AN1262 APPLICATION NOTE
1.316
Lp IpRMS
Apmin = 103
[cm4]
---------------------------------------
(6)
1
--
∆ T2 K u B max
∆
In this equation T is the hot-spot temperature rise (located in the core center leg, where heat can be re-
∆
moved more difficultly), defined as T = T
- T
. For reliability reasons T
is usually limited at 100°C
max
amb
max
where, by the way, ferrites usually feature minimum losses. K is the window utilization factor, that is the por-
u
tion of the total core window area occupied by the windings, which can be estimated equal to 0.4 for margin
wound construction and to 0.7 for triple insulated wire construction.
The smallest core with an AP greater then AP
will be chosen from the catalog data (the core list of table
min
10 can be used as a reference). If there is a core with an AP < AP
but very close to, it might be worthwhile
min
trying to design with this smaller core before trying the larger one.
Calculate the required minimum number of primary turns of the primary winding.
2)
3)
It will be given by:
Lp 0.7
Bmax Ae
104
------------------------
Npmin
=
Define primary and secondary windings' turns number.
secondary winding turns number Ns will be simply:
In the case of single-output under consideration, the
Np
n
Ns
= ------- + 1
,
that is, the result of the division will be rounded up to the next larger integer. The actual primary turns will then
be calculated, rounding the result to the closest integer.
Np = [Ns · n + 0.5].
It can be convenient to round to the next even number when interleaved winding technique is to be used for
transformer construction, so as to split the primary in two equal halves.
Calculate the air gap length.
4)
The gap length (l ) needed to get the desired inductance Lp will be calculated
g
with the following empirical formula:
1
------
k2
Lp 109
---------- ---------
I g
=
[mm]
(7)
Np2
k1
If the calculated value is not available as a standard part, if possible, the primary turns number can be adjust-
ed a little bit to get an off-the-shelf part.
The air gap should be located on the core center leg only, to minimize radiated fields. In prototyping, center
leg grinding to get nonstandard gap values can be avoided by keeping the two half-cores apart by about half
the calculated value with spacers.
5) Calculate transformer total losses. The allowed total transformer losses (P ) can be calculated by dividing
tot
∆
the hot-spot temperature rise T by the thermal resistance of the wound core R
:
th(core)
∆T
Ptot = ---------------------- [W ]
Rth(core)
If the manufacturer does not provide thermal data, R
can be estimated. It has been shown [1] that there
th(core)
is a good correlation between core's area product and thermal resistance, regardless of its shape:
-0.37
≈
R
23 · AP
[°C/W];
th(core)
12/42
STMICROELECTRONICS [ ST ]
