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FlyBack Converter design Equations

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Advanced Member level 1
Oct 6, 2006
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What are the design equations for the calculation of fly back Converter

Peak Primary Current
Primary Average Current
Priamry RMS Current

How it can be ensured that converter is working in discontinuous mode at all conditions of load?


The whole flyback system is so complex it can not explained in a few sentences.
While the principle is relatively simple, there are a lot of details to watch.

To be able to answer your questions we need more details where you want to measure the currents.

A fly back topology is often used with AC mains input. If you now ask about this AC input current, then usually there is a filter, followed by a bridge rectifier and a bulk capacitor. Often a PFC is involved.

For the lowest possible input RMS current, it is: I = P / U. Where P is the input power, U is the RMS input voltage and I is the RMS input current. The current is considered here as ideal: pure sine without overtones and no phase shift with respect to voltage, which you never will have. You will always see higher input RMS current.

For primary RMS current on a bridge rectified system it is easy: It simply is zero, because positive and negative waveform is symmetric and therefore will cancel out.

For primary peak current. The lowest theoretically possible is U_RMS x sqrt (2). In reality you always will see a higher value.


Pout = 0.5 Lpri. Ipk^2. freq. efficiency.

also Vmin/L = Ipk/Ton (Ton = half of period)

Using algebra you can solve for Ipk & L in the above, this gives you the one solution for your desired freq of operation, Vin min, and power out (eff = 78% a good starting point) for a fully discontinuous design (lowest RFI).

Then you can design the transformer for Lpri & Ipk & freq of operation.

Regards, EP.

[ just for completeness in the above it is assumed the flyback voltage is = the input voltage (Vin min), where this is not the case, say Vin min = 250v and Vfly = 125V, then Ton = 0.333 of Tperiod, and Vfly exists for 0.667 of Tperiod ]
The turns ratio must be scaled for this voltage ratio, so for 24.7V out, V fly = 125V, so for 20T of secondary , there will be 125/24.7 x 20Turns of primary turns, Bpk should be 160mT for 100kHz with a good quality ferrite...
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thanks for reply.

I have designed a wide input range fly back converter using the attached application note.
I have found differences in design equations in different application notes.

Can you explain the equations on page 8 in the attached .pdf file. What will happen if there is more or less primary inductance? What is the figure of merit for discontinuous fly back converter?


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  • Very Wide Input Voltage Range, Off-Line Flyback Switching Power Supply.pdf
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What will happen if there is more or less primary inductance?

Greater primary inductance will require longer time to rise to a desired Ampere level. If nothing else is changed then it generally requires a slower frequency, or longer duty cycle.

I have recovered a Ferrite core transformer (ETD) from an old 100 watt (12@ 10amps) switching supply.
The air gap is 0.5 mm.

32 closely spaced turns of 26 AWG gives 220uH inductance.

How can i use this information to design the fly back transformer for any spec?

The terms you are interested in are what peak current and therefore flux density you are running this at and the frequency of operation, and whether it is continuous or discontinuous. Your output power is basically the energy built up in the inductor, E = 1/2*L*I^2 multiplied by the operating frequency.

To make a more powerful supply, you would have to run at a fairly high frequency in order to get the number of energy pulses up per second. You will also have to drop the inductance in order to build up sufficient current in order to provide a big enough energy pulse. This then starts to increase the flux density in the magnetic material thus increasing its losses. As with all things engineering it's a trade off.

There are loads of examples of designing an inductor on theinternet but you need to understand how materials are specced. They almost always have a power loss rating at a certain Δ flux density, and operating frequency. The datasheet will almost always suggest a flux density at a certain frequency. For instance my latest design runs at 200mT at 50kHz and will go about 20°C above ambient. I think I used N85 material from Epcos/TDK from memory.
Currently i can't get new cores with specification.

I have to use the available core. As i mentioned it is a ETD core from Chinese 100 watt (12@ 10amps) switching supply. The air gap is 0.5 mm.

I need 20 watts at output.

Suppose i have 220uH inductance. @ 32 closely spaced turns of 26 AWG.

VDc min 130v.
Pout 20 watts @ 12 Volt.
Efficiency 75%
Discontinuous Mode.
frequency 140Khz.
Duty cycle 0.45
PWM controller uc3845
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Well, if you are seeing 220uH, and your DC link volts are 130V min...

I peak = (V/L) * (1/f) * .45 = 1.89A

Based on 1/2*L*I^2, E = 392uJ

So at 130kHz your maximum output power at a .45pu duty will be about 55W (in a perfect world). This suggests it will run in a discontinuous mode of operation.

Are you trying to make an isolated supply?

Do you know anything about the material property of the core material? If not then you are just going to have to run it and see what it does as regards core heating. If you are designing a power supply then the first thing you would want to know is the core material, core area, and what gaps are available.

"So at 130kHz your maximum output power at a .45pu duty will be about 55W (in a perfect world). This suggests it will run in a discontinuous mode of operation."

How discontinuous mode is achieved?

Does secondary turn ration has any effect on mode of operation?

At page 13 of the attached application note Dmax is based on Vreflected. How Vreflected is selected?

I need isolated supply with four isolated outputs total (30 watts). I have studied TL431 and loop compensation techniques. And will discuss it later.


  • Design Guide for Off-line Fixed Frequency DCM Flyback Converter.pdf
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It will be discontinuous mode because the required power is less than that developed at lowest volts and maximum duty factor.

For isolated supplies, do you actually know what you are doing as regards isolation strategies and primary screening for EMC?

Secondary does not affect whether the converter operated in discontinuous mode or not.

What will happen if we reduce the primary inductance to 80uH?

Currently i don't know about standards.
What are the standards which are followed in the design of flyback converters?

The peak current will go up possibly to a dangerous level, and the losses in the core will increase too.

I'm afraid I cannot help you on the standards but a Google search will help you find out what you want. It depends what region you are wanting the power supply to operate in.

How discontinuous mode is achieved?

ETD core from Chinese 100 watt (12@ 10amps) switching supply

Pout 20 watts @ 12 Volt.

To get DCM, allow enough time (a low enough frequency) so that current waveforms drop to zero. The coil is then idle for a portion of the cycle.

Your specs calculate to 1.8 A continuous. So suppose your secondary carries sawtooth shaped bursts, at a 50% duty cycle, and at a fast enough rate, to be equivalent to 1.8 A continuous. Then you are talking about 1.8 x 2 x 2 = 7.2 A peak from your secondary.

This is only theoretical, but it's to get a rough idea what to expect. You can get this with the correct step-down ratio, and operating frequency.

Does secondary turn ration has any effect on mode of operation?

This is where it helps to do some experimenting with a simulator. Several factors come into play. Including step up/down ratio, and frequency, and duty cycle, and primary Henry value.

Your 220 uH transformer looks as though it ought to work (in simulation). You do not necessarily have to operate it at 140 kHz. It may be more efficient at a faster switching frequency, say 200 kHz.

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