Switching Power Supply Principle and Design (Series 57)

2-1-1-8. Analysis of hysteresis loss in switching power supply transformer

Due to the magnetic coercive force of the transformer core, when the magnetic field generated by the excitation current completes magnetizing the transformer core, the magnetic flux density cannot drop to zero along with the magnetic field strength; that is, the excitation current or magnetic field strength drops from the maximum value to zero, but the magnetic flux density does not drop to zero along with the magnetic field strength, but stays at a residual magnetic flux density Br position called "remanence".

Therefore, when the AC magnetic field repeatedly magnetizes the transformer core, an additional portion of the magnetic field energy is always needed to overcome the magnetic coercive force and eliminate the residual magnetic flux. This portion of the magnetic field energy used to overcome the magnetic coercive force and eliminate the residual magnetic flux does not play a role in enhancing the magnetic flux density of the transformer core, and it is a kind of loss. In addition, because the change in magnetic induction intensity always lags behind the magnetic field intensity by one phase, this loss is called hysteresis loss.

For simplicity, we use the concepts of ideal magnetization curve and equivalent magnetization curve of transformer core to analyze the hysteresis loss of transformer core.

In Figure 2-11, straight line doa is the ideal magnetization curve of the transformer core; when the input voltage is AC, the magnetic flux density changes back and forth from the negative maximum value - Bm to the positive maximum value Bm.

When the positive half-cycle voltage of the first AC pulse is input, the magnetic flux density will rise along the ideal magnetization curve oa and reach point a, the corresponding magnetic field strength is Hm, and the magnetic flux density is Bm; when the first AC pulse voltage input ends, the magnetic field strength is 0, but the magnetic flux density does not return to 0 along the original ideal magnetization curve oa, but drops to point b along another new magnetization curve ab, that is, the residual magnetic flux density Br. Obviously, the magnetization curve ab is a new equivalent magnetization curve, because the maximum magnetic flux density increment is Bm, the maximum magnetic field intensity increment is the algebraic sum of -Hc and Hm, and the slope of the equivalent magnetization curve is equal to the ratio of the maximum magnetic flux density increment to the maximum magnetic field intensity increment.

When the positive half-cycle voltage of the first AC pulse ends and the negative half-cycle voltage begins, the magnetic flux density will continue to decrease along the bc equivalent magnetization curve and reach point c, where the corresponding magnetic field strength is -Hc and the magnetic flux density is 0; then, the amplitude of the negative half-cycle voltage remains unchanged, but the magnetic field strength continues to increase in the negative direction on the basis of -Hc, and finally reaches the negative maximum value -Hm, and the corresponding magnetic flux density increases from 0 to -Bm along the equivalent magnetization curve cd.

When the negative half-cycle voltage of the first AC pulse ends, the magnetic field strength is 0, but the magnetic flux density is not equal to 0, but it drops along another new equivalent magnetization curve de to point e, that is, the residual magnetic flux density -Br. When the positive half-cycle voltage of the input pulse arrives, the magnetic flux density rises from -Br along the equivalent magnetization curve ef to 0, and then continues to rise along the equivalent magnetization curve fa to reach point a, the corresponding magnetic field strength is Hm, and the magnetic flux density is Bm.

It can be seen from Figure 2-11 that the hysteresis loop curve abcdefa (dashed line) composed of multiple equivalent magnetization curves takes many detours compared with the ideal magnetization curve doa (solid line). Obviously, the larger the area of ​​the hysteresis loop curve encircled by the dashed line abcdefa, the more detours the equivalent magnetization curve takes. These detours will consume electromagnetic energy, and this loss is hysteresis loss.

Now let's further analyze what the area enclosed by the dotted line abcdefa represents. First, we take a small area ΔA from the closed curve abcdefa for analysis, as shown in Figure 2-12.

In Figure 2-12, ΔA is an area randomly selected from the hysteresis loop of the transformer core for analysis. The value of the ΔA area can be arbitrarily small to ensure that the magnetic permeability of the transformer core can be regarded as a constant in this area. The area ΔA corresponds to the magnetic induction intensity increment ΔB, the magnetic field intensity increment ΔH, and the time increment Δt. According to the definitions of magnetic field intensity and magnetic flux density, as well as the theorem of electromagnetic induction, the following relationship can be listed:

(2-21), (2-22), (2-23), (2-24) are completely equivalent. In (2-21), (2-22), (2-23), (2-24), ΔB is the increment of magnetic flux density, ΔH is the increment of magnetic field intensity, μ is the magnetic permeability, Δt is the time increment, or unit time; E is the induced electromotive force generated by the unit length of the wire, E = ΔB/Δt; iμ is the excitation current, which is related to the input voltage, the magnetic permeability of the transformer core, and the size of the pulse width, iμ=E*Δt/μ; since the unit of is Henry/meter (inductance per unit length of wire), we regard it as the inductance of a unit length of wire.