Planar transformer: technology, calculations, cost

    Not so long ago, I was approached by a company that needed to develop a line of LED drivers. The name of the company and TTX drivers will not be called, the NDA did not sign, but ethics are ethics. It seems to be a regular order for a driver, of which a dozen are typed per year, but there were two mutually exclusive requirements: cost and dimensions .

    The task from the point of view of circuitry is simple, but from the point of view of production and design it turned out to be very interesting. And so - it was required to make a network driver for LED with a power factor corrector (power of about 100 W), which cost around $ 3 per series and had dimensions of no more than 11 mm in height! Many will say: “What is the problem of making a deshman driver?”, But Deshman will not work, because one more requirement - it is possible to give a 5 year guarantee without fear . And here the fun begins.

    The choice of topology, circuitry was made, everything fit into the dimensions and cost, but the "classic" transformer spoiled such a wonderful picture. He is huge, he is expensive, he is technologically difficult to manufacture. It remained to solve the last problem and after two days in thought and calculation it was found - a planar transformer .

    If you are interested between what and what the choice was made, on what arguments it was based and how it was possible to get the cost of the transformer less than $ 0.5, then I invite you to a tackle. Well, to improve the "appetite" I am attaching you a photo of the finished transformer:




    The main disadvantages of the "classic" transformers


    I think it’s not a secret to anyone what an ordinary transformer looks like, but suddenly someone has missed the last 150 years of the industrial revolution, so I’ll remind you:




    It looks like an ordinary transformer wound on a frame from the core RM12. Why is he so bad? There are several reasons, of course, some of them lose relevance in certain tasks, but the story will be conducted in the context of the task that confronted me. And here are the main ones:

    • Height. Even a person with a poor eye can roughly estimate the size of a transformer from a photograph and say with confidence: "It is definitely more than 11 mm." Indeed, the height of the transformer on the RM12 is about 24 mm, which is more than 2 times the required value
    • Manufacturability. When you need to wind 1-2 transformers, then you take the frame, wire and wind. When you need to wind 100-200 pieces, then you can order winding in your own country, the price does not bite yet. When you need to wind 10,000 pieces, and then another 50,000, then a bunch of nuances arise: price, quality, the choice of another contractor in Asia. All this increases the final cost of the product when I just need super cheap and very high quality.
    • Repeatability It is very difficult to wind and assemble two identical transformers; it is impossible to make 10,000 identical transformers. This I have experienced in my own skin more than once, especially when it comes to production in South Africa. Now imagine
      that you have to “modify the file” these 10,000 transformers in the final assembly. Presented? Did you feel sad about the amount of labor, and therefore the cost? I think it has become.
    • Cost price. This is generally a very difficult point, but let's look at the photo above and see that to build a classic transformer we need a frame, core, brackets, copper wire, insulation and all this with our hands or on a semi-automatic machine. Let's say all this costs "X dollars". For the manufacture of a planar transformer, only a core is needed. I think it’s obvious here that 1 part is clearly cheaper than 1 same part + 4 more components?

    At this moment, you will probably be tormented: “If everything is so bad, then why are ordinary transformers so common?” A little earlier I said that part of these minuses in certain tasks is not a minus. For example, if you open UPS on-line, you will see that the transformer there is not the most dimensional element. Yes, and if you collect small batches of up to 100-200 devices per month, then for sure the cost will even out, because 100-200 pieces can already be made in Russia or hire a winder, buy a Chinese machine tool or make it yourself for 100-200 thousand rubles. and enjoy life.
    And perhaps the main place where planar transformers will not supersede conventional ones - converters with a rated power of more than 2000 watts .

    Planar Transformer Device


    In the very first picture you see this type of transformer already assembled, the view is very unusual, is not it? Although people who opened modern TVs, charging laptops (not cheap) have probably already seen such transformers or the like.

    Planar transformers can be made in different designs, a clear classification does not exist as far as I know, but I divide them into 2 types:

    • Independent. The transformer is a separate electronic component that can be separately supplied and manufactured. Such a solution is good if there is a large line of devices where the transformer is unified. This is not my case. I need cheap, and unification always requires sacrifice in the form of a slight increase in price.


    • With a common core. This is just my case. With this design, the transformer windings are made on the main circuit board of the device and is not an integral part of it. The core is simply put on the board and attached using brackets or otherwise, for example, glue or compound.



    Whatever type of planar transformer is considered, they have one thing in common - all windings are made in the form of copper tracks on a printed circuit board .

    If you decide to familiarize yourself with this technology in more detail and go to Google, you will probably find the phrase in many articles: "... and finally, in recent years, planar transformers have become affordable. This is due to the fact that multi-layer boards have become cheaper." When I designed my first planar transformer, the year so in 2010-11, this phrase baffled me. I naively thought what gliders do exclusively on multilayer printed circuit boards. At that time, I was still studying at a university, and although I worked and received a good scholarship, this type of board was not financially very affordable for me. I thought and decided to make my facebook !!!!to reduce the cost of this technology, as it turned out later - came up with a bicycle.

    The essence of the cost reduction was to use a “pie” of several two-layer printed circuit boards of small thickness (0.8 or 1 mm). For me, this seemed like brilliant and simple solutions. The only problem was that, as always, I looked at the solutions of top companies engaged in power electronics, such as Texas Instruments, Linear, Infineon, Murata, and they used printed circuit boards in 6-8 layers and in 2010 they even standard 4 class (0.15 / 0.15 mm) were very expensive. Then it turned out that they called me to a good company for summer practice and there they told me and showed me that they had been doing such “pies” for planar transformers for 10 years already. Other companies also did a lower rank than TI and Infineon. The main thing isthe idea was true and such a solution is not just right, but also time-tested .

    All elements of the “pie” are ordinary two-layer boards of the standard accuracy class, which means they are sooooo cheap and any manufacturer of printed circuit boards can make them. The elements of the “pie” of a planar transformer look like this:



    As you can see, there are only 3 elements in my transformer, although there could have been more. Why 3? According to my calculations, in order to gain the required inductance in the primary winding, I will need 6 layers. 2 layers gives me the main board + 2 layers “piece of cake” + 2 layers “piece of cake”. The secondary winding only fit on 2 layers, from here another "piece of cake". As a result, it has a stack of 4 two-layer printed circuit boards. Further arithmetic is even simpler: I use the ELP18 / 4/10 core, which means that the distance under the “windings” is 4 mm. We divide this distance by the number of boards: 4 mm / 4 boards = 1 mm - the thickness of each printed circuit board. Everything is simple!

    If you suddenly do not understand where the 4 mm gap came from, you can see the datasheet on the core here. And for those who are not comfortable following links or don’t want to spend traffic on a large pdf, a small clipping:



    As you can see, the size of the core window in one half is 2 mm, in the second half it is also 2 mm. We get the total window size in height - 4 mm.

    Now you can make out what the cost of a planar transformer consists of. In fact, there are only 2 components: a core and 3 printed circuit boards. A bulk core costs $ 0.14, printed circuit boards 3 pieces of $ 0.11 each for the same on the series. We get $ 0.47 worth the transformer itself. I did not include here the compound for gluing the cores, because if we scatter its value for the whole batch, then even 1 cent does not work there and did not consider the assembly work. Work is not considered for one simple reason - the transformer is assembled at the stage of manual installation, but it costs a penny in Asia. For comparison, soldering 2 transistors in a TO-220 package costs the same as installing a planar transformer, that is, a minuscule again. That's how we get the figure of $ 0.5 for 1 transformer up to 100 watts .

    A little about my results ... I managed to fit in the overall height and even do better - instead of the maximum 11 mm, I got 9.6 mm. On the one hand, it is not noticeable, but in practice this is a decrease in size by about 13%. Moreover, the main height dimension was no longer set by a transformer, but electrolytic SMD capacitors at the input and output.
    At cost - I can’t tell you the exact number, but it turned out to meet the demand. It is worth noting the efforts of the customer himself, he managed to find suppliers who, on a large series, were able to give prices at the level, and sometimes even slightly lower, than on digikey. Personally, my merit is that I solved the technical problem and did it cheaply, and the customer himself already made super-cheap without loss of quality.

    Technical possibilities offered by a planar transformer


    Further, my article takes on a more technical character than narrative, and if you are not interested in power electronics, dry calculations and other nasty things, then you can stop reading and proceed to the discussion in the commentary. There will be no more beautiful pictures. If you plan to take this technology into service, then for you everything is just beginning.

    Planar transformers, due to their physical and structural properties, allow us to get not only a gain in terms of manufacturability, and therefore cost, but also open up new horizons for us in the design. Let's look at the main advantages that we get when using planar transformers:

    • Low thermal resistance. It is due to the higher ratio of the surface area of ​​the core to its volume. Due to this, the cooling capacity of planar transformers is significantly higher compared to the "classical" transformers by 50-70% . This allows us to lay a higher current density during design, and therefore provide a higher energy density with the same effective core volume (V e ). In this case, the temperature increase remains within acceptable limits
    • High current density. The increased current density is a consequence of the previous “plus” of a planar transformer. Typically, for a transformer with a wire winding, the standard value of the current density is a figure of about 6-7-8 A / mm 2 , when for a planar transformer it is a figure of about 15-25A / mm 2 . This, of course, all other things being equal, such as overheating temperature
    • Excellent repeatability of spurious parameters. The geometry of printed circuit boards during production is maintained very precisely, which ensures almost perfect repeatability of spurious parameters. This allows you to easily design resonant converters, for example, LLC half-bridge and achieve very high switching frequencies up to 2-4 MHz
    • High coupling ratio. Everything is simple here - less losses in the windings,
      which means we get a higher converter efficiency
    • Low leakage inductance. Due to this, the amplitude of EMF emissions and voltage fluctuations is lower, which in turn increases the reliability of transistors
    • Very high energy density. Due to the combination of all the previously described properties of a planar transformer.

    So that you can more clearly assess the full potential of this type of transformer, I can say that in this project, I managed to build a 65 W resonant converter on one pair of ELP18 / 4/10 cores. And now look at its overall dimensions, is it not bad for such a trifle?

    Planar Transformer Calculation Method


    There are a lot of techniques that allow you to calculate this type of transformer. True, the main literature, including scientific, is mainly in English, German and Chinese. In practice, I tried several, they were all taken from English-speaking sources and all showed an acceptable result. In the course of several years of work, I made small corrections that allowed me to slightly increase the accuracy of the calculations, and I will demonstrate this very technique to you.

    I don’t have any ambitions for its uniqueness, nor do I guarantee that its results are accurate enough in all ranges of frequencies and powers. Therefore, if you plan to use in your work, then be careful and always monitor the adequacy of the results.

    A little bit about modeling ... It can, and sometimes needs to be done, but working even with such a monster as Comsol, I could not get an accuracy higher than the usual methods described everywhere give. I tried to take into account a greater number of parasitic parameters, and more accurately describe the skin effect, and take into account magnetic changes in the core material and much more - it was better to get + -3-5% accuracy. Therefore, at powers up to 150-200 W, I don’t see any sense in modeling (you can certainly not agree), but after 200 W you can’t do without it, especially if you have a resonant converter.

    Planar Transformer Calculation


    When calculating any transformer, the first step is to find the maximum value of magnetic induction. Losses in the core and in copper conductors lead to heating of the transformer, therefore, calculations must be carried out regarding the maximum permissible overheating of the transformer. The latter is selected on the basis of operating conditions and requirements for the device.

    The case is an empirical assumption in which we assume that half of the total losses on the transformer are core losses. Based on this assumption, we calculate the maximum density of core losses according to the empirical formula:

    Where is the effective magnetic volume V E taken from the core documentation in [cm 3 ], the value of the maximum overheating ΔT is selected based on the calculations (for example, I usually take into account 50-60 degrees ). The dimension of the obtained value is [mW / cm 3 ] .

    Please note that many of the formulas that I describe are obtained empirically. Others are recorded in their final form without writing down their mathematical derivation. For those who are interested in the origin of the latter, I advise you to simply familiarize yourself with foreign literature on magnetic materials, for example, Epcos and Ferroxcube also have books.

    Now, knowing the maximum density of losses in the core, we can calculate the maximum value of the inductance at which the superheat temperature will not be exceeded above the calculated one.

    Where C M , C T , x , y are the parameters obtained empirically by the method of approximating the loss curve, and f is the conversion frequency. You can get them in two ways: by processing the data (graphs) from the documentation on your core or by building these graphs yourself. The latter method will allow you to get more accurate data, but you will need a full-fledged thermal imager.

    As an example, I will share with you these values ​​for cores from Epcos N49Its counterpart from Ferrocube is also the popular and affordable 3F3 material . Both materials make it possible to build transducers with a resonant frequency up to 1 MHz inclusively. It is also worth noting that these parameters depend on the frequency; these figures are for frequencies of 400-600 kHz . This is the most popular frequency range and material that I use.

    • With M = 4.1 * 10 -5
    • With T = 1.08 * 10 -2
    • x = 1.96
    • y = 2.27

    Next, it is worth recalling the second component of the losses in the transformer - losses in the copper winding . They are considered easy, according to our favorite Ohm's law, which additionally took into account quite logical points: our current is pulsed and it does not flow 100% of the time, that is, the duty cycle. I will not tell you how to calculate the resistance of a copper winding according to its geometry, it is too commonplace, and I will probably recall the general formula:

    Losses in copper are calculated for each winding separately, and then they add up. Now we know the losses in each layer of the “pie” and in the core. Those who wish can simulate the overheating of the transformer, for example, in Comsol or Solidworks Flow Simulation.

    Continuing the theme of copper conductors, let's recall a phenomenon such as the skin effect. If to explain “on the fingers”, then this is the effect when, with an increase in the frequency of the current flowing in the conductor, the current is “squeezed out” of the conductor (from the center to the surface) by another current - eddy current .
    Speaking more scientifically, as a result of the flow of alternating current in the conductor, a variable induction is induced, which in turn causes eddy currents. These eddy currents have a direction opposite to our main current and it turns out that they are mutually subtracted and in the center of the conductor the total current is zero.
    The logic is simple - the higher the frequency of the current flow, the more the skin effect affects and the lower the effective cross section of the conductor. You can reduce its influence by optimizing the geometry of the windings, parallelizing them and other methods that probably deserve, if not a whole book, then a large separate article.
    For our calculations, it is enough to roughly estimate the effect of the skin effect using another empirical formula:

    Where ∆δ is the thickness of the zone with zero current, f is the frequency of the transducer in [kHz] . As you can see, this effect is entirely tied to the switching frequency.

    And now let's calculate how many turns and other things we will need to manufacture a forward-running transformer. The first thing we consider is how many turns we need in the primary winding:


    Where U minIs the minimum input voltage, D is the duty cycle, f is the frequency of operation, A e is the effective core cross section. Now we consider the number of turns for the secondary winding:

    Where N 1 is the number of turns in the primary winding, D is the duty cycle, U out is the nominal output voltage, U min is the minimum input voltage.

    The next step is to calculate the inductance of the primary winding. Since the current in the winding has an impulse response, it will also depend on the inductance. We calculate it according to the following formula:

    Where μ 0 is the effective magnetic permeability, μ a is the amplitude magnetic permeability, A e- effective core section, N 1 - number of turns in the primary winding, I e - effective path length. Missing parameters, such as permeability and magnetic line length, you can take in the documentation for a specific core.

    Now the final step that we need to take is to calculate the current acting in the primary winding. This will allow in the future to calculate the cross section for the primary winding and, accordingly, the width of the conductor. The current value consists of two components and looks as follows:

    Here, it seems that all the components of the formula are already familiar and calculated, the only parameter I note is P max. This is not just the value of the rated output power, it is the total power of the converter taking into account the efficiency at least approximately (I usually put 95-97% for resonant converters) and the margin that you put in the device. In my devices, there is usually a 10% margin in power, in especially critical devices and nodes it is sometimes necessary to lay a 20-25% margin, but this causes a rise in price.

    So we got all the parameters that are necessary for the calculation and design of a planar transformer. Of course you have to calculate the cross-section for the windings yourself, but this is elementary arithmetic, which I do not want to clutter up the article. All the rest has already been calculated and all that remains is to design the boards in any CAD system.

    Total


    I hope my article will help you start using planar transformers both in your home projects and in commercial ones. This technology must be used carefully, because depending on the task, it may turn out to be more expensive than “classic” transformers.

    The use of planar transformers also undoubtedly opens up new technical possibilities, and modern Mosfets and new GaN transistors only contribute to this, making it possible to create converters with frequencies from 400 kHz and higher. However, the cost of these "capabilities" is not always low enough, and for the design of resonant converters at such frequencies requires a large set of knowledge and experience.

    But don't be upset! For any of you, even a beginner electronics engineer, it’s easier to collect topologies, for example, ZVS bridge (Full bridge). This topology allows you to get a very high efficiency and does not require any super-secret knowledge. It is only necessary to make a prototype or layout and experiment well. Good luck in exploring new horizons!

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