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6/96
AN-19
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operating from 100/115/230 VAC mains, for reasons of cost,
size, efficiency, and EMI.  For this reason, 
TOPSwitch
 has a
fixed operating frequency of 100 kHz.
Transformer Construction
In a flyback converter, the transformer is the main energy
storage and processing element.  Therefore, it has a large effect
on the efficiency of the power supply as a whole.  An efficient
flyback transformer will have low DC losses, low AC losses,
low leakage inductance, and low winding capacitance.
DC Losses
The only significant DC losses in a power transformer will be
due to the copper losses in the transformer windings.  For a high-
efficiency design, the transformer wire gauge should be
sufficiently large to reduce the copper losses to an acceptable
level.  A traditional design guideline is to size each winding for
a current capacity of 200 to 500 circular mils per RMS ampere
of current.  The power windings in the transformer of the
ST204A example circuit were designed for a current density of
approximately 300 circular mils per RMS ampere.
function  of  frequency  is  shown  in Figure 12.  As an example,
for 100 KHz, 26 AWG is the largest wire size that allows full
utilization of the cross-section of the wire.  High current
windings at 100 KHz should be constructed using several
strands of  26 AWG or smaller wire rather than one large
diameter conductor in order to allow full utilization of the
conductor.  Foil conductors with a thickness less than or equal
to twice the skin depth can also be used for high current
windings to reduce skin effect losses.
Core losses can also add significantly to the power loss of a
transformer.  These losses are due to the AC component of the
flux in the transformer.  The AC flux density in a flyback
transformer can be estimated using either of two formulas:
B
N
2
I
K
l
V
D
×
N
A
f
AC
P
P
RP
g
MIN
×
MAX
P
e
S
=
×
×
×
×
=
×
×
×
0 4
.
 π
10
2
8
B
 is half of the peak to peak flux density in Gauss, N
 is the
number of primary turns, I
is the primary peak current, K
 is
the ripple current to peak current ratio (refer to Appendix A), l
g
is the transformer core gap in centimeters, V
 is the minimum
DC input voltage to the transformer, D
 is the duty cycle at
minimum input voltage, A
 is the core cross-sectional area in
square centimeters, and f
 is the operating frequency in Hertz.
The first equation calculates the flux excursion using ampere-
turns, and the second expression determines the flux excursion
using the volt-second product.  Both equations should yield the
same result for the same operating conditions.  The choice of
using one expression versus the other is determined by the basic
information about the transformer that is readily available.  For
a transformer designed to operate in the continuous mode,
typical values of B
 will be around 400-750 Gauss.  For high-
efficiency operation, a material should be selected that will
keep core losses under  50 mW/cm
3
 at 100 KHz.  Refer to the
core loss curves published by ferrite manufacturers in order to
select a suitable core material.  A few examples of appropriate
ferrite materials for 100 KHz designs are Philips 3C85 and 3F3,
Magnetics, Inc. P and R, TDK PC40, Siemens N67 , Tokin
2500B and 2500B2, and B2 material from Thomson.
Leakage Inductance
A very important consideration in designing a low-loss
transformer is minimizing the amount of leakage inductance.  A
transformer with high leakage inductance will dissipate large
amounts of energy in the primary clamp components.  The
energy dissipated in the clamp is wasted and detracts from the
overall efficiency.
For a transformer meeting international insulation and safety
requirements, a practical value for leakage inductance is about
1-3% of the open circuit primary inductance.  Values much
(4)
AC Losses
AC losses in the transformer arise from skin effect losses in the
transformer windings, and AC core losses.  High frequency
currents tend to flow close to the surface of a conductor rather
than its interior.  This phenomenon is called the skin effect.  The
penetration of AC current into a conductor varies as the square
root of the frequency, so for a higher frequency, currents will
flow closer to the surface of the conductor and leave the interior
underutilized.  The result is a higher effective resistance for AC
current versus DC current.  To minimize the AC copper losses
in a transformer, no conductor should be used that has a
thickness greater than 2 times the skin depth at the operating
frequency of the supply.  A graph of usable  wire  gauge  as  a
40
20
15
104
105
Frequency (Hz)
106
107
A
SKIN DEPTH/AWG vs. FREQUENCY
25
30
P
35
Partial
Utilization
Full
Utilization
Figure 12. Skin Depth vs. Frequency.