Let’s discuss the relationship between transformers and inductors again.
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The issue discussed this time is the relationship between transformers and inductors. It should be noted that the scope of this topic is limited to "the relationship between transformers and inductors" and no other issues should be involved. This is just to be able to draw a conclusion.
Last time this issue was discussed in the forum, someone said that the coil of the transformer has nothing to do with the transformer design. It may be because they think that the inductance of the source and secondary windings is not considered in the actual design. When testing the transformer, the source and secondary inductance are measured only because the inductance can easily test the quality of the transformer, because the inductance of the coil can reflect the "quality control parameters" of the coil. My colleague also told me about this result, but I still want to use the problem of transformers and inductors as a breakthrough in the design.
Known basic problems
1. Current can generate a magnetic field, and the intensity H of the magnetic field is related to the line integral of the current flowing through the conductor. Here, the conductor is regarded as a wire. For a strict discussion, please refer to "Ampere's Loop Theorem".
Select a loop in space (called Ampere's loop) and define a positive direction. Then the line integral of the magnetic induction intensity on the loop is equal to the total current passing through the loop (the positive direction of the current is determined by the right-hand rule) multiplied by the magnetic permeability in the vacuum.
We assume that the wire is the wire of the transformer. As for what kind of core the transformer is, we will not discuss the shape of the transformer or consider it. First, consider the transformer as a "mouth"-shaped transformer without leakage inductance. Of course, I also know that B=uH, but let's not discuss it first.
2. First consider a cross-sectional area of the transformer. The line integral of the multiple strands of the transformer wire forms a magnetic field H, which is only distributed in the "mouth"-shaped transformer skeleton. That is, there is no leakage inductance.
3. The transformer can transform voltage and current at the same time. There should be no objection to this. Don't argue about isolation transformers or something. The reason for the voltage transformation is that the magnetic field changes of the source winding and the secondary winding of the coil are the same. The source side generates a changing magnetic field H and the secondary side converts the magnetic field H.
4. Whether the source side or the secondary side is a "coil" individually, it can also be said that they are inductors. Then let me talk about the "relationship between inductance and transformer"
5. Inductance is an inherent property of the coil. Once the coil is determined, the inductance is determined. Don't consider the transformer material, leakage inductance, magnetic saturation, shape, wire resistance and other issues first.
6. According to Ampere's loop theorem, the more turns the coil has, the stronger the intensity H of the magnetic field it generates. The stronger H is, the larger the range of magnetic field change is, and the more energy can be converted. The larger the capacity of the transformer is.
7. The magnetic field intensity is not only related to the current intensity I, but also to the area S. Let's ignore the area S for now. Just talking about the current I, if you want to unilaterally increase the rate of change of the current, it will be affected by the inductance. Due to the effect of inductance: the current cannot change suddenly, so the more turns the coil has, the greater the inductance is, and the greater the inductance is, the greater the resistance to the current is. For the transformer, the more turns the coil has, the lower the rate of change of the current is, because the greater the inductance of the coil is.
8. Then the first design problem of the transformer comes, how to design a reasonable inductance value? At first, I thought it was relatively simple. I thought that the rate of change of the transformer's H was only related to the inductance of the source side. In fact, it is also related to the inductance and load of the secondary side. If the inductance of the secondary side is very small, the induced electromotive force that can be generated will be lower, so the coil on the secondary side cannot be too few. Although the turns ratio meets the requirements of the transformation ratio, it may not be able to generate enough electromotive force. If the inductance of the secondary side is larger, the electromotive force that can be generated will be higher, but the current cannot be too large.
9. The faster the frequency of the transformer, the faster the rate of change of the magnetic field H. This is why the switching power supply can reduce the size of the transformer. However, the frequency cannot be too fast. If it is too fast, the rate of change of the current will be low due to the effect of the inductance, and the capacity of the transformer will also be affected.
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