Switching Power Supply Principle and Design (Series 54)

2-1-1-5． Calculation of the volt-second capacity and primary coil turns of a double-excitation switching power supply transformer

In Figure 2-7, for the dual-excitation switching power supply transformer, each time an AC pulse voltage is input, except for the first input pulse whose magnetic flux density changes from 0 to the maximum value Bm, the range of the magnetic flux density changes for the remaining input pulses is from the negative maximum value -Bm to the positive maximum value Bm, or from the positive maximum value Bm to the negative maximum value -Bm, that is: each time an AC pulse voltage is input, the increment ΔB of the magnetic flux density is twice the maximum magnetic flux density Bm (2Bm).

Therefore, substituting this result into equations (2-13) and (2-14), we can obtain:

Formulas (2-17) and (2-18) are the formulas for calculating the number of turns of the primary coil N1 winding of the dual-excitation switching power supply transformer. In the formula, N1 is the minimum number of turns of the primary coil N1 winding of the transformer, S is the magnetic conductive area of ​​the transformer core (unit: square centimeters), Bm is the maximum magnetic flux density of the transformer core (unit: Gauss), τ is the pulse width, or the width of the power switch conduction time (unit: seconds), E is the amplitude of the pulse voltage, that is, the operating voltage amplitude of the switching power supply, in volts, and F is the operating frequency of the switching power supply, in Hertz.

Similarly, we define the product of the input pulse voltage amplitude E and the pulse width τ in formula (2-17) as the volt-second capacity of the transformer, expressed as US (unit: volt-second), that is: US = E×τ.

It should also be pointed out here that the use of (2-17) and (2-18) to calculate the number of turns of the primary coil N1 winding of the double-excitation switching power supply transformer is conditional, that is, the volt-second capacity Us of the positive and negative half-cycles of the input AC pulse voltage must be equal. If they are not equal, the flux density increment ΔB in (2-17) and (2-18) cannot be expressed by 2Bm, but should be expressed by the difference between the two actual variables Bm and -Bm, that is: ΔB = Bm-(-Bm). Here, it is more appropriate to regard Bm and -Bm as variables.

Comparing equations (2-17) and (2-18) with equation (2-16), it is easy to see that, under the condition that the magnetic conductive area of ​​the transformer core and the input voltage amplitude are completely equal, the range of variation of the magnetic flux density in the iron core of the dual-excitation switching power supply transformer is much larger than that in the iron core of the single-excitation switching power supply transformer; or under the condition that the volt-second capacity is completely equal, the number of turns of the primary coil of the dual-excitation switching power supply transformer is much less than that of the primary coil of the single-excitation switching power supply transformer. Therefore, for dual-excitation switching power supply transformers, it is generally not necessary to leave an air gap in the transformer core.

In equations (2-17) and (2-18), for the core of a high-power dual-excitation switching power supply transformer, the maximum magnetic flux density Bm is generally not to exceed 3000 Gauss. If the Bm value is too high, when the switching device is accidentally triggered and the phase in Figure 2-7 is wrong, it is easy to cause magnetic saturation of the transformer core, causing the switching power supply to be damaged by excessive operating current.