11

Magnetics Modeling In Spice

Proximity Loss

Dr. Ray Ridley

www.ridleyengineering.com

PSMA Magnetics Session

2

The Biggest Problem with Magnetics Design

The single biggest issue with magnetics design is that 99.9% of engineers don’t

understand or apply proximity loss properly.

Example: Forward converter transformer

Winding loss if you don’t do proximity analysis:

1.04 W

Winding loss with full harmonic analysis

10.77 W

33

Proximity Effects Current Distribution

1

2

3

4

5

Relative Current Density (A)

Current into page

Current out of page

Core

44

1-Dimensional Field Solution from Dowell’s Equation

1

sinh 2 sin 2( )

cosh 2 cos 2iG

2

sinh cos cosh sin( )

cosh 2 cos 2iG

2 2

1

1

2

1(1 () 4 )( )

n

d w i i i i

i i

ii

i

G GP b l Hh

i

i

i ii

w

l

h

n IH

b

Mean turn length of layer

Porosity of layer (fill factor)

Height of layer

H field at boundary of layer

i

ii

h

Ratio of fields on either side of layer

Skin depth of layer including porosity

Normalized height of layer relative to skin depth

55

Proximity Loss Example

300 -

425 V

12 V 30 A100 kHz

Primary 51 turns 20 awg 3 layers

Secondary 5 turns 10 mil foil

66

Primary Proximity Loss

DC 0.097 Ohm100 kHz 2.42 Ohm

77

Primary Proximity Loss

Magnetics Test Setup

Clear Transformer Design

0

0.5

1

1.5

2

2.5

3

3.5

4

0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 0.020

Time (ms)

Switch Current (A)

88

Primary Proximity Loss

Magnetics Test Setup

Clear Transformer Design

0.010

0.100

1.000

10.000

100.000

10 100 1000 10000 100000 1000000 10000000 100000000

Resistance (Ohm)

Frequency (Hz)

Transformer Primary AC Resistance vs Frequency

DC Resistance = 0.09657

Ripple Frequency Resistance = 2.4239

Ohm

Ohm

99

Primary Proximity Loss

Magnetics Test Setup

Clear Transformer Design

0.010

0.100

1.000

10.000

100.000

10 100 1000 10000 100000 1000000 10000000 100000000

Resistance (Ohm)

Frequency (Hz)

Transformer Primary AC Resistance vs Frequency

DC Resistance = 0.09657

Ripple Frequency Resistance = 2.4239

Ohm

Ohm Transformer Primary Winding Proximity Model Transformer Secondary Winding Proximity Model

Proximity model active? 1 1=yes

Rac1 1.32 mΩ

Rac2 234.43 mΩ

Rac3 2938.35 mΩ

Rac4 6590.55 mΩ

Rac5 21402.18 mΩ

Lac1 41.39685 uH

Lac2 41.0829 uH

Lac3 29.89081 uH

Lac4 8.84732 uH

Lac5 2.55406 uH

1010

Primary Proximity Loss

Magnetics Test Setup

Clear Transformer Design

1111

Magnetics Test Setup

Clear Transformer Design

Primary Proximity Loss

1212

Secondary Proximity Loss 10 mil Foil

DC 0.00145 Ohm100 kHz 0.0102 Ohm

1313

Secondary Waveforms and Proximity Loss

0

5

10

15

20

25

30

35

40

0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 0.020

Time (ms)

Forward Diode Current (A)

1414

Secondary Proximity Loss

Secondary Winding

Primary Winding

0.0014569

0.0102

0.001

0.010

0.100

1.000

10 100 1000 10000 100000 1000000 10000000 100000000

Resistance (Ohm) Transformer Secondary AC Resistance vs Frequency

Frequency (Hz)DC Resistance =

Ripple Frequency Resistance =

Ohm

Ohm

1515

Secondary Proximity Loss Reduced Foil Thickness

10 mil Reduced to 5 mil Foil

10 mil Foil

2.93 W

1616

Secondary Proximity Loss Simulation

17

Winding Structure to Spice Model in 1 Step

Transformer Primary Winding Proximity Model Transformer Secondary Winding Proximity Model

Proximity model active? 1 1=yes

Rac1 1.32 mΩ

Rac2 234.43 mΩ

Rac3 2938.35 mΩ

Rac4 6590.55 mΩ

Rac5 21402.18 mΩ

Lac1 41.39685 uH

Lac2 41.0829 uH

Lac3 29.89081 uH

Lac4 8.84732 uH

Lac5 2.55406 uH

Transformer Secondary Winding Proximity Model

Proximity model active? 1 1=yes

Rac1 0.00 mΩ

Rac2 0.02 mΩ

Rac3 1.80 mΩ

Rac4 108.50 mΩ

Rac5 319.92 mΩ

Lac1 0.15451 uH

Lac2 0.15451 uH

Lac3 0.15451 uH

Lac4 0.14178 uH

Lac5 0.03818 uH