**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 spread-sheet programs such as Excel and Lotus 123

After the first economical 8-bit 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, easy-to-use tools for use throughout the industry.

**Designing with the Rale Design Software**

The Rale Design Software 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* (Ismax-Ismin)/(Ismax+Ismin) =(Bmax-Bmin)/(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, high-frequency 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, high-frequency transformers should be manufactured for low leaking reactance , with single-section 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 high-frequency 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 AC-component (the ripple of the input current) of the induction automatically. But this indicates that the selected ferrite quality is not optimal.

**Copper additional losses**

- Eddy current losses
- Skin effect losses
- Proximity effect losses
- Losses due to circulating currents through the parallel-connected wires.

Proximity losses are smaller in the case of a winding that takes up only 30-60% 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 parallel-connected 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 parallel-connected wires. The value is normally set between 1.25 and 3.

Losses of circulating currents through the parallel-connected 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 qnom 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: qmax = Unom/(Umin + Unom) = 296/(125+296) = 0.7.
- Th duty cycle at the input voltage Upmax = 700V will be: qmin = Upnom/(Upmax+Upnom) = 296/(700+296) = 0.3
- Input voltage : U(V) = 125V
- Duty cycle : Formfactor = 0.7
- Ripple of the primary current (induction) : dI/Io = 17%
- Output DC-voltage : Voltage = 2 x 24V
- Output DC-current ; Current = 2 x 4A
- Ambient temperature : Amb. Temp. = 40°C
- Temperature rise : Temp. rise = 60°K
- Induction = 0.275T
- Single-section bobbin with the primary between 2 secondary : Bobbin = 11
- Max. Build 50%: Space = 0.5
- Factor for additional Cu-losses : Rac/Rdc = 3
- The winding filling factor :44%<100%
- The maximum temperature of the windings is 40°C+57°K = 97°C < 115°C.
- 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 : 0.25-0.28T
- 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
- Min. input voltage and the duty cycle at this voltage
- Dc-output voltages and dc-output currents
- The ripple of the input current (induction)
- Frequency
- Continuous mod Bmin>0
- Discontinuous mode Bmin=0
- Min. input voltage and the duty cycle at this voltage
- DC-output voltages and dc-output currents (output power)
- Inductance of the primary winding
- Frequency
- Pout Output power in W
- L Inductance in H
- F Frequency in Hz
- Imax Max. primary current (peak)
- Imin Min. primary current
- Ripple%= 100 x (Imax-Imin)/(Imax+Imin)
- Iav = (Imax+Imin)/2
- Pout = Uin x Iav x q
- Uin Min. input voltage
- q Duty cycle of the primary
- Ripple% Ripple of the
**primary current dIo/I**= 100 x (Imax-Imin)/(Imax+Imin) - Min. input voltage
- DC-output voltages and dc-output 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)
- (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)
- Min. input voltage
- DC-output voltages and dc-output currents (output power)
- Inductance of the primary winding
- Frequency
- Ratio of the primary and secondary turns (T1/T2)
- Discontinuous operation mode (s
- 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)****dIo/I = 100 x (1- q) / s****Formfactor = 1 / 2 / q**

**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:

Ripplemin = Ripplemax *(Upmin*qmax/Upmax/qmin)^2 = 100*(0.7*125/750/0.3)^2 < 17%

The duty cycle q is defined as follows:

**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:

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 number of parallel-connected 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 |
Iprms |
2xIsrms |
2xUodc |
2xIodc |
Pcu |
Pfe |
Q |
Ripple |
DTcu |

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:

The parameters of the designs are core size, output power and eddy current losses (Rac/Rdc)

/ |
Primary |
Secondary |
|||||

Core |
Rac/Rdc |
Power |
Inductance |
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:

In the following Figure are 2 typical operation modes:

**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:

Then you need to calculate the ripple of the primary

Pout = L x (Imax^2-Imin^2) x f / 2 = L x (Imax+Imin) x (Imax-Imin) x f /2

Where:

Using:

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:

**Ration of the primary and secondary turns in continuous operation mode**

You know:

Now you need to calculate the duty cycle **(Formfactor)** and the input **dIo/I**:

Where:

A = (Uout/Uin) x (T1/T2)

**Ration of the primary and secondary turns in discontinuous operation mode**

You know:

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:

and