅጡᄃपࣃ࿪߹ଠטඉர̝ᇴጯሀ ݭĄ҃ޢĂੵͽᖎಏ۞៍هᄲځपࣃ࿪߹ଠטඉரྃᐺጡ

۞నࢍࣧநγĂ֭೩΍˘ᖎಏͷ၁ϡ̝ਫ਼ྮྃᐺጡనࢍ͞

ڱĄٙ೩΍̝ਫ਼ྮྃᐺጡనࢍ͞ڱੵࠎుซё(step by step) γĂ֭ΞᅅٽгӀϡт Excel 5.0 ̝࿪ཝइ྅హវ૟׎ր௚

̼Ăซ಼҃̂г೩੼ਫ਼ྮྃᐺጡ̝నࢍड़தĄགྷሀᑢᄃ၁ រീྏඕڍ଀ۢᑕϡٙ೩నࢍԫఙٙనࢍ۞ਫ਼ྮྃᐺጡĂ ӈֹ׍ΠΗπࢬ࿬ᕇপ̷ّ̝ೱёᘦᑅጡĂϺΞᅅٽгֹ

ᘦᑅጡ႕֖ٙᅮّ̝ਕఢॾࢋՐĄ

௑ཱི৶͔

c ᘦᑅጡ࿪˧࿪ट

c ,2 c ₃ ਫ਼ྮྃᐺጡ࿪ट d యЇฉഇ

dˆ యЇฉഇ̈ੈཱིϹ߹ត̼ณ D యЇฉഇۡ߹ณ

F i ࿪߹ਫ਼ྮᖼொבᇴ F j ฟྮᖼொבᇴ

F m యЇฉഇਫ਼ྮᖼொבᇴ F v ࿪ᑅਫ਼ྮྃᐺጡᖼொבᇴ ωs ฟᙯ̷ೱᐛத

G c ਫ਼ྮྃᐺጡᖼொבᇴ

CL

Gaud_, ౕਫ਼ྮ̝ᓏᐛୂຏޘ H j पࣃ࿪߹ଠטਫ਼ྮણᇴ

iˆ o ࢑ྶ࿪߹តજณ I ಏҜ৏ੱ

L p ᘦᑅጡ˘Ѩ઎࿪ຏ L s ᘦᑅጡ˘Ѩ઎࿪ຏ R ࢑ྶ࿪ܡ

R ,1 R ₂ ਫ਼ྮྃᐺጡ࿪ܡ R c ᘦᑅጡ࿪˧࿪ट̰ܡ

LP

R ᘦᑅጡ˘Ѩ઎࿪ຏ̰ܡ RLs ᘦᑅጡ˘Ѩ઎࿪ຏ̰ܡ R s פᇹ࿪߹̝פᇹ࿪ܡ s ٛёᖼೱྻზ̄

s e γొྃᐺ୆த s f פᇹ࿪߹̝˭ࢫ୆த s n פᇹ࿪߹̝˯̿୆த T 1 ਫ਼ྮᆧৈ

T i ࿪߹ਫ਼ྮᆧৈ

T s ฟᙯ̷ೱฉഇ T v ࿪ᑅਫ਼ྮᆧৈ

vˆ g Ꮾˢ࿪ᑅត̼ณ vˆ o Ꮾ΍࿪ᑅត̼ณ V g Ꮾˢ࿪ᑅ V o Ꮾ΍࿪ᑅ

Z o Ꮾ΍ܡԩᖼொבᇴ

CL

Zo_, ౕਫ਼ྮ̝Ꮾ΍ܡԩ ωci ࿪߹ਫ਼ྮϹ෸ᐛத

ωciv ࿪ᑅᄃ࿪߹ਫ਼ྮᆧৈ̝Ϲᕇᐛத ωcp ਫ਼ྮྃᐺጡໂᕇᐛத

ωcz ਫ਼ྮྃᐺጡ࿬ᕇᐛத ωza צଠវΠΗπࢬ࿬ᕇ ωzc ᕭگጡВॎᐛத

࡭ ᔁ

ώ ࡁ տ ຏ ᔁ ઼ ࡊ ົ གྷ ෱ ྃ ӄ Ă ࢍ ൪ በ ཱི Ĉ NSC 90-2516-S-233-001Ą

ણ҂͛ᚥ

1. Middlebrook, R. D., and Cuk, S., “A General Unified Approach to Modeling Switching-Converter Stages,”

IEEE Power Electronics Specialist Conference, Cleveland, OH, USA, pp. 18-34 (1976).

2. Middlebrook, R. D., “Small-Signal Modellng of Pulse- Width Modulated Switched-Mode Power Converter,”

Proceedings of the IEEE, Vol. 76, No. 4, pp. 343-354, (1988).

3. Severns, R. P., and Bloom, G., Modern DC-to-DC Switchmode Power Converter Circuits, Van Nostrand Reinhoid, New York (1985).

4. Kuo, C. C., and Tzou, Y. Y., “Frequency Response Curve Fitting Design of the Loop Compensator of a Switching Mode DC-DC Regulator,” The 11th Symposium on Elect- rical Power Engineering, Taipei, pp. 319-333 (1990).

5. Qiu, S. S., Filanovsky, I. M., and Lin, B. T., “A New Method of Analysis for PWM Switching Power Con- verters,” International Journal of Electronics, J. Electro- nics, Vol. 86, No. 11, pp. 1395- 1410 (1999).

6. Kislovski, A. S., Redl, R., and Sokal, N. O., Dynamic Analysis of Switching-Mode DC/DC Converters, Van Nostrand Reinhoid, New York (1991).

7. Unitrode Application Note, UC3842/3/4/5 Provides Low-Cost Current-Mode Control, U-100A (1994).

8. Wang, S. S., “Stability Analysis and Control Design of PWM Switched Mode Power Converters,” Ph. D.

Dissertations, Electrical Engineering, National Tsing Hua University, Hsinchu, Taiwan, R.O.C. (1989).

9. Ridley, R. B., Cho, B. H., and Lee, F. C., “Analysis and Interpretation of Loop Gains of Multiloop-Controlled Switching Regulators,” IEEE Transactions on Power Electronics, Vol. 3, No. 4, pp.545-554 (1988).

10. Chio, B., Cho, B. H., and Lee, F. C., “Three-Loop Control Multimodule Converter Systems,” IEEE Transactions on Power Electronics, Vol. 8, No. 4, pp.466-474 (1993).

11. Middlebrook, R. D., “A Unified Model for Current- Programmed Converter,” IEEE Transactions on Power Electronics, Vol. 10, No. 4, pp. 397-408 (1995).

12. Lin, C. S., and Chen, C. L., “Single-Wire Current-Share Paralleling of Current-Mode-Controlled DC Power Sup- plies,” IEEE Transactions on Industrial Electronics, Vol.

47, No. 4, pp. 780-786 (2000).

13. Sanders, S. R., and Verghese, G. C., “Synthesis of Averaged Circuit Models for Switched Power Converters,”

IEEE Transactions on Circuits and Systems, Vol. 38, No.

8, pp. 905-915 (1990).

14. Vincenti, D., and Jin, H., “A Generalized Approach for Input Unbalance Correction in Polyphase Converters,”

IEEE Industrial Electronics, Control and Instrumentation Conference, Orlando, FL, USA, pp. 365-369 (1995).

15. Pan, C. T., and Shieh, J. J., “A Closed form Duty Cycle Control for Advanced Static VAR Compensators,” The 2nd International Power Electronics and Motion Control Conference, Hangzhou, China, pp. 477-482 (1997).

16. Shieh, J. J., Wang, S. S., and Wu, M., “Loop Compensator Design for Combining Secondary Output Filter Switching Mode Step Down DC/DC Regulator,” The 21th Sympo- sium on Electrical Power Engineering, Taipei, Taiwan, pp.

848-852 (2000).

17. Ridley, R. B., “Secondary LC Filter Analysis and Design Techniques for Current-Mode-Controlled Converters,”

IEEE Transactions on Power Electronics, Vol. 3 No. 2, pp.

499- 507 (1988).

18. Chetty, P. R. K., Switch-Mode Power Supply Design, TAB BOOK/s, Inc., New York (1986).

2001 ѐ 04 ͡ 11 ͟! ќቇ 2002 ѐ 03 ͡ 18 ͟! ܐᆶ 2002 ѐ 08 ͡ 29 ͟! ኑᆶ 2002 ѐ 09 ͡ 09 ͟! ତצ