Designing Planar Magnetic.pdf

Topic 4

Designing Planar Magnetics

Designing Planar Magnetics

Lloyd Dixon, Texas Instruments

A BSTRACT

Planar magnetic devices offer several advantages over their conventional counterparts. This paper dis-

cusses the magnetic fields within the planar structure and their effects on the distribution of high fre-

quency currents in the windings. Strategies for optimizing planar design are presented, and illustrated

with design examples. Circuit topologies best suited for high frequency applications are discussed.

I. A DVANTAGES OF P LANAR M AGNETICS

In contrast to the helical windings of conven-

tional magnetic devices, the windings of planar

transformers and inductors are located on flat sur-

faces extending outward from the core centerleg.

Magnetic cores used with planar devices have

a different shape than conventional cores used

with helical windings. Compared to a conven-

tional magnetic core of equal core volume, de-

vices built with optimized planar magnetic cores

usually exhibit:

• Significantly reduced height (low profile)

• Greater surface area, resulting in improved

heat dissipation capability.

• Greater magnetic cross-section area, enabling

fewer turns

• Smaller winding area

• Winding structure facilitates interleaving

• Lower leakage inductance resulting from

fewer turns and interleaved windings

• Less AC winding resistance

• Excellent reproducibility, enabled by winding

structure

Fig. 1. Planar transformer.

Magnetic / electric relationships are much simpler

and easier to understand when using the SI system

of units (rationalized MKS). When core and winding

materials are specified in CGS or English units, it is

nevertheless best to think in SI units throughout the

design process, and then if necessary convert to

other unit systems as the final step in the process.

In transformer applications, the winding con-

figurations commonly employed in planar de-

vices are advantageous in reducing AC wind-

ing losses. However, in inductors and flyback

transformers using gapped centerlegs, the

winding configuration often results in greater

AC winding loss.

II. M AGNETIC F IELD P ROPERTIES

A magnetic field is actually stored energy.

The physical distribution of the magnetic field

represents the distribution of this energy. Un-

derstanding the properties of the magnetic field

not only reveals the amount of stored energy

and its locations, it also reveals how and where

this energy is coupled to various electrical cir-

cuit elements.

Tutorials on magnetics design have been pre-

sented at previous Unitrode/TI seminars. Most of

this material has been consolidated into a “Magnet-

ics Design Handbook, MAG100A”. This handbook,

as well as all past seminar topics, is available for

downloading from the web site http://power.ti.com.

Click on [Design Resources] Æ

[Power Management Training].

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Inductance is simply an electrical circuit con-

cept which enables the circuit designer to predict

and quantify the effects of magnetically stored

energy in the electrical circuit.

Applying the basic principles of magnetic

field behavior (discussed in earlier seminars) to

planar magnetic structures enables us to optimize

the design and predict the magnitude of parasitic

circuit elements such as leakage inductance. The

magnetic field also is the dominant influence on

the distribution of high frequency AC current in

the windings, thereby determining AC winding

losses.

Fig. 2. Cross-section of equipotentials and flux

lines within a planar transformer (one-half of

transformer shown).

DC and AC current distributions within the

windings usually differ significantly. At high fre-

quencies, the magnetic field arranges itself so as

to minimize the rate of energy transfer between

the electrical circuit and the field. The field

“pulls” the opposing currents to the conductor

surfaces closest to each other, as shown in Fig. 2.,

thereby minimizing the volume of the field

(skin/proximity effect). Also, the currents spread

across the opposing conductor surfaces so as to

minimize energy density.

However, at low frequencies, the rate of en-

ergy transfer between the circuit and the mag-

netic field is very small. The rate of energy trans-

fer into the conductor resistance is greater. There-

fore, DC and low frequency currents distribute

uniformly throughout the conductors so as to

minimize I 2 R loss.

A. Review of Magnetic Field Fundamentals

Rules governing magnetic field behavior are

summarized in Appendix I.

Every magnetic field has two components:

Magnetic force, F, (magnetic potential), and

magnetic flux, Ф . Magnetic force is directly pro-

portional to current (Ampere’s Law). In fact, in

the SI system of units, magnetic force, F , directly

equals current – units of magnetic force are ex-

pressed in Amperes. Thus, 1 Ampere of current

flowing in a conductor inevitably results in 1

Ampere of magnetic force.

Magnetic force can be described as a series of

equipotential surfaces. The spacing of these sur-

faces defines a force gradient – a magnetic poten-

tial gradient. The magnitude of this gradient at

any location is called field intensity, H.

Fig. 2. shows the leakage inductance in the

left half of a planar transformer structure. (In or-

der to provide clarity of illustration, only three

primary turns are used, and spacing between pri-

mary and secondary is greatly exaggerated.) The

light dash lines show the edge view of the mag-

netic force equipotentials between primary and

secondary windings. The light solid lines repre-

sent flux. The equipotential surfaces can be

thought of as elastic membranes which terminate

on current flow and are “anchored” on the oppos-

ing currents which produce the field.

III. T HE “T RUE ” T RANSFORMER

Transformers in switching power supplies are

used primarily in buck-derived topologies (for-

ward converter, full bridge, half bridge, etc.) In a

transformer, energy storage is usually undesir-

able, but unavoidable – appearing in the trans-

former equivalent circuit as parasitic leakage in-

ductance and magnetizing inductance. (Flyback

transformers are misnamed – they are actually

coupled inductors. Energy storage is essential to

their function.)

In a “true” transformer (Fig. 2.), opposing

currents flow simultaneously in primary and sec-

ondary windings. The Ampere-turns in the sec-

ondary winding, resulting from load current, are

canceled by equal and opposite Ampere-turns

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flowing in the primary. A small additional unop-

posed magnetizing current also flows in the

windings. This magnetizing current provides the

small magnetic force necessary to push flux

through the very low reluctance of the high per-

meability magnetic core. The closed loops of this

magnetizing flux link the primary and secondary

windings to each other, thus providing the cou-

pling which is essential for transformer operation

(shown in Fig. 3.). Magnetizing flux and its asso-

ciated magnetizing current change as a function

of Volt-seconds per turn applied to the windings

(Faraday's Law) independently of load current .

Magnetizing inductance appears in the trans-

former equivalent electrical circuit as a shunt

element.

Much of the energy stored in the magnetizing

inductance goes into hysteresis loss, the rest is

usually dissipated in snubbers or clamps. If the

core were ideal – with infinite permeability – the

magnetizing inductance value would be infinite,

and thus have no effect on circuit performance.

ries leakage inductances, (L LP , L LS ) . Each time

the power switch turns off, energy stored in the

leakage inductance usually ends up dissipated in

snubbers or clamps, thus degrading power supply

efficiency.

Fig. 4. shows the electrical equivalent circuit

of the transformer, including the magnetizing in-

ductance and parasitic leakage inductance appor-

tioned to primary and secondary windings. The

“ideal transformer” is used to account for the ac-

tual turns ratio and primary-secondary isolation.

Leakage inductances are usually so small com-

pared to the magnetizing inductance value that

they can be combined, with negligible error, into

a single leakage inductance value in an equiva-

lent “L” network. Magnetizing inductance can be

assigned to either the primary or secondary side.

L LP

L LS

Primary

L M

Ideal

XFMR

Secondary

Fig. 3. Magnetizing flux links the windings.

Excluding magnetizing current, load-related

Ampere-turns in primary and secondary windings

cancel completely. Load current has no effect on

the magnetizing flux in the core. Magnetic force

related to load current exists in only one place

within the transformer – in the region between

primary and secondary windings where the cur-

rents do not cancel. As shown in Fig. 2., the flux

lines associated with this field between the wind-

ings link half the energy of the field to primary

and half to the secondary winding. But these flux

lines do not link the windings to each other.

Thus, the coupling between windings is impaired.

The energy stored in this inter-winding region

appears in the equivalent electrical circuit as se-

Fig. 4. Transformer equivalent electrical circuit.

The leakage inductance value can be calcu-

lated from the physical dimensions of the wind-

ings [1] . Leakage inductance is minimized by:

• minimizing the number of turns

• using a core with a large winding “breadth”

• interleaving windings

• minimizing the spacing between primary and

secondary windings

Bifilar windings approach the ideal, but this

is usually not possible in a planar transformer,

especially when high voltage isolation is re-

quired.

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