
AN-17
C
6/96
10
CMA
CM
I
RMS
=
This completes all calculations necessary for the primary
winding.  Secondary peak current, RMS current, average output
current, output capacitor ripple current, and secondary minimum
and maximum conductor diameter must also be calculated.
Peak secondary current I
 is a simple function of peak primary
current I
P
, primary turns N
P
, and secondary turns N
S
.
I
I
N
N
SP
P
P
S
=
×
Secondary RMS current I
 is found from maximum duty
cycle D
, secondary peak current I
, and ripple to peak
current  ratio K
RP
 (K
RP
 is identical for primary and secondary).
I
I
D
K
K
SRMS
SP
MAX
RP
3
RP
=
×
×
+
(
)
(
)
1
1
2
Output current I
O
 is simply the ratio of output power P
O
 to output
Voltage V
O
:
I
P
V
O
O
O
=
Output capacitor ripple current I
 is not a true transformer
parameter but is needed for capacitor selection and easy to
calculate from other transformer parameters.  I
 is found
from secondary RMS current I
SRMS
 and output current I
O
.
I
I
I
RIPPLE
SRMS
O
=
2
2
Minimum secondary bare conductor diameter DIA
 (in mm)
based on previously calculated current capacity CMA and
secondary RMS current must be determined.
From the primary CMA and secondary RMS current I
SRMS
, the
minimum secondary bare conductor CM
S
 is calculated.
CM
CMA
I
S
SRMS
=
×
Minimum secondary AWG
 is then calculated from another
empirical equation.  Secondary calculated wire gauge AWG
 is
always rounded down to the next integer value which selects the
next larger standard wire size.
Primary insulated wire diameter OD in mm is found from
effective bobbin width BW
E
 and number of primary turns N
P
:
OD
BW
N
E
P
=
The bias winding is usually wound with the same wire diameter
as the primary to reduce the number of different wire gauges
necessary for production.
Actual magnet wire outside diameter OD is slightly larger than
the diameter DIA of the bare copper conductor.  Insulation
thickness varies inversely with bare copper conductor  American
Wire Gauge (AWG) size which means that smaller diameter
conductors have thinner insulation thickness.  Data from several
different manufacturers were tabulated to generate an empirical
expression for total insulation thickness INS (in mm) as a
function  of  heavy  insulated  magnet  wire  outside  diameter
(in mm).
INS
LOG OD
=
×
+
(0 0594
(
))
.
0 0834
DIA
OD
INS
=
Another empirical equation determines the AWG for magnet
wire with a given bare conductor diameter DIA.  Integer AWG
values are the standard sizes of available wire so the calculated
AWG value should always be rounded up to the next integer or
standard value (the next smaller standard conductor diameter)
before proceeding with the current capacity or CMA calculation.
AWG
LOG DIA
(
=
×
×
9 97
.
1 8277
2
(
)))
Magnet wire for transformer winding usually has the cross
sectional area specified in circular mils. A circular mil is the
cross  sectional area  of  a  wire  with  a  diameter of 1 mil (or
0.0254 mm).  The effective cross sectional area in circular mils
(CM) of a standard AWG size bare conductor wire is found
from the following simple expression.
CM
AWG
3
=
2
50
“Circular mils per Amp” or CMA is a convenient way to specify
winding current capacity.  CMA, which is the inverse of current
density,  is simply the ratio of cross sectional area in circular
mils to the RMS value of primary current.  CMA should be
between 200 and 500 and is calculated from cross sectional
wire area in CM and RMS primary current I
RMS
.