Switching Power Supply Principle and Design (Series 72)

2-1-1-18. Distributed capacitance of switching power supply transformer

The distributed capacitance of the primary and secondary coils of the switching transformer also has an important impact on the performance indicators of the switching power supply. It will form an oscillation circuit with the leakage inductance of the transformer coil to produce oscillation. When the rising or falling rate of the input pulse voltage is greater than the rising or falling rate of the oscillation waveform, the oscillation circuit absorbs energy, making the leading and trailing edges of the input pulse waveform worse; and when the rising or falling rate of the input pulse voltage is less than the rising or falling rate of the oscillation waveform, the oscillation circuit will release energy and cause the circuit to oscillate. If the quality factor of the oscillation circuit is relatively high, the circuit will produce parasitic oscillations and generate EMI interference.

In addition, the size of the distributed capacitance of the filter inductor of the switching power supply voltage input circuit has a great influence on the EMC index, so here we also need to have a full understanding of the distributed capacitance composition and principle of the filter inductor coil. In principle, there is basically no fundamental difference between the distributed capacitance of the filter inductor coil and the distributed capacitance of the switching transformer coil. Therefore, the analysis and calculation method of the distributed capacitance of the transformer coil is also effective for the filter inductor coil.

The distributed capacitance of the primary and secondary coils of the switching transformer is related to the structure. Therefore, it is difficult to accurately calculate the distributed capacitance of the primary and secondary coils of the switching transformers with different structures. Let's take the simplest double-layer coil structure of the switching transformer as an example to calculate the distributed capacitance of their primary or secondary coils.
Figure 2-41 is a schematic diagram for analyzing and calculating the distributed capacitance between the coils of the switching transformer.

Assume that the distance between the two layers of cylindrical coils is d, the height is h, and the average circumference is g. Assume that the potential difference between the two layers of coils along the height changes linearly, that is:

Ux=Ua+(Ub-Ua) x/h (2-112)

Where: Ux is the potential difference between the two layers of coils along the height change, Ua and Ub are the potential differences corresponding to x=0 and x=h respectively. Usually Ua=0, or Ua=Ub.
Assume that the electric field between the two surfaces corresponding to the two coils is approximately uniformly distributed, that is, the electric field of a flat plate capacitor, then, according to formula (2-112), the energy stored in the electric field can be obtained as:

Where, Cs is the distributed capacitance between the primary or secondary coils of the transformer; U is the operating voltage between the two coils of the transformer; Ua and Ub are the potential differences corresponding to x=0 and x=h respectively.

For transformers with only two layers of coils on the primary or secondary side, there are only two ways to connect them, as shown in Figure 2-42. In Figure 2-42-a, Ua=0, Ub=U2-U1=U; in Figure 2-42-b, Ua=Ub=(U2-U1)/2=U/2.

For Figure 2-42-a, the distributed capacitance between the primary or secondary coils of the transformer can be obtained as:

Cs=εrε0gh/3d ——Ua=0 (2-115)

For Figure 2-42-b, the distributed capacitance between the primary or secondary coils of the transformer can be obtained as:

Cs=εrε0gh/4d ——When Ua=Ub (2-116)

From this, we can see that the distributed capacitance between the primary or secondary coils of the transformer is not only related to parameters such as the height, circumference, and distance between the two coils of the transformer coil, but also to the potential difference between the two coils.