# Choking Coil

 Main page | Use of the tables | Calculations | Tips | Mathematics used in the program | Literature Notes

## Use of the choking-coil/flyback transformer core tables

Choking coils and the transformer of the flyback converter must store energy. The stored energy is stored as magnetic field-energy in the ferrite-core, more exactly: stored in the air-gap.

The energy which has to be stored amounts to: The values L and Imax have been determined on the simulation side.
In order to choose a suitable core, the following requirements for the core must be considered,

• that the magnetic energy storage capacity is at least as big as the above calculated energy ½ ·L I2max and
• that the core is as small as possible, so that it is inexpensive.

The core table for the selection of suitable cores includes 11 columns, and 12 for the flyback transformer. These are:

• NO.: current number to the list of different cores
The next three columns serve the identification of the core. They are not required for calculations within the program.
• Core: Core type
• Identification: Further identification-charictoristics, e.g. air-gap, material or order code
• Manufacturer: Manufacturer of the core, so more information about the core can be requested if required
The next four columns contain data from the data sheet, which are required by the program for the calculations.
• AL/NH: The magnetic conductance. With this one can calculate the number of turns needed for L.
• Ae/mm2: The effective magnetic cross section of the core.
• le/mm: The effective magnetic length of the core.
• Amin/mm2: Minimal core cross-section to calculate the maximum magnetic flux-density.
The next four columns are calculated by the program
• Wmax/mWs: The magnetic energy storage capacity of the core, for a maximum magnetic flux density of 0.3T
• Bmax/mT: The maximum magnetic flux density in the core. This magnetic flux density is calculated for the worst case scenario within the input voltage range Vin and nominal load. It is calculated for the minimal cross-section area of the core Amin. The maximum flux density is given as an additional important piece of information in order to help the user to select a suitable core. In order to influence Bmax you can change L or ΔIL on the simulation-side.
• N1: The number of turns for the required inductance L, as well as for L1 of the flyback converter.
• N2: The secondary number of turns required for the flyback converter. This column only appears if a flyback converter is calculated. To change the secondary number of turns you can change the ratio N1/N2 on the simulation side. If the ratio is changed it will influence the maximum drain-source voltage of the transistor. The lower the ratio N1/N2 the smaller the drain-source voltage of the transistor Vds_max will be.

The program suggests suitable cores:

• Green writing: Very well-suited cores, whose magnetic energy storage capacity Wmax exceeds the required value by a marginal quantity and also has the smallest possible core-volume. The maximum flux-density in these cores approximately reach the saturation point of 0.3T.
• Brown writing: Well suited cores, whose magnetic energy storage capacity clearly lies over the required value. Its core-volume is up to twice as large as the smallest very-well suited core. The maximum flux density for these cores usually lie between 0.2...0.25T.
• Black writing: Suitable cores, whose magnetic energy storage capacity lie very far over the required value. These cores are uneconomically large.
• Gray writing: Inappropriate cores. Under the condition that Bmax < 0.3T at every point in the core, the magnetic energy storage capacity lies under the necessary value. The column "Bmax/mT" gives information about the actual maximum flux density. If the core material chosen by you has a higher flux density capibility, you can use this core at your own discretion.

Under the core table are seven input-fields. The fields 'core', 'ID' and 'manufacturer', all serve for the identification of the core and are irrelevant for calculations in the program. The fields 'Al', 'Ae', 'le', and 'Amin' must be filled corresponding to the data sheet. To complete your input click "ADD". The inputed core will be added to the table and treated in the same way as the rest of the pre-determined cores in the table.

Note:
The Wire-diameters proposed by us as well as the Wire-cross-section is always for a declared current density of 3A/mm2.

## Calculation of choking-coils and flyback transformers On the simulation side an inductor and the related inductor current proposed by us or chosen by you, was calculated. The inductor and the maximum current determine the election of a suitable core.

Choking-coils shall store energy. The stored energy amounts to: W = ½ L I 2max. This energy is stored in the form of magnetic field energy. In fact, as well as being stored in the ferrite it is also stored in the air-gap of the core (see right of illustration).

• The required physical size of a choking-coil is approximately proportional to the amount of energy to be stored.
The field energy in the storage inductor amounts to: (1)

The magnetic flux-density B is continuous and is approximately the same in the ferrite and the air gap, i.e. BBFeBg. The magnetic field-strength H is not continuous, it is higher in the air-gap rather than the ferrite by a factor of μr. This is introduced in equation (1), which results in B = μ0μr ·H, IFe = lFe ·A and Vg = g ·A: (2)

μr in the ferrite amounts to approximately 1000...4000. The effective magnetic core-length only goes into the energy calculation with lFe/μr. Therefore one can say that with usual core-dimensions energy is stored mainly within the air-gap.
• This leads to the following: Choking coils need an air-gap. The energy is stored within this gap.
Since the energy is stored in the air-gap, one requires a certain air-gap volume in order to store the demanded energy. The maximum capable flux-density within customary ferrite amounts to approximately Bmax = 0.3T
• Therefore it follows that: The bigger the air-gap the larger the magnetic energy storage capacity.
The manufacturers of ferrite cores give substitutional values for the term (lFe/μr+g)·A) in equation (2), namely
• effective magnetic core-cross-section Ae,
• the effective magnetic core-length le and
• the effective permeability μe.
This implies: The value μe can be calculated by means of magnetic conductance AL: The magnetic energy storage capacity then amounts to: Therefore from the table-values Ae, le, AL and Amin, our program first calculates the magnetic energy storage capacity, and from the result of this produces suggestions for suitable cores.

The number of turns N1 are calculated with the help of the magnetic conductance AL: Calculation of wire-diameter:

The current density S of the winding can be chosen between 2 and 5 A/mm2, (depending on the thermal resistance of the transformer). For this it follows that for the wire-cross-section and the wire-diameter: Note:
The wire-diameters proposed by us are calculated for a current density of 3A/mm2.

## Tips

• Don't use cores which are too small (Grey Writing) at first, unless you know what you are doing.
• For high frequencies (>50kHz) and larger current ripples (continuous mode) you should select somewhat larger cores (Brown writing). With these the change in flux-density is smaller and with it the hysteresis losses.
• Choose ΔIL so that it is not too big. The suggestions proposed by us have adequately small current ripple along with physically small inductor size. With a larger current ripple, the voltage ripple of the output voltage Vout becomes clearly bigger while the physical size of the inductor decreases marginally.

## Mathematics used in the program

The columns Wmax, Bmax, and N1 are calculated as follows: Let W be the maximum energy, that the core has to store. This energy amounts to W = ½ L I2. From the data-sheet of the core, the following values are required for further calculation:
• AL is the magnetic conductance
• Ae is the effective core cross section
• le is the effective core-length
• Amin is the minimum core-cross-section for calculating the maximum magnetic flux density
From this it follows:
• Wmax: The maximum magnetic energy storage capacity of the core
Wmax is the amount of energy that a core can handle, if the maximum flux-density in the minimal cross-section Amin is exactly B = 0.3T.  For the core selection Wmax must be larger than W = ½ L I2. A core is economically favorable if it can handle the necessary energy and also have a volume which is as small as possible. According to their volumes Ae·le cores are marked with a colour:

• Cores which are too small (where B in Amin would exceed 0.3T) are written in bright-grey.
• Cores, whose effective volumes are as small as possible are written in green.
• Cores that lie 50 to 100% over the smallest volume, are written in brown.
• Cores, which are even bigger (uneconomically big) are written in black.
• Bmax: Maximum flux-density, in the smallest core-cross-section Amin.
It amounts to:  • N1: The number of turns of the inductor or of the flyback converter primary coil.
The number of turns N1 amounts to: N2: Secondary number of turns of the flyback converter transformer.
N2 is calculated by using the chosen turns ratio N1/N2: Main page | Use of the tables | Calculations | Tips | Mathematics used in the program | Literature Notes | Top of page