Designing
100kHz, flyback transformers
for input voltage125700Vdc and power up to 500W
In the beginning…
Thirty years ago, designers calculated
transformers on their pocket calculators. The designer had to
pencil in all the input and output fields onto a form and then
feed them into the calculator. Today, he can forget the pencil,
but he still has to enter the figures into spreadsheet programs
such as Excel and Lotus 123
After the first economical 8bit computer became available in
1978, professionals could begin to develop programs to design
transformers and inductors. This development went in two
directions:
First, companies developed their own computer programs to
meet their own specific requirements. These usually used
already available algorithms and experience. After reaching
acceptable levels to meet the company’s needs both in
technical capability and ease of use, further development
ceased.
Secondly, small companies began to develop professional
computer programs which are sold or leased to the
manufacturers of transformers and inductors.
With continuous input from the various manufacturers, they
were able to develop universal, powerful, easytouse tools
for use throughout the industry.
Designing with the Rale Design System
The Rale Design system automatically calculates designs for
transformers and inductors. Consequently, its data base
incorporates all the necessary materials including cores,
bobbins, wires, steels, etc. in both metric and USA units. This
data base is totally user expandable. To use the programs, the
designer needs only a basic knowledge of transformers or
inductors and their operation mode. The designer does not need to
use any complicated formulas, he only needs to follow two simple
phases:
The user only fills in the input mask with the global
parameters (voltage, current, temperature rise, regulation,
etc.) and runs the program.
After the design is finished by the program the user can
switch to the Test Mode and change by hand the parameters of
the designed transformer (turns, wire sizes, steel, ...) and
run the program in order to redesign it. In this phase the
user can also test his design, changing the input voltage,
frequency, load, duty cycle,...
The Operating Modes of a Flyback
Transformer
The following flyback transformer diagram illustrates only the
parameters relating to its design.
With a flyback transformer, the distinction is drawn between
two modes of operation:
Mode with continuous secondary current ( Fig. 1,
t3=0).
Mode with intermittent DC secondary current (Fig. 2,
t3>0).
Continuous mode (Fig.1)
In this mode, secondary current ripple is less than 100%:
Ripple = 100* (IsmaxIsmin)/(Ismax+Ismin)
=(BmaxBmin)/(Bmax+Bmin) < 100
In the flyback transformer’s continuous mode, the output
voltage is "impressed" for practical purposes, and is
not greatly dependent upon load. Because the variation of the
duty cycle is not directly proportional to the variation of the
input voltage, this mode is preferred for a wide range of the
input voltages (min. 3:1). Secondly, the flyback transformer is
larger with less ripple in the primary current. For that reason,
the choice of ripple (10% to 100%) of the secondary current has
to be harmonized between the transformer manufacturer and the
electronics engineer.
Intermittent mode (Fig.2)
If the range of the input is not too wide (max. 3:1) then this is
the most common operation mode because the flyback transformer is
smaller than in the continuous operation mode:
t1=t2 at minimal input voltage
Ripple => 100%.
Input only relevant to the design of a
flyback
Criterion for design
Normally, highfrequency transformers have very low regulation
and are designed according to the prescribed temperature rise.
Since these transformers are manufactured almost exclusively
using ferrite, the optimum operating temperature is around
100°C.
Bobbin
In order to protect the transistors, highfrequency transformers
should be manufactured for low leaking reactance , with
singlesection bobbin units. For this reason, they often require
bifilar or interleaved windings.
Ferrite, Induction and Temperature rise
Since the optimum operating temperature of ferrite for
highfrequency transformers is around 100°C and their ambient
temperature is 40°C , our design assumption must be for a
temperature rise of 60°K. The program calculates both the active
and the reactive core losses by hypothesizing the ferrite type,
the frequency, the form of input voltage, induction and core
temperature. The induction should be selected so that the
transformer does not saturate at minimum input voltage, maximum
duty cycle and maximum core temperature. If the core losses in
relation to temperature rise are not economically acceptable,
then the computer program will optimize or reduce the
ACcomponent (the ripple of the input current) of the induction
automatically. But this indicates that the selected ferrite
quality is not optimal.
Copper additional losses
With a highfrequency transformer, the distinctions are drawn
between the following additional losses in a winding, over and
above the dccurrent losses:
1. Eddy current losses
2. Skin effect losses
3. Proximity effect losses
4. Losses due to circulating currents through the
parallelconnected wires.
Proximity losses are smaller in the case of a winding that
takes up only 3060% of the available winding space. For that
reason, one should always set the input for the Space between
0.3 and 0.6 for purposes of automatic core selection by the
program.
The input for Rac/Rdc will limit the extent of additional
losses. The computer program selects a high enough number of
parallelconnected wires for the eddy current losses and skin
effect losses to fall short of the prescribed value for Rac/Rdc.
For that reason, the input for Rac/Rdc is also used for
monitoring parallelconnected wires. The value is normally set
between 1.25 and 3.
Losses of circulating currents through the parallelconnected
wires are not calculated. It is assumed that these additional
losses have been eliminated by suitable design precautions. In
particular, it should be ensured, for a given litz, that the
twisting for the winding maintains the same position at the input
and at the output of the winding for any given winding.
Duty cycle at minimal input voltage
The duty cycle q is defined as follows:
A flyback transformer with an automatic controller of output
voltage and current ripple less than 100% is normally designed
with the following parameters:
"Nominal" input voltage Upnom= (Upmin*Upmax)1/2 = (125*700) 1/2=
296V. At this input voltage the duty cycle q_{nom}
will be 0.5.
This flyback transformer has to be designed at the
input voltage Upmin = 125V. At this input voltage the
duty cycle will be:
q_{max} = Unom/(Umin + Unom) = 296/(125+296) =
0.7.
Th duty cycle at the input voltage Upmax = 700V will
be:
q_{min} = Upnom/(Upmax+Upnom) = 296/(700+296) =
0.3
Ripple of the input current at the minimal input voltage =
17%
In order to have the ripple smaller than 100% at the maximal
input voltage, you have to prescribe the ripple at the minimal
input voltage as follows:
Ripple_{min }= Ripple_{max }*(Upmin*q_{max}/Upmax/q_{min})^2
= 100*(0.7*125/750/0.3)^2 < 17%
Procedure to design a 200W flyback
transformer
Normally the user loads the standard input file for the
flyback transformer and fills in the input mask in accordance
with the discussion above. Note that all other parameters (such
as chassis, insulation, case, impregnation,…) are generally
relevant to the transformer design and will not be discussed:
Input voltage : U(V) = 125V
Duty cycle : Formfactor = 0.7
Ripple of the primary current (induction) : dI/Io = 17%
Output DCvoltage : Voltage = 2 x 24V
Output DCcurrent ; Current = 2 x 4A
Ambient temperature : Amb. Temp. = 40°C
Temperature rise : Temp. rise = 60°K
Induction = 0.275T
Singlesection bobbin with the primary between 2
secondary : Bobbin = 11
Max. Build 50%: Space = 0.5
Factor for additional Culosses : Rac/Rdc = 3
If the core size is not prescribed by the user the
input field Selection is set at 0. This
means that the program should search for a suitable core
for this application from your selected core family. In
the system for automatic selection of the core from your
prescribed core family, the program will offer you an
adequately sized core for your application.
On completion of the design work, the following
design data will be available, which can be saved and/or
printed on 3 pages:
Checking the design
However, there are two parameters, which relate
exclusively to the flyback transformer: primary winding
inductance (1.12 mH) and the gap (2x0.014") for
calibration of the primary winding inductance at the
nominal frequency.
The winding filling factor :44%<100%
The maximum temperature of the windings is 40°C+57°K
= 97°C < 115°C.
The number of parallelconnected wires (litz) for the
secondary only is
30 x WG 29. A copper foil can replace this litz. The foil
thickness should correspond to the wire diameter of the litz
(11.3 mill or less). The foil width should be matched to the
width of the bobbin. The number of foils connected in parallel is
determined in accordance with the following illustration.
Using the Test Mode
If the design data is not satisfactory, then you can access
the test mode, modify the designed transformer manually (turns,
wire size, steel, input voltage, load, duty cycle,…) and
redesign the transformer by that means. The following output mask
in the test mode shows the results by checking the output voltage
for the maximal input voltage of 700V and the duty cycle of 0.3:
Uin = 700/125 = 5.6.
The following table shows the summary of the most important
parameters, calculated by the program in the test mode. Note that
the duty cycle (q) was changed in order to get the nominal input
voltage that a voltage controller would give.
Ui
V

Iprms
A

2xIsrms
A

2xUodc
V

2xIodc
A

Pcu
W

Pfe
W

Q

Ripple
%

DTcu
°K

125

1.87

7.22

23.6

3.93

4.62

0.55

0.7

17.7

57.4

296

1.01

5.98

24.1

4.03

2.50

1.7

0.5

47.4

46.5

700

0.62

5.58

24.5

4.11

1.28

3.53

0.3

93

49.4

In order to get the constant total losses in the whole range of
the input voltage, select the ferrite and the operation frequency
at the nominal input voltage so that you get approximately Pfe =
Pcu
Technical specification common for
all designs
All flyback transformers in the following table were
calculated under the same conditions:
Input voltage : 125Vdc  700Vdc
Output voltages : 2 x 24Vdc
Frequency : 100kHz
Duty cycle : 0.7 at the input voltage 125V
Ripple of the induction : 17% at the input voltage 125Vdc
Peak induction : 0.250.28T
Build of the windings : approx. 50%
Ambient temperature : 40°C
Temperature rise : 60°K
Core family and ferrite : ETD, N27 or better
Order of the windings : Primary between both secondary
The parameters of the designs are core size, output power and
eddy current losses (Rac/Rdc)

/


Primary

Secondary

Core

Rac/Rdc

Power
W

Inductance
mH

Turns

Parallel x Wire Gauge

Turns

Parallel x Wire Gauge

ETD 19

1.3

23

8.8

242

1x37

2x5

1x29

ETD24

2

38

5.54

185

1x33

2x16

1x25


1.20

48

4.47


1x33


10x34

ETD29

2.9

60

3.34

142

1x30

2x12

1x22


1.9

75

2.8


1x29


9x30


1.20

85

2.43


2x32


40x36

ETD34

1.65

95

2.26

117

1x28

2x10

30x32


1.25

110

1.91


3x33


65x36

ETD39

2,75

125

1.73

94

1x25

2x8

22x29


1.90

145

1.46


2x29


50x32


1.25

177

1.19


6x33


140x33

ETD44

1.80

230

0.89

71

5x29

2x6

90x33


1.25

280

0.75


15x34


300x38

ETD49

2.00

330

0.65

59

10x30

2x5

200x34


1.20

423

0.50


40x36


750x40

About Designing of Flyback Transformers
About Rale Input
In order to design a flyback transformer with the Rale Design Software you
need the following inputs:
 Min. input voltage and the duty cycle at this voltage
 Dcoutput voltages and dcoutput currents
 The ripple of the input current (induction)
 Frequency
In the following Figure are 2 typical operation modes:
 Continuous mod Bmin>0
 Discontinuous mode Bmin=0
User Input
Some of customers use other inputs for designing of a flyback. Here are some
typical cases
Inductance of the primary winding
You know:
 Min. input voltage and the duty cycle at this voltage
 DCoutput voltages and dcoutput currents (output power)
 Inductance of the primary winding
 Frequency
Then you need to calculate the ripple of the primary
Pout = L x (Imax^2Imin^2) x f / 2 = L x (Imax+Imin) x (ImaxImin) x f /2
Where:
 Pout Output power in W
 L Inductance in H
 F Frequency in Hz
 Imax Max. primary current (peak)
 Imin Min. primary current
Using:
Ripple%= 100 x (ImaxImin)/(Imax+Imin)
Iav = (Imax+Imin)/2
Pout = Uin x Iav x q
We can calculate:
Pout = 2 x L x Iav^2 x (Ripple%/100) x f
or
Ripple% = 100 x Uin^2 x q^2 / L / Pout / f / 2 (<=100)
Formfactor = 1 / 2 / q
Where:
 Uin Min. input voltage
 q Duty cycle of the primary
 Ripple% Ripple of the primary current dIo/I = 100 x (ImaxImin)/(Imax+Imin)
Ration of the primary and secondary turns in continuous operation mode
You know:
 Min. input voltage
 DCoutput voltages and dcoutput currents (output power)
 Inductance of the primary winding
 Frequency
 Ratio of the primary and secondary turns (T1/T2)
 Continuous operation mode (s=p, Bmin>0, see Figure)
Now you need to calculate the duty cycle (Formfactor) and the input dIo/I:
(Uin x q) / (Uout x s) = (T1/T2)
s= p = 1  q
q = A/(1+A)
and
Formfactor = 1 / 2 / q
Ripple% = 100 x Uin^2 x q^2 / L / Pout / f / 2 (<=100)
Where:
A = (Uout/Uin) x (T1/T2)
Ration of the primary and secondary turns in discontinuous operation mode
You know:
 Min. input voltage
 DCoutput voltages and dcoutput currents (output power)
 Inductance of the primary winding
 Frequency
 Ratio of the primary and secondary turns (T1/T2)
 Discontinuous operation mode (s<p, Bmin=0, see Figure)
Now you need to calculate the duty cycle (Formfactor) and the input dIo/I:
The ripple of the primary current is 100% and the primary duty cycle can be
calculated:
Ripple% = 100 x Uin^2 x q^2 / L / Pout / f / 2 (<=100)
and
q = (2 x L x Pout x f)^0.5 / Uin (q has to be <1)
s = q x (Uin/Uout) / (T1/T2) (s <= 1  q)
and
dIo/I = 100 x (1 q) / s
Formfactor = 1 / 2 / q
