Switching Power Supply Principle and Design (Serial 59) Switching Power Supply Transformer Core Hysteresis Loop Measurement - Part 1

2-1-1-9. Measurement of the hysteresis loop of the switching power supply transformer core

Modern electronic equipment has higher and higher requirements for the working efficiency, volume and safety of power supplies. Many factors that determine the working efficiency, volume and safety requirements of switching power supplies are basically related to the switching transformer, and the most relevant to the technical performance of the switching transformer is the transformer core material. The hysteresis loss and eddy current loss of the transformer core material are the most important factors that determine the technical performance of the transformer core material. Therefore, it is necessary to measure the hysteresis loop of the transformer core material.

The iron core of the transformer is generally made of ferromagnetic materials. In addition to high magnetic permeability, another important magnetic characteristic of ferromagnetic materials is that during the magnetization process, the magnetic flux density B and the magnetic field intensity H are out of phase. This characteristic is called hysteresis. Therefore, when the iron core of the transformer is magnetized by an alternating magnetic field, the magnetization curve of the transformer core is also called a hysteresis loop. The hysteresis loop is a curve of the relationship between the magnetic field intensity H and the magnetic flux density B inside the medium. By testing the hysteresis loop of the transformer core, it is easy to see the main electrical properties of the transformer core material.

It is rather troublesome to conduct rigorous testing on the parameters of the hysteresis loop of ferromagnetic materials, but it is relatively simple to display the hysteresis loop with an oscilloscope. Figure 2-15 is a schematic diagram of measuring the hysteresis loop of the transformer core with an oscilloscope. In Figure 2-15, transformer T1 is the signal source. By selecting the tap of the secondary coil of transformer T1 through K1, the voltage output of the signal source can be changed; T2 is the transformer sample to be tested, and Dp is the oscilloscope; R1, R2, R3, and R4 are sampling resistors for displaying the magnetic field intensity H. The sampling voltage u1 is used as the input voltage for the oscilloscope's X-axis deflection display. The sampling voltage output can be selected through K2, thereby changing the width of the oscilloscope's X-axis deflection display; the resistor R and the capacitor C are an integration circuit. The integrated voltage u2 is output from both ends of the capacitor C as the input voltage for the oscilloscope's Y-axis deflection display to display the magnetic flux density B.

Let's analyze the working principle of Figure 2-15 in detail. According to Ampere's circuit law: the line integral of the magnetic field intensity vector along any closed path is equal to the algebraic sum of the currents passing through the area enclosed by the closed path. And Kirchhoff's law of magnetic circuit: in the magnetic field loop, the algebraic sum of the magnetic flux potential NI (N is the number of coil turns, I is the current intensity) in any winding direction is always equal to the algebraic sum of the magnetic voltage drop Hili (Hi is the magnetic field intensity, li is the average length of the magnetic field intensity Hi in the magnetic circuit). Assuming that the excitation current flowing through the primary coil of transformer T2 is i1, the magnetizing field intensity in the iron core of the sample transformer can be obtained as:

H = N1i1/l (2-32)

Where: l is the average magnetic path length of the transformer sample core. Assuming the terminal voltage of R1 is u1, we can get:

i1 = u1/R1 (2-33)

H = N1*u1/R1*l (2-34)

Formula (2-34) shows that: in Figure 2-15, the sampled voltage u1 at any time is proportional to the magnetic field strength H. Therefore, the voltage u1 can be used as the X-axis input voltage of the oscilloscope, and the horizontal direction of the oscilloscope is used to display the magnetic field strength H.
Let's see how to display the magnetic flux density B. According to Faraday's law of electromagnetic induction, under the action of the alternating magnetic field, the magnitude of the electromotive force e2 induced in the secondary coil of transformer T2 is:

e2 =N2dΦ/dt =N2SdB/dt (2-35)

In formula (2-35), e2 is the induced electromotive force generated by the secondary coil of transformer T2, N2 is the number of turns of the secondary coil of transformer T2, Φ is the magnetic flux in the transformer core, and S is the effective magnetic conductive cross-sectional area of ​​the transformer core.
The magnetic flux density B can be obtained by integrating formula (2-35):

It can be seen from equations (2-35) and (2-36) that the induced electromotive force is the differential of the magnetic flux density with respect to time, so the magnetic flux density should be the integral of the induced electromotive force with respect to time. Therefore, the display of the magnetic flux density B must be composed of an integration circuit. In Figure 2-15, the RC circuit has exactly this integration characteristic.