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AN4105

Design Considerations for Switched Mode Power Supplies Using A Fairchild Power Switch (FPS) in a Flyback Converter

Fairchild Semiconductor 

AN4105

APPLICATION NOTE

IP

IS

Ideal Transform er

VP

VS

IP

I*

P

IS

NP : N S

VP : VS =N P : N S

IP : IS = N S : N P

Figure 20. Ideal transformer.

The input to output voltage ratio of an ideal transformer is

directly proportional to the turns ratio. This is the ratio of the

number of turns on the primary winding to the number of

turns on the secondary. The polarity is represented schemati-

cally by the placement of a dot on each winding. Since n =

Vp/Vs, and an ideal transformer has no loss, the current ratio

is inversely proportional to the turns ratio. The current direc-

tion is such that it enters on one side and leaves at another.

Thus the sum of all the nI that flow into the dot is zero. The

dot, indicating the winding polarity, is placed to make the

flux direction in the transformer core uniform when current

flows into the dot. Furthermore, in the case of an ideal trans-

former, if the path on the secondary side windings is opened,

there is no secondary current flow, and the current on the pri-

mary side also goes to zero.

5.3 The Real Transformer

Significant differences exist between an ideal transformer

and a real one. In a real transformer:

1. The coupling coefficient between each coil is finite, and

when a gap is placed in the core as is done in many power

transformers, the coupling coefficient becomes still smaller

(i.e., there is leakage flux);

2. There are losses, such as iron (hysteresis) loss, eddy current

loss, coil resistance loss, etc.; and,

3. The inductance of each coil is finite. When a gap is

placed in the core the inductance becomes still smaller.

In a real transformer, should the secondary side be opened

current would continue to flow in the primary (as in 3,

above). So, while energy cannot be stored in the ideal

transformer, it is stored in a real transformer. The so-called

magnetizing inductance accounts for this energy storage

phenomenon. The circuit of Figure 21 is a simplistic view of

an actual transformer and shows the magnetizing inductance.

Figure 22 presents a more complete equivalent circuit of a

real transformer, showing inductances and loss resistances

VP

Lm

VS

NP : N S

VP : VS =N P : N S

I*

P

:

IS

=NS

:

NP

Figure 21. A model of an actual transformer showing the

magnetizing inductance Lm, which accounts for energy

storage.

Rp Llp

Ideal Transformer Lls

Rs

Rm Lm

- Rp:Primary side winding resistance

- Rs:Secondary side winding resistance

- Llp:Primary side leakage inductance

- Lls:Secondary side leakage inductance

- Lm:Magnetizing inductance

- Rm:Transform er core loss resistance

Figure 22. A more complete equivalent circuit of an

actual transformer, showing inductances and loss

resistances.

18

©2002 Fairchild Semiconductor Corporation

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