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Idecided to write a Blog on the basics of transformer design as I believe there are a lot of members that may not have been exposed to it before. Some think it's a black art or black magic, but it's actually based on rock solid science. I'm going to stick with the basics and not get too deep in this blog. And I'm planning on writing a companion Blog on Inductor design soon.

Number one rule: a transformer only operates on a changing input voltage. This usually means AC or pulses, but let's stick with AC for this blog. To keep things simple, let's use a sine-wave for an AC input. A transformer has some pretty great properties. It can step-up or step-down voltages. It can do the same with currents. It can even do the same with impedances and hence, can match an input impedance to an output impedance so as to obtain a maximum transfer of power from an input source to a load. The ability to change voltage, current, or impedance is controlled by the turns ratio between primary and secondary. The equation that governs this is: Vsec = (N2/N1)*Vpri, where Vpri is the primary winding voltage, Vsec is the secondary winding voltage, N1 is the primary number of turns and N2 is the secondary number of turns. For impedance, we simply use the ratio of secondary to primary turns squared instead of the ratio of turns itself. In equation form, it is: ZSec/Zpri = (Nsec/Npri)^2, which is N^2sec/N^2pri.

Another amazing property of a transformer is it's ability to isolate the primary circuit from the secondary circuit, yet, it can transfer power from one side to the other. This is true only for an isolation transformer. There is also an Autotransformer which is the equivalent of an isolation transformer with the bottom leads connected together so that isolation is no longer possible, but the step-up and step-down property still works.

Most transformers require a ferromagnetic core made of typically, Silicon Steel for frequencies up to 1 KHz, or Ferrite for frequencies from about 10 KHz up to several MHz. There are other, specialized core materials, but we won't get into them here. When using a magnetic core, if enough voltage is applied to the winding, which in turn creates a magnetic flux in the core, the core will saturate. When this happens, the core no longer functions as a magnetic core and a large current will flow in the primary. In order to avoid core saturation, the transformer must be designed for a certain range of input voltage and frequencies. Actually, it's the product, called volt-seconds that's important. The flux density must be kept below the saturation value for the type of core material used. For magnetic Silicon Steel, this is between 12.5 to 16 KiloGauss in the CGS system of units, which is equivalent to 1.25 to 1.6 Tesla in SI units. For Ferrite, saturation typically happens at 3.0 to 3.5 KG (0.3 to 0.35 Tesla). In order to design a transformer that will not be in saturation, the following formula is used for a sine-wave input: N = E*10^8/(4*1.11*F*A*B), where N= number of primary turns, E= primary voltage in volts, F = sine frequency in Hz, A = core cross sectional area in cm^2, and B= flux density in Gauss. As an example, if we were going to use a standard EI-150 core for a 120 VAC, 60 Hz transformer, the core area for a square stack can be found in the core manufacturer's datasheet as 1.5" x 1.5" x 6.45 cm^2/in^2 = 14.5 cm^2. For a core grade of 29 gauge M6, the maximum flux density is rated at 14.5 KG at a loss of about 6 watts/Lb. The primary turns needed,therefore, will be: N = 125E8/(4*1.11*60*14.5*14.5E3) = 223.17 turns, which can get rounded down to 223 turns in this case. The primary wire size needed depends on the primary current. Note that we used 125 VAC for the primary voltage. This is to give us a little safety marking against core saturation.

In our example, let's say the transformer secondary output power shall be 150 watts, and will be 10 VAC RMS at 15 Amps. For a power line frequency transformer such as this, we can use the current density to determine the wire sizes, starting with the secondary. A good value of current density is 600 C.M./A (circular mils/amp). We need to multiply the secondary current by the current density to get the needed wire cross sectional area. 15 Amps * 600 C.M./Amp = 9,000 circular mils. Next, using a magnet wire chart for round wire, we find that the closest wire size in the American Wire Gauge (AWG) is AWG #10 at 10,384 C.M. Using a current density of 600 C.M./Amp should give an output voltage regulation of approximately 5% from no load to full load.

Some of you may wonder how the core size is chosen. It's largely done by using the Area Product, which is Aw*Ac*k, where Aw is the window area (the available area the wire must fit into), Ac is the core area, and k is a constant that depends on factors I won't get into here. For those that are interested, a great book on the subject is by the late, Col William T. McLyman of CalTech who came up with this concept of numerically determining the smallest core needed for a given set of transformer parameters. The name of the book is: Transformer_&_Inductor_Design_Handbook.

And if your using a standard transformer lamination, there's no need to always use a square stack. Sometimes, depending on the available space, it's better to use a stack longer than square. Rarely have I seen transformers with a stack shorter than square, but it's sometimes done. The standard laminations have are sized and named after their center leg width in inches. For example, an EI-100 has a 1.00 inch wide center leg. The outer legs are half the width of the center leg, as are the I pieces.

I'll be glad to answer any questions as I didn't cover all aspects of transformer design. And although most of this material does apply to high-frequency transformers, the primary turns equation usually needs to be modified, especially for unidirectional waveforms (pulsed DC).

I understand you cover most of electric transformer, how about toroidal chapel, can one use or applies the same formulas too which you have just given and how do go to select core for transformer or inductor iron and powder ones? Hope I will get reply from your rocking.

planar transformers are not that different from normal ones technique wise... back in the day the go to company was philips.... then ferroxcube bought the division and rebranded all the stuff

how to design them including safety issues, though it references outdated standards:

www.ferroxcube.com/.../plandesi.pdf

and the magnetics designer that even transformer shop engineers are impressed by:

that said you did not say if you needed safety isolation. planars lend themselves to higher powers than 10W and you can not get safety isolation in one under a 60W capable core due to spacing and isolation ratings. For DC/DC converters i recommend clip cores with separate high turns side in a separate multilair PBC... for the real small stuff you run into winding depth not holding the PCBs instead of winding width holding turns

I measured no voltage on the auxiliary winding. I believe this is because the device is not switching. The input voltage during testing were between 230-240VAC, rectified was around 330VDC to the primary.

To better understand what's going on could you provide transformer inductance(primary magnetizing), and waveforms showing Vcc, DRV, and the aux winding waveform at the transformer? (Preferabley together on the same scope shot if possible). If we get all those signals we should be able to understand how the controller IC itself is behaving on your board.

Webench doesn't support multiple outputs yet so if you did not do already I suggest to be sure you add up the total output power and use that to calculate as if it was a single output design with the total output power of your full design. That will ensure the peak current and magnetizing inductance are more realistic.

That will allow you to see more on the impacts of each component selection. You would still need to add the total power and use that in the calculations as the calculator is focused on a single output design.

The information in the datasheet, also show that the auxiliary winding voltage sometime goes below 0V, during the energy transfer state. I think the LDO on auxiliary winding method will have a problem here.

i have replace the diode on the secondary side with low Vf Schottky and done some measurements but the isolation transformer that i was using, decided to stop working. So i will give you what i have from the last measurement session until the replacement transformer arrive.

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Purpose: To investigate the usefulness and effectiveness of a dual beam-current transformer (BCTs) design to monitor and record the beam dosimetry output and energy of pulsed electron FLASH (eFLASH) beams in real-time, and to inform on the usefulness of this design for future eFLASH beam control.

Methods: Two BCTs are integrated into the head of a FLASH Mobetron system, one located after the primary scattering foil and the other downstream of the secondary scattering foil. The response of the BCTs was evaluated individually to monitor beam output as a function of dose, scattering conditions, and ability to capture physical beam parameters such as pulse width (PW), pulse repetition frequency (PRF), and dose per pulse (DPP), and in combination to determine beam energy using the ratio of the lower-to-upper BCT signal.

Results: A linear relationship was observed between the absorbed dose measured on Gafchromic film and the BCT signals for both the upper and lower BCT (R2 > 0.99). A linear relationship was also observed in the BCT signals as a function of the number of pulses delivered regardless of the PW, DPP, or PRF (R2 > 0.99). The lower-to-upper BCT ratio was found to correlate strongly with the energy of the eFLASH beam due to differential beam attenuation caused by the secondary scattering foil. The BCTs were also able to provide accurate information about the PW, PRF, energy, and DPP for each individual pulse delivered in real-time.

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