Ferrite Core Transformer Winding Formula

[Rosham Rosebure]

Inthis article, you will learn how to calculate the turns ratio of a ferrite core transformer for high-frequency switch mode power supply inverters. High-frequency ferrite core transformers are used in almost every power electronics circuit, such as inverters and pure sine wave inverters. They are used to boost up or step up the low DC voltage of a battery and other DC sources, like solar panels. Ferrite core transformers are also used in isolated DC to DC converters to step down or step up the DC voltage. For example, in an isolated buck converter, it is used to step down the DC voltage, and in an isolated boost converter, they are used to step up the DC voltage. In this article, we will learn how to calculate the turns ratio of a high-frequency ferrite core transformer with examples.

A Ferrite Core Transformer is a type of transformer that uses a ferrite core instead of an iron core. Ferrite cores are made from a mixture of iron oxide and other metals, and they have unique magnetic properties that make them suitable for use in high-frequency applications. Ferrite core transformers are commonly used in power electronics circuits, such as inverters and DC to DC converters, to step up or step down voltage levels. They are known for their high efficiency and compact size, making them ideal for applications where space and energy efficiency are important.

For example, in the boost-up stage we have two options to choose from in power electronics converters: push-pull topology and full bridge. I will explain both methods one by one. The turns ratio calculation formula and concept remain the same for both topologies. The only difference between the push-pull topology and the full bridge transformer design is that the push-pull ferrite core transformer requires a center tap in the primary winding. In other words, the push-pull transformer has twice the number of primary turns than the full bridge transformer.

As you know, battery voltage does not remain the same all the time. As the load on the battery increases, the battery voltage will be less than 12 volts. With no load and a fully charged battery, the battery voltage will be near 13.5 volts. Therefore, the input voltage is not constant, and we must consider it while calculating the turns ratio of the ferrite core transformer. The cutoff voltage for the battery is usually 10.5 volts. We can take it as the smallest possible value of the input voltage to boost up the DC converter. So, we have the following parameters now:

Where Npri is the number of primary turns and Nsc is the number of secondary turns. We have three known variables like turns ratio, which can be calculated by the above equation, input voltage, and output voltage. But we need to calculate the primary turns to find the secondary turn of a ferrite core transformer. The formula to calculate the primary turns for a ferrite core transformer is given below:

So the calculated value of Bmax is 1600G, which is within the acceptable range of the maximum flux density. This means we can take Npri = 3 for further calculations. The primary number of turns for the push-pull ferrite center-tap transformer is 3 turns + 3 turns. In any design, you will need to adjust the value of Npri if it is in fraction. You can easily adjust it. But you need to check the value of Bmax every time. We start with an assumed value of Bmax and calculate Npri. But you can also start with an assumed value of Npri and check the value of the maximum flux density Bmax. For example, suppose a value of Npri = 1 and check the value of Bmax, and keep repeating this process until it falls within an acceptable range.

So, the transformer must be able to supply a 330-volt output with an input range of 13.5 volts to 10.5 volts. The maximum duty cycle for PWM is 98%, leaving the remaining 2% for dead time. During the minimum possible input voltage, the duty cycle will be at its maximum. At a maximum duty cycle of 98%, the input voltage to the transformer is 0.98 * 10.5 = 10.29 volts.

So the number of primary turns is equal to 3, and the number of secondary turns is equal to 96. This is all about the turns ratio calculation for high-frequency transformers. If you have any issues, please let me know in the comments.

Sir i respect your efforts

Formula given for high frequency or ferrite transformer is only for input output voltage .

But what about input output current ,gauge of wire, size of ferrite core available.

Thanks for this article;it was usefull,..sir u said the output of the ferrite transformer will always be 50kHz in the given example, what if the load operates on 50 or 60 Hz wont it be a problem?? If yes, please what are the necessary changes??

hi malik

thanks for the post

I have an issue with the calculation for Npri

my core is EE65 and the Ac is 5.3cm2 by observation.

now, after I calculated for Npri using Vpx10^8/4BmaxAcF which you gave, my result is 0.75471698turns

I feel something is wrong with this calculation

can you please help me with what I am missing?

thanks

please provide all values. Also have you checked and mentioned switching frequency and voltage?

But if you have assumed the Bmax value and Frequency as mentioned in this post then maybe it will make difference with your real number of turns of your transformer.

Hi Excellence,

Since you have not provided all the values, let us assume Bmax = 1500 G, Switching Frequency f = 50KHz. Also Effective Area ( Ac ) of EE65 Ferrite core is 540mm^2 or 5.4cm^2 (As per datasheet ). Now put the Vin value in this formula to calculate Npri :

Npri = (Vin * 10^8) / (4 * f * Bmax * Ac).

After calculating Npri you may check Bmax value (if you wish). Then follow those steps and use the formula I have mentioned above in my comment. And if you are facing problems, let me know with more details next time. Have a nice day ?

Thanks very much replying me.

And sorry for giving little details.

My concern is this:

After employing the formulae for the calculation, my Np is less than 1.

Here is the breakdown:

12 10^8/450,00015005.4

My result is 0.74074074 which is less than 1 turn

This looks too little for Primary Turns

Am I still missing something?

Please help me

I am certain sir. Its 12v

I intend using it for step up

I actually wanted to use it for Inverter using Switch Mode Topology.

I will be glad if you can give me some practical hints concerning that too.

Its my first attempt.

Consider Case 3 : If your core is different then the cross section area may also differ. It could be same too or maybe higher or smaller to 540mm^2. Only in case when it is smaller can result to non-zero primary turns.

Okay

If the higher the core size, the lower the frequency, then could it be possible that the core is supposed to operate at the 20kHz to at least get tangible Np using Vp=12v, and maintaining the Bmax=1300

For example:

1210^8/420,00013005.4 = 2.14turns = 2turns approx

But, my question is that what will be the consequence of using 20kHz instead of 50kHz?

Thanks for your responses

Thanks so much I made an inverter using sg3524 ..I got an output of 320v on no load but once I place a load of 26watts d voltage drop to 150v..one side of the MOSFET is also heating Dan d other..d ferrite core I used is removed from a factory inverter and slated to handle not less Dan 500watts load

Now, cores are of varied materials such as ferrites, steel, silicon, and many more. This article will focus solely on ferrite cores and expound on the different types, benefits, and applications. Additionally, we may give other knowledge that may be of importance to you.

Often, the magnetic ferrite cores have a combination of manganese, zinc, nickel compounds, and iron oxides. Since the compounds have low coercivity, they fall under soft ferrites. Ferrite core types comprise shell, toroidal, cylindrical, and closed-core.

Ferrite core transformers usually have a higher demand when compared to iron core transformers. The ferrite transformers have advantages, including resistance to elevated currents, low hysteresis losses, and no lamination required.

ETD cores; First, we have the ETD cores with minimum winding resistance at their center post. The winding resistance allows optimization of dimensions for increased power efficiencies. Furthermore, they suit inductors and power transformers efficiently.

EER cores; Secondly, there are EER cores with a round center post feature. Most times, the round center post will permit a shorter winding path length when compared to a square center post.

E, I core; Its feature is a bobbin winding. And you can assemble it with ease. E, I core uses are; inverter transformers, broadband, power, converters, telecom inductors, and differentials.

Different applications and core types have varying names and topologies based on the circuit design. Some of the topologies include flyback, push-pull, half-bridge, and shell-type. Nonetheless, when designing any ferrite transformer with any topology form, consider the shape, unit cost, optimum temperature, size, and frequency. The mentioned points should uphold the transformer by minimizing core losses, providing electrical isolation, and preventing core saturation.

All in all, ferrite core transformers are the best option when considering high-frequency applications since they have efficient performance. The transformers have high magnetic permeability, high coercivity, and they conduct low electrical power. The high-frequency applications include switched-mode power supply, noise filters, RF (radio frequency) inductors, transformers, etc.

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