Basic concepts and working principles of transformers

Modern electronic equipment has higher and higher technical performance indicators such as power supply efficiency, volume and safety requirements. Among the many factors that determine these technical performance indicators in the switching power supply, they are basically related to the technical indicators of the switching transformer. The switching power supply transformer is a key component in the switching power supply. Therefore, in this section, we will conduct a theoretical analysis of many technical parameters related to the switching power supply transformer in great detail.

When analyzing the working principle of the switching transformer, we will inevitably involve concepts such as magnetic field intensity H, magnetic induction intensity B, and magnetic flux. For this reason, we first briefly introduce their definitions and concepts here.

Electric fields and magnetic fields exist everywhere in nature. There must be an electric field around a charged object. Under the action of the electric field, the surrounding objects will be induced to become charged. Similarly, there must be a magnetic field around a magnetic object. Under the action of the magnetic field, the surrounding objects will also be induced to produce magnetic flux.

Modern magnetic research shows that all magnetic phenomena originate from electric current. Magnetic materials or magnetic induction are no exception. The origin of ferromagnetic phenomena is due to the microcurrent formed by the movement of electrons outside the atomic nucleus inside the material, also known as molecular current. The collective effect of these microcurrents makes the material present various macroscopic magnetic properties to the outside. Because each microcurrent produces a magnetic effect, a unit of microcurrent is called a magnetic dipole. Therefore, the magnitude of the magnetic field strength is related to the distribution of magnetic dipoles.

Under macroscopic conditions, magnetic field strength can be defined as the size of the magnetic field at a certain point in space. We know that the concept of electric field strength is defined by the force generated by a unit charge in an electric field, but it is difficult to find a magnetic substance similar to a "unit charge" or a "unit magnetic field" in a magnetic field to define the magnetic field strength. For this reason, the definition of electric field strength has to borrow the concept of current flowing through a conductor of unit length to define the magnetic field strength, but this concept should be used to define the electromagnetic induction strength, because electromagnetic fields can induce each other.

Fortunately, the electromagnetic induction intensity is not only related to the current flowing through the conductor per unit length, but also to the properties of the medium. Therefore, the electromagnetic induction intensity can be expressed by multiplying the magnetic field intensity by a coefficient representing the medium properties. This coefficient representing the medium properties is called magnetic permeability.

In electromagnetic field theory, the definition of magnetic field intensity H is: the ratio of the force F of the magnetic field on a straight wire in a vacuum perpendicular to the magnetic field to the product I of the current I and the length of the wire is called the magnetic field intensity at the location of the current-carrying straight wire. Or: when a 1-meter-long wire in a vacuum perpendicular to the magnetic field passes through a current of 1 ampere and is subjected to a magnetic field force of 1 Newton, the magnetic field intensity at the location of the wire is 1 Oersted.

Electromagnetic induction intensity is also generally called magnetic induction intensity. Since the magnetic induction intensity and the magnetic field intensity in a vacuum are exactly equal in value, the definition of magnetic induction intensity in a vacuum is exactly the same as the definition of magnetic field intensity in a vacuum. The difference is that the magnetic field intensity H has nothing to do with the properties of the medium, while the magnetic induction intensity B is related to the properties of the medium.

However, many books use the above method to define the intensity of electromagnetic induction, which is unreasonable; because the intensity of electromagnetic induction is related to the properties of the medium, then, for example, in a solid medium, it is difficult for people to use the method of a straight current conducting wire to measure the force exerted on a straight current conducting wire in a magnetic field. Since it cannot be measured, it should not be assumed that the force exerted on it is related to the properties of the medium. In fact, the magnetic permeability of the medium is not measured by force, but by electromagnetic induction. The intensity of electromagnetic induction is generally referred to as magnetic induction. The magnetic field intensity H and the magnetic induction intensity B are expressed by the following formula:

In the formula (2-1), the unit of magnetic field intensity H is Oersted (Oe), the unit of force F is Newton (N), the unit of current I is Ampere (A), and the unit of wire length is meter (m). In the formula (2-2), the unit of magnetic induction intensity B is Tesla (T), is the magnetic permeability, the unit is Henry/meter (H/m), and the magnetic permeability in vacuum is recorded as, = 1. Because the unit of Tesla is too large, people often use Gauss (Gs) as the unit of magnetic induction intensity B. 1 Tesla is equal to 10000 gauss (1T=104Gs).

Since magnetic phenomena can be vividly represented by magnetic lines of force, the magnetic induction intensity B can be defined as the density of magnetic line flux, that is, the magnetic line flux per unit area. The magnetic line flux density can be referred to as magnetic flux density. Therefore, the electromagnetic induction intensity can be expressed as:

In formula (2-3), the unit of magnetic flux density B is Tesla (T), the unit of magnetic flux is Weber (Wb), and the unit of area is square meter (m2). If the magnetic flux density B is expressed in Gauss (Gs), the unit of magnetic flux is Maxwell (Mx), and the unit of area is square centimeter (cm2). Among them, 1 Tesla is equal to 10,000 Gauss (1T = 104Gs), and 1 Weber is equal to 10,000 Maxwell (1Wb = 104Mx).

In addition to being called magnetic induction intensity and magnetic flux density, many people also call it magnetic induction density. So far, it has been explained that electromagnetic induction intensity B, magnetic induction intensity B, magnetic flux density B, magnetic induction density B, etc. are completely interchangeable in concept.

By the way, in other books, some people define the magnetic induction intensity B as: B = (H+M), where H and M are the magnetization intensity and magnetic field intensity respectively, and M is the vacuum permeability. For simplicity, we do not intend to introduce too many other concepts. If there is a special need, the definition of formula (2-2) can be used to convert with other concepts.

It is also necessary to point out that the magnetic permeability used to represent the properties of the medium is not a constant, but a nonlinear function. It is not only related to the medium and the magnetic field strength, but also to the temperature. Therefore, the definition of magnetic permeability is not a simple coefficient, but people are using it to cover up the inherent relationship between the magnetic field strength and the electromagnetic induction strength, which has not yet been fully revealed by humans. However, for the sake of simplicity, when we analyze the magnetic field strength and the electromagnetic induction strength, we can still treat the magnetic permeability as a constant, or take its average value or effective value for calculation.

Switching transformers generally work in a switching state; when the input voltage is a DC pulse voltage, it is called a unipolar pulse input, such as a single-excitation transformer switching power supply; when the input voltage is an AC pulse voltage, it is called a bipolar pulse input, such as a dual-excitation transformer switching power supply; therefore, the switching transformer can also be called a pulse transformer, because its input voltage is a sequence of pulses; however, when it comes to a real comparison, there are still differences in the working principles between the switching transformer and the pulse transformer, because the switching transformer is also divided into forward and reverse outputs, which will be explained in detail later. Assume that the cross-section of the switching transformer core is S. When a rectangular pulse voltage with an amplitude of U and a width of τ is applied to the primary coil of the switching transformer, an excitation current flows through the primary coil of the switching transformer; at the same time, a magnetic field will be generated in the core of the switching transformer, and the core of the transformer will be magnetized. Under the action of a magnetic field with a magnetic field strength of H, a magnetic flux line flux with a magnetic flux density of B will be generated, referred to as magnetic flux, represented by ""; the process in which the magnetic flux density B or magnetic flux changes under the action of the magnetic field strength H is called the magnetization process. The so-called excitation current is the current that magnetizes and demagnetizes the transformer core.

According to Faraday's electromagnetic induction theorem, when the magnetic field or magnetic flux density in the inductor changes, an induced electromotive force will be generated in the coil; the induced electromotive force in the coil is:

Where N is the number of turns of the primary coil of the switching transformer; is the magnetic flux of the transformer core; and B is the magnetic induction intensity or average magnetic flux density of the transformer core.

The concept of average value of magnetic flux density is introduced here because the magnetic flux in the transformer core is not uniformly distributed, and the magnetic flux density is related to the actual distribution of magnetic flux on the core or the cross section of the core. Therefore, when analyzing certain macroscopic characteristics such as transformers, it is sometimes necessary to use the concept of average value to simplify the problem.

From formula (2-4), it can be seen that the change of magnetic flux density is carried out at a constant speed, that is:

Assuming that the initial value of the magnetic flux density is B(0) = Bo (take t = 0), when t > 0, the magnetic flux density increases linearly, that is:

When t = τ, that is, when the time reaches the trailing edge of the pulse, the magnetic flux density reaches its maximum value Bm = B(τ). The magnetic flux density increment (the difference between the initial value and the final value of the magnetic flux density) ∆B = B(τ)-B(0) = Bm-Bo. When the input voltage is a sequence of unipolar rectangular pulses, according to the law of electromagnetic induction, a magnetic flux density increment will be generated in the transformer core corresponding to it, that is:

If the influence of eddy current can be ignored, the average value of magnetic field intensity H depends on the properties of the magnetic material. The increase of magnetizing current in the primary coil of the transformer is proportional to H. In the straight line section of the characteristic curve, magnetic field intensity H, magnetizing current and magnetic flux density B all change linearly.

After the pulse voltage ends (t>τ), the magnetizing current in the transformer will decrease according to the transformer output circuit characteristics, that is, the law determined by the circuit parameters, and the magnetic field strength and flux density in the transformer core will also weaken. At this time, a reverse polarity voltage, that is, back electromotive force, is generated in the transformer coil. The transformer output circuit characteristics are actually the forward and flyback voltage output circuit characteristics that have been introduced in detail in Chapter 1.

Although the above analysis is based on unipolar pulse input as an example, it is also valid for bipolar pulse input. In terms of method, it is only necessary to regard the bipolar pulse input as two unipolar pulse inputs separately.

The switching power supply transformer is divided into single-excitation switching power supply transformer and dual-excitation switching power supply transformer. The working principle and structure of the two switching power supply transformers are not exactly the same. The input voltage of the single-excitation switching power supply transformer is a unipolar pulse, and it is also divided into forward and reverse voltage output; while the input voltage of the dual-excitation switching power supply transformer is a bipolar pulse, which is generally a bipolar pulse voltage output.

In addition, in order to prevent magnetic saturation, an air gap is generally required in the core of a single-excitation switching power supply transformer; while the core magnetic flux density variation range of a dual-excitation switching power supply transformer is relatively large, and magnetic saturation is generally not prone to occur. Therefore, an air gap is generally not required.

Single-excitation switching power supply transformers are divided into forward and flyback types, and the technical parameter requirements for the two types of switching power supply transformers are also different; the primary inductance requirement for the forward switching power supply transformer is relatively large, while the requirement for the primary inductance of the flyback switching power supply transformer is related to the output power.

The hysteresis loss of the iron core of the dual-excitation switching power supply transformer is relatively large, while the hysteresis loss of the iron core of the single-excitation switching power supply transformer is relatively small. These parameters are basically related to the magnetization curve of the transformer core. Historical anecdotes:

The concepts of magnetic induction intensity and magnetic field intensity have always been confusing. This is due to historical reasons. In 1900, the International Conference of Electrologists agreed with the proposal of the American Institute of Electrical Engineers (AIEE) to decide that the unit name of the CGSM system magnetic field intensity is Gauss, which is actually a misunderstanding. The original proposal of AIEE was to use Gauss as the unit of magnetic flux density B, but it was mistakenly translated into magnetic field intensity when translated into French, causing confusion. At that time, the vacuum magnetic permeability in the CGSM system and the Gauss unit system was a dimensionless pure number 1, so there was no difference between B and H in the vacuum, resulting in B and H using the same unit - Gauss.

It was not until July 1930 that the International Electrotechnical Commission made a decision based on extensive discussions: the magnetic permeability of vacuum has dimensions, B and H have different properties, B and D correspond, H and E correspond, and in the CGSM unit system, Gauss is the unit of B and Oersted is the unit of H.

It was not until the 11th International Conference on Weights and Measures in 1960 that the concepts of magnetic induction intensity and magnetic field intensity were basically unified, when the system of units based on six basic units, namely meter, kilogram, second, ampere, kelvin and candela, was named the International System of Units and expressed as SI (the abbreviation of the French Le System International el"Unites).

Due to historical reasons, two units are often used in electromagnetic units, one is the SI international unit system, and the other is the CGSM (centimeter, gram, second) absolute unit system; the main difference between the two units is that in the CGSM unit system, the vacuum permeability , in SI units, the magnetic permeability of a vacuum Therefore, we only need to multiply the CGSM unit by a coefficient to convert the CGSM unit into the SI unit, which can generally be written asor, you can see this symbol to know that the SI unit system is used; but here or It is generally called relative permeability, which is a coefficient without units. You must bring your unit.