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Flyback Transformer Design ForTOPSwitch ® Power SuppliesApplication Note AN-17

total flyback component cost is lower when compared to othertechniques. Between 75 and 100 Watts, increasing voltage andcurrent stresses cause flyback component cost to increasesignificantly. At higher power levels, topologies with lowervoltage and current stress levels (such as the forward converter)may be more cost effective even with higher component counts.

Flyback transformer design, which requires iteration through aset of design equations, is not difficult. Simple spreadsheetiteration reduces design time to under 10 minutes for a transformer

When developing TOPSwitch flyback power supplies,transformer design is usually the biggest stumbling block.Flyback transformers are not designed or used like normaltransformers. Energy is stored in the core. The core must begapped. Current effectively flows in either the primary orsecondary winding but never in both windings at the sametime.

Why use the flyback topology? Flyback power supplies use theleast number of components. At power levels below 75 watts,

®

Figure 1. ST202A Power Supply Operates from Universal Input Voltage and Delivers 15 Watts.

PI-1787-021296

7.5 V

RTN

C547 µF

D2UG8BT

D31N4148

R268 Ω

VR21N5995B

6.2 V

C3120 µF

25 V

D1

UF4005

C2680 µF

25 V

VR1P6KE200

CIRCUIT PERFORMANCE:

Line Regulation - ±0.5%(85-265 VAC)

Load Regulation - ±1%(10-100%)

Ripple Voltage ± 50 mVMeets VDE Class B

BR1 C133 µF(CIN)

R139 Ω

U2NEC2501-H

U1TOP202YAI

DRAIN

SOURCE

CONTROL

C40.1 µF

C71000 nF

Y1

L13.3 µH

J1

C60.1 µF

L222 mH

L

N

IPRI

ISEC

VDIODE

VDRAIN

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that usually works the first time. This method, used forcontinuous mode as well as discontinuous mode designs, hasthree distinct steps:

1) Identify and estimate a set of independent variables(input) depending on application details, transformercore, and selected TOPSwitch .

2) Identify and calculate a set of dependent parameters(output).

3) Iterate specified independent variables until selecteddependent parameters fall within defined limits for apractical flyback transformer.

A simple PC spreadsheet (available from Power Integrationsfor Excel or compatible spreadsheet programs) automates thetransformer design method presented in this application note.(Note: this improved version has been completely revised andmay give slightly different answers compared to earlier versions.Refer to the last page of this application note for a completedescription of the changes.)

A new parameter, the ratio of primary ripple current to peak current (K RP), is introduced to describe the TOPSwitch draincurrent waveform shape and simplify subsequent calculationssuch as RMS current and AC flux density.

Application specific independent variables include minimumand maximum AC input voltage, line frequency, TOPSwitchswitching frequency, output and bias voltages, output power,bridge rectifier conduction time, size of input energy storage

capacitor, power supply efficiency and power loss allocationbetween primary and secondary circuitry. Variables dependingon the transformer core and construction include effective corecross sectional area and magnetic path length, ungappedeffective inductance, bobbin physical winding width, marginwidth (for creepage distance and safety isolation), number of primary layers, and number of secondary turns. Variablesdepending on TOPSwitch include switching frequency, reflectedoutput voltage, ripple to peak current ratio, and TOPSwitchvoltage drop.

For a given application and transformer core, 20 of these 23independent variables will be calculated or estimated once and

then remain fixed during iteration. Only three variables,number of secondary turns N S, ripple to peak current ratio K RP,and number of primary winding layers L will be changed duringthe iteration process.

Dependent parameters are divided into four groups: DC inputvoltage, primary current waveform shape, transformer design,and voltage stress. DC input voltage parameters are simply theminimum and maximum DC input voltage after the AC mainshave been rectified and filtered. Primary current waveform

shape parameters include maximum duty cycle, average current,peak current, ripple current, and RMS current to completelydefine transformer primary current and determine operation ineither continuous or discontinuous mode. Transformer designparameters include primary inductance, number of primaryturns, number of bias winding turns, gapped effective inductance,maximum flux density, AC flux density, ungapped core relativepermeability, estimated gap length, effective bobbin width,insulated primary wire diameter, insulation thickness, bareconductor cross section, primary current capacity, and secondarydesign parameters. Voltage stress parameters determine themaximum TOPSwitch off-state drain voltage and output rectifierpeak inverse voltage.

Of all these dependent parameters, only three require examinationand comparison within limits during iteration. Maximum fluxdensity B M, gap length L G , and primary current capacity CMAare checked with each iteration until all three parameters arewithin specified limits. The remaining dependent parametersare either intermediate calculations or parameters used by themanufacturer for construction or the designer for specifyingcomponents.

Understanding primary and secondary current waveform shapein both continuous and discontinuous mode operation isnecessary before beginning transformer design.

Figure 1 shows a typical flyback power supply using theTOP202 TOPSwitch from Power Integrations, Inc. TOPSwitchcombines an integrated high voltage MOSFET switch with acomplete switching power supply controller and protectioncircuitry in a single 3 pin TO220 package. The TOPSwitch

power supply operates from 85 to 265 VAC and delivers 15Watts at 7.5 Volt output. AC power is rectified and filtered byBR1 and C1 (C IN) to create the high voltage DC bus applied tothe primary winding of T1. The other side of the transformerprimary is driven by TOPSwitch . D1 and VR1 clamp voltagespikes caused by transformer leakage inductance. D2, C2, L1,and C3 rectify and filter the power secondary. TOPSwitch biasvoltage is provided by D3 and C4 which rectify and filter thebias winding. EMI filter components L2, C6, and C7 reduceconducted emission currents. Bypass capacitor C5 filtersinternal TOPSwitch gate charge current spikes and alsocompensates the control loop. Regulation is achieved when theoutput voltage rises sufficiently above Zener diode voltage

(VR2) to cause optocoupler photodiode current to flow.Optocoupler phototransistor current flows into the TOPSwitchcontrol pin to directly control the duty cycle and output voltage.R1 together with series impedances of VR2 and TOPSwitchdetermine the control loop DC gain. R2 and VR2 provide aslight preload to improve regulation at light loads.

Figures 2 and 3 show typical voltage and current waveformstaken from the same power supply delivering 15 Watts from110 VAC input voltage but with different flyback transformer

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BIAS

BIAS(ALTERNATELOCATION)

PRIMARY

PI-1678-091395

SECONDARY(INSULATED)

BIAS

MM

PRIMARY

(Z WOUND)

ALTERNATEPRIMARYWINDING

SECONDARY

SAFETYINSULATIONTAPE

(a) MARGIN WINDING

(b) C WINDINGPI-1521-091395

Figure 5. Triple Insulated Wire Wound Transformer.Figure 4. Margin Wound Transformer.

Teflon sleeving with a minimum wall thickness of 0.41 mmshould be used to meet the safety agency requirements. Considerthe core as isolated dead metal (which means the core isconductive but not part of any circuit and safely insulated fromthe consumer). The sum of distance from primary winding (orlead exits) to the core added to the distance from the core to thesecondary (or lead exits) must be equal to or greater than therequired creepage distance.

Both Z winding (Figure 4a) and C winding (Figure 4b) techniquesfor multiple primary layers are shown. Note that the “dot” sidewhich connects to TOPSwitch is buried under the second layer

for self shielding to reduce EMI (common mode conductedemission currents). Z winding decreases transformercapacitance, decreases AC TOPSwitch losses, and improvesefficiency but is more difficult and costly to wind. TheC winding is easier and lower cost to wind but at the expense of higher loss and lower efficiency.

Figure 5 shows a new technique using double or triple insulatedwire on the secondary to eliminate the need for margins (insulatedwire sources can be found at the end of this application note).In double insulated wire, each layer is usually capable of meeting the electric strength requirement of the safety agency.In triple insulated wire, all three combinations of two layerstaken together must usually meet the electric strengthrequirement. Special care is necessary to prevent insulationdamage during winding and soldering. This technique reducestransformer size and eliminates the labor cost of adding marginsbut has higher material cost and may increase winding costs.The primary winding is wound over the full width of the bobbinflange. The bias winding can be wound if desired over theprimary. One layer of tape is usually necessary betweenprimary or bias and secondary to prevent abrasion of the

insulated wire. The double or triple insulated wire is thenwound. Another layer of tape is added to secure insulatedwinding.

Figure 5 also shows an alternate position for the bias windingwound directly over the secondary to improve coupling to thesecondary winding and reduce leakage inductance (to improveload regulation in bias winding feedback circuits). Note thatbecause the bias winding is a primary circuit, margin woundtransformers must have another layer of supplementary orreinforced insulation between the secondary and alternate biaswinding.

Refer to AN-18 for more information regarding transformerconstruction guidelines.

Flyback transformer design now begins by specifying the threegroups of independent variables shown in the spreadsheet(Figure 6).

Application Variables:

Output power P O, output voltage V O, AC mains frequency f L,TOPSwitch switching frequency f S (100KHz), minimum(VACMIN ), and maximum (V ACMAX ) AC mains voltage comedirectly from the application.

For efficiency ( η), start with an estimate based on measurementsin similar power supplies (or use a value of 0.8 if data isunavailable).

Efficiency can be used to calculate total power loss P L in thepower supply as shown below. Some power losses occurring inseries primary components such as the bridge rectifier, common

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Figure 6. Spreadsheet for ST202A Flyback Transformer Design .

1

2

3

4

5

6

7

8

9

1 0

1 1

1 2

1 3

1 4

1 5

1 6

1 7

1 8

1 9

2 0

2 1

2 2

2 3

2 4

2 5

2 6

2 7

2 8

2 9

3 03 1

3 2

3 3

3 4

3 5

3 6

3 7

3 8

3 9

4 0

4 1

4 2

4 3

4 4

4 5

4 6

4 7

4 8

4 9

5 05 1

5 2

5 3

5 4

5 5

5 6

5 7

5 8

5 9

6 0

6 1

6 2

6 3

6 4

6 5

6 6

6 7

6 8

6 9

7 0

7 1

7 2

7 3

7 4

7 5

7 6

7 7

7 8

7 9

8 0

8 1

8 2

A B C D E F

INPUT OUTPUT

ENTER APPLICATION VARIABLES

VACMIN 8 5 Volts Minimum AC Input VoltageVACMAX 265 Volts Maximum AC Input VoltagefL 6 0 Hertz AC Mains FrequencyfS 100000 Hertz TOPSwitch Switching FrequencyVO 7.5 Volts Output VoltagePO 1 5 Watts Output Powern 0.8 Efficiency EstimateZ 0.5 Loss Allocation FactorVB 10.4 Volts Bias VoltagetC 3.2 mSeconds Bridge Rectifier Conduction Time EstimateCIN 3 3 uFarads Input Filter Capacitor

ENTER TOPSWITCH VARIABLES

VOR 8 5 Volts Reflected Output VoltageVDS 1 0 Volts TOPSwitch on-state Drain to Source VoltageVD 0.4 Volts Output Winding Diode Forward Voltage DropVDB 0.7 Volts Bias Winding Diode Forward Voltage DropKRP 0 . 9 2 Ripple to Peak Current Ratio (0.4 < KRP < 1.0)

ENTER TRANSFORMER CORE/CONSTRUCTION VARIABLES

EE22-Z Core TypeAE 0.41 cm^2 Core Effective Cross Sectional AreaLE 3.96 cm Core Effective Path LengthAL 2400 nH/T^ 2 Ungapped Core Effective InductanceBW 8.43 mm Bobbin Physical Winding WidthM 0 mm Safety Margin Width (Half the Primary to Secondary Creepage Distance)L 2 Number of Primary Layers

NS 5 Number of Secondary Turns

DC INPUT VOLTAGE PARAMETERS

VMIN 9 3 Volts Minimum DC Input VoltageVMAX 375 Volts Maximum DC Input Voltage

CURRENT WAVEFORM SHAPE PARAMETERS

DMAX 0.51 Duty Cycle at Minimum DC Input Voltage (VMIN)IAVG 0.20 Amps Average Primary CurrentI P 0.74 Amps Peak Primary CurrentI R 0.68 Amps Primary Ripple CurrentIRMS 0.32 Amps Primary RMS Current

TRANSFORMER PRIMARY DESIGN PARAMETERS

LP 623 uHenries Primary InductanceNP 5 4 Primary Winding Number of TurnsNB 7 Bias Winding Number of TurnsALG 215 nH/T^ 2 Gapped Core Effective InductanceBM 2 0 8 5 Gauss Maxim um Fl ux De ns it y (2000 < BM < 3000)BAC 959 Gauss AC Flux Density for Core Loss Curves (0.5 X Peak to Peak)ur 1845 Relative Permeability of Ungapped CoreLG 0 . 2 2 mm Gap Length (Lg >> 0.051 mm)BWE 16.86 mm Effective Bobbin WidthOD 0.31 mm Maximum Primary Wire Diameter including insulationINS 0.05 mm Estimated Total Insulation Thickness (= 2 * film thickness)DIA 0.26 mm Bare conductor diameterAWG 3 0 AWG Primary Wire Gauge (Rounded to next smaller standard AWG value)CM 102 Cmils Bare conductor effective area in circular milsCMA 3 2 1 Cmils/Amp Primary Winding Current Capacity (200 < CMA < 500)

TRANSFORMER SECONDARY DESIGN PARAMETERS

ISP 7.95 Amps Peak Secondary CurrentISRMS 3.36 Amps Secondary RMS CurrentIO 2.00 Amps Power Supply Output CurrentIRIPPLE 2.70 Amps Output Capacitor RMS Ripple Current

CMS 1079 Cmils Secondary Bare Conductor minimum circular milsAWGS 1 9 AWG Secondary Wire Gauge (Rounded up to next larger standard AWG value)DIAS 0.91 mm Secondary Minimum Bare Conductor DiameterODS 1.69 mm Secondary Maximum Insulated Wire Outside DiameterINSS 0.39 mm Maximum Secondary Insulation Wall Thickness

VOLTAGE STRESS PARAMETERS

VDRAIN 573 Volts Maximum Drain Voltage Estimate (Includes Effect of Leakage Inductance)PIVS 4 2 Volts Output Rectifier Maximum Peak Inverse VoltagePIVB 5 9 Volts Bias Rectifier Maximum Peak Inverse Voltage

ADDITIONAL OUTPUTS

VX 1 2 Volts Auxiliary Output VoltageVDX 0.7 Volts Auxiliary Diode Forward Voltage DropNX 8.04 Auxiliary Number of TurnsPIVX 6 8 Volts Auxiliary Rectifier Maximum Peak Inverse Voltage

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mode choke, and TOPSwitch are not associated directly withenergy stored in the flyback transformer core. The remainingpower losses, occurring in the output rectifier and clamp Zenerdiode when energy is released from the flyback transformer, arenow defined as secondary loss P LS. Loss Allocation Factor Z,defined below as the ratio of secondary loss P LS to total loss P L,is a scaling factor which distributes the losses between primaryand secondary. Loss allocation factor Z is typically between 0.4and 0.6 which means that secondary loss P LS is usually 40% to60% of total power supply loss P L .

P P L O= × −

( )1 η

η

Z P

P LS

L

=

Bias voltage VB is determined by the feedback control circuit

and is usually between 10 volts and 30 volts (see AN-16).

For bridge rectifier conduction time t C, 3 milliSeconds is typical(measure on a similar power supply or set equal to zero for aconservative first design).

For input filter capacitor C IN , start with a standard value inmicroFarads between two and three times the output power inWatts (appropriate for universal or 115 VAC input). Forexample: 30 µF to 45 µF is a suitable capacitance range for a15 Watt supply. 33 µF is the lowest standard value within therange.

TOPSwitch Variables:

Reflected output voltage V OR appears across the transformerprimary when TOPSwitch is off and current is flowing throughthe secondary and output rectifier diode. Transformers optimizedfor TOPSwitch applications should be designed with a maximumreflected voltage V OR of 60V or less for the TOP1XX series and135V or less for the TOP2XX series. For more information,refer to AN-16.

VDS is the on-state TOPSwitch voltage from the data sheet(typically 10 volts) at the specified value for peak TOPSwitch

drain current I P.

Output rectifier forward voltage drop V D depends on output voltage.For lower output voltages (typically 8 Volts and below) a Schottkydiode is commonly used and V D is typically 0.4 Volts. In some cases,a Schottky diode can be used for output voltages as high as 12Vdepending on input voltage range and transformer turns ratio. Forhigher output voltage, an ultrafast recovery PN junction diode is

Figure 7. Bridge AC Current, AC Voltage, and DC Voltage Waveforms.

normally used and V D is typically 0.7 Volts.

Bias winding diode forward voltage drop (V DB) is also typically0.7 Volts

Ripple current to peak current ratio K RP determines how far intothe continuous mode a flyback transformer will operate.Continuous mode transformers optimized for TOPSwitchapplications operating from 100/115 VAC or universal inputvoltage should have a minimum K RP of 0.4. Applicationsoperating from 230 VAC input voltage should have a minimumKRP of 0.6. Discontinuous mode transformers optimized forTOPSwitch applications always have a K RP equal to 1.0.

K I I RP

R

P

=

Transformer Core/Construction Variables:

The following effective parameters are specified by the coreand bobbin manufacturer in data sheets: cross sectional area A e(cm 2), path length L e (cm), ungapped inductance A L (specifiedin either mH/(1000 turns) 2 or nH/T 2), and physical bobbinwinding width B W (mm).

Margin width M, determined by insulation methods and

regulatory requirements discussed above, is usually between2.5 to 3.0 mm for margin wound or set to zero for insulated wirewound transformers.

For number of layers L, one or two layers of primary windingare normally used. Higher number of layers increase cost,increase capacitance, reduce coupling, and increase leakageinductance.

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Number of secondary turns N S is a key iteration variable. Oneturn per Volt of output voltage is a good value to begin with forNS (for example: start with 5 turns for a +5V output).

The four groups of dependent parameters can now be calculated.

DC Input Voltage Parameters:

Minimum DC input voltage V MIN depends on the AC inputvoltage, bridge rectifier, and energy storage capacitor.Figure 7 shows how C IN charges to the peak of the AC inputvoltage during a short conduction time t C. Because of full waverectification, C IN has a ripple voltage at twice line frequency.CIN must supply the entire average primary current during thedischarge time between the peaks of the AC input voltage.Minimum DC voltage V MIN can be found from the followingequation where P O is the power supply output power, η is anestimate of efficiency, f L is line voltage frequency, V ACMIN is theminimum AC mains voltage, C IN is the value of the filtercapacitor, and t

C is an estimate for conduction time. As an

example, for 60 Hz, 85 VAC input voltage, efficiency of 0.8,15 Watt output power, 33 uF input filter capacitance, andestimated conduction time of 3.2 mS, V MIN is 93 Volts DC.

V V P

f t

C MIN ACMIN O

LC

IN

= × −× × × −

×( ) (

( ))2

2 1

22η

= × −× ×

× −

× =( ) (

( . )

.)2 85

2 15 1

2 603 2

0 8 33932

mS

F V

µ

Maximum DC input voltageV MAX is simply the peak value of the highest AC input voltage (V ACMAX ) expected in theapplication. Operation from 265 VAC input results in amaximum DC bus voltage V MAX of 375 Volts DC.

V V V MAX ACMAX = × = × =2 265 2 375

Current Waveform Shape Parameters:

DMAX is the actual duty cycle occurring when the TOPSwitchpower supply delivers maximum output power from minimuminput voltage. D MAX has an upper limit equal to the minimumvalue of the TOPSwitch Data Sheet parameter DC MAX (64%).DMAX is calculated from reflected voltage V OR, minimum DCinput voltage V MIN , and TOPSwitch on-state Drain to Source

voltage V DS:

D V V V V MAX

OR

OR MIN DS

= + −( )Average current I AVG is calculated from minimum DC inputvoltage V MIN , output power P O, and efficiency η:

I P

V AVGO

MIN

= ×ηPeak primary current Ip is calculated from average current I AVG ,ripple to peak current ratio K RP, and maximum duty cycle D MAX :

I I K DP AVG RP MAX

= × − ×2

2( )

Ripple current I R is calculated from average current I AVG , peak

primary current I P, and maximum duty cycle D MAX :

I I I

D R P AVG

MAX

= × −2 ( )

RMS current I RMS is calculated from maximum duty cycle D MAX ,peak primary current I P, and ripple to peak ratio K RP. I RMS canalso be calculated directly from D MAX , IP, and ripple current I R.

I I D K

K RMS P MAX RP

RP= × × − +( )2

3

1

= × − × + D I I I I MAX P P R R( ( ) )22

3

Transformer Design Parameters:

Primary inductance L P (in µH) is determined by the flyback transformer energy equation defined below. The flyback transformer stores energy proportional to the square of primarycurrent. When TOPSwitch is on, primary current linearly rampsup over a current range, defined earlier as ripple current I R, andincreases the energy stored in the flyback transformer core.When TOPSwitch turns off, the stored energy incrementassociated with ripple current I R is delivered to the load andsecondary losses (rectifier and clamp). Inductance L P can nowby calculated from output power P O, efficiency η, loss allocationfactor Z, peak current I P, switching frequency f S, and ripplecurrent to peak current ratio K RP (which determines I R).

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9

LP

Z

f I K K P

O

S P RP RP

= ×× × − +

× × × −10

1

12

6

2

(( ( ))

)

( )

η η

η

Primary inductance L P (in µH) can also be determined from asimple function of ripple current I R, effective primary voltage(V MIN-VDS), maximum duty cycle D MAX , and switching frequencyf S as shown below but the resulting value for primary inductancemay be slightly different due to the selected value for lossallocation factor Z and TOPSwitch on-state Drain to Sourcevoltage V DS. The energy equation given above is preferred forselecting the value of inductance L P while the ripple currentequation given below is best for verifying the L P value usingin-circuit measurements.

L V V D

I f P MEASURED

MIN DS MAX

R S ( )

( )= × − ×

×10 6

Number of primary turns N P depends on number of secondaryturns N S, output voltage V O, diode forward voltage drop V D,effective primary voltage (V MIN -VDS), and maximum duty cycleDMAX :

N N V V

V V D

DP S MIN DS

O D

MAX

MAX

= × −+ × −1

The number of bias winding turns N B is calculated from theoutput voltage V O, output diode voltage V D, secondary numberof turns N S, target bias voltage V B, and bias diode voltage V BD:

N V V

V V N B

B BD

O DS

=+

+×

ALG is the effective inductance for the gapped core in nH/T2.

Some core vendors offer standard gapped core sets with specifiedALG . The transformer manufacturer either procures the gappedcore for the given A LG value or grinds the gap to meet theinductance specification in the finished transformer. A LG is

also used to simplify subsequent calculations. A LG is calculatedfrom primary inductance L P (in µH) and number of primaryturns N P. Note that A LG is specified in nH/(turn)

2.

A L

N LGP

P

= ×10002

Maximum flux density B M is a dependent iteration variable tobe manipulated between the limits of 2000 and 3000 Gauss byvarying number of secondary turns N S which directly variesnumber of primary turns N P as previously shown. B M iscalculated from peak current I P, number of primary turns N P,effective gapped inductance A LG , and effective core crosssectional area A e. B M can also be calculated from effectiveprimary voltage (V MIN -V DS), output voltage V O, output diodevoltage V D, and maximum duty cycle D MAX :

B N I A

A M P P LG

e

= × ××10

= × ×× × −

+ × − N I A

AV V

V V D

DS P LG

e

MIN DS

O D

MAX

MAX 10 1

BAC is the AC flux density component. The equation gives peak

AC flux density (rather than peak to peak) to use with core losscurves provided by the core vendor. B AC can be calculated frommaximum flux density B M and ripple to peak current ratio K RP.BAC can also be calculated from effective primary voltage(VMIN -VDS), duty cycle, frequency, effective core cross sectionalarea, and number of primary turns N P:

B B K V V D

f A N AC M RP MIN DS MAX

S e P

= × = − × ×× × ×210

2

8( )

Relative permeability µr of the ungapped core must be calculatedto estimate the gap length L g. µr is found from core parametersAe (cm

2), L e (cm), and ungapped effective inductance A L:

µ π

r L E

e

A L A

= ×× × ×0 4 10.

Gap length L g is the air gap ground into the center leg of thetransformer core. Grinding tolerances and A LG accuracy placea minimum limit of 0.051 mm on L g. L g (in mm) is calculatedfrom number of primary turns N P, core effective cross sectionalarea A e, primary inductance L P (in µH), core effective pathlength L e, and relative permeability µr:

L N A L LgP e

P

e

r = × × ×× − ×0 4 100 10

2

. π µ

Effective bobbin width BW E takes into account physical bobbinwidth BW, margins M, and number of layers L:

BW L BW M E = × − ×( ( ))2

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CMA CM

I RMS =

This completes all calculations necessary for the primarywinding. Secondary peak current, RMS current, average outputcurrent, output capacitor ripple current, and secondary minimumand maximum conductor diameter must also be calculated.

Peak secondary current I SP is a simple function of peak primarycurrent I P, primary turns N P, and secondary turns N S.

I I N

N SP PP

S

= ×

Secondary RMS current I SRMS is found from maximum dutycycle D MAX , secondary peak current I SP, and ripple to peak current ratio K RP (K RP is identical for primary and secondary).

I I D K K SRMS SP MAX RP

RP= × − × − +( ) ( )1 3 12

Output current I O is simply the ratio of output power P O to outputVoltage V O:

I P

V OO

O

=

Output capacitor ripple current I RIPPLE is not a true transformerparameter but is needed for capacitor selection and easy tocalculate from other transformer parameters. I RIPPLE is foundfrom secondary RMS current I SRMS and output current I O.

I I I RIPPLE SRMS O= −2 2

Minimum secondary bare conductor diameter DIA S (in mm)based on previously calculated current capacity CMA andsecondary RMS current must be determined.

From the primary CMA and secondary RMS current I SRMS , theminimum secondary bare conductor CM S is calculated.

CM CMA I S SRMS = ×

Minimum secondary AWG S is then calculated from anotherempirical equation. Secondary calculated wire gauge AWG S isalways rounded down to the next integer value which selects thenext larger standard wire size.

Primary insulated wire diameter OD in mm is found fromeffective bobbin width BW E and number of primary turns N P:

OD BW

N E

P

=

The bias winding is usually wound with the same wire diameteras the primary to reduce the number of different wire gaugesnecessary for production.

Actual magnet wire outside diameter OD is slightly larger thanthe diameter DIA of the bare copper conductor. Insulationthickness varies inversely with bare copper conductor AmericanWire Gauge (AWG) size which means that smaller diameterconductors have thinner insulation thickness. Data from severaldifferent manufacturers were tabulated to generate an empiricalexpression for total insulation thickness INS (in mm) as afunction of heavy insulated magnet wire outside diameter(in mm).

INS LOG OD= × +( . ( )) .0 0594 0 0834

DIA OD INS = −

Another empirical equation determines the AWG for magnetwire with a given bare conductor diameter DIA. Integer AWGvalues are the standard sizes of available wire so the calculatedAWG value should always be rounded up to the next integer orstandard value (the next smaller standard conductor diameter)

before proceeding with the current capacity or CMA calculation.

AWG LOG DIA= × − ×9 97 1 8277 2. ( . ( ( )))

Magnet wire for transformer winding usually has the crosssectional area specified in circular mils. A circular mil is thecross sectional area of a wire with a diameter of 1 mil (or0.0254 mm). The effective cross sectional area in circular mils(CM) of a standard AWG size bare conductor wire is foundfrom the following simple expression.

CM AWG

=−

250

3

“Circular mils per Amp” or CMA is a convenient way to specifywinding current capacity. CMA, which is the inverse of currentdensity, is simply the ratio of cross sectional area in circularmils to the RMS value of primary current. CMA should bebetween 200 and 500 and is calculated from cross sectionalwire area in CM and RMS primary current I RMS .

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AWG LOG CM S S = × −9 97 5 017. ( . ( ))

(Secondary conductors larger than 26 AWG should not be useddue to skin effects. Refer to AN-18 for suggestions on parallelconductor techniques.)

Bare conductor diameter (in mm) is now determined.

DIAS

AWGS

= × × ×−

4 2

1 2725 41000

503

..

π

The maximum wire outside diameter OD S (in mm) for a singlelayer based on number of secondary turns and bobbin widthmust also be calculated:

OD BW M

N S

S

= − ×( )2

Secondary wire insulation thickness can now be calculatedfrom the bare conductor outside diameter (determined byCMA) and the insulated wire outside diameter (determined bynumber of turns and effective bobbin width). Note that secondaryinsulation thickness INS S (in mm) is the insulation wall thicknessrather than the total insulation thickness used in the primarywinding calculation.

INS OD DIA

S S S = −

2

Obviously, if insulation thickness INS S is not a positive number,another transformer design iteration is necessary with eithermore secondary layers, a smaller number of secondary turns, ora transformer core with a wider bobbin.

For insulated wire secondaries, INS S must be equal to or greaterthan insulation thickness of the selected wire.

Parallel combinations of wire with half the diameter may beeasier to wind and terminate but the effective secondary CMAwill be half the value of the single winding.

Voltage Stress Parameters:

Maximum drain voltage is the sum of maximum DC inputvoltage V MAX , an estimated drain clamp voltage term based onVOR , and an estimated voltage term related to typical blockingdiode forward recovery. Refer to AN-16 for more detail.

V V V V DRAIN MAX OR= + × × +( . . )1 4 1 5 20

Maximum peak inverse voltage PIV S for the output rectifier isdetermined by transformer primary and secondary number of turns N P and N S, maximum DC input voltage V MAX , and outputvoltage V O.

PIV V V N

N S O MAX

S

P

= + ×( )

Maximum peak inverse voltage PIV B for the bias rectifier isdetermined from a similar equation using number of bias turnsNB.

PIV V V N

N B B MAX B

P

= + ×( )

Additional or auxiliary output winding number of turns N X andrectifier diode peak inverse voltage PIV X can be determined

from the desired value for auxiliary output voltage V X, auxiliaryrectifier diode forward voltage drop V DX , output voltage V O,output rectifier diode forward voltage drop V D, and number of secondary turns N S.

N V V

V V N X

X DX

O DS =

++ ×

PIV V V N

N X X MAX X

P

= + ×( )

Iteration can now be used to reach a final and acceptablesolution for the flyback transformer design.

Iterate number of secondary turns N S or primary ripple to peak current ratio K RP until maximum flux density B M is betweenindicated limits and check that gap length L g is higher thanindicated minimum value. B M will decrease and L g will increaseas N S or K RP is increased.

Examine primary current capacity in Circular Mils per Amp(CMA). If CMA is below the specified lower limit of 200,consider increasing number of primary layers from one to twoor use the next larger core size and perform new iteration. If CMA is greater than 500, consider using the next smaller coresize. (CMA greater than 500 simply means that the wirediameter is oversized for the expected RMS current).

The transformer design is now complete. The transformer

8/16/2019 an17

12/12

AN-17

C 6/96 12

manufacturer needs the following information:

Core part number and gapped effective inductance A LGBobbin part numberWire gauge and insulation style on all windingsSafety or Electric strength and Creepage distance

specificationsPrimary Inductance L PNumber of turns (N P, NS, NB, etc.) for each windingBobbin pin connectionsWinding layer placement and winding instructionsTemperature class of operation (class A is 105 °C, class B

is 130 °C, etc.)

Spreadsheet Improvements

The order of the spreadsheet has been changed to simplify the iterationprocess. Reflected voltage V OR and ripple to peak current ratio K RP arenow independent variables which make peak current Ip and duty cycleD

MAX dependent variables. Loss allocation factor Z is introduced to

distinguish between power losses occurring before energy is stored inthe transformer (primary losses) and power losses occurring afterenergy is released from the transformer (secondary losses). Primaryinductance L P is now calculated from output power P O, KRP, efficiencyη, and loss allocation factor Z. The spreadsheet now takes into accountprimary magnet wire insulation thickness as well as the discrete stepsof standard AWG wire sizes. Metric dimensions are used throughout(with the exception of Circular mils for wire cross sectional area).Drain Voltage V DRAIN now includes an estimate for the effect of leakageinductance induced voltage spikes on typical primary clamp circuits.

References

Bisci, J., Part IV: Magnet Wire: Selection DeterminesPerformance, PCIM, October 1994, pp. 37.

Leman, B., Finding the Keys to Flyback Power SuppliesProduces Efficient Design, EDN, April 13, 1995, pp. 101-113.

McLyman, C., Transformer and Inductor Design Handbook,Marcel Dekker, Inc. 1978

Insulated Wire Sources

Rubudue Wire Company5150 E. LaPalma Ave, Suite 108Anaheim Hills, CA 92807 USA(714) 693-5512(714) 693-5515 FAX

Furukawa Electric America, Inc.200 Westpark Dr., Suite 190Peachtree City, GA 30269 USA(770) 487-1234(770) 487-9910 FAX

The Furukawa Electric Co., Ltd.6-1, Marunouchi 2-chome,Chiyoda-ku, Tokyo 100, Japan81-3-3286-322681-3-3286-3747 FAX

Power Integrations reserves the right to make changes to its products at any time to improve reliability or manufacturability.Power Integrations does not assume any liability arising from the use of any device or circuit described herein, nor does itconvey any license under its patent rights or the rights of others.

PI Logo and TOPSwitch are registered trademarks of Power Integrations, Inc.©Copyright 1994, Power Integrations, Inc. 477 N. Mathilda Avenue, Sunnyvale, CA 94086

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