By Victor W. Quinn, Chief Technology Ofﬁ cer, Tabtronics ... · conductor layer, R is the ratio of sinusoidal surface magnetic-ﬁ eld intensities, B is the ratio of conductor thickness

Power Electronics Technology October 2005 www.powerelectronics.com October 2005 www.powerelectronics.com14

Intuitive design techniques based on normalized loss and energy densities demonstrate real benefi ts for optimizing transformer confi gurations.

By Victor W. Quinn, Chief Technology Offi cer, Tabtronics Inc., Geneseo, N.Y.

TThe size, performance and cost of a power electronic system are closely linked to the like parameters of the magnetic components. Since custom power transformers are widely used, transformer design is a frequent design used, transformer design is a frequent design

process that has a signifi cant impact on system performance. Yet most high-frequency transformers use less than 25% of the available core window for effi cient current conduction. Two factors cause this relatively poor utilization: insulation requirements and eddy current losses.

Insulation requirements generally limit the total winding conductor cross-sectional area to less than half of the available core window. Induced high-frequency eddy currents often increase the apparent winding resistances by 50% or more. Therefore, less than 25% of the available core window is used effectively (Fig. 1). Interleaved windings, multifi lar conduc-tors, Litz wire and other approaches can decrease eddy current effects. However, these techniques add additional insulation penalties, which further reduce the net cross-sectional win-dow area available for the winding conductors.

Insulationand Shields

Eddy Current Loss Penalty

Net Conductor Area

100%

75%

50%

25%

0%

Typical Core Window Utilization

Fig. 1. Typical core window utilization in a high-frequency transformer.

Despite much published literature concerning the evalua-tion of transformer loss and energy at high frequencies, con-tinued widespread interest in transformer design methods indicates that many designers seek more intuitive techniques to evaluate tradeoffs and assure an optimal confi guration. to evaluate tradeoffs and assure an optimal confi guration. This interest is understandable because many methods lead the designer to make repeated trial confi gurations until obtaining a satisfactory result. While Finite Element Analysis (FEA) and commercial software facilitate the evaluation of many trial confi gurations, the designer’s imagination of improved confi gurations is fueled by understanding and insight.

A transformer design approach using normalized loss and energy densities inspires concepts of equivalent winding thicknesses that intuitively display optimal conductor and interleaving confi gurations.

Low-Frequency Transformer DesignClassical transformer design methods evaluate the

potential volt-ampere (VA) capacity of a selected core in comparison to the VA requirement of a given power supply application. The VA capacity of a selected core is fundamentally limited by a consideration of losses with respect to temperature rise or effi ciency requirements. At low frequencies, currents within conductors are largely uniform throughout the conductors’ cross-sections. Therefore, dissipation for a given winding is readily calculated using the material resistivity and the geometric parameters of length and cross-section for the conductor. At low frequencies, for coils with multiple windings having uniform mean lengths of turn, minimum total loss is achieved by selecting appropriate conductors for each winding to yield uniform current density throughout the coil. For uniform resistivity, mean length of turn and current density, the low-frequency dissipation of a coil is given by:

Low-frequency coil loss = ρ × ×Cond JVOL2


DESIGN METHODS

where is the conductor resistivity, CondVOL

denotes the effective total conductor volume, and J is the winding RMS current density.

Low-frequency loss can be rewritten using the concept of normalized resistance:

Low-frequency coil loss = Ω NIii

∑

2

where is the resistance of a theoretically equivalent single-turn winding yielding the specifi ed total Cond

VOL,

and NIi represents the RMS

amp-turn product for the ith

winding in the coil.The single-turn resistance

is given by the expression:

Ω∆

∆=

×ρ y∆y∆x T×x T× hickness

where y is the effective conductor length (or mean length of turn), x is the conductor width, and Thickness is the conductor thickness (Fig. 2). The denominator of this expression is equivalent to the total conductor cross-sectional area.

Therefore, low-frequency coil loss can be readily estimated using the normalized single-turn resistance and the square of the sum of the RMS amp-turn products for all windings in the coil. The accuracy of this loss estimate depends on the accuracy of the estimate for the total conductor cross-sectional area. Insulation considerations generally limit the conductor area to less than half of the available core window area. The dominant insulations are those that isolate windings from core (bobbin), windings from other windings (interwinding) and layers from other layers (interlayer). The conductor thickness of the normalized winding can be estimated by reducing the available core window height by the anticipated bobbin, interwinding and interlayer thicknesses.

This approach may be extended to low-frequency magnetic energy in the coil. For a normalized, nonmagnetic, single-portion primary conductor, having uniform mean

length of turn and uniform current density, the low-frequency magnetic energy is:

Normalized low-frequency magnetic energy =µ0

6

∆Normalized low-frequency magnetic energy =

∆Normalized low-frequency magnetic energy =

∆y∆y∆x

Thickness

where 0 is the permeability constant for free space.

While coil insulation increases loss by decreasing the effective thickness of the conductor for the normalized winding, coil insulation increases magnetic energy in the portion by increasing the effective thickness of coil regions subject to magnetic-fi eld penetration:

Normalized low-frequency magnetic energy =

µ0

6 23

∆∆6 2∆6 2

y

6 2x6 2Thickness

IL n n

nIWCU6 2CU6 2

L Ln nL Ln n

L

+n n− −n n

+

6 26 2

6 26 26 26 2

( )2 1( )2 1n n( )n n2 1n n2 1( )2 1n n2 1L L( )L Ln nL Ln n( )n nL Ln n2 1n n2 1L L2 1n n2 1( )2 1n n2 1L L2 1n n2 1n n− −n n( )n n− −n n2 1n n2 1− −2 1n n2 1( )2 1n n2 1− −2 1n n2 1 ( )1( )1n n( )n nL L( )L Ln nL Ln n( )n nL Ln n− −( )− −n n− −n n( )n n− −n n

where ThicknessCU

denotes the thickness of the accu-mulated copper conductors, n

L is the number of conductor

layers in the winding portion, IL is the interlayer insulation thickness, and IW is the interwinding insulation thickness (Fig. 3). (Note that total interwinding insulation thickness is 2IW since each portion is taken to contribute half of the total interwinding insulation thickness.) Following the result for normalized resistance, low-frequency magnetic energy for a selected winding portion can be estimated using normal-ized low-frequency magnetic energy (LFME

NORM) with the

square of the sum of the RMS amp-turn winding product in the portion:

Low-frequency magnetic energy =

LFME NINORM iPORTION∑

2

For a specifi c application and a transformer having given conductor and core regions, the normalized expression for low-frequency winding loss can be combined with an empirically derived core loss result to yield:

Total low-frequency transformer loss =

F NF

NCOILF NCOILF NpCOREFCOREF

Pn

× +F N× +F Np× +p2× +2× +

x

y

Thickness

NormalizedConductor

ConductorCross-SectionCurrent

Fig. 2. Depiction of a normalized conductor.

Seco

ndar

yPr

imar

y

IW = GW

2 IW = 2 GW

IL = GI

Fig. 3. Cross-sectional view of winding with defi nitions of insulation thickness.

Insulation considerations generally limit the conductor area to less than half of the available core window area.

www.powerelectronics.com Power Electronics Technology October 2005www.powerelectronics.com Power Electronics Technology 17

DESIGN METHODS

where FCOIL

and FCORE

are parameters relating exponential functions of primary turns (N

P) to coil and core losses,

respectively, and n is the empirically derived exponential variation of core loss with magnetic fl ux density. Without a constraint of core saturation, the value of primary turns that minimizes this expression for total low-frequency transformer loss is given by:

Nn F

FPCOREn FCOREn F

COILFCOILFn=

n F×n F

×+

22

Therefore, low-frequency transformer design involves normalized empirical core loss data and estimation of effective total conductor volume considering insulation, clearances, electrostatic shields and other coil cross-sectional area penalties.

High-Frequency Transformer DesignHigh-frequency power electronic applications cause added

transformer design considerations. Coil loss is signifi cantly affected by induced eddy currents within the conductors as a result of magnetic-fi eld intensities. Further, high-frequency excitation and circuit topology requirements generate constraints on leakage inductance (stray magnetic energy). The inherent complex waveshapes necessitate consideration of dc and higher-order harmonic components.

For a single-conductor layer, having one conductor surface at zero magnetic-fi eld intensity, high-frequency conductor loss and magnetic-energy storage can be calculated using the concept of dimensionless density functions[1]:

Conductor layer power =

p R By

xNI0p R0p R 2( ,p R( ,p R 0( ,0 ) () (

y) (

y)= ×B= ×B( ,= ×( ,0( ,0= ×0( ,0 ) (= ×) (

×ρ) (ρ) (

δ) (

δ) (

∆y∆y) (

∆) (

y) (

y∆y) (

y

∆) (

∆) (

Conductor layer magnetic energy =

e R By

xNI0 0e R0 0e R B0 0B 2( ,e R( ,e R0 0( ,0 0e R0 0e R( ,e R0 0e R 0( ,00 000 0( ,0 000 0) (0 0) (0 0 )= ×B= ×B0 0= ×0 0B0 0B= ×B0 0B( ,= ×( ,0 0( ,0 0= ×0 0( ,0 0( ,= ×( ,0 0( ,0 0= ×0 0( ,0 00( ,0= ×0( ,00 000 0( ,0 000 0= ×0 000 0( ,0 000 0) (= ×) (0 0) (0 0= ×0 0) (0 0µ δ

yµ δ

yµ δ0 0µ δ0 0) (µ δ) () (µ δ) (

y) (

yµ δ

y) (

y0 0) (0 0µ δ0 0) (0 0

∆y∆yµ δ

∆µ δ

yµ δ

y∆yµ δ

y) (µ δ) (

∆) (µ δ) (

y) (

yµ δ

y) (

y∆y) (

yµ δ

y) (

y

∆µ δ

∆µ δ) (µ δ) (

∆) (µ δ) (

where is the skin depth for the conductor material at the specifi ed frequency, x represents the width of the conductor layer, y represents the mean length of turn of the conductor layer, R is the ratio of sinusoidal surface magnetic-fi eld intensities, B is the ratio of conductor thickness to skin depth, and p

0 and e

0 are the dimensionless density functions

for loss and magnetic energy, respectively.Although p

0 and e

0 are functions involving complex terms,

the resultant expressions are similar to the low-frequency expressions presented earlier because they largely depend on simple geometric factors and the square of the amp-turn product. As a mathematical approach for calculation of dissipation, effective conductor thickness can be taken as the skin depth divided by the loss-density function. The loss-density function adjusts the effective thickness as a result of induced magnetic-fi eld and current distributions within the conductor layer. In truth, conductor thickness is not changing with excitation. The theoretical convenience of equivalent thickness is merely a simplifying calculation method to evaluate net dissipation and stored energy effects in a conductor layer. Effective thickness represents the effects of complex current density and magnetic-fi eld distributions, which vary greatly within the conductor cross-sections. Therefore, the dimensionless density functions yield intuitive calculations of loss and magnetic energy using the equivalent low-frequency expressions. Further derivations will be required to consider the general case for a multiple-layer winding undergoing complex excitation.

Nonsinusoidal CurrentsTransformer winding current may contain a bias

component, and in this event, the winding current can be represented by the harmonic decomposition:

Fig. 4. Loss-equivalent thickness for a bridge transformer primary. Fig. 5. Energy-equivalent thickness for a bridge transformer primary.

0 2 4 6 8

2

0

-2Phase

Sum of 10 Harmonics

150%

125%

100%

75%

50%

25%

0%0 1/4 1/2 3/4 1

Magnetic Energy Model6- Thick Single-Turn ReferenceLayer Insulation = 0.5 Interwinding Insulation =

Available Winding Height

1 Layer2 Layers

3 Layers

4 Layers

5 Layers

Ampl

itude

Effe

ctive

Win

ding

Thi

ckne

ss R

atio

0 2 4 6 8

2

0

-2Phase

Sum of 10 Harmonics

Ampl

itude

40%

35%

30%

25%

20%

15%

10%

5%

0%0 1/4 1/2 3/4 1

Dissipation Model6- Thick Single-Turn ReferenceInterlayer Insulation = 0.5 Interwinding Insulation =


Effe

ctive

Win

ding

Thi

ckne

ss R

atio

1 Layer

2 Layers

3 Layers4 Layers

5 Layers


DESIGN METHODS

I I

I I

I I

DCI IDCI IRMS

RMI IRMI IS RI IS RI I MS

RMI IRMI ISkI ISkI IK RI IK RI I MS

I I= ×I I

I I= ×I II IS RI I= ×I IS RI I

I I= ×I II IK RI I= ×I IK RI I

αI IαI II I= ×I IαI I= ×I I

I I= ×I IαI I= ×I II IS RI I= ×I IS RI IαI IS RI I= ×I IS RI I

αI IαI II I= ×I IαI I= ×I I

0I I0I II I= ×I I0I I= ×I I

S R1 1S RI IS RI I1 1I IS RI II IS RI I= ×I IS RI I1 1I IS RI I= ×I IS RI IS RαS R1 1S RαS RI IS RI IαI IS RI I1 1I IS RI IαI IS RI II IS RI I= ×I IS RI IαI IS RI I= ×I IS RI I1 1I IS RI I= ×I IS RI IαI IS RI I= ×I IS RI I

where IRMSk

is the RMS current value at the kRMSk

is the RMS current value at the kRMSk

th is the RMS current value at the kth is the RMS current value at the k harmonic, I

RMS is the RMS value of the complex waveshape, and

K is

the ratio of the RMS value of the kththe ratio of the RMS value of the kththe ratio of the RMS value of the k harmonic to the RMS value of the complex waveshape.

The equivalent loss-density function for a given layer is then given by:

p R BB

i p R iR i Bp Requip Requii

0 1p R0 1p R B0 1B0 1p R0 1p Requi0 1equip Requip R0 1p Requip Rv0 1vp Rvp R0 1p Rvp R 02

2

1

0i p0i p2i p2i p0 10 1R i0 1R iR i0 1R i B0 1B( ,p R( ,p R0 1( ,0 1p R0 1p R( ,p R0 1p R )( )R( )R1( )1

( ,R i( ,R i0 1( ,0 1R i0 1R i( ,R i0 1R i )=( )−( )

+ ×R i+ ×R iR i+ ×R i0 1+ ×0 1R i0 1R i+ ×R i0 1R iR i0 1R i+ ×R i0 1R i+ ×+ ×i p+ ×i pi p0i p+ ×i p0i pi p2i p+ ×i p2i p0 1+ ×0 1( ,+ ×( ,R i( ,R i+ ×R i( ,R i0 1( ,0 1+ ×0 1( ,0 1R i0 1R i( ,R i0 1R i+ ×R i0 1R i( ,R i0 1R i+ ×∑+ ×∑+ ×α αα αα αi pα αi p0α α02α α2 ( )

α α( )

+ ×α α+ ×+ ×α α+ ×i p+ ×i pα αi p+ ×i p+ ×α α+ ×∑α α∑+ ×∑+ ×α α+ ×∑+ ×

where B1 is the ratio of conductor thickness to skin depth

for the fi rst harmonic.Similarly, the equivalent ac magnetic-energy density

function for a given layer is:

e R Bi

e Requie Requie R i

i0 1e R0 1e R B0 1Bequi0 1equie Requie R0 1e Requie Rv0 1ve Rve R0 1e Rve R

2

0 1e R0 1e R( ,e R( ,e R0 1( ,0 1e R0 1e R( ,e R0 1e R ) () (e R) (e Ri) (i0 1) (0 1e R0 1e R) (e R0 1e R, ), )i B, )i B0 1, )0 10 1, )0 1i B0 1i B, )i B0 1i B= ×e R= ×e R0 1= ×0 1e R0 1e R= ×e R0 1e R) (= ×) () (= ×) () (= ×) (e R) (e R= ×e R) (e Ri) (i= ×i) (i e R0 1e R) (e R0 1e R= ×e R0 1e R) (e R0 1e R, )= ×, ), )= ×, )i B, )i B= ×i B, )i B0 1, )0 1= ×0 1, )0 10 1, )0 1= ×0 1, )0 1i B0 1i B, )i B0 1i B= ×i B0 1i B, )i B0 1i B∑) (∑) () (= ×) (∑) (= ×) (

α) (

α) (

These equivalent density functions can be used to derive expressions for loss- and energy-equivalent conductor thicknesses:

Loss-equivalent thickness =

δ

n

np

nB

Lequi

n

nL

−

=∑

2

0 1B0 1B0 1equi0 1equiv0 1v 0 10 11

10 110 1

1,0 1,0 1

Magnetic-energy-equivalent thickness =

δ[32

6 16 11

2

0 16 10 16 1

× +− −

+

6 1

6 1

6 1

6 16 16 16 1

6 16 1

6 1

6 1

6 16 1

6 1

6 1

6 1

6 1

6 16 16 16 1

6 16 1

6 1

6 1

6 16 1

6 1−6 1

6 1

6 1

6 10 10 16 10 16 1

6 10 16 16 1

6 1

6 1

6 1

6 1

6 16 1

6 1

6 1

6 16 1

6 10 10 10 10 16 10 16 1

6 10 16 16 10 16 1

6 10 16 16 1

6 1

6 1

6 16 1

6 1

6 1

6 1

G× +G× +G n

n

n

n6 1e6 1

nB0 1B0 1

W× +W× + I LG nI LG n L

L

L

equi6 1equi6 10 1equi0 16 10 16 1equi6 10 16 10 1v0 16 10 16 1v6 10 16 1

( )2 1( )2 1− −( )− −2 1− −2 1( )2 1− −2 1G n( )G n2 1G n2 1( )2 1G n2 1I L( )I L2 1I L2 1( )2 1I L2 1G nI LG n( )G nI LG n2 1G n2 1I L2 1G n2 1( )2 1G n2 1I L2 1G n2 1 ( )1( )1− −( )− −n( )n− −n− −( )− −n− −L( )L

,0 1,0 1nnn

nL

=∑6 1∑6 1

1

]

where nl is the number of layers, G

1 is the interlayer

insulation thickness and GW is the interwinding insulation

thickness for the selected winding portion.Although the expressions for loss and magnetic energy

invoke complex density terms that appear formidable, let’s turn our attention to simple graphical methods using concepts of effective normalized winding thickness and normalized winding height. These concepts are readily accomplished using common computer methods and facilitate graphical recognition of optimal coil designs considering insulation and eddy current penalties.

Equivalent Thickness MethodsAs described earlier, the transformer design process

involves the calculation of coil loss in consideration of a VA requirement arising from circuit application conditions. For low frequencies, the total coil loss can be evaluated using the product of the single-turn resistance of a volume-equivalent single-turn conductor and the square of the amp-turn product through the conductor cross-section. We will seek a similar intuitive calculation method for loss and magnetic energy in a winding portion undergoing complex excitation.

To this end, we will develop a graphical relationship between the effective winding thicknesses and the physical utilization of an available winding height. This graphical approach facilitates the selection of optimal layers and winding interleaves, including the effects of layer-insulation thickness and considering constraints of maximum leakage-inductance energy and maximum coil height. Loss and magnetic energy can then be evaluated following the expressions for low frequency applied to a normalized conductor having the appropriate equivalent thickness.

This method is illustrated in Figs. 4 through 9 as applied to a winding portion with maximum overall winding thickness of six skin depths, fi ve conductor layers maximum, and

Fig. 7. Energy-equivalent thickness for a bridge transformer secondary.Fig. 6. Loss-equivalent thickness for a bridge transformer secondary.

0 2 4 6 8

2

1

0Phase

Sum of 10 Harmonics

40%

35%

30%

25%

20%

15%

10%

5%

0%0 1/4 1/2 3/4 1

Dissipation Model6- Thick Single-Turn ReferenceInterlayer Insulation = 0.5 Interwinding Insulation =


Effe

ctive

Win

ding

Thi

ckne

ss R

atio

Ampl

itude

1 Layer

2 Layers

3 Layers4 Layers

5 Layers

0 2 4 6 8

2

1

0Phase

Sum of 10 Harmonics

150%

125%

100%

75%

50%

25%

0%0 1/4 1/2 3/4 1



1 Layer2 Layers

3 Layers4 Layers

5 Layers

Effe

ctive

Win

ding

Thi

ckne

ss R

atio

Ampl

itude


interlayer- and interwinding-insulation thicknesses of half a skin depth each. Figs. 4 and 5 pertain to the primary winding of a transformer used in a bridge confi guration operating at 62.5% duty cycle. The current was normalized to yield unity RMS value.

Fig. 4 shows that maximum loss-equivalent-wind-ing thickness is achieved when 88% of the winding height is used with fi ve conductor layers. For this con-fi guration, the loss-equivalent-winding thickness is 28% of the available winding height. However, as a result of

Fig. 9. Energy-equivalent thickness for a forward transformer primary.Fig. 8. Loss-equivalent thickness for a forward transformer primary.

0 2 4 6 8

210

Phase

Sum of 10 Harmonics

0 1/4 1/2 3/4 1

Dissipation Model6- Thick Single-Turn ReferenceInterLayer Insulation = 0.5 Interwinding Insulation =


1 Layer

2 Layers3 Layers

4 Layers

5 Layers

40%

35%

30%

25%

20%

15%

10%

5%

0%

Effe

ctive

Win

ding

Thi

ckne

ss R

atio

Ampl

itude

0 2 4 6 8

210

Phase

Sum of 10 Harmonics

0 1/4 1/2 3/4 1



1 Layer2 Layers

3 Layers4 Layers

5 Layers

150%

125%

100%

75%

50%

25%

0%

Effe

ctive

Win

ding

Thi

ckne

ss R

atio

Ampl

itude

High Energy & Surface MountMOVsEXACTING

PERFORMANCE

CKE manufactures a wide range of metal oxide CKE manufactures a wide range of metal oxide varistors (MOVs) for your unique requirements. varistors (MOVs) for your unique requirements. From low voltage radial lead styles to high From low voltage radial lead styles to high energy packages, we build to OEM specs energy packages, we build to OEM specs or provide direct replacements.or provide direct replacements.

For FREE SAMPLES, visit our Web site www.cke.com

CKE also offers: Selenium Surge Suppressors Silicon Rectifiers Custom Assemblies Silicon Carbide Varistors

Lucernemines, PA 15754Lucernemines, PA 15754(724) 479-3533(724) 479-3537 (Fax)(724) 479-3537 (Fax)[email protected]

PET ad-4c 1/2pg•9-05 9/12/05 5:05 PM Page 1


magnetic energy stored in insulation regions, the corresponding magnetic-energy-equivalent-winding thickness is 92% of the available winding height (Fig. 5). Interleaving effects can be readily evaluated by considering con-structions that fit within a fraction of the available winding height. For example, a simple interleave of two por-tions can be examined by considering winding confi gurations that fi t within half of the available winding height.

In Fig. 4, when winding height is limited to 50%, two layers provide a maximum equivalent thickness of 20%. However, two portions can be used with an interleave strategy to double

the equivalent wind-ing thickness and in this case achieve 40% of the available wind-ing height. Therefore, an interleaved con-figuration that splits the winding into two portions of two lay-ers each dissipates 30% less power than the optimal single-winding-portion configuration. This analysis can be read-ily extended to other interleave strategies by considering the constraint on avail-able winding height to be 1/n, where n is the number of in-terleaved winding portions. Resultant-loss and energy-equivalent thickness-es will respectively increase and decrease by a factor of n with appropriate inter-leaving.

When an opti-mal winding strat-egy is selected, the resultant-loss and magnetic-energy-equivalent winding thicknesses can be used to determine

the normalized dissipation and en-ergy storage for equivalent single-turn conductors. These results are readily scaled for the specifi c application using the square of the amp-turn product through the cross-section.

The secondary current of the bridge transformer contains a dc bias compo-nent because rectifier elements force unidirectional currents. Figs. 6 and 7display the results for one of the half secondaries again operating at 62.5% duty cycle. The signifi cant dc compo-nent causes thicker conductors to have greater benefit; therefore, two por-tions of a single layer each provide the lowest winding dissipation with a

Winding lossCore loss

Bridge Transformer Dissipation at 80°C720-W output

Duty Cycle

5.0

4.5

4.0

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0.070.0% 62.5% 60.0% 55.0% 50.0%

Winding lossCore loss

Forward Transformer Dissipation at 25°C100-W output

Duty Cycle

1.00

0.75

0.50

0.25

0.0040.0% 35.2% 30.0% 25.0%

Fig. 10. Measured total loss of 150-kHz bridge transformer providing 12 V at 60 A.

Fig. 11. Measured total loss of 100-kHz forward transformer providing 20 V at 5 A.

DESIGN METHODS

For high performance and reliability,For high performance and reliability,

Datatronics is the magnetics solutions

leader in mil-aero electronics. Our high

voltage,Data Bus and LAN components

offer exceptional reliability in harsh

environments for critical avionics,

navigation and control applications.

High Voltage Magnetics

Single, Dual and Low Profile1553 Data Bus Magnetics

Military and Space LevelLAN Magnetics

LAN 10baseT, 10/100base T

MIL-PRF-27, MIL-PRF-21038,MIL-STD-981 Compliance

ISO 9001/ 9002

> Free white paper and catalog

We offer a range of custom& standard devices including:

Hi-RelMil/AeroMagnetics Solutions

Visit us on the web for ourVisit us on the web for ourfree White Paper entitledfree White Paper entitled“Measuring Transformer“Measuring TransformerDistributed Capacitance” &Catalog or call 888-889-5391.Catalog or call 888-889-5391.

datatronicsromoland.com

See us atPower Systems WorldOct 25-27, Baltimore

Booth 828


combined loss-equivalent thickness of 48%. Fig. 7 indicates that the lowest ac magnetic energy is also achieved with two single-layer portions, yield-ing a total magnetic-energy-equiva-lent thickness of 17%. Note that this equivalent thickness is correlated to the RMS current of the total waveshape, including the dc bias component.

The forward-converter application also generates a significant bias component in the current waveshape. For a duty cycle of 35.2%, Fig. 8indicates that two portions of two layers each are the preferred choice to minimize loss with a combined loss-equivalent thickness of 40%. The harmonic distribution of the forward converter causes thick single-layer portions to be less benefi cial. Clearly, optimal transformer design depends on an accurate defi nition of application waveshapes and constituent harmonic components.

Transformer Examples Two transformers were designed

using the methods outlined earlier. Fig. 10 summarizes total transformer dissipation at 80°C as a function of duty cycle for a bridge transformer operating at 150 kHz and providing 12 V at 60 A. Fig. 11 displays the results at 25°C for a forward transformer operating at 100 kHz and providing 20 V at 5 A.

Open-circuit test methods were used to measure core loss at each of the harmonic components of application voltage. Short-circuit test methods were used to measure ac resistance and evaluate ac winding loss at each of the harmonic components of application current. DCR test methods were used to evaluate dc loss of windings conducting bias currents. Figs. 10 and 11 summarize total dissipation using these comprehensive methods. Both transformers achieve efficiencies in excess of 99%. PETech

References1. Quinn, V. “New Technology Reduces Eddy Current Dissipation in Windings,” Properties and Applications of Magnetic Materials Conference Record, 2005.

DESIGN METHODS

Documents

By Victor W. Quinn, Chief Technology Ofﬁ cer, Tabtronics ... · conductor layer, R is the ratio of sinusoidal surface magnetic-ﬁ eld intensities, B is the ratio of conductor thickness