Switching Power Supply Principle and Design (Series 78)

In a flyback switching power supply, when the core area of ​​the switching transformer is fixed, the volt-second capacity of the switching transformer is mainly determined by the size of the flux increment ⊿B (⊿B = Bm-Br) and the number of turns N1 of the primary coil of the switching transformer, as shown in Figure 2-50.

As can be seen from Figure 2-50, the magnetic induction intensity is determined by the magnetic field intensity, that is, the magnetic flux increment ⊿B is also determined by the magnetic field intensity. In Figure 2-50, the dotted line B is the initial magnetization curve of the switching transformer core. The so-called initial magnetization curve is the magnetization curve when the switching transformer core is not yet magnetized and is used for the first time. Once the switching transformer core is magnetized, the initial magnetization curve no longer exists. Therefore, in the switching transformer, the magnetization of the switching transformer core is generally not carried out according to the initial magnetization curve, but as the magnetic field intensity increases and decreases, the magnetic induction intensity will change back and forth along the magnetization curves ab and ba, or the magnetization curves cd and dc. When the magnetic field intensity increases, the magnetic field intensity magnetizes the switching transformer core; when the magnetic field intensity decreases, the magnetic field intensity demagnetizes the switching transformer core.

Figure 50 Magnetic induction intensity is determined by the magnetic field intensity

In Figure 2-50, when the magnetic field strength increases from 0 to H1, the corresponding magnetic induction intensity also increases from Br1 along the magnetization curve ab to Bm1; and when the magnetic field strength decreases from H1 to 0, the corresponding magnetic induction intensity will decrease from Bm1 along the magnetization curve ba to Br1. If the direction of the magnetic flux is not considered, the change in magnetic flux is ⊿B1, that is, the magnetic flux increment ⊿B1 = Bm1-Br1.

If the magnetic field strength is further increased from 0 to H2, the magnetization curve will follow the curves cd and dc, and the corresponding magnetic flux increment ⊿B2 = Bm2-Br2.

It can be seen from Figure 2-50 that for different magnetic field strengths, that is, different excitation currents, the change in magnetic flux is also different, and the change in magnetic flux is not linearly related to the magnetic field strength. Figure 2-51 is a function curve of the mutual change of magnetic induction intensity and magnetic field intensity. In Figure 2-51, curve B is the curve of the corresponding change of magnetic induction intensity and magnetic field intensity; curve μ is the curve of the corresponding change of magnetic permeability and magnetic field intensity; curve iμ is the curve of the corresponding change of excitation current and magnetic field intensity.

Figure 51. Function curve of the mutual change of magnetic induction intensity and magnetic field intensity

For Figure 2-51:

B=μH (2-147)

iμ= Uτ /L （2-148）

In formulas (2-147) and (2-148), B is the magnetic induction intensity, H is the magnetic field intensity, μ is the magnetic permeability, iμ is the excitation current, U is the voltage applied to the primary coil of the switching transformer, L is the inductance of the primary coil of the switching transformer, and τ is the pulse width.

As can be seen from Figure 2-51, the place with the largest magnetic permeability is not the place where the magnetic induction intensity or magnetic field intensity is the smallest or largest, but the place where the magnetic induction intensity or magnetic field intensity is at a certain intermediate value. After the magnetic permeability reaches the maximum value, the magnetic permeability will drop rapidly as the magnetic induction intensity or magnetic field intensity increases; when the magnetic permeability drops to nearly 0, we think that the switching transformer core has begun to saturate, as shown in Bs and Hs in the figure. At this time, the inductance of the primary coil of the switching transformer will drop to 0, and the excitation current will become infinite.

[page]

Figure 2-52 (a) Schematic diagram of a switching transformer core with an air gap in the middle

Figure 2-52 (b) Magnetization curve of the switching transformer core with an air gap in the middle

Since the permeability has a large variation range and is prone to saturation, the switching transformer used in general switching power supplies must leave an air gap in the middle of the switching transformer core. Figure 2-52-a) is a schematic diagram of a switching transformer core with an air gap in the middle, and Figure 2-52-b) is a magnetization curve diagram of a switching transformer core with an air gap in the middle, and a schematic diagram for calculating the optimal air gap length of the switching transformer core.

In Figure 2-52-b), the dotted line is the magnetization curve of the switching transformer core without an air gap, and the solid line is the magnetization curve of the switching transformer core with an air gap; curve b is the equivalent magnetization curve of the switching transformer core with an air gap, and its equivalent magnetic permeability, that is, the slope of the curve is tgβ; μa is the average magnetic permeability of the switching transformer core with an air gap; μc is the magnetic permeability of the switching transformer core when no air gap is left.

As can be seen from Figure 2-52, the longer the air gap length of the switching transformer core is, the smaller its average magnetic permeability is, and the switching transformer core is not easy to saturate; but the smaller the average magnetic permeability of the switching transformer core is, the greater the leakage inductance between the primary and secondary coils of the switching transformer. Therefore, the design of the air gap length of the switching transformer core is a relatively complex calculation process, and it must also be considered comprehensively based on the output power of the switching power supply and the voltage variation range (duty cycle variation range). However, we can measure the volt-second capacity of the switching transformer and check whether the air gap length of the switching transformer core is appropriate.

Regarding the design of the air gap length of the switching transformer core, please refer to the previous section "2-1-13. Selection of the air gap of the switching transformer core". More detailed content will be analyzed later when designing the switching transformer.

It should be pointed out here that for the same switching transformer, due to the different duty cycles when the switching power supply is working, or the duty cycle is constantly changing, the magnetization curve of the switching transformer core is also constantly changing, that is: the maximum magnetic induction intensity Bm and the residual magnetism Br in the magnetization curve are not a fixed value; when the duty cycle is relatively large, due to the increase in the excitation current, the maximum magnetic induction intensity Bm will also increase accordingly, at this time the current of the secondary coil of the switching transformer will also increase, thereby increasing the demagnetization current. The increase in demagnetization current is very beneficial to reducing the residual magnetism Br of the switching transformer core, so that the flux increment ⊿B also increases accordingly. Therefore, the formula (2-146) used to calculate the volt-second capacity of the switching transformer is actually only meaningful when calculating the maximum volt-second capacity of the switching transformer.

In addition, the curve of magnetic permeability in Figure 2-51 is not static, and it is greatly affected by temperature. Because, at present, the core materials used in most switch transformers are basically ferrite magnetic materials. These ferrite transformer cores are made by mixing a variety of ferromagnetic metal materials with non-metallic materials, and then stamping the ferromagnetic mixed materials into shape according to the ceramic production process, and finally sintering them at high temperature. Since ferrites are metal oxides, most metal oxides have the common properties of semiconductor materials, that is, the resistivity changes with temperature, and the rate of change is very large. Thermistors are manufactured based on these properties. Every time the temperature doubles, the resistivity will drop (or rise) several times, or even hundreds of times. Most thermistor materials are metal oxides, so ferrites also have the properties of thermistors.

Although the resistivity of the ferrite transformer core is very high at room temperature, when the temperature rises, the resistivity will drop rapidly, causing the eddy current loss to increase; when the temperature rises to a certain limit, the effective inductance of the transformer primary coil drops to almost 0, which is equivalent to the magnetic permeability also dropping to 0, or equivalent to the transformer secondary coil being short-circuited. The temperature at this time is called the Curie temperature, represented by Tc. Therefore, the resistivity and magnetic permeability of ferrite are unstable, and the operating temperature of ferrite switching transformers cannot be very high, generally not exceeding. Figure 2-53 is a curve of the initial magnetic permeability μi of the high magnetic permeability material H5C4 series core of Japan TDK Company as a function of temperature. Its Curie temperature Tc is about 120℃.

Figure 2-53 Curve of initial magnetic permeability μi of high magnetic permeability material H5C4 series core of TDK Corporation of Japan versus temperature