AN4105 APPLICATION NOTE
20
©2002 Fairchild Semiconductor Corporation
6.2 Determining The Number of Turns
Although the equation for the minimum number of flyback
transformer turns can be determined using applied voltage
and maximum turn on time, the equations used here are
derived from the relationship between L and I
P
.
For an AP determined from equation (a), above, calculate
N
MIN
using the following eq uations:
For an AP determined from equation (b), above, calculate
N
MIN
using the following eq uations:
6.3 The Windings
The cross sectional area of the winding must be obtained
from the calculated effective current and the current density
(from the appropriate equation above), factoring in the
number of turns (as determined from a calculation of
NMIN). If eddy current loss is not a serious problem simply
divide the effective current by the current density, thereby
determining the coil cross sectional area.
Be aware, however, that as the coil becomes thicker, the
problem of eddy current loss will arise. Using twisted thin
coil strands (Litz wire), instead of a single heavy wire, can
reduce the eddy current loss, but K
U
will become smaller.
6.4 Determining The Gap
It is not easy to precisely calculate the required gap
.
However, the gap can be calculated from the following
equation. It is based on the fringing effect of the surrounding
flux. Note that the calculated value of L is usually larger than
required.
Therefore, the gap must be changed to obtain the required
value of L
.
References
1. Transformer and Inductor Design Handbook. 2nd ed.
Col. Wm. T. McLyman. Marcel Dekker, Inc., 1988.
2. Switch Mode Power Supply Handbook. Keith H.
Billings. McGraw-Hill, Inc., 1989.
KA1H0280RB, KA1M 02 80 RB, KA1H0380RB, KA1M0380RB,
KA1L0380RB, KA1L03 80B, KA1H0680B, KA1M0680B,
KA1H0680RF B , KA1M 068 0RB, KA1M0880B, KA1L0880B,
KA1M0880BF, KA1M0880D, KA2S0680B, KA2S0880B,
KA3S0680RB, KA3S0680RFB, KA3S0880RB, KA3S0880RFB,
KA1H0165RN, KA1H0165R, KA1H0265R, KA1M02 65 R ,
KA1H0365R, KA1M 0365R, KA1L0365R, KA1H0565R,
KA1M0565R, KA1M0765RC, KA1M 07 65 R , KA1M0965R,
KA2S0765, KA2S0965, KA2S09655, KA2S1265, KA3S0765R,
KA3S0765RF, KA3S0965R, KA3S09 65RF, KA3S1265R,
KA3S1265RF, KA5H0280R, KA5M0280R, KA5H0380R,
KA5M0380R, KA5L0380R, KA5P0680C, KA5H0165R,
KA5M0165R, KA5L0165R, KA5H0 165RV, KA5M0165RV,
KA5L0165RV, KA5M0165RI, KA5L0 165RI, KA5H0165RN,
KA5M0165RN, KA5L0165RN, KA5H0165RVN,
KA5M0165RVN, KA5L0165RVN, KA5H02659RN,
KA5M02659RN, KA5H026 5RC, KA5M0265R, KA5L0265R,
KA5M0365RN, KA5L0365RN, KA5H0365R, KA5M0365R,
KA5L0365R, KA5M0765RQC, KA5M0965Q, KA5S0765C,
KA5S09654QT, KA5S0965, KA5S12656, KA5 S1 265,
KA5Q0740RT, KA5Q0945RT, KA5Q0765RT, KA5Q126 56RT,
KA5Q126 5R F, KA5Q1565R F, FSDH0165, FSDH565,
FS6M07652RTC, FS6M12653RTC, FS6S0765RCB,
FS6S0965RT, FS6S0965RC, FS6S1265RB, FS6S1565RB,
FS7M 08 80 , FS8 S0 765RC
Table 1. K
U
, K
P
, and K
K
U
K
P
K = K
U
K
P
CCM Buck, Boost Inductor 0.7 1.0 0.7
DCM Buck, Boost Inductor 0.7 1.0 0.7
CCM Flyback Transformer 0.4 0.5 0.2
DCM Flyback Transformer 0.4 0.5 0.2
N
MIN
LI
P
B
MAX
A
C
-----------------------10
4
=
L = Inductance of Transformer
Ip = Operating peak current
Bmax = Maximum operating flux density
Ae = Effective cross-sectional area of core
N
MIN
L∆I
m
∆B
m
A
C
--------------------10
4
=
L = Inductance of Transformer
Ip = Operating peak current
Bmax = Maximum operating flux density
Ae = Effective c ross-sectional area of core
I
g
u
O
u
r
N
2
A
C
L
---------------------------- 10
2
–
cm
[]
=
Uo = Permeability of free space
Ur = Relative permeability