Revealed: Fundamental magnetic phenomena in electronic transformers

Electrons always flow along the path with the least resistance in a conductor. The structural elements on the surface of the conductor and near the surface are basically parallel to the surface of the conductor, and the resistance of electrons to transposition and flow is small. In the interior of the conductor, the structural elements are arranged in the vertical, left-right, front-back spatial arrangement, and the directional flow of electrons in them is subject to resistance in five directions (while there is only resistance in three directions on the surface). It can be seen that the resistance of electrons running near the surface of the conductor is much smaller than that inside, which leads to the skin effect of the current.

Secondly, when electrons move in the wire, a magnetic field is generated in the direction perpendicular to their movement (right-hand rule). Under the action of the magnetic field, other electrons gradually diverge toward the periphery and move toward the surface of the wire, forming a skin effect of the current.

Third, of course, there is the influence of temperature: inside the conductor, the heat generated by the resistor is not easy to dissipate, the temperature is high, the valence and electron movement rates are high, and the circuit is not very flat, which leads to a relatively narrow electron path and high resistance. On the surface of the conductor, the heat dissipation is fast, the temperature is low, the valence and electron movement rates are low, and the circuit is flat, which leads to a relatively wide electron path, so the surface resistance of the conductor is small, and the external electrons run faster, which is one of the reasons for the current skin collection. Tip discharge When a part of the conductor is made very thin and sharp, the surface area of ​​the tip is relatively large, and the density of electrons that move here by transposition is relatively large. There is even some crowding at the tip, and some electrons overflow from the tip in the crowd, thus leading to tip discharge.

Basic Phenomena of Magnetism

From the "Source of Magnetism", we know that the spin magnetic moment of the electrons outside the nucleus of some atoms cannot be offset, thus generating a residual magnetic moment. However, if the magnetic moment of each atom is still arranged chaotically, the entire object still cannot be magnetic. Only when the magnetic moments of all atoms are neatly arranged in one direction, just like many small magnets connected end to end, can the object show magnetism to the outside and become a magnetic material. This phenomenon of neat arrangement of atomic magnetic moments is called spontaneous magnetization. Since there is spontaneous magnetization inside magnetic materials, are all the atoms in the object neatly arranged in one direction? Of course not, otherwise, all steel and other materials will always be magnetic, becoming a large magnet that can always attract each other (in fact, two pieces of soft iron will not attract each other by themselves). In fact, most magnetic materials have a magnetic domain structure, which makes them not magnetic when they are not magnetized.

Magnetic domain:

The so-called magnetic domain refers to a small area inside the magnetic material. Each area contains a large number of atoms. The magnetic moments of these atoms are neatly arranged like small magnets, but the directions of the atomic magnetic moments between adjacent areas are different, as shown in the right figure. The interface between each magnetic domain is called the domain wall. Macroscopic objects generally always have many magnetic domains. In this way, the directions of the magnetic moments of the magnetic domains are different, and the result is that they cancel each other out, the vector sum is zero, and the magnetic moment of the entire object is zero, so it cannot attract other magnetic materials. In other words, magnetic materials do not show magnetism to the outside under normal circumstances. Only when the magnetic material is magnetized can it show magnetism to the outside. The figure below shows the common magnetic domain shapes in magnetic materials observed under a microscope. The left side is the common strip domain of soft magnetic materials. The black and white parts have different brightness because the directions of the magnetic moments of different magnetic domains are different. Their interface is the domain wall; the middle is the dendritic domain and the domain wall; the right side is the magnetic domain shape that can be seen in thin film materials. In actual magnetic materials, magnetic domains have various forms, such as strip domains, maze domains, wedge domains, ring domains, dendritic domains, bubble domains, etc.

Since the magnetic moments inside the magnetic domain are arranged neatly, how are the atomic magnetic moments arranged at the magnetic domain wall? On one side of the domain wall, the atomic magnetic moment points in a certain direction. Assume that the direction of the atomic magnetic moment on the other side of the domain wall is opposite. Then, inside the domain wall, the atomic magnetic moment must be in some form of transition state. In fact, the domain wall is composed of many layers of atoms. In order to achieve the turning of the magnetic moment, starting from one side, the magnetic moment of each layer of atoms is deflected by an angle relative to the direction of the magnetic moment in the magnetic domain, and the deflection angle of the atomic magnetic moment of each layer gradually increases. When it reaches the other side, the magnetic moment has completely turned to the same direction as the magnetic moment of the magnetic domain on this side. The figure above shows a typical schematic diagram of the magnetic domain wall structure.

Curie temperature:

For all magnetic materials, they are not magnetic at all temperatures. Generally, magnetic materials have a critical temperature Tc. Above this temperature, due to the violent thermal motion of atoms at high temperatures, the arrangement of atomic magnetic moments is chaotic and disordered. Below this temperature, the atomic magnetic moments are arranged neatly, spontaneous magnetization occurs, and the object becomes ferromagnetic.

Taking advantage of this feature, people have developed many control components. For example, the rice cooker we use takes advantage of the Curie point of magnetic materials. A magnet and a magnetic material with a Curie point of 105 degrees are installed in the center of the bottom of the rice cooker. When the water in the pot dries up, the temperature of the food will rise from 100 degrees. When the temperature reaches about 105 degrees, the magnetism of the magnetic material attracted by the magnet disappears, and the magnet loses its attraction to it. At this time, the spring between the magnet and the magnetic material will separate them, and at the same time, the power switch will be turned off, and the heating will stop. [page]

Common physical quantities related to magnetic materials:

Magnetic field strength: refers to the size of the magnetic field at a certain point in space, expressed by H, and its unit is ampere/meter (A/m).

Magnetization intensity: refers to the sum of magnetic moment vectors per unit volume inside the material, represented by M, and the unit is ampere/meter (A/m).

Magnetic induction intensity: The definition of magnetic induction intensity B is: B=m0(H+M), where H and M are magnetization intensity and magnetic field intensity respectively, and m0 is a coefficient called vacuum permeability. Magnetic induction intensity is also called magnetic flux density, and its unit is Tesla (T).

Magnetic permeability: The definition of magnetic permeability is m=B/m0H, which is the ratio of B to H at any point on the magnetization curve (see static magnetization of materials). Magnetic permeability actually represents the ease with which magnetic materials are magnetized, or the sensitivity of materials to external magnetic fields.

Static magnetization and common performance indicators of magnetic materials:

We already know that magnetic materials have magnetic domains inside, which are like numerous small magnets piled up in a disordered manner, and the whole has no magnetism to the outside. At this time, we say that the material is in a magnetic neutral state. However, if the material is in an environment with an external magnetic field, then these small magnets (actually the magnetic moments of the magnetic domains) will interact with the magnetic field, resulting in the rotation of the magnetic moments in the material in the direction of the external magnetic field, causing these magnetic moments to no longer cancel each other out, that is, the vector sum of all magnetic moments is not equal to zero. Under the action of an external magnetic field, the process of a magnetic material changing from a magnetic neutral state to a state showing magnetic moments to the outside is called magnetization.

So what changes actually occur in magnetic materials during the magnetization process?

In the magnetically neutral state (i.e., without an external magnetic field), the magnetic moments inside the material are arranged in a chaotic manner, the total magnetic moment is zero, and therefore the magnetization intensity displayed by the material is also zero.

When a magnetic material is placed in an external magnetic field, the magnetic moment inside the material will be affected by the force of the magnetic field, and the magnetic moment will rotate in the direction of the external magnetic field, just like a magnet rotating in a magnetic field. At this time, the magnetic moment is no longer completely chaotically arranged, but a total magnetization intensity is generated along the direction of the external magnetic field. At this time, we say that the material is magnetized. Moreover, the larger the external magnetic field, the greater the number and degree of rotation of the magnetic moment inside the material in the direction of the external magnetic field. When the external magnetic field is large enough, all the magnetic moments inside the material will be neatly arranged along the direction of the external magnetic field. At this time, the magnetization intensity displayed by the material to the outside reaches the maximum value. We say that the material is magnetized to saturation. After reaching saturation, no matter how the magnetic field is increased, the magnetization intensity of the material will no longer increase. Therefore, the magnetization intensity when the material is magnetized to saturation is called saturation magnetization intensity, which is represented by Ms.

From the above analysis, we know that the magnetization intensity of the material changes with the external magnetic field. In scientific experiments and production practice, the relationship between the magnetic field and the magnetization intensity is often drawn as a curve, called the magnetization curve, as shown in the figure. Among them, the horizontal axis represents the size of the external magnetic field, and the vertical axis represents the level of magnetization intensity. The magnetization curve can generally be divided into three stages: reversible magnetization stage, irreversible magnetization stage, and saturation stage.

In engineering, the magnetization curve is usually drawn using the relationship between magnetic intensity and magnetic field instead of the relationship between magnetization intensity and magnetic field. At this time, when the magnetization is saturated, there is a saturation magnetic induction intensity (or saturation magnetic flux density), which is represented by Bs. In the future, if there is no special explanation, we will use the B-H magnetization curve. The saturation magnetic induction intensity is an important indicator of magnetic materials.

On the magnetization curve, each point has a ratio of magnetic induction intensity to magnetic field, which is called magnetic permeability. At different stages of magnetization, the magnetic permeability of the material is also different. The magnetic permeability at the highest point is called the maximum magnetic permeability. The magnetic permeability at the starting point of magnetization is called the initial magnetic permeability. Magnetic permeability is another very important indicator of soft magnetic materials.

So, how does the magnetic moment inside the material rotate during the magnetization process? There are two ways to make the magnetic moment of the material rotate: one is domain wall displacement: when the material is magnetized, the atomic magnetic moment inside the domain wall gradually turns to the direction of the external magnetic field, and the domain wall gradually moves. In this way, the area of ​​the magnetic domain close to the direction of the external magnetic field gradually expands, while the magnetic domain opposite to the direction of the external magnetic field gradually shrinks. This method generally occurs in the non-saturation stage. The second is the consistent rotation of the magnetic moment: under the action of the external magnetic field, the magnetic moment in the magnetic domain opposite to the direction of the external magnetic field rotates as a whole in the direction of the external magnetic field, just like a magnet rotates. This method mainly occurs in the near saturation stage. [page]

The remagnetization process of magnetic materials:

Now, let's assume that the magnetic material is magnetized gradually. As the magnetic field increases, the magnetic induction intensity also increases until it reaches saturation. The entire magnetization process can be represented by the curve Oabc in the figure.

Then, the external magnetic field is gradually reduced. What will happen to the material? It is not difficult to imagine that the reduction of the external magnetic field will definitely reduce the magnetic induction of the material, but the interesting thing is that the magnetic induction does not return along the original path of cba, but decreases along the curve cde. In other words, when the external magnetic field is reduced from the saturation point, the corresponding magnetic induction is higher than the magnetic induction at the initial magnetization. It seems that the reduction of the magnetic induction is "lag" or "lag" behind the reduction of the magnetic field. This characteristic of magnetic materials is called hysteresis. Hysteresis is an extremely important feature of magnetic materials.

Due to the hysteresis phenomenon, if the external magnetic field of a magnetic material is removed from the saturation point, that is, the external magnetic field is returned to zero, the magnetic induction of the material cannot be reduced to zero at the same time, but a part of the magnetic induction Br still exists, which is called residual magnetic induction intensity, or remanence for short. The reason for the remanence phenomenon is that after the external magnetic field is reduced, the magnetic moment inside the material cannot completely return to the original direction, but will stay in a certain direction before due to various resistances. This is the so-called irreversible magnetization. Only in extremely low magnetic fields can the material undergo complete reversible magnetization. In general, magnetization is not completely reversible.

So, if we want to return the magnetic induction to zero intentionally, what should we do? It can be inferred that a reverse magnetic field should be applied to the material. Yes, applying a reverse magnetic field will further reduce the magnetic induction, and the magnetic induction is exactly zero at a certain characteristic magnetic field Hc, which is called coercive force. If the reverse magnetic field continues to increase, the magnetic induction will also reverse, and gradually tend to the reverse saturation point g as the reverse magnetic field increases. Similarly, gradually reducing the reverse magnetic field from point g, the magnetic induction will saturate along the curve ghi, and finally reach the positive saturation point c.

In this way, when the external magnetic field changes from positive to negative, the magnetic induction will change along cdefghijc. This closed curve is called a hysteresis loop. The area contained in the hysteresis loop represents the work done by the external magnetic field on the material, that is, the energy consumed, which is called hysteresis loss.

Dynamic magnetization and common performance indicators of magnetic materials:

If magnetic materials are exposed to a changing magnetic field, their magnetization undergoes some interesting changes compared to their static magnetization.

First, during dynamic magnetization, the magnetic permeability of the material changes. We already know that during repeated magnetization, the magnetic induction intensity inside the material always lags behind the change of the magnetic field, which is called hysteresis. Assuming that the magnetic field during dynamic magnetization changes sinusoidally, the hysteresis phenomenon during dynamic magnetization is manifested as the magnetic induction intensity always lags behind the change of the magnetic field by one phase, and the direct consequence is that the magnetic permeability of the material becomes a complex number. This permeability is divided into two parts: one is the part with the same direction (or phase) as the magnetic field, which is called the real part of the complex permeability, also known as elastic permeability, which represents the energy that can be stored when the material is magnetized; the other is the part that is 90 degrees in phase with the magnetic field, which is called the imaginary part of the complex permeability (loss permeability), which represents the energy consumed by the material during dynamic magnetization.

Secondly, the material will generate eddy currents during dynamic magnetization, resulting in eddy current losses. Eddy current losses are harmful in soft magnetic materials. In order to reduce eddy current losses, when manufacturing transformer cores, the materials are generally made into multiple layers of stacked, mutually insulated thin sheets. Since the core is composed of thin sheets and the thin sheets are insulated, the eddy currents generated by the thin sheets during dynamic magnetization will be confined inside the thin sheets. If the core is made of a whole piece of material, the eddy currents will be very serious because the conductor loop composed of the core material is very large. In addition, the size of the eddy current during dynamic magnetization is also related to the resistivity of the core material. For example, although the core made of ferrite is a whole, its resistivity is extremely large, so the eddy current loss can still be very low.

There are many ways of dynamic magnetization depending on the type of magnetic field during dynamic magnetization.

The most common magnetizing field is a sine wave. If the magnetic field is relatively low and the material has not yet been magnetized to saturation, then the waveform of the magnetic induction intensity is also a sine wave, so the dynamic hysteresis loop is an ellipse, as shown in the figure. If the magnetic field is large, causing the material to saturate, then the hysteresis loop will no longer be an ellipse, but will be deformed: the magnetic field becomes a peaked shape, and the waveform of the magnetic induction intensity becomes a flat top, and the entire hysteresis loop is similar to the static saturation hysteresis loop.

In some cases (such as single-ended pulse transformers), the magnetizing field to which the material is subjected is a unidirectional square wave pulse, and the hysteresis loop is shown in the figure on the right. In addition, some materials are affected by both AC and DC magnetic fields, which is called AC and DC superposition magnetization, and the hysteresis loop becomes asymmetric.