Design Considerations for Asymmetric Half Bridge Converters

7/23/2019 Design Considerations for Asymmetric Half Bridge Converters

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FN@]EL@BC UOG@EDHC_SD] QD[O] UOG@HN] =11< - =110

>

Lnhksodi Eld`

Nmstrnet – Ngdhk vnr`dus i`hcs df sdft-sw`tel`hk

edhvortors, nsyggotrè Q[G lnbf-mr`cko edhvortors lnvo

crnwh nttoht`dh cuo td tlo`r s`gpbè`ty, `hloroht zord vdbtnko

sw`tel`hk (ZVU) enpnm`b`ty, nhc f`xoc-froquohey dpornt`dh.

Sl`s pnpor prosohts nh nhnbys`s nhc rovòws prnetènb cos`kh

edhs`cornt`dhs fdr nh nsyggotrè lnbf-mr`cko edhvortor. @t

`hebucos cos`kh`hk tlo trnhsfdrgor nhc soboet`hk edgpdhohts.

N stop-my-stop cos`kh prdeocuro w`tl n cos`kh oxngpbo w`bb

lobp ohk`hoors cos`kh nh nsyggotrè lnbf-mr`cko edhvortor.

@. @HS]DC_ES@DHSlo offdrt td dmtn`h ovor-`herons`hk pdwor cohs`ty

df sw`teloc-gdco pdwor suppbòs lns mooh b`g`toc

my tlo s`zo df pnss`vo edgpdhohts. Dpornt`dh nt

l`klor froquoheòs edhs`cornmby rocueos tlo s`zo df

pnss`vo edgpdhohts, suel ns trnhsfdrgors nhc

f`btors9 ldwovor, sw`tel`hk bdssos lnvo l`hcoroc

l`kl-froquohey dpornt`dh. Sd rocueo sw`tel`hk

bdssos nhc nbbdw l`kl-froquohey dpornt`dh, rosdhnht

sw`tel`hk nhc sdft-sw`tel`hk toelh`quos lnvo mooh

covobdpocY>-?W

.

Slo rosdhnht sw`tel`hk gotldc prdeossos pdwor

`h n s`husd`cnb gnhhor my ut`b`z`hk tlo rosdhnheo

cur`hk tlo oht`ro sw`tel`hk por`dc. Kohornbby, tlo

dutput vdbtnko `s rokubntoc my vnr`nmbo froquohey

edhtrdb nhc tlo eurroht dr vdbtnko wnvofdrg `h tlo

rosdhnht hotwdri lns n s`husd`cnb slnpo.

Gonhwl`bo, sdft-sw`tel`hk toelh`quos ut`b`zo tlo

rosdhnheo dpornt`dh dhby cur`hk tlo sw`tel`hk

trnhs`t`dh td sdftoh tlo sw`tel`hk elnrnetor`stès df

tlo covèos. [loh tlo sw`tel`hk trnhs`t`dh `s dvor,

tlo edhvortor rovorts td Qubso-[`ctl-Gdcubnt`dh

(Q[G) gdco. U`heo rosdhnht dpornt`dh dhby deeurs

cur`hk tlo sw`tel`hk trnhs`t`dh, tlo pnrngotors df

rosdhnht edgpdhohts nro hdt ns er`tènb ns `h n

rosdhnht edhvortor. Gdrodvor, tlo sw`tel`hk

froquohey `s f`xoc nhc ons`by syhelrdh`zoc td tlo

dtlor pdwor stnkos td g`h`g`zo OG@.

Ngdhk vnr`dus i`hcs df sdft-sw`tel`hk

edhvortors, tlo nsyggotrè Q[G lnbf-mr`cko

edhvortor lns crnwh nttoht`dh cuo td `ts s`gpbè`ty

nhc `hloroht zord vdbtnko sw`tel`hk (ZVU)

enpnm`b`ty. F`kuro > nhc = sldw tlo mnsè e`reu`t nhc

typènb dpornt`dh wnvofdrgs df tlo nsyggotrè

Q[G lnbf-mr`cko edhvortor. Sl`s edhvortor lns

sovornb ncvnhtnkos dvor dtlor sdft-sw`tel`hk

tdpdbdkòs: bdw GDUFOS vdbtnko nhc eurroht

stross, sgnbb dutput enpne`tdr nhc `hcuetdr,g`h`gug edgpdhoht eduht, nhc s`gpbo edhtrdb.

+

VD

-

] d

^=

(>-C)

h:> @ p

Bbip

Bg

EM @

cs=

@ g

V ̀h

+

Vc

-

@ cs>

^>

(C)

+

Vroe

-

VEM

F`k.>. Nsyggotrè Q[G lnbf-mr`cko edhvortor.

F`k.=. Sypènb wnvofdrgs df nh nsyggotrè Q[G lnbf-mr`cko edhvortor.

Cos`kh Edhs`cornt`dhs fdr Nsyggotrè

Lnbf-Mr`cko Edhvortors




=

Sl`s pnpor prosohts cos`kh edhs`cornt`dhs df nh

nsyggotrè Q[G lnbf-mr`cko edhvortor. @t `hebucos

cos`kh`hk tlo trnhsfdrgor nhc soboet`hk tlo

edgpdhohts. Slo stop-my-stop cos`kh prdeocuro

oxpbn`hoc w`tl n cos`kh oxngpbo w`bb lobp ohk`hoors

cos`kh nh nsyggotrè Q[G lnbf-mr`cko edhvortor.

@@. @CONB@ZOC DQO]NS@DH Q]@HE@QBO DF

NUPGGOS]@E Q[G LNBF-M]@CKO EDHVO]SO]

F`kuro 5 `bbustrntos tlo s`gpb`fòc e`reu`t c`nkrng

df nh nsyggotrè Q[G lnbf-mr`cko edhvortor nhc

`ts `conb wnvofdrgs, wloro tlo boninko `hcuetnheo

df tlo trnhsfdrgor `s `khdroc. Slo CE mbdei`hk

enpne`tdr (EM) nets hdt dhby ns nh ohorky sdureo

fooc`hk tlo bdnc wl`bo tlo uppor sw`tel (^=) `s

edhcuet`hk, mut nbsd ns n mbdei`hk enpne`tdr td

provoht trnhsfdrgor snturnt`dh.

F`k. 5. U`gpb`fòc e`reu`t c`nkrng df nh nsyggotrè Q[G lnbf-mr`cko

edhvortor nhc `ts wnvofdrgs.

Nppby`hk n vdbtnko-soedhc mnbnheo oqunt`dh

nerdss tlo trnhsfdrgor pr`gnry s`co ns:

( ) (> )`h EM EMV V C V C∝ ⋏ 7 ⋏ ∝ (>)

Slo vdbtnko nerdss EM `s dmtn`hoc my:

EM `hV V C7 ⋏ (=)

wloro C `s tlo cuty eyebo rnt`d df bdw-s`co

GDUFOS (^>).

@conb`zoc dutput vdbtnko `s dmtn`hoc my nvornk`hk

tlo soedhcnry-s`co roet`fòr vdbtnko (Vroe) ns:

( )(> )`h EM EM

d

V V V V C C

h h

∝7 ⋏ + ⋏ ∝ (5)

wloro h `s tlo trnhsfdrgor turhs rnt`d (H p/Hs).

Uumst`tut`hk Oqunt`dhs = `htd 5, tlo `conb`zoc

dutput vdbtnko `h Oqunt`dh 5 `s s`gpb`fòc ns:

=(> )`hd

V C CV

h

⋏ ∝ ⋏7 (3)

F`kuro 3 sldws tlo hdrgnb`zoc kn`h us`hk

Oqunt`dh 3. Slo dpornt`dh sldws syggotry fdr tlotwd dpornt`dh rnhkos df C frdg 1% td ?1% nhc

frdg ?1% td >11%. U`heo tlo sbdpo df tlo kn`h

eurvo `s rovorsoc nt ?1% cuty eyebo, cuty eyebo

sldubc mo o`tlor mobdw dr nmdvo ?1% fdr dutput

vdbtnko rokubnt`dh. @h kohornb, dpornt`dh rnhko frdg

1% td ?1% `s proforroc s`heo tlo edhvoht`dhnb

Q[G edhtrdbbor enh mo usoc ns `t `s. Gonhwl`bo,

dpornt`dh rnhko nmdvo n ?1% cuty eyebo roqu`ros

ncc`t`dhnb e`reu`try td n edhvoht`dhnb Q[G

edhtrdbbor cuo td tlo rovorsoc edhtrdb pdbnr`ty.

F`k. 3. Hdrgnb`zoc vdbtnko kn`h wloh `khdr`hk tlo cuty eyebo bdssos

enusoc my boninko `hcuetnheo.

F`kuro ? sldws s`gpb`fòc pr`gnry-s`co eurroht

wnvofdrgs. Slo trnhsfdrgor pr`gnry-s`co eurroht (@ p) `s

tlo sug df tlo dutput `hcuetdr eurroht roforroc td ns tlo

pr`gnry s`co (@BD /h) nhc tlo gnkhot`z`hk eurroht (@G).

F`k. ?. Qr`gnry-s`co eurroht wnvofdrgs.




5

@h stoncy-stnto dpornt`dh, tlo gnkhot`z`hk eurroht

`s nutdgntènbby ncjustoc sd tlnt tlo nvornko

elnrk`hk eurroht df EM dvor dho eyebo `s zord. Slo

gonh vnbuo df tlo trnhsfdrgor gnkhot`z`hk eurroht,

@G.nvk, `s dmtn`hoc frdg tlo edhc`t`dh fdr zord hot

eurroht tlrdukl tlo CE mbdei`hk enpne`tdr (EM):

. .( ) ( )(> )D D G nvk G nvk

@ @ @ C @ Ch h

+ 7 ∝ + ∝ (?)

. (> = ) D G nvk

@ @ C

h7 ∝ ⋏ (6)

wloro @d `s tlo dutput bdnc eurroht.

Ns dmsorvoc, tlo gonh vnbuo df tlo trnhsfdrgor

gnkhot`z`hk eurroht `s zord wloh cuty eyebos fdr tlo

GDUFOSs nro ovoh (?1% nhc ?1%). Gonhwl`bo,

tlo gonh vnbuo df tlo gnkhot`z`hk eurroht `heronsos

ns tlo cuty eyebo gdvos nwny frdg ?1%, wlèl

sldubc mo tlo wdrst enso fdr trnhsfdrgor cos`kh. @h

dtlor wdrcs, g`h`gug nhc gnx`gug cuty eyebos

nro tlo wdrst ensos fdr dpornt`dh rnhko mobdw ?1%

cuty eyebo nhc nmdvo ?1% cuty eyebo, rospoet`voby.

@@@. USONCP-USNSO NHNBPU@U DF NES_NB

NUPGGOS]@E Q[G LNBF-M]@CKO EDHVO]SO]

F`kuro 6 sldws tlo selogntè df nh nsyggotrè

Q[G lnbf-mr`cko edhvortor nhc F`kuro ; sldws `ts

typènb wnvofdrgs. @h F`kuro 6, Bg nhc Bbi nro tlo

gnkhot`z`hk `hcuetnheo nhc offoet`vo boninko

`hcuetnheo `h tlo trnhsfdrgor pr`gnry s`co,rospoet`voby, nhc EM `s tlo CE mbdei`hk enpne`tdr

wldso vdbtnko `s nbgdst edhstnht cur`hk dho

sw`tel`hk eyebo.

F`k. 6. Uelogntè df nh nsyggotrè Q[G lnbf-mr`cko edhvortor.

F`k. ;. Sypènb wnvofdrgs df nh nsyggotrè Q[G lnbf-mr`cko edhvortor.

@h kohornb, tlo nsyggotrè Q[G lnbf-mr`cko

edhvortor edhs`sts df tlroo stnkos, ns sldwh `h F`kuro 6:

n squnro wnvo kohorntdr, ohorky trnhsfor hotwdri, nhc

roet`fòr hotwdri.

Slo squnro wnvo kohorntdr prdcueos n squnro wnvo

vdbtnko (V c ) my cr`v`hk sw`telos ^> nhc ^=

edgpbogohtnr`by. @h drcor wdrcs, tlo bdwor nhc

uppor GDUFOSs cuty eyebos sldubc mo C nhc >-C,

rospoet`voby. N sgnbb conc t`go `s usunbby

`htrdcueoc motwooh tlo edhsoeut`vo trnhs`t`dhs.

Slo ohorky trnhsfor hotwdri edhs`sts df n CE

mbdei`hk enpne`tdr nhc trnhsfdrgor. Slo ohorky

trnhsfor hotwdri rogdvos tlo CE dffsot df tlo




3

squnro wnvo vdbtnko (Vc) us`hk tlo CE mbdei`hk

enpne`tdr (EM), tloh trnhsfors tlo puro NE

squnro wnvo vdbtnko td tlo soedhcnry s`co

tlrdukl tlo trnhsfdrgor. Slo trnhsfdrgor

pr`gnry-s`co eurroht, @ p, bnks tlo vdbtnko nppbòc

td tlo trnhsfdrgor pr`gnry s`co cuo td tlo

boninko `hcuetnheo, wlèl nbbdws tlo GDUFOSs

td mo turhoc dh w`tl zord vdbtnko. Ns sooh `h

F`kuro ;, nftor dho df tlo sw`telos lns mooh

turhoc dff, @ p elnrkos (dr c`selnrkos) tlo

GDUFOS dutput enpne`tnheos nhc ovohtunbby

sw`hks tlo sw`tel vdbtnkos frdg dho `hput rn`b td

tlo dtlor (frdg V`h td krduhc dr frdg krduhc td

V`h). Sloh, @ p edht`huos td fbdw tlrdukl tlo nht`-

pnrnbbob mdcy c`dco. Ns bdhk ns tlo mdcy c`dco

edhcuets, tlo edrrospdhc`hk GDUFOS enh mo

turhoc dh w`tl zord vdbtnko.

Slo roet`fòr hotwdri prdcueos n CE vdbtnko myroet`fy`hk tlo NE vdbtnko w`tl roet`fòr c`dcos

nhc n bdw-pnss BE f`btor. Slo roet`fòr hotwdri

enh mo `gpbogohtoc ns n fubb-wnvo mr`cko dr

eohtor-tnppoc edhf`kurnt`dh.

@h stoncy-stnto nhnbys`s, tlo fdbbdw`hk

nssugpt`dhs nro gnco:

Slo conc t`go `s hokb`k`mbo s`heo `t `s vory sgnbb

edgpnroc td tlo sw`tel`hk eyebo.

Slo boninko `hcuetnheo `s guel sgnbbor tlnh tlognkhot`z`hk `hcuetnheo.

Slo CE mbdei`hk enpne`tdr, EM, `s bnrko ohdukl

td hokboet tlo vdbtnko r`ppbo nerdss EM.

Slo dutput f`btor `hcuetdr dporntos `h edht`hudus

edhcuet`dh gdco.

Nbb e`reu`t obogohts nro `conb nhc bdssboss.

Slo cuty eyebo fdr bdwor GDUFOS, C, `s b`g`toc

mobdw ?1%.

Slo enpne`tdrs E> nhc E= `hebuco hdt dhby tlo`htorhnb dutput enpne`tnheo df GDUFOSs, mut

nbsd tlo oxtorhnb pnrns`tè enpne`tnheos.

N. Dpornt`dh Gdco Nhnbys`s

Slo nsyggotrè lnbf-mr`cko edhvortor lns o`klt

dpornt`dh gdcos cur`hk dho sw`tel`hk eyebo. Slo

oqu`vnboht e`reu`t df onel gdco `s `bbustrntoc `h

F`kuro <.

(n)

(m)

(e)

(c)

(o)




?

(f)

(k)

(l)

F`k. <. Dpornt`dh gdcos df nh nsyggotrè Q[G lnbf-mr`cko edhvortor.

Gdco @ (td~t>): Slo bdwor sw`tel (^>) `s

edhcuet`hk nhc n vdbtnko df (V`h-VEM) `s nppbòc td

tlo trnhsfdrgor pr`gnry s`co (V pr ). Slo trnhsfdrgor

pr`gnry-s`co eurroht (@ p) `s tlo sug df tlo dutput

`hcuetdr eurroht roforroc td ns tlo pr`gnry s`co

(@BD/h) nhc tlo gnkhot`z`hk eurroht (@G). Sl`s gdco

`s s`g`bnr td tlo pdwor trnhsforr`hk gdco df n

edhvoht`dhnb lnbf-mr`cko edhvortor.

Gdco @@ (t>~t=): Slo bdwor sw`tel (^>) `s turhoc

dff nt t> nhc tlo pr`gnry s`co eurroht, @ p, elnrkos E>

nhc c`selnrkos E=. Sl`s gdco edht`huos uht`b tlo pr`gnry-s`co vdbtnko crdps td zord (uht`b E= `s

c`selnrkoc td VEM) nt t=. U`heo tlo soedhcnry s`co `s

edhhoetoc td tlo pr`gnry s`co, E= `s c`selnrkoc

us`hk tlo ohorky stdroc `h tlo boninko `hcuetnheo

nhc dutput `hcuetdr.

Gdco @@@ (t=~t5): Nt t=, tlo trnhsfdrgor pr`gnry-

s`co nhc soedhcnry-s`co vdbtnkos moedgo zord nhc

tlo soedhcnry s`co `s coedupboc frdg tlo pr`gnry

s`co. Sloh, tlo dutput `hcuetdr eurroht, @BD, mok`hs

td froowloob `h tlo soedhcnry s`co tlrdukl tlo

roet`fòrs wl`bo E= edht`huos td mo c`selnrkoc. U`heo

tlo soedhcnry-s`co `hcuetdr (Bd) `s c`sedhhoetoc

frdg tlo pr`gnry s`co, E= `s c`selnrkoc us`hk tlo

ohorky stdroc `h tlo boninko `hcuetnheo dhby. Nftor

E= `s fubby c`selnrkoc, tlo mdcy c`dco df ^

= mok`hs

edhcuet`hk mofdro t5.

Gdco @V (t5~t3): Slo mdcy c`dco df ^= `s

edhcuet`hk nhc tlo vdbtnko nerdss tlo sw`tel ^= `s

ebngpoc nt zord. My turh`hk dh ^= wl`bo tlo mdcy

c`dco `s edhcuet`hk, zord vdbtnko sw`tel`hk (ZVU)

`s nelòvoc. Cur`hk tl`s gdco, n vdbtnko df -VEM `s

nppbòc nerdss tlo boninko `hcuetnheo nhc tlo

pr`gnry-s`co eurroht (@ p) coeronsos. Sl`s gdco

edht`huos uht`b @ p, pbus tlo gnkhot`z`hk eurroht (@G),

moedgos -@BD/h. Cur`hk tl`s gdco, tlo trnhsfdrgor

soedhcnry-s`co vdbtnko rogn`hs zord, wlèl enusoscuty eyebo bdssos df ns guel ns:

3 5>

=d bi

B

s U `h

t t @ B C

S S h V C

∝7 7

⋏ ⋏ ⋏ (;)

wloro Ss `s tlo sw`tel`hk por`dc.

Gdco V (t3~t?): Slo uppor sw`tel (^=) `s

edhcuet`hk nhc -VEM `s nppbòc td tlo trnhsfdrgor

pr`gnry s`co (V pr ). Slo trnhsfdrgor pr`gnry-s`co

eurroht (@ p) `s tlo sug df tlo dutput `hcuetdr eurroht

roforroc td ns tlo pr`gnry s`co (-@BD/h) nhc tlo

gnkhot`z`hk eurroht (@G). Sl`s gdco `s s`g`bnr td

tlo pdwor trnhsforr`hk gdco df n edhvoht`dhnb lnbf-

mr`cko edhvortor.

Gdco V@ (t?~t6): Slo uppor sw`tel (^=) `s turhoc

dff nt t? nhc tlo pr`gnry-s`co eurroht @ p elnrkos E=

nhc c`selnrkos E>. Sl`s gdco edht`huos uht`b tlo

pr`gnry-s`co vdbtnko moedgos zord (uht`b E> `s

c`selnrkoc td V`h-VEM) nt t6. U`heo tlo soedhcnry-

s`co `hcuetdr (Bd) `s edhhoetoc td tlo pr`gnry s`co,

E> `s c`selnrkoc us`hk tlo ohorky stdroc `h tlo

boninko `hcuetnheo nhc dutput `hcuetdr.

Gdco V@@ (t6~t;): Nt t6, tlo trnhsfdrgor pr`gnry-

s`co nhc soedhcnry-s`co vdbtnkos moedgo zord nhc

tlo soedhcnry s`co `s coedupboc frdg tlo pr`gnry

s`co. Sloh, tlo dutput `hcuetdr eurroht, @BD, mok`hs

td froowloob `h tlo soedhcnry s`co nhc E> edht`huos

td mo c`selnrkoc. U`heo tlo soedhcnry s`co `s

c`sedhhoetoc frdg tlo pr`gnry s`co, E> `s

c`selnrkoc us`hk tlo ohorky stdroc `h tlo boninko




6

`hcuetnheo dhby. Nftor E> `s fubby c`selnrkoc, tlo

mdcy c`dco df ^> mok`hs edhcuet`hk mofdro t;.

Gdco V@@@ (t;~t<): Slo mdcy c`dco df ^> `s

edhcuet`hk nhc tlo vdbtnko nerdss tlo sw`tel ^> `s

ebngpoc nt zord vdbtnko. My turh`hk dh ^> wl`bo tlo

mdcy c`dco `s edhcuet`hk, zord vdbtnko sw`tel`hk

(ZVU) `s nelòvoc. Cur`hk tl`s gdco, n vdbtnko df

(V`h-VEM) `s nppbòc nerdss tlo boninko `hcuetnheo

nhc tlo pr`gnry s`co eurroht (@ p) `heronsos. Sl`s

gdco edht`huos uht`b @ p g`hus tlo gnkhot`z`hk

eurroht moedgos @BD /h. Cur`hk tl`s gdco, tlo

trnhsfdrgor soedhcnry s`co vdbtnko rogn`hs zord,

wlèl enusos cuty eyebo bdssos df ns guel ns

< ;=

=

(> )

d bi B

s U `h

t t @ B C

S S h V C

∝7 7

⋏ ⋏ ⋏ ∝ (<)

M.

Zord-Vdbtnko Uw`tel`hk Edhc`t`dh

Ns c`seussoc `h tlo oxpbnhnt`dh df dpornt`dh gdco,

nftor ^> `s turhoc dff nt t>, E= `s c`selnrkoc frdg V`h

td VEM my tlo ohorky stdroc `h tlo boninko

`hcuetnheo nhc dutput `hcuetdr. Sloh E= `s fubby

c`selnrkoc my tlo ohorky stdroc `h tlo boninko

`hcuetnheo dhby. Slorofdro, tlo ZVU edhc`t`dh fdr

sw`tel ^= `s k`voh ns:

= =

= > =Y ( )W ( )Y Wbi p `h B @ t E E CV 8 + (0)

wloro Bbi `s tlo offoet`vo boninko `hcuetnheo `htlo trnhsfdrgor pr`gnry s`co nhc @ p(t=) `s tlo pr`gnry

s`co eurroht nt t=, k`voh ns:

= .

(> )( )

=

d `h U p G nvk

g

@ V C CS @ t @

h B

∝7 + + (>1)

Nftor ^= `s turhoc dff nt t?, E> `s c`selnrkoc frdg

V@H td V@H-VEM my tlo ohorky stdroc `h tlo boninko

`hcuetnheo nhc dutput `hcuetdr. Sloh E> `s fubby

c`selnrkoc my tlo ohorky stdroc `h tlo boninko

`hcuetnheo dhby. Slorofdro, tlo ZVU edhc`t`dh fdr

sw`tel ^> `s k`voh ns:

= =

6 > =Y ( )W ( )Y(> ) Wbi p `h

B @ t E E C V 8 + ∝ (>>)

wloro @ p(t6) `s tlo pr`gnry-s`co eurroht nt t6, k`voh ns:

6 .

(> )( )

=

d `h U p G nvk

g

@ V C CS @ t @

h B

∝7 ∝ + ∝ (>=)

U`heo @ p(t=) `s nbwnys bnrkor tlnh |@ p(t6)| nhc CV`h `s

nbwnys sgnbbor tlnh (>-C)V`h fdr cuty eyebos sgnbbor

tlnh ?1%, tlo ZVU edhc`t`dh df Oqunt`dh 0 `s

snt`sfòc gdro ons`by tlnh tlnt df Oqunt`dh >>. Slus,

tlo edhc`t`dh k`voh my Oqunt`dh >> sldubc mo

snt`sfòc td nelòvo ZVU fdr mdtl GDUFOSs. @t `s

roqu`roc td `heronso tlo boninko `hcuetnheo (Bbi

) dr

`heronso tlo vnbuo df |@ p(t6)| td kunrnhtoo ZVU fdr

mdtl sw`telos dvor w`co bdnc rnhko. Sdd bnrko n

boninko `hcuetnheo `heronsos tlo vdbtnko dvorslddt

nhc r`hk`hk `h tlo roet`fòr c`dcos, wlèl rosubts `h

us`hk l`klor vdbtnko rntoc roet`fòrs nhc pdwor

c`ss`pnt`dh `h tlo shummor e`reu`t td ebngp tlo

vdbtnko dvorslddt. Nhdtlor wny td kunrnhtoo ZVU

dvor n w`co bdnc rnhko `s td `heronso tlo vnbuo df

|@ p(t6)| my rocue`hk tlo gnkhot`z`hk `hcuetnheo.

Ovoh tldukl tl`s gotldc `heronsos edhcuet`dh

bdssos dh tlo pr`gnry s`co, `t `s gdro offoet`vo tlnh`herons`hk tlo boninko `hcuetnheo fdr l`kl `hput

vdbtnko nppbènt`dhs wloro tlo edhcuet`dh bdssos `h

tlo pr`gnry s`co nro hokb`k`mbo.

Vks>

Vks=

Vcs>

Vks>

Vcs=

@Q

Vpr

C >-C

V`h

V`h

V`h-V

EM VEM

Vks>

Vks>

Vks=

Vks=

Vpr V

`h-V

EM

VEM

V`h-VEM VEM

Vcs=

Vcs>

gdco @@ nhc @@@ gdco V@ nhc V@@

t>

t5

t=

t?

t;

t6

VEM

V`h-V

EM

F`k. 0. Cotn`boc wnvofdrgs cur`hk tlo sw`tel`hk trnhsòht.




;

E. CE Elnrnetor`stès Edhs`cor`hk Cuty Eyebo

Bdssos

@h tlo `hput td dutput vdbtnko robnt`dhsl`p df

Oqunt`dh 3, tlo cuty eyebo bdssos enusoc my boninko

`hcuetnheo `s `khdroc. @h prnetènb cos`kh, ldwovor,

cuty eyebo bdssos tnio n edhs`cornmbo ngduht df tlo

sw`tel`hk eyebo nhc sldubc mo edhs`coroc td dmtn`htlo edrroet dutput vdbtnko oqunt`dh. Ns dmsorvoc `h

F`kuro ;, cuty eyebo bdssos tnio pbneo hdt dhby

cur`hk tlo ^> edhcuet`dh por`dc (CB>), mut nbsd

cur`hk tlo ^= edhcuet`dh por`dc (CB=). Edhs`cor`hk

tlo cuty eyebo bdssos frdg Oqunt`dhs ; nhc <, tlo

dutput vdbtnko df Oqunt`dh 3 `s gdc`fòc ns:

= >

( )( ) (> )`h EM EM

d B B

V V V V C C C C

h h

∝7 ⋏ ∝ + ⋏ ∝ ∝ (>5)

Uumst`tut`hk Oqunt`dhs =, ;, nhc < `htd >5, tlo

dutput vdbtnko `h Oqunt`dh >5 `s s`gpb`fòc ns:== =

(> ) ( )`h d bi d

U

V @ BV C C

h h S 7 ⋏ ∝ ∝ (>3)

Ns dmsorvoc `h Oqunt`dh >3, cuty eyebo bdssos

`heronso ns tlo boninko `hcuetnheo `heronsos. Ovoh

tldukl bnrko boninko `hcuetnheo `heronsos ZVU bdnc

rnhko nhc nbbov`ntos tlo rovorso-roedvory prdmbog

my rocue`hk c`/ct, `t rosubts `h rocueoc trnhsfdrgor

turhs rnt`d, wlèl enusos gdro vdbtnko stross dh tlo

roet`fòr c`dcos nhc `heronsoc edhcuet`dh bdssos cuotd cuty eyebo bdssos. Edhs`cor`hk tlo dvornbb

offèòhey, boninko `hcuetnheo rosubt`hk `h ?~>1%

cuty eyebo bdssos (CB>+CB=) `s prdpor.

@V. COU@KH Q]DEOC_]O

@h tl`s soet`dh, n cos`kh prdeocuro `s prosohtoc

us`hk tlo selogntè df F`kuro >1 ns n roforoheo. N

eohtor tnppoc trnhsfdrgor `s usoc `h tlo roet`fòr

stnko nhc tlo `hput vdbtnko `s nssugoc td mo

suppbòc frdg pdwor fnetdr edrroet`dh (QFE) pro-

rokubntdr. N CE-CE edhvortor w`tl n >0=[/=3Vdutput lns mooh soboetoc ns n cos`kh oxngpbo. Ns n

gnjdr covèo, FUFN-soròs Fn`rel`bc Qdwor Uw`tel

(FQUSG

) `s ogpbdyoc, wlèl `s nh `htokrntoc Qubso

[`ctl Gdcubnt`dh (Q[G) edhtrdbbor nhc

GDUFOSs spoe`fènbby cos`khoc fdr Zord Vdbtnko

Uw`tel`hk (ZVU) lnbf-mr`cko edhvortors w`tl

g`h`gnb oxtorhnb edgpdhohts. Edgpnroc w`tl n

c`seroto GDUFOS nhc Q[G edhtrdbbor sdbut`dh, tlo

FUFN-soròs enh rocueo tdtnb edst, edgpdhoht eduht,

s`zo, nhc wo`klt, wl`bo s`gubtnhodusby `herons`hk

offèòhey, prdcuet`v`ty, nhc systog rob`nm`b`ty.

Slo cos`kh spoe`fènt`dhs nro ns fdbbdws:

Hdg`hnb @hput Vdbtnko: 311VCE (dutput df QFE

stnko)

Dutput: =3V/<N (>0=[)

Ldbc-up S`go ]oqu`rogoht: =1gs (?1Lz B`ho

Froquohey)

CE B`hi Enpne`tdr df QFE Dutput: 551¿F

Uw`tel`hk Froquohey: >11iLz Gnx`gug Cuty Eyebo df Q[G Edhtrdbbor: ?1%

Edhtrdb

@E

Vee

VCBBVee

UK QK

VES]

LVee

Hs

Vd

Hp Hs

C]>

_5

IN35>

V`h

(QFE dutput)

C]=

BD

ED

EM

] sohso

E`h

]S

FM

EUFUFN=>11

F`k. >1. ]oforoheo e`reu`t df nh nsyggotrè Q[G lnbf-mr`cko edhvortor fdr tlo cos`kh oxngpbo.




<

YUSOQ->W Cof`ho tlo Uystog Upoe`fènt`dhs

Slo fdbbdw`hk spoe`fènt`dh sldubc mo cof`hoc.

Ost`gntoc Offèòhey ( O ff ): Slo pdwor edhvors`dh

offèòhey gust mo ost`gntoc td enbeubnto tlo

gnx`gug `hput pdwor w`tl n k`voh gnx`gug

dutput pdwor. @f hd roforoheo cntn `s nvn`bnmbo, uso O ff 7 1.<<~1.0= fdr bdw-vdbtnko dutput nppbènt`dhs

nhc O ff 7 1.0=~1.06 fdr l`kl-vdbtnko dutput

nppbènt`dhs. [`tl tlo ost`gntoc offèòhey, tlo

gnx`gug `hput pdwor `s:

d

`h

ff

Q Q

O 7 (>?)

@hput Vdbtnko ]nhko (V ̀hg`h

nhc V ̀hgnx

): Slo

gnx`gug `hput vdbtnko wdubc mo tlo hdg`hnb QFE

dutput vdbtnko:

gnx.`h D QFE V V 7 (>6)

Sldukl tlo `hput vdbtnko `s rokubntoc ns n

edhstnht my tlo QFE pro-rokubntdr, `t crdps cur`hk

tlo ldbc-up t`go. Slo g`h`gug `hput vdbtnko,

edhs`cor`hk tlo ldbc-up t`go roqu`rogoht, `s k`voh

ns:

g`h =

.

=`h L_

`h D QFE

`h

Q S V V

E 7 ∝ (>;)

wloro VD.QFE `s tlo hdg`hnb QFE dutput vdbtnko,

SL_ `s tlo ldbc-up t`go, nhc E`h `s tlo CE b`hi mubienpne`tdr dh tlo `hput s`co.

(Cos`kh Oxngpbo) Nssug`hk tlo offèòhey `s 0=%,

>0==10

1.0=d

`h

ff

Q Q

O [ 7 7 7

gnx

. 311`h D QFE V V V 7 7

5g`h = =

. 6

= = =10 =1 >1311 56;

551 >1

`h L_ `h D QFE

`h

Q S V V V

E

∝

∝

⋏ ⋏ Û7 ∝ 7 ∝ 7

Û

YUSOQ-=W Cotorg`ho tlo Srnhsfdrgor Surhs]nt`d (h7Hp /Hs)

Ns dmsorvoc `h Oqunt`dh >3, boninko `hcuetnheo

df tlo trnhsfdrgor rosubts `h cuty eyebo bdssos nhc

nffoets tlo `hput td dutput vdbtnko rnt`d. Edhs`cor`hk

tlo fdrwnrc vdbtnko crdp `h tlo roet`fòr c`dco,

Oqunt`dh >3 `s gdc`fòc ns:

== =(> ) ( ) d BI

d F `h

U

@ BV V V C C

h h S + 7 ∝ ∝ (><)

wloro VF `s tlo soedhcnry-s`co roet`fòr c`dco

vdbtnko crdp.

Sloro nro tlroo cos`kh pnrngotors `h Oqunt`dh ><:

cuty eyebo (C), trnhsfdrgor turhs rnt`d (h), nhc

boninko `hcuetnheo. @t `s hoeossnry td cotorg`ho tloboninko `hcuetnheo pr`dr td tlo trnhsfdrgor turhs

rnt`d nhc cuty eyebo. ]ntlor tlnh eldds`hk tlo

boninko `hcuetnheo nrm`trnr`by, `t `s ronsdhnmbo td

cotorg`ho tlo boninko `hcuetnheo my edhs`cor`hk tlo

cuty eyebo bdssos. Slo cuty eyebo bdssos nro

npprdx`gntoby:

> = gnx =

>6

( )

`h bi Bdss B B

`h U

Q B C C C

V S

⋏ ⋏7 + ≏

⋏ (>0)

@t `s typènb td sot tlo cuty eyebo bdssos ns ?~>1%

df tlo sw`tel`hk eyebo. Dheo tlo boninko `hcuetnheo`s cotorg`hoc, tlo trnhsfdrgor turhs rnt`d `s

enbeubntoc my sdbv`hk Oqunt`dh >< fdr h w`tl n k`voh

C ns:

=(> ) ( (> )) 3( )

( )

`h `h d F d bi s

d F

V C C V C C V V @ B f h

V V

∝ + ⋏ ⋏ ∝ ∝ +7

+(=1)

[loh enbeubnt`hk tlo trnhsfdrgor turhs rnt`d w`tl

g`h`gug `hput vdbtnko nhc gnx`gug cuty eyebo

edhc`t`dh, tloro sldubc mo sdgo gnrk`h dh tlo

gnx`gug cuty eyebo df tlo Q[G edhtrdbbor td

kunrnhtoo dutput vdbtnko rokubnt`dh.

(Cos`kh Oxngpbo) My eldds`hk cuty eyebo bdssos ns

0% df tlo sw`tel`hk eyebo, tlo boninko `hcuetnheo `s

dmtn`hoc ns:gnx =

= 6

( )

>6

1.10 311 >1 >135

>6 =10

Bdss `h U bi

`h

C V S B

Q

L ¿

∝

⋏ ⋏7

⋏

⋏ ⋏ Û7 7

⋏

Edhs`cor`hk ?% gnrk`h dh tlo gnx`gug cuty eyebo df

tlo Q[G edhtrdbbor (?1¾5%), tlo wdrst-ensognx`gug cuty eyebo td enbeubnto tlo trnhsfdrgor turhs

rnt`d `s eldsoh ns 3=%. Nssug`hk tlo fdrwnrc vdbtnko

crdp df tlo roet`fòr `s >.=V, tlo turhs rnt`d `s k`voh ns:




0

(Cos`kh Oxngpbo – Edht`huoc)

g`h

gnx gnx

g`h =

gnx gnx

= 6 5

(> )

( )

( (> )) 3( )

( )

56; 1.3= (> 1.3=)

(=3 >.=)

(56; 1.3= (> 1.3=)) 3(=3 >.=) < 35 >1 >11 >1

( )

6.=

`h

d F

`h d F d bi s

d F

d F

V C Ch

V V

V C C V V @ B f

V V

V V

∝

⋏ ∝7

+

⋏ ⋏ ∝ ∝ ++

+

⋏ ⋏ ∝7 +

⋏ ⋏ ∝ ∝ + ⋏ ⋏ Û ⋏ Û+

+

7

YUSOQ-5W Enbeubnto tlo Hdg`hnb Cuty Eyebo

fdr Gnx`gug @hput Vdbtnko nhc Fubb-Bdnc

Edhc`t`dh

U`heo tlo turhs rnt`d `s cotorg`hoc `h USOQ-=, tlo

hdg`hnb cuty eyebo fdr gnx`gug `hput vdbtnko nhcfubb bdnc edhc`t`dh `s dmtn`hoc my sdbv`hk:

gnx == =(> )( ) ( ) d bi

d F `h hdg hdg

U

@ BV V V C C

h h S + 7 ⋏ ∝ ∝ (=>)

Slo hdg`hnb cuty eyebo `s k`voh ns:

gnx gnx

( ) => > 3Y W

=

=

d F d bi

`h `h U

hdg

h V V @ B

V hV S C

+∝ ∝ +

7 (==)

(Cos`kh Oxngpbo)

gnx gnx

6

6

( ) => > 3Y W

=

=

6.= =?.= = < 35 >1> > 3Y W

= 311 6.= 311 >1 >11.53

=

d F d bi

`h `h U

hdg

h V V @ B

V hV S C

∝

∝

+∝ ∝ +

7

⋏ ⋏ ⋏ Û∝ ∝ +

⋏ ⋏ ⋏ Û7 7

YUSOQ-3W Dutput @hcuetdr Cos`kh

Slo eurroht r`ppbo df tlo dutput f`btor `hcuetdr `s

k`voh ns:(> )

( )=

Y W(> )

`hd F

D bi B U

d `h

V CV V

@ Bh @ CS B h V C

∝∝ ∝

∆ 7 Û ∝⋏ ∝ (=5)

wloro Bd `s tlo dutput `hcuetdr.

@t `s typènb td sot tlo r`ppbo ns >1~=1% df tlo

rntoc dutput eurroht.

(Cos`kh Oxngpbo) My eldds`hk tlo eurroht r`ppbo df

tlo dutput `hcuetdr ns =1% df tlo rntoc dutput eurroht,

tlo dutput `hcuetnheo `s k`voh frdg Oqunt`dh =5 ns:

66

(> )( )

=Y W

(> )

311 (> 1.53)( =?.=)

= < 35 >16.= Y1.53 >1 >1 W< 1.= 6.= 311 (> 1.53)

5=.5

`hd F

D bi d U

B `h

V CV V

@ Bh B CS @ h V C

L ¿

∝∝

∝∝ ∝

7 Û ∝∆ ⋏ ∝

⋏ ∝ ∝ ⋏ ⋏ Û7 Û ⋏ Û ∝

Û ⋏ ⋏ ∝

7

Slo dutput `hcuetdr `s sgnbbor tlnh tlo fdrwnrc

edhvortor w`tl tlo sngo eurroht r`ppbo nhc dutput

pdwor.

YUSOQ-?W Cotorg`ho tlo Gnkhot`z`hk

@hcuetnheo

Ns dmsorvoc `h Oqunt`dhs >1 nhc >=, tlognkhot`z`hk `hcuetnheo vnbuo `s ebdsoby robntoc td

tlo ZVU edhc`t`dh, s`heo `t cotorg`hos tlo poni

eurroht bovob cur`hk tlo sw`tel`hk trnhs`t`dh. Df tlo

twd ZVU edhc`t`dhs `h Oqunt`dhs 0 nhc >>,

Oqunt`dhs >> `s tlo wdrst enso fdr dpornt`dh w`tl n

cuty eyebo mobdw ?1%. Slus, Slo ZVU edhc`t`dh fdr

mdtl GDUFOSs `s k`voh ns:

=

.

=

> =

(> )Y W

=

( ) Y(> ) W

d `h U bi G nvk

g

`h

@ V C CS B @

h B

E E C V

∝∝ +

8 + ⋏ ∝

(=3)

wloro E> nhc E= nro tlo offoet`vo dutput

enpne`tnheos (pnrns`tè nhc oxtorhnb enpne`tnheo) fdr

^> nhc ^=, rospoet`voby.

(Cos`kh Oxngpbo)

Loro, `t `s cos`khoc td kunrnhtoo ZVU frdg fubb bdnc td

=1% bdnc. F`rst, tlo cuty eyebo fdr =1% bdnc edhc`t`dh `s

dmtn`hoc ns:

gnx gnx

A=1%

6

6

( ) => > 3Y W

=

=

6.= =?.= = (< 1.=) 35 >1> > 3Y W

= 311 6.= 311 >1 >11.=<

=

d F d bi

`h `h U

h V V @ B

V hV S C

∝

∝

+∝ ∝ +

7

⋏ ⋏ Û ⋏ Û∝ ∝ +

⋏ ⋏ ⋏ Û7 7

[`tl tlo cuty eyebo nt =1% bdnc edhc`t`dh, tlo

gnx`gug gnkhot`z`hk ̀ hcuetnheo vnbuo td kunrnhtoo

ZVU `s dmtn`hoc my sdbv`hk (=3) fdr Bg ns:




>1

gnx

6

>=

6

(> )

==Y (> ) = W

311 (> 1.=<) 1.=< >1 >1

= >?1 >1 < 1.==Y (> 1.=<) 311 = 1.=<W35 >1 6.=

6?3

`h U g

dss d`h

bi

V C CS B

E @ C V C

B h

L ¿

∝

∝

∝

∝2

∝ ∝

⋏ ∝ ⋏ ⋏ Û7

⋏ Û Û∝ ⋏ ∝ ⋏ ⋏Û7

Slo gnkhot`z`hk `hcuetnheo `s cotorg`hoc ns 651¿L.

YUSOQ-6W Cos`kh tlo Srnhsfdrgor

Slo poni gnkhot`z`hk eurroht `s k`voh ns:

gnx

.

(> )(> = )

=

`h U d G pi

g

V C C S @ @ C

B h

∝7 + ∝ (=?)

Cur`hk trnhsòht dr stnrtup, tlo cuty eyebo enh monbgdst zord. Slus, tlo gnkhot`z`hk eurroht sldubc

mo enbeubntoc fdr tlo wdrst enso df zord cuty eyebo.

Slo g`h`gug turhs fdr tlo trnhsfdrgor pr`gnry s`co

`s k`voh ns:

.g`h

nx

g G pi

p

o

B @ H

N M7 (=6)

wloro No `s tlo edro erdss-soet`dhnb nron `h gg=

nhc Mgnx `s tlo gnx`gug fbux cohs`ty `h Sosbn.

Sloh, elddso tlo prdpor hugmor df turhs fdr tlosoedhcnry s`co tlnt rosubts `h pr`gnry s`co turhs

bnrkor tlnh H pg`h

ns:

`h

p s p H h H H 7 ⋏ 8 (=;)

Slo w`ro c`ngotor sldubc mo eldsoh mnsoc dh tlo

eurroht cohs`ty. Slo eurroht cohs`ty `s typènbby

?N/gg= wloh tlo w`ro `s bdhk (8>g). [loh tlo

w`ro `s sldrt w`tl n sgnbb hugmor df turhs, n eurroht

cohs`ty df 6->1 N/gg= `s nbsd neeoptnmbo. Nvd`c

us`hk w`ro w`tl n c`ngotor bnrkor tlnh 1.3 gg td

nvd`c si`h-offoet bdssos ns wobb ns td gnio w`hc`hkonsòr. Fdr n l`kl-eurroht dutput, `t `s mottor td uso

pnrnbbob w`hc`hks w`tl gubt`pbo strnhcs df tl`hhor

w`ro td g`h`g`zo tlo si`h offoet.

F`kuro >> sldws tlo pr`gnry-s`co eurroht

wnvofdrgs. Slo rgs vnbuo df tlo pr`gnry s`co

eurroht `s npprdx`gntoby k`voh ns:

= = = =

1 1 5 5 3 3 ; ;( ) ( )(> )

5 5

rgs Q Q Q Q Q Q Q Q p

@ @ @ @ @ @ @ @ @ C C

+ + + +7 + ∝ (=<)

1 .

(> )

=

d `h U Q G nvk

g

@ V C CS @ @

h B

∝7 + ∝ (=0)

5 .

(> )

=

d `h U Q G nvk

g

@ V C CS @ @

h B

∝7 + + (51)

3 .

(> )

=

d `h U Q G nvk

g

@ V C CS @ @

h B

∝7 ∝ + + (5>)

; .

(> )

=

d `h U

Q G nvk g

@ V C CS

@ @ h B

∝

7 ∝ + ∝

(5=)

@Q

@Q;

@Q5

C >-C

@Q1

@Q3

F`k. >>. Qr`gnry-s`co eurroht wnvofdrgs.

Slo rgs eurroht fdr soedhcnry w`hc`hks nro

uhovoh fdr cuty eyebos sgnbbor tlnh ?1%. Sloeurroht `h tlo w`hc`hk fdr c`dco CF> `h hdrgnb

dpornt`dh `s:

>

rgs

CF d @ @ C≏ (55)

Gonhwl`bo, tlo eurroht `h w`hc`hk fdr CF= c`dco

`h hdrgnb dpornt`dh `s:

= (> )rgs

CF d @ @ C≏ ∝ (53)

(Cos`kh Oxngpbo) Fdr wdrst enso zord cuty eyebo

(C71), tlo gnx`gug gnkhot`z`hk eurroht ̀ s:gnx

.

(> )

(> = )=

<(> = 1) >.=0

6.=

`h U d G pi

g

V C C S @

@ C B h

N

∝7 + ∝

7 ∝ ⋏ 7

U`heo tlo pr`gnry-s`co eurroht oqunbs tlo gnkhot`z`hk

eurroht pbus tlo dutput eurroht roforroc td tlo pr`gnry,

gnkhot`z`hk eurroht enh ronel tlo pubso-my-pubso

eurroht b`g`t bovob k`voh my Q[G edhtrdbbor cur`hk

trnhsòht. Sloro sldubc mo ohdukl gnrk`h `h

trnhsfdrgor cos`kh, ldwovor, Mgnx71.>?S `s usoc td

kunrnhtoo hdh-snturnt`dh df tlo trnhsfdrgor cur`hk

trnhsòht (OO]5?3=, No7>10gg=). Slo gnx`gug fbux

cohs`ty `h tlo wdrst enso seohnr`d w`bb mo eloeioc `hUSOQ-< nftor eurroht b`g`t bovob ̀ s cotorg`hoc. Slo

g`h`gug hugmor df turhs fdr tlo pr`gnry w`hc`hk `s

k`voh ns:6

.g`h

6

gnx

651 >1 >.=030.;

>10 >1 1.>?

g G pi

p

o

B @ turhs

N M

∝

∝

Û ⋏7 7 7

Û ⋏

Slo pr`gnry nhc soedhcnry-s`co turhs nro cotorg`hoc

ns ?1 turhs nhc < turhs, rospoet`voby.

Slo rgs vnbuo df tlo pr`gnry-s`co eurroht `s k`voh my:




>>

6

1 6

< 311 (> 1.53) 1.53 >1 >11.3> 1.00

6.= = 651 >1 Q

@ N∝

∝

⋏ ∝ ⋏ ⋏ Û7 + ∝ 7

⋏ Û

6

5 6

< 311 (> 1.53) 1.53 >1 >11.3> =.3=

6.= = 651 >1 Q @ N

∝

∝

⋏ ∝ ⋏ ⋏ Û7 + + 7

⋏ Û

6

3 6

< 311 (> 1.53) 1.53 >1 >11.3> 1.>;

6.= = 651 >1 Q

@ N∝

∝

⋏ ∝ ⋏ ⋏ Û7 ∝ + + 7 ∝

⋏ Û

6

; 6

< 311 (> 1.53) 1.53 >1 >11.3> >.?0

6.= = 651 >1

Q @ N∝

∝

⋏ ∝ ⋏ ⋏ Û7 ∝ + ∝ 7 ∝

⋏ Û

>.=0rgs

p @ N7

Slo eurroht `h tlo w`hc`hk fdr CF> c`dco `h hdrgnb

dpornt`dh `s

> < 1.53 3.;rgs

CF d @ @ C N≏ 7 ⋏ 7

Gonhwl`bo, tlo eurroht `h tlo w`hc`hk fdr CF= c`dco

`h hdrgnb dpornt`dh `s:

= (> ) < (> 1.53) 6.?rgs

CF d @ @ C N≏ ∝ 7 ⋏ ∝ 7

Fdr tlo pr`gnry w`hc`hk, 1.>=φÛ51 (B`tz w`ro) `s

soboetoc nhc tlo eurroht cohs`ty `s 5.<N/gg=. @h tlo

enso df tlo soedhcnry w`hc`hk, 1.>φÛ>11 (B`tz w`ro)

`s soboetoc nhc tlo eurroht cohs`tòs nro ?.0N/gg

=

nhc<.=N/gg= fdr CF> nhc CF=, rospoet`voby.

YUSOQ-;W CE Mbdei`hk Enpne`tdr Uoboet`dh

Ovoh tldukl `t lns mooh nssugoc tlnt tlo CE

mbdei`hk enpne`tdr EM `s bnrko ohdukl td hokboet tlo

vdbtnko r`ppbo nerdss EM, tdd bnrko n enpne`tdr

rosubts `h sbdw cyhngè rospdhso. Slus, `t `s typènb

td soboet tlo enpne`tdr sd tlnt tlo r`ppbo `s ?~>1% df

tlo `hput vdbtnko. Slo vdbtnko r`ppbo df CE mbdei`hk

enpne`tdr `s k`voh ns:

1

> >Y (> = )W

U CS

d dEM p

M M

@ @ V ` ct C

E E h h∆ ≏ 7 + ∝∩ (5?)

(Cos`kh Oxngpbo)

Sd sot tlo vdbtnko r`ppbo mobdw 51V, tlo g`h`gug

CE mbdei`hk enpne`tdr vnbuo `s dmtn`hoc frdg

1

> >Y (> = )W 51

U CS

d d p hdg

M M

@ @ ` ct C V

E E h h7 + ∝ 2∩

6

>Y (> = )W

51

> < <Y (> = 1.53)W 1.53 >1 >1 >05

51 6.= 6.=

d d M hdg hdg U

M

@ @ E C C S

V h h

E hF V

∝

8 + ∝

8 + ∝ ⋏ ⋏ ⋏ Û 7

Slo vdbtnko df EM `s k`voh ns V@HÛC my (=) nhc

tlo gnx`gug enpne`tdr vdbtnko `s tlodrotènbby

lnbf df tlo `hput vdbtnko. Ldwovor, `t enh ronel tlo

`hput vdbtnko wl`bo tlo edhvortor `s hdt dpornt`hk

`f tlo boninko eurrohts df tlo GDUFOSs nro

uhmnbnheoc. Slus, vdbtnko rnt`hk sldubc mo l`klor

tlnh gnx`gug `hput vdbtnko (311V).

Nhdtlor `gpdrtnht fnetdr td edhs`cor wloh

soboet`hk tlo enpne`tdr `s tlo eurroht rnt`hk. U`heo

tlo pr`gnry-s`co eurroht df >.=;N enbeubntoc `h

USOQ-6 fbdws tlrdukl tlo enpne`tdr, n bdw-OU]

enpne`tdr sldubc mo eldsoh. Slus, n

==1hF/=;?VNE f`bg enpne`tdr `s soboetoc.

YUSOQ-<W Eurroht Uohs`hk

Sd cotorg`ho tlo pubso-my-pubso eurroht b`g`t

bovob, tlo poni eurroht `h tlo pr`gnry s`co sldubc mo

dmtn`hoc f`rst ns:

(> )(= = )

=

pi d `h hdg hdg U p hdg

g

@ V C C S @ C

h B

∝7 ∝ + (56)

(Cos`kh Oxngpbo)

Slo poni eurroht `s dmtn`hoc ns:

6

6

(> )(= = )

=

< 311 1.53 (> 1.53) >1 >1(= = 1.53)

6.= = 651 >1

=.3>

pi d `h hdg hdg U p hdg

g

@ V C C S @ C

h B

N

∝

∝

∝7 ∝ +

⋏ ⋏ ∝ ⋏ Û7 ∝ ⋏ +

⋏ Û7

Eurroht b`g`t bovob `s cotorg`hoc ns 5N, us`hk

1.=Π ros`stdr s`heo tlo eurroht b`g`t tlrosldbc

vdbtnko `s 1.6V.

Ns goht`dhoc `h USOQ-6, tlo trnhsfdrgor

gnkhot`z`hk eurroht enh ronel tlo pubso-my-pubsoeurroht b`g`t bovob k`voh my tlo Q[G edhtrdbbor

cur`hk trnhsòht. Slorofdro, tlo gnx`gug fbux

cohs`ty df trnhsfdrgor sldubc mo eloeioc ns.6

gnx g`h 6

651 5>11.5?

>10 >1 ?1

wdrst g B@G

o p

B @ M S

N H

∝

∝

⋏Û7 7 7

Û ⋏

YUSOQ-0W C`dco Uoboet`dh

Slo vdbtnko stross fdr onel roet`fòr c`dco (CF>

nhc CF=) `s k`voh ns:

>

= CF `hV V C

h7 ⋏ ⋏ (5;)

=

=(> ) CF `hV V C

h7 ⋏ ∝ ⋏ (5<)




>=

(Cos`kh Oxngpbo)

Edhs`cor`hk n wdrst enso df C7?1% fdr CF>:

>

=311 1.? 63

6.= CF V V 7 ⋏ ⋏ 7

Edhs`cor`hk n wdrst enso df C71% fdr CF=:

=

=311 > >=<

6.= CF

V V 7 ⋏ ⋏ 7

Edhs`cor`hk vdbtnko dvorslddt nhc r`hk`hk, >11V

nhc =11V c`dcos nro soboetoc fdr CF> nhc CF=,

rospoet`voby. Slo eurroht fdr onel c`dco dmtn`hoc `h

USOQ-6 `s:

>< 1.53 3.;rgs

CF d @ @ C N≏ 7 ⋏ 7

=(> ) < (> 1.53) 6.?rgs

CF d @ @ C N≏ ∝ 7 ⋏ ∝ 7

V. COU@KH S@QU

N.

_hmnbnheoc Uoedhcnry Surhs Srnhsfdrgor[loh n eohtor-tnppoc w`hc`hk `s usoc `h tlo

trnhsfdrgor soedhcnry w`hc`hk, uhmnbnheoc turhs

enh mo usoc td dpt`g`zo tlo trnhsfdrgor cos`kh, ns

sldwh `h F`kuro >=. Slo gnkhot`z`hk eurroht df tlo

trnhsfdrgor `s sl`ftoc, ns sldwh `h F`kuro >5, my

us`hk n trnhsfdrgor w`tl uhmnbnheoc soedhcnry

turhs. Slo nvornko vnbuo df tlo gnkhot`z`hk eurroht,

dr tlo CE dffsot df tlo gnkhot`z`hk eurroht, `s k`voh

ns:

= >. (> )U U

G nvk d d

p p

H H @ @ C @ C H H

7 ∝ ∝ (50)

Sl`s moedgos zord ospoe`nbby wloh:

=

> =

U

U U

H C

H H 7

+ (31)

Slus, tlo gnkhot`z`hk eurroht CE dffsot fdr sdgo

dpornt`hk pd`ht enh mo gnco v`rtunbby zord us`hk

uhmnbnheoc turhs. Ldwovor, tl`s `heronsos eurroht

r`ppbo `h tlo dutput `hcuetdr, wlèl rosubts `h n

bnrkor `hcuetdr dh tlo soedhcnry s`co. Slo

uhmnbnheoc trnhsfdrgor sldubc mo cos`khoc us`hk

trnco-dffs motwooh tlo trnhsfdrgor s`zo nhc tlo

`hcuetdr s`zo. Hdtèo tlnt tlo c`dco vdbtnko stross

rogn`hs uhelnhkoc, ovoh wloh uhmnbnheoc turhs

nro usoc.

+

VD

-

] d

=̂

>̂

Hp @ p

Bbip

Bg

EM

@ cs >

@ g

@ BD

V ̀h

@ d

+

Vc

-

VEM

+

V pr

-

+

Vroe

-

Hs>

Hs=

C>

C=

>-C

C

F`k. >=. Srnhsfdrgor w`tl uhmnbnheoc soedhcnry turhs.

>U BD

p

H @

H

=U BD

p

H @

H > =U U H 8

1.? C 2

F`k. >5. Ul`ft df gnkhot`z`hk eurroht my n trnhsfdrgor w`tl uhmnbnheoc

soedhcnry turhs.

M. Oxtorhnb Udft-Utnrt

Ovoh tldukl tlo FUFN-soròs lns `htorhnb sdft-

stnrt, eurroht dvorslddt enh deeur cur`hk stnrtup

wloh tlo boninko `hcuetnheo `s vory sgnbb, ns

copètoc `h F`kuro >3.

[loh ^> `s f`rst turhoc dh, tlo pr`gnry-s`co

vdbtnko `s dhby `gpdsoc dh tlo boninko `hcuetnheo

uht`b tlo soedhcnry-s`co roet`fòr c`dco `s turhoc dh.

Sl`s `hcueos l`kl c`/ct eurroht `h tlo pr`gnry s`conhc tlo eurroht enh oxeooc tlo pubso-my-pubso

eurroht b`g`t bovob cur`hk tlo bonc`hk-ocko mbnhi`hk

(BOM) t`go nhc turh-dff cobny t`go. Sd rocueo tlo

eurroht dvorslddt, QFG (pubso-froquohey-

gdcubnt`dh) sdft-stnrt enh mo nccoc td tlo `htorhnb

Q[G sdft-stnrt us`hk nh oxtorhnb enpne`tdr nhc

ros`stdr dh tlo ]S p`h, ns sldwh `h F`kuro >3.




>5

(> )`h

bi

V Cc`

ct B

∝

7

(> )`h

bi

V Cc`

ct B

∝7

F`k. >3. Udft-stnrt wnvofdrgs edgpnr`sdh.

V@. O\QO]@GOHSNB VO]@F@ENS@DH

Sd sldw tlo vnb`c`ty df tlo cos`kh prdeocuro

prosohtoc `h tl`s pnpor, tlo edhvortor df tlo cos`kh

oxngpbo wns mu`bt nhc tostoc. Nbb e`reu`t

edgpdhohts nro usoc ns cos`khoc. F`kuro >? sldws

tlo f`hnb selogntè df tlo nsyggotrè Q[G lnbf-

mr`cko edhvortor cos`kh oxngpbo. U`heo tlo boninko`hcuetnheo `s robnt`voby sgnbb, froquohey gdcubntoc

sdft-stnrt `s `hedrpdrntoc w`tl tlo dr`k`hnb Q[G

sdft-stnrt td rocueo tlo eurroht dvorslddt. F`kuro >6

sldws tlo trnhsfdrgor strueturo. Sd dmtn`h tlo

cos`kh boninko `hcuetnheo vnbuo, ocko w`hc`hk

rntlor tlnh eohtor w`hc`hk `s usoc fdr tlo soedhcnry-

s`co turhs.

F`kuro >; sldws tlo crn`h-td-sdureo vdbtnko df ^>

nhc tlo trnhsfdrgor pr`gnry-s`co eurroht (@ p)

wnvofdrgs nt fubb bdnc edhc`t`dh. Frdg tlo crn`h-td-

sdureo vdbtnko df ^>, tlo cuty eyebo fdr ^> `s nmdut

53% ns cos`khoc `h USOQ-5. F`kuro >< sldws tlo

crn`h-td-sdureo vdbtnko df ^> nhc trnhsfdrgor

pr`gnry-s`co eurroht (@ p) wnvofdrgs nt hd-bdnc

edhc`t`dh. Ns dmsorvoc, tlo edhvortor dporntos `h

murst gdco cuo td tlo mu`bt-`h murst gdco dpornt`dh

df tlo FUFN=>11. Slo pdwor edhsugpt`dh nt hd

bdnc `s 1.5[, `hebuc`hk tlo pdwor edhsugpt`dh df

tlo edhtrdbbor. F`kuro >0 sldws tlo crn`h-td-sdureo

vdbtnko nhc eurroht wnvofdrgs df ^> nt fubb-bdnc

edhc`t`dh. Slo crn`h vdbtnko crdps td zord nhc tlo

mdcy c`dco edhcuets mofdro tlo sw`tel `s turhoc dh.

Slo poni vnbuo df tlo crn`h eurroht `s nmdut =.3N, ns

cos`khoc. F`kuro =1 sldws tlo crn`h-td-sdureo

vdbtnko df ^> nhc vdbtnko nhc eurroht df tlo roet`fòr

c`dco C=>>. Ns dmsorvoc, tlo edhcuet`dh curnt`dh

df tlo c`dco C=>> `s boss tlnh lnbf df tlo sw`tel`hkeyebo. F`kuro => sldws tlo crn`h-td-sdureo vdbtnko

df ^> nhc vdbtnko nhc eurroht df roet`fòr c`dco

C=>=. Ns dmsorvoc, tlo edhcuet`dh curnt`dh df tlo

c`dco C=>= `s gdro tlnh lnbf df tlo sw`tel`hk eyebo.

Ns dmsorvoc frdg F`kuro =1 nhc =>, tlo vdbtnko

strossos df tloso c`dcos nro uhovoh. Slus, n =11V

rntoc c`dco `s roqu`roc fdr C=>= td lnhcbo tlo

vdbtnko dvorslddt wl`bo n >11V rntoc c`dco `s usoc

fdr C=>>. Slnhis td tlo rocueoc c`/ct my tlo

boninko `hcuetnheo, tloro `s nbgdst hd rovorso

roedvory, ovoh tldukl tlo =11V ubtrn-fnst c`dco `susoc. F`kuro == sldws tlo sdft-stnrt wnvofdrgs.

U`heo tlo boninko `hcuetnheo `s robnt`voby sgnbb,

froquohey gdcubntoc sdft-stnrt `s `hedrpdrntoc w`tl

tlo dr`k`hnb Q[G sdft-stnrt td rocueo tlo eurroht

dvorslddt. F`kuro =5 sldws tlo gonsuroc offèòhey

fdr c`fforoht bdnc edhc`t`dhs. Slo offèòhey nt fubb-

bdnc edhc`t`dh `s nmdut 05%.




>3

F`k. >?. Uelogntè df nh nsyggotrè Q[G lnbf-mr`cko edhvortor.

- Edro: OO]5?3= (No7>10 gg=)

- Mdmm`h: OO]5?3= (Ldr`zdhtnb)

F`k. >6. Srnhsfdrgor strueturo.

Q`h(U ↝ F) [`ro Surhs [`hc`hk Gotldc

Hp > ↝ < 1.>=φÛ51 (B`tz w`ro) ?1 Udbohd`c [`hc`hk

Hs> >6 ↝ >5 1.>φÛ>11 (B`tz w`ro) < Udbohd`c [`hc`hk

Hs= >= ↝ 0 1.>φÛ>11 (B`tz w`ro) < Udbohd`c [`hc`hk

Q`h Upoe. ]ognri

@hcuetnheo >＇< 651¿L ¾ ?% >11iLz, >V

Boninko >＇< 3?¿L ¾ >1%Uldrt dho df tlo soedhcnry

w`hc`hks.




>?

F`k. >;. Dpornt`dh wnvofdrgs nt fubb bdnc edhc`t`dh. F`k. ><. Dpornt`dh wnvofdrgs nt hd bdnc edhc`t`dh.

F`k. >0. Zord vdbtnko sw`tel`hk wnvofdrgs nt fubb bdnc edhc`t`dh. F`k. =1. ]oet`fòr c`dco (C=>>) wnvofdrgs nt fubb bdnc.

F`k. =>. ]oet`fòr c`dco (C=>=) wnvofdrgs nt fubb bdnc. F`k. ==. Udft-stnrt wnvofdrgs nt fubb bdnc.

<?

<6

<;

<<

<0

01

0>

0=

05

03

0?

1 =? ?1 ;? >11 >=? >?1 >;? =11Qd ([)

O f f ( %

)

F`k. =5. Gonsuroc offèòhey.




>6

V@@. EDHEB_U@DH

Sl`s pnpor prosohts cos`kh edhs`cornt`dhs df nh

nsyggotrè Q[G lnbf-mr`cko edhvortor. Slo prnetènb

cos`kh prdeocuro ohcs w`tl n cos`kh oxngpbo df n

=3V/<N (>0=[) nsyggotrè lnbf-mr`cko edhvortor,wlèl vnb`cntos tlo c`seuss`dh.

V@@@. ]OFO]OHEOU

Y>W ]dmort B. Uto`korwnbc, ‒N Edgpnr`sdh df Lnbf-mr`cko ]osdhnht

Edhvortor Sdpdbdkòs,‗ @OOO Srnhsnet`dhs dh Qdwor Oboetrdhès, Vdb. 5,

Hd. =, Npr`b >0<<.

Y=W N. F. [`tubsi` nhc ]. [. Orèisdh, ‒Cos`kh df tlo Uoròs ]osdhnht

Edhvortor fdr G`h`gug Utross,‗ @OOO Srnhsnet`dhs dh Nordsp. Oboetrdh.

Uyst., Vdb. NOU-==, pp. 5?6-565, Juby >0<6.Y5W ]. Druknht`, J. Pnhk, nhc F.E. Boo, ‒@gpbogohtnt`dh df Dpt`gnb

Srnjoetdry Edhtrdb df Uoròs ]osdhnht Edhvortors,‗ Qrde. @OOOQOUE ‐<;, >0<;.

Y3W V. Vdrpor`nh nhc U. Eui, ‒N Edgpboto CE Nhnbys`s df tlo Uoròs

]osdhnht Edhvortor,‗ Qrde. @OOO QOUE‐<=, >0<=.Y?W ]ngosl Druknht`, Qlun Eloo Johk, Joffroy S. I. Kunh nhc B̀ ow N.

Eldy, ‒Udft-sw`tel`hk CE/CE Edhvortor w`tl Q[G Edhtrdb‗, @OOO

Srnhsnet`dhs dh Qdwor Oboetrdhès, Vdb. >5, Hd. >, pp. >1=->>3, Jnh.

>00<.

Lnhksodi Eld` roeo`voc M.U., G.U.,

nhc Ql.C cokroos `h oboetrènb

ohk`hoor`hk frdg Uodub Hnt`dhnb

_h`vors`ty, `h >006, >000, nhc =11=,

rospoet`voby. Frdg =11= td =11;, lowdrioc fdr Fn`rel`bc Uogèdhcuetdr `h

Idron ns n systog nhc nppbènt`dh ohk`hoor. Lo `s eurrohtby

wdri`hk fdr Fn`rel`bc Uogèdhcuetdr `h Mocfdrc, HL, _UN, ns

n pr`he`pnb systog nhc nppbènt`dh ohk`hoor. L`s rosonrel

`htorosts `hebuco sdft-sw`tel`hk toelh`quos, gdcob`hk, nhc

edhtrdb df edhvortors. Lo lns pumb`sloc >? pnpors `h @OOO

edhforoheos nhc trnhsnet`dhs nhc >= nppbènt`dh hdtos fdr

Fn`rel`bc Uogèdhcuetdr.

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Design Considerations for Asymmetric Half Bridge Converters

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