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TIDA-00688: Query in Transformer design

Part Number: TIDA-00688

The above data i have taken from TIDA-00688    page no.7  .   The above design is with Planar transformer .  consider  a normal E type ferrite core( not planar core)  E 20/10/6   &    its magnetic mean length from datasheet is 46.mm .  Let us assume turns as 6  &  peak current  (200 +  (307/2))mA  .  Now in this case the maximum magnetic field strength will be equal to   =   (6  * 0.3535)/46mm  =  46.1 A/m  .

confirm me whether the above maximum magnetic filed strength calculation correct or not?

  • Naga, hello and thank you for your interest in Texas Insruments.  Your inquiry has been received, however the design owner is currently out of the office.  We are looking to determine if we can have your answer provided from another Texas Instruments colleague.  Please allow us another 1-2 business days before we are able to respond here. 

    Best Regards,

    John Fullilove

    Texas Instruments

  • please solve my query
  • please respond to my query
  • Dear Sahitya-san,

    I think you found an error in our user guide. It has the wrong formula at this place. Because I'm not the author of the guide I'd need some time to work on the correct formula.

    In the mean time please have a look at following TI designs which are equivalent but use a dedicated transformer. A typical transformer for this type of converter needs an air gap like a fly-back transformer. TIDA-00688 however uses a larger core to create the required inductance and handle the flux.

    Here the designs with transformer: TIDA-00129, TIDA-00237 and TIDA-00689

    Kind regards,

    Ingolf

  • lDear Sahitya-san,

    The guide has to be updated as there has been used a formula for air coils. On top we don't need the H field. As per core datasheet we need to ensure B(max) below ~400mT. As a good practice for higher frequency B should be limited to ~200mT for N87 material.

    The new calculation would be as following:

    We have a DC current of 0.2A and a ripple of 0.3A so peak current is 0.35A (Idc+Iripp/2).
    B = N * I * u0 * ue / l
    With N=6, I=0.35, u0 = 1.26e-7, ue = 1180 and l = 0.0203 (see page 3 of https://en.tdk.eu/inf/80/db/fer/elp_18_4_10.pdf)
    we get B = 156 mT which is fine.

    In your case it looks even better. B would be only 96mT which would be perfect for N87 material in your core (https://en.tdk.eu/inf/80/db/fer/e_20_10_6.pdf). The only problem is the tolerance. Ungapped cores lead to significant manufacturing variation in inductance. If there is no need for such low number of turns it is better to use a core with an air gap and more windings. This reduces tolerance on inductance because the air gap allows you tighter manufacturing control. On top you can select a smaller core because energy is stored now in the air gap instead of in the magnetic material. Please let us know whether you need assistance on calculation of transformers with air gap.

    Kind regards,

    Ingolf

  • Dear Frank,

                            In your calculation you have taken ue  as constant & its value as 1180. This type of calculating B , may be correct in case of cores with air gap , where the B-H curve is linear.  But if we observe the B-H curve for ungapped cores , it is linear for some portion only .  Any way in my point of view , we should first calculate  H  which  is (N * I)/L   from the value of H we should check the B  from the   B-H curve   &  we should ensure that  core wont saturate.  

    I need your assistance to calculate the required air  gap  &  Inductance calculation with air gap.

    Kindly correct me if i am wrong.

    Regards

    Naga sahitya

  • Dear Sahitya,

    The ue I used is the relative effective permeability of the ungapped core and as such I felt free to use it for the calculation. It includes the unavoidable manufacturing air gap. Calculating H is part of the equation. As magnetic path length we use the datasheet value of the core which is 20.3mm in "our" core and 46.3mm in "your" core. In case of "our" core we get 103 A/m and with "your" core it is 45 A/m. With these values for H we are still OK as per SIFERRIT N87 datasheet. It shows for 100C around 350mT for 103 A/m and 150mT to 200mT for 45A/m. In reality we will most likely experience less mT because the two halves of the core always have some unavoidable manufacturing air gap. Therefore no problem in the application with the numbers we discussed.

    Now the calculation with the air gap. Here I'd use the formulas B = N * I * u0 / ((l_Fe / u_Fe) + l_air) and L = (N^2) * u0 * A / (l_air + l_Fe / u_Fe) with B = field strength, N = number of windings, I = current, u0 = magnetic field constant, l_Fe = magnetic path length in ferrite, u_Fe relative permeability of ferrite, l_air = thickness of air gap (sum of all), A = core cross sectional area and L = inductance. I did a quick calculation with N = 15 and an air gap of 0.1 mm with the planar core and I got 95 uH, B = 65mT using the effective permeability ue = 1180 (H=23.6). A quick check of the H/B diagrams in the N87 datasheet shows that we are in the linear region but the resolution is too coarse for an exact B reading.

    When you calculate a transformer with a fixed inductance you would need to trade the core size against the wire diameter (number of turns, core losses vs. copper losses). A smaller core requires more turns which leads to even smaller wire diameter and higher DC resistance. Same time the air gap is calculated so that B stays below 200mT. In any case the wire diameter must be big enough to support your average current. This is an iterative process and could be quite some effort. This is why many designers focus on defining the key parameters only (inductance, power, operating and isolation voltages) and let a transformer manufacturer do the calculation and/or simulation.

    When I calculate with an E13/6.5/3.7 core from N87 material and 0.1mm air gap I get 28 turns for 100uH which sounds reasonable. As a first estimate we could use AWG26 wire with around 70 - 80 cm length for the 28 turns which gives an R_DC of about 0.1 Ohm. This would be fine for our application. In our example B would be 120mT and H is 43 so such transformer design could be a first step.

    Please let me know whether you get similar results.

    Best regards,

    Ingolf