Switching Power Supply Principle and Design (Series 67)

2-1-1-14. Measurement of pulse permeability and average permeability of transformer core

We have already introduced the concepts of pulse permeability of pulse transformer and average permeability of switching transformer in the previous equations (2-11) and (2-12). The pulse permeability μ△ of pulse transformer is expressed by the following equation:

μ△=△B/△H —— Pulse transformer (2-11)

The average magnetic permeability μa of the switching transformer is:

μa=△Ba/△Ha —— Switching transformer (2-12)

In the formula (2-11), μ△ is called the pulse static magnetization coefficient, or the pulse permeability of the pulse transformer; △B is the increment of magnetic flux density in the pulse transformer core; △H is the increment of magnetic field strength in the pulse transformer core. In the formula (2-12), μa is the average permeability of the switching transformer; △Ba is the increment of average magnetic flux density in the switching transformer core; △Ha is the increment of average magnetic field strength in the switching transformer core.

To a certain extent, switching transformers are also pulse transformers, because they input voltage pulses; but the amplitude and width of the pulse voltage input of a general pulse transformer are basically fixed, and it is a unipolar voltage pulse, and the area of ​​its hysteresis loop is relatively small, so the transformer's pulse permeability μ△ can almost be regarded as a constant. However, the amplitude and width of the switching transformer input pulse voltage are generally not fixed, and the area of ​​its hysteresis loop varies relatively widely, and the range of variation of the core permeability is also relatively large, especially for double-excitation switching transformers. Therefore, it can only be described by the concept of average permeability μa.

If it is not particularly emphasized that the input voltage of the pulse transformer is a unipolar pulse voltage, and the amplitude and width of the input pulse voltage are basically fixed; then, it is not a bad idea to use formula (2-11) to calculate the average magnetic permeability of the switching transformer; because when people measure the average magnetic permeability μa of the switching transformer, it is impossible to use many pulse voltages with different amplitudes and widths to test the switching transformers one by one, and then take the average value of the test results.

We can imagine that if we only select one group of voltage pulses with different amplitudes and widths from the many voltage pulses used for testing, whose amplitude and width are relatively medium among these test voltage pulses, then there will not be much difference in using the test result of formula (2-11) to replace the result of formula (2-12); in this way, the measurement of the average magnetic permeability of the transformer becomes simple. Therefore, when we test the average magnetic permeability of the switching transformer, we can also use formula (2-11) to measure it, but we must choose a more appropriate test pulse voltage amplitude and width.

Based on this idea, the measurement method of the average permeability of the switching transformer is basically the same as the measurement method of the pulse permeability of the pulse transformer. The average permeability of the switching transformer can be measured while measuring the hysteresis loss and eddy current loss of the transformer core.

According to Ampere's circuit law of magnetic field intensity: the line integral of magnetic field intensity along any closed loop l is equal to the algebraic sum of all current intensities passing through the loop. Or Kirchhoff's law of magnetic circuit: in the magnetic field loop, the algebraic sum of magnetic flux potential NI (N is the number of coil turns, I is the current intensity) in any circling direction is always equal to the algebraic sum of magnetic voltage drop Hili (Hi is the magnetic field intensity, li is the average length of the magnetic field intensity in the magnetic circuit). It can also be interpreted as: the product of the average value of magnetic field intensity and the average length l of any closed loop is equal to the algebraic sum of all current intensities passing through the loop. This law has been used in the previous equations (2-32) and (2-72), and is repeated here, that is:

△H●l=N●△I (2-90)

In formula (2-90), △H is the increment of magnetic field strength in the transformer core, N is the number of turns of the transformer primary coil, and △I is the increment of excitation current flowing through the transformer primary coil.

It can be seen from Figure 2-26 or Figure 2-28 that △I in formula (2-90) is the maximum value of the excitation current Iμm. In addition, according to the relationship between input voltage, magnetic flux, magnetic flux change rate, and magnetic flux and magnetic flux density in the electromagnetic induction theorem, we can get:

μa≈μ△=△B/△H=Ulτ/SNIμm (2-91)

In the formula (2-91), μa is the average magnetic permeability of the switching transformer; μ△ is the pulse magnetic permeability of the pulse transformer, or the pulse static magnetizing coefficient; △B is the increment of magnetic flux density in the switching transformer core under the conditions of a certain test pulse voltage amplitude and width; △H is the increment of magnetic field strength in the switching transformer core under the conditions of a certain test pulse voltage amplitude and width; U is the amplitude of the input pulse voltage; S is the cross-sectional area of ​​the transformer core; N is the number of turns of the primary coil of the switching transformer; l is the average length of the magnetic circuit of the switching transformer core; Iμm is the maximum value of the excitation current flowing through the primary coil of the switching transformer; τ is the width of the voltage pulse.