Keith Billings April 2003

7/25/2019 Keith Billings April 2003

1/6ower Electronics Technology April 2003 www.powerelectronics.com 42

MAGNETIC COMPONENTS SPECIAL REPORT

Designing Flyback Trans ormer or Discontinuous Mode

By Keith Billings DKB Power Inc., Ontario, Canada

Lt s return to t e question, W y Have an Air Gap? ini-ia y pose in t e Power Design artic e in t e Decem er002 issue of Power Electronics Technology. In that article,e found that although an air gap wont prevent satura-

ion in true transformer applications, it does reduce thes ope o t e B/H oop, re ucing permea i ity an in uctance,an increasing t e magnetizing current in t e primary. Weoun even a sma air gap ene ts iscontinuous orwar

esigns, as t e resi ua ux va ue wi e nearer zero, a owinga arger wor ing ux ensity range.

Now, et s examine one more examp e o t e unctionan air gap in a errite core, w i e provi ing a etter un-

erstan ing o y ac trans ormers. g. 1s ows a typicaff-line flyback converter found in a low-power multipleutput application. A major advantage of this topology is

ts low cost and simplicity. In multiple output applications,t e a ition o a secon ary win ing, a sing e io e, an an

utput capacitor is a t at s require or eac a itionaso ate or common output. I one output is c ose - oop

vo tage sta i ize , t en a ot er outputs wi e semi-sta i-ize , wit in imits o oa ing an vo tage typica y requiren many app ications . A common i cu ty in t e esign

suc converters is t e so-ca e trans ormer. We can seeow its esign requires more care an un erstan ing t an

ts counterpart in t e orwar converter.esign i cu ties stem rom t e act t at y ac trans-

ormers aren t rea y trans ormers. More accurate y, t ey rein uctors or c o es, epen ing on t e mo e o operation.They have additional windings called the secondaries. How-ver, the secondary voltages arent related to the primary to

secondary turns ratio, as they would normally be with a truetrans ormer. W y is t is?

oo again at t e p asing o t e win ings an io es inig. 1. W en Q1 is ON t e input vo tage is app ie to t e

start o t e primary win ing t e ot en . T is is positive,an an increasing current is owing in t e primary t emagnetizing current . T e p asing o t e secon ary win -ings an recti er io es is suc t at t e secon aries aren ton ucting uring t is perio . Hence, t e secon ary win -

ings effectively dont exist, or at least the primary cant seethem. As a result, theres no usable transformer action duringthe ON period of Q1.

W en Q1 turns OFF, t e magnetizing current in t e pri-mary win ing imme iate y stops. However, t e core mustnow return to its previous con ition o near-zero ux, ant e vo tage on a win ings wi reverse, creating t e y ac

action. T is rings t e secon ary win ings an io es intoon uction an a ecreasing emagnetizing current nowows in t e secon aries. In ot er wor s, t e energy store

in t e magnetic e uring t e ON perio o Q1, spi sut into the secondary during the OFF period of Q1. Once

again, during this OFF period, the primary winding is notonducting and effectively does not exist. So, once again,

t ere s no usa e trans ormer action etween primary ansecondary. However, the secondary windings do see each

t er, ecause t ey re a con ucting at t e same time. Asa resu t, t e vo tage on t e contro e output e nes t evo tage on a ot er outputs. In t is respect, t ere s e ective

trans ormer action etween t e secon aries.Wit a t is in min , we now not to try to esign y ac

trans ormers as i t ey were trans ormers, ecause t ey ontwork that way. What, then, is the best design approach forthem? The first step is to decide on the required mode of op-rationeither discontinuous (complete energy transfer or

inductor type operation) or continuous (incomplete energytrans er or c o e type operation . To e p wit t is ecision,et s oo at t e wave orms o ig. 2, on page 45.

n t e iscontinuous mo e, t e secon ary current a s tozero e ore t e next Q1 ON perio . T e current wave ormis sawtoot , as s own in igs. 2aor 2 , an t e pea cur-ent is at east twice t e mean current. T e isa vantage o

t is mo e o operation is t e ig pea ripp e current in

F g. 1 Typical off-line flyback converter.


2/6www.powerelectronics.com Power Electronics Technology April 2003 45

POWER DESIGNS

the transformer windings, diodes, transistors, and caps.

Hence, this mode is more suitable for low power applica-tions. Advantages are no dc component in the transformer;no reverse recovery pro ems in t e output recti er io est ey re OFF e ore Q1 turns ON again ess turns; an no

rig t- a -p ane-zero in t e trans er unction 1].In t e continuous mo e, t e secon ary current is greater

t an zero w en Q1 turns ON or t e next perio . You can see

t is in g. 2c. T e main a vantage is re uce ripp e current.Unfortunately, the transformer must now support a dc cur-rent component. The output diodes are conducting when Q1turns ON (presenting diode reverse recovery problems), andit requires more turns w i e t ere s a rig t- a -p ane -zeroin t e trans er unction. However, t e a vantage o muc

re uce ripp e currents ma es t is mo e more suita e orig er power app ications.You can e ne t e mo e o operation y a justing t e

in uctance. In t is examp e, you can o t is y a justing t esize o t e air gap. Low in uctance ea s to t e iscontinu-ous mo e, w i e arge in uctance ea s to t e continuousconduction mode. In general, the inductance may be adjustedby changing the turns, core material (permeability) or thesize of the air gap, or a combination of these.

Design ExampleDiscontinuous ModeAt t is stage, t e esign approac is est i ustrate y con-

si ering a speci c examp e. Assume a iscontinuous mo eo operation as een c osen a so nown as t e comp eteenergy trans er mo e wit 50 Hz operating requencyan a power o 100W. T e ON perio o Q1 is to e 40%o t e tota perio or 8 s an t e OFF perio wi e 12 s.This provides a 2 s margin to ensure the mode remainsdiscontinuous. As shown in ig. 2b, other values can be used.

IRCLE 234 on Reader Service Card freeproductinfo.net/pet

g. 2. (a) iscontinuous mode (boundry conditions); (b) iscontinuous

ode (working condition with safety margin);( ) Continuous mode

higher power condition).



T is 40% con uction perio occurs atthe minimum input voltage of 100Vdcand full load. A gapped ferrite core is

sed, which has a center pole area ofsay 100 mm.

At 100V input an 100W power, t e

time average primary input currentwi e 1A. T e mean current in Q1 ant e primary win ing P1 , uring t e8 s 40% ON perio is 2.5A. T e peanput current is twice t e average or

5A in t is examp e see t is wave ormn Fig. 2b).

he required primary inductancean now be calculated using formula

i/ t = V, w ere i = 5A, t = 8 san V = 100V. L wi e 160 H seequations , on page 48 .

ow, t e minimum primary turnsan e ca cu ate . T ey are e ne y

t e nee to support t e app ie vo tsecon s not y t e in uctance!T e app ie vo t secon s equate to t eparameter on the B/H loop shownn ig. 3. This change in magnetic fluxensity B will be maintained irre-

spective o t e size o t e air gapitgenerates within the primary windinghe back mmf required to offset the

applied volt seconds.We c oose a maximum core ux

ensity o 0.2 Tes a to provi e a goo

wor ing margin on t e saturationeve o 0.35 Tes a. Hig er ux va ueswi increase core oss ut wi resu tn ess copper oss ecause ess turns

are require , an converse y . T eptimum c oice is w ere copper anore loss are equal. This is an iterativerocess, and cannot be finalized at this

stage; it must be checked in the finalesign. T e o owing ormu a wi

yie t e minimum primary turns ore c osen parameters:

V tA

min

See equationssing t e c osen va ues in t e

a ove ormu a, we n t e minimumrimary turns are 40.

imilarly, the secondary turns areefined by the need for the secondary

current to a to zero e ore t e nextON period of Q1. Once again, the turnsare not calculated by transformer ac-tion, although they are a function oft e require secon ary vo tage seeFigs. 2a an . Fig. 2a s ows t e

oun ary con ition w ere t e secon -ary current just a s to zero just e oret e next ON perio . ig. 2 s owsa etter con ition wit more wor -ing margin w ere t e current a s tozero in 10 s, 2 s e ore t e next ONperiod. This allows for some load andtolerance variations but also increasesthe peak current slightly.

Assume t e secon ary vo tage is toe 20V. T e y ac perio is 60% 12

s , an t e time average secon ary

current or 100W output wi e 5A.We ave c osen to ma e secon arycon uction perio 10 s. Hence, t emean current uring t e secon arycon uction perio o 10 s is 10A,and the peak current is 20A. In thissimplified example, weve not madeany allowance for diode drop and effi-ciency oss. Note t e ig output ripp ecurrent, pea ing at 20A. C ear y, t isisn t a practica esign an s ows w yt e iscontinuous mo e is norma y

imite to ow power app ications.However, i t e output vo tage was to

e arger1000V, or examp e youcan o t is wit t e y ac topo -ogy)then the peak current would beonly 400mA, which is fine.

The secondary inductance requiredor 20V output an 10 s con uction

perio may now e ca cu ate in t esame way as t e primary in uctance.Vs is now 20V an i/ t is 2A/s.Eva uating, we get 10 H see ap-

pen ix . Since t e gap as a rea yeen e ne y t e primary esign,

we must now se ect t e secon aryturns to get this value of inductancein the secondary.

The primary inductance (Lp) is160 H for 40 turns, and inductanceratios as N so 10 turns wi give 10H see appen ix . Less turns may euse , resu ting in t e current roppingto zero in a s orter y ac perio ,moving more into t e iscontinuousmo e, increasing t e pea secon arycurrent, an provi ing a wi er zero


POWER DESIGNS



current margin. Converse y, more secon ary turns may notallow the secondary current to reach zero during the flybackperiod, and the continuous mode of operation will be en-tered. Neither the primary or secondary turns are definedy trans ormer action. However, i a itiona secon ary

win ings are to e provi e , t eir vo tages wi e e ne y

t e trans ormer ratio etween t e various outputs, ecauset ey a con uct at t e same time.To speci y t e output vo tage, t e contro oop is c ose

to t e c osen output an a justs t e uty ratio to maintaint e output vo tage at t e c osen va ue or variations in inputvo tage an re uce oa ing. Increasing t e oa ing eyonthe designed 100W moves the action into the continuousmode. While this is possible, it complicates the design ofboth transformer and control loop because it introducesa RHP zero into t e trans er unction an intro uces a ccomponent into t e win ings. I t e contro oop ai s, t eoutput vo tage goes to a ig an uncontro e va ue, t us,

overvo tage protection is a wise precaution.To optimize t e esign, ca cu ate t e core an copper

oss at u oa . T ey s ou e near equa or optimumesign. I necessary, a just t e c osen ux va ue an turns

to o tain t is equa ity. Remem er: Increasing t e ux wiincrease core loss and decrease copper loss, since there willbe less turns.

POWER DESIGNS

g. 3. Top right quadrant of the B/H loop of the gapped core.




We can now win t e trans ormer.The primary is wound using a wiregauge to fill less than 50% of the bob-bin area to allow for insulation. Theest o t e space is use or t e secon -

aries. Severa sma er iameter stran s

ay e use in para e to re uce s inects.At t e moment o turn OFF o Q1,

t e primary current more correct y,ampere turns pro uct must com-

utate to t e secon ary. Any ea agenductance opposes this action, and a

large voltage overshoot will be gener-ated on the primary needing aggres-sive snu ing action. T is pro em ise uce y inter eaving primary an

secon ary as you wou in a orwar

trans ormer esign.W en nis e , t e core is tte us-

ng an e astic an to o it toget er,an t e core gap a juste to o taint e require primary in uctance o160 H. For a better understanding,onsider the action of the core gap in

CIRCLE 237 on Reader Service Card freeproductinfo.net/pet CIRCLE 238 on Reader Service Card freeproductinfo.net/pet

POWER DESIGNS

a somew at i erent way. Energy isstored in the magnetic field during theON period of Q1 and transferred to thesecondary during the OFF period ofQ1. ig. 3s ows t e top rig t qua rant

t e B/H oop o t e gappe core,

wit t e wor ing va ue o ux ensityswing B impose on it. T e area toe e t o t e B/H oop is proportiona

o t e store energy per cyc e, w i e t euc sma er area containe wit ine B/H oop is an in ication o core

oss (not to scale). In general,ower = f Ve H dB

quationsrimary In uctance

t

=

W ere:

P=Primary in uctance

P= Primary vo tage V

t = Q1 ON time ( s) = Peak primary current (A)

r mary turnsV t

AP

Where:t = Q1 ON time sB = Pea ux ensity tes a

Ae = e ective area o center po e mm2

= Minimum primary turnsIn uctance actor

ALP

W ere:A

L= Inductance of a single turn ( )

Secondary inductance LS= N 2 A

Where:L

S= Secon ary in uctance H= Secon ary turns

Secon ary turns

SS

L

=

Primary store /trans erre energy percyc e j = L

P P jou es

W ere:I

P= Peak primary current (A)

LP

= primary inductance (H)



Trans erre power P = LP

2 = WWhere:f = Frequency (Hz)

Air e

P

Ga =

W ere:

Air gap = mmr = 4 10 7

P= Primary turns

Ae = Po e area mm= Primary in uctance mH

Increasing the Air GapIncreasing the air gap will swing theB/H loop more to the right, increasingt e area an ence t e store energy.Most o t e energy is store in t e airgap ecause t is is t e owest perme-

a i ity part o t e magnetic pat , get-ting somet ing- or-not ing.

T e remnant ux Br a so re ucesas t e core gap increases, s ig t y in-creasing t e usa e ux wor ing range.The peak primary current increases asthe inductance reduces. Since stored

POWER DESIGNS

nergy is proportiona to Lp Ip,nergy still increases with the larger

gapeven though inductance falls.elow the B/H loop is shown the

primary magnetizing current uringt e ON time o Q1. In pec e orm, it

s ows t e e ective secon ary emag-netizing current as wou e re ecteto t e primary win ing in terms oampere-turns. O course, it oes notactua y ow in t e primary. T e ac

ux swing rema ns constant rre-spective of the core gap: It is a function

f applied primary volt seconds. Thepeak current and stored energy are the

epen ant varia es set y t e size ot e air gap. So now we see one moreapp ication or t e air gap.

or mu tip e outputs, simp y sumt e tota output power an use t isva ue in t e equations w en ca cu atingt e primary an secon ary in uctance

t e main contro e output. T esecondary currents will sort themselves

ut, depending on the loading appliedFor more information on this article,CIRCLE 339 on Reader Service Card


o eac output.ven while ignoring the transform-

r action, (because its not a designarameter), it still exists. The flyback

vo tage is re ecte ac to t e primarywin ing uring t e OFF perio o

Q1. Hence, re ucing secon ary turnsncreases secon ary pea currents anncreases t e vo tage stress on Q1 ur-ng t e OFF perio .

oo or t e o ow-up artic e in t eext issue o PETec . It wi cover t e

ransformer design for the continuousode (or incomplete energy transfer

hoke mode). PETech

Keit Bi ings is presi ent o DKB PowerInc., [email protected].

eference1. Keit Bi ings, Switc mo e PowerSupp y Han oo , McGraw-Hi ISBN0-07-006719-8.

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Keith Billings April 2003

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