Switching Power Supply Principle and Design (Series 49)

2-1-1-1. Magnetization of the core of a single-excitation switching power supply transformer by pulse train

For the sake of simplicity, we equate the single-excitation transformer switching power supply to the circuit shown in Figure 2-1, in which we regard the DC input voltage as a series of DC pulse voltages, i.e., unipolar pulse voltages, through the on-off function of the control switch, to directly supply power to the switching transformer. Here we specifically call the transformer a switching transformer to indicate that the circuit shown in Figure 2-1 is different from the general power transformer circuit in terms of working principle.

In a general power transformer circuit, when the input voltage across the power transformer is 0, it means that the input end is short-circuited, because the internal resistance of the power supply can be regarded as 0; while in a switching transformer circuit, when the input voltage across the switching transformer is 0, it means that the input end is open-circuited, because the internal resistance of the power supply can be regarded as infinite.

In Figure 2-1, when a set of DC pulse voltages with serial numbers 1, 2, 3, ... are respectively applied to both ends of the primary coils a and b of the switching transformer, an excitation current will flow through the primary coil of the switching transformer. At the same time, a magnetic field will be generated in the iron core of the switching transformer. Under the action of the magnetic field with a magnetic field strength of H, a magnetic line flux with a magnetic flux density of B will be generated, referred to as magnetic flux, and represented by "Φ".

The process in which the magnetic flux density B or magnetic flux Φ changes under the influence of the magnetic field strength H in the transformer core is called the magnetization process; therefore, the curve used to describe the corresponding changes between the magnetic flux density B and the magnetic field strength H is called the magnetization curve. Figure 2-2 is a curve diagram showing the corresponding changes between the magnetic flux density B and the magnetic field strength H when the single-excitation switching transformer core is magnetized.

By the way, in the analysis of the magnetization process of the transformer core, the two names of magnetic flux density and magnetic induction intensity are often used. There is no difference between these two names in essence and they can be used interchangeably. Different names are used in different occasions just for convenience.

If the core of the switching transformer has never been magnetized by any magnetic field before and the volt-second capacity of the switching transformer is large enough, then when the first DC pulse voltage is applied to the ends of the primary coils a and b of the transformer, an excitation current will flow in the primary coil of the transformer and generate a magnetic field in the core of the transformer.

Under the action of magnetic field intensity H, the magnetic induction intensity B in the transformer core will rise according to the 0-1 magnetization curve in Figure 2-2; when the first DC pulse voltage is about to end, the magnetic field intensity reaches the first maximum value Hm1, and the magnetic induction intensity will be magnetized to the first maximum value Bm1 by the magnetic field intensity; thus, a magnetic induction intensity increment ΔB is generated, ΔB = Bm1- 0. The increase in magnetic induction intensity indicates that the magnetic field generated by the excitation current flowing through the primary coil of the transformer is magnetizing the transformer core.

When the sequence pulse voltage is applied to the primary coils a and b of the switching transformer, a magnetic field will be generated in the transformer core. This magnetic field is completely generated by the excitation current flowing through the primary coil of the transformer. The excitation current flowing through the primary coil of the transformer is:

In formula (2-8), iμ is the excitation current flowing through the primary coil of the transformer, E is the voltage applied to both ends of the primary coil of the transformer, L1 is the inductance of the primary coil of the transformer, t is the time, and iμ(0) is the initial current, that is, the excitation current flowing through the primary coil of the transformer at t = 0.

If the duty factor (duty cycle) of the pulse sequence satisfies that the magnetizing current drops to zero before the next pulse enters, that is, the switching power supply operates in the critical continuous or discontinuous state of current.
After the first DC pulse ends, since the primary coil of the switching transformer is open, although the excitation current flowing through the primary coil of the transformer drops to zero, the magnetic field intensity H will not drop to zero immediately; at this time, the primary and secondary coils of the transformer will simultaneously generate back electromotive force. Due to the effect of the back electromotive force, current will flow in the primary and secondary coil loops of the transformer. This loop current is an induced current, or induced current.

When the first DC pulse ends, if the primary coil of the switching transformer is not open, the back electromotive force will reversely charge the input voltage; if the primary coil of the switching transformer is open, the back electromotive force will charge and discharge the distributed capacitance in the primary coil, thereby generating high-frequency oscillations inside the primary coil.

The induced current generated by the back electromotive force will generate a reverse magnetic field in the transformer core, demagnetizing the transformer core, and the magnetic field intensity H begins to gradually decrease from the first maximum value Hm1 to 0; but the magnetic flux density B in the transformer core does not return to the original path of the 0-1 magnetization curve during magnetization, following the magnetic field intensity to zero, but returns to point 2 according to another new magnetization curve 1-2; that is: the first residual magnetic flux density Br1. Therefore, people are accustomed to calling the value of the magnetic flux density at point 2 as residual magnetic flux density, or "residual magnetism" for short. The residual magnetism of the transformer core indicates that the transformer core has memory characteristics, which is a basic characteristic of ferromagnetic materials.

——Regarding the concept that the primary and secondary coils of the transformer will simultaneously generate back electromotive force to demagnetize the transformer core, please refer to the content of Chapter 1 "1-5-1. Working Principle of Single-Excitation Transformer Switching Power Supply".