Principle and design of switching power supply (Part 6) Calculation of energy storage inductance of reverse series switching power supply

1-3-2. Calculation of energy storage inductance of reverse series switching power supply

The calculation method of the energy storage inductor of the reverse series switching power supply is basically the same as the method of "calculation of the energy storage filter inductor of the series switching power supply" mentioned above. The calculation of the value of the energy storage inductor in the reverse series switching power supply is also analyzed from the critical continuous current state of the current flowing through the energy storage inductor. However, it should be noted that the energy storage inductor in the reverse series switching power supply only generates back electromotive force to provide energy to the load during the period when the control switch K is turned off. Therefore, the current flowing through the load is half of the current flowing through the load of the series switching power supply, that is, when the duty cycle is less than 0.5, the current Io flowing through the load R in the reverse series switching power supply is only one-fourth of the maximum current iLm flowing through the energy storage inductor L.

According to formula (1-21):

iLm =Ui*Ton/L —— The moment before K is turned off (1-21)

Formula (1-21) can be rewritten as:

4Io = Ui*T/2L —— The moment before K turns off (1-28)

Where Io is the current flowing through the load. When D = 0.5, its magnitude is equal to one quarter of the maximum current iLm. T is the duty cycle of the switching power supply, which is exactly equal to 2 times Ton.

From this we obtain:

L = Ui*T/8Io —— When D = 0.5 (1-29)

or:

L > Ui*T/8Io —— When D = 0.5 (1-30)

Formulas (1-29) and (1-30) are the formulas for calculating the energy storage inductance in the reverse series switching power supply. Similarly, the calculation results of formulas (1-29) and (1-30) only give the intermediate value or average value of the energy storage filter inductance L of the reverse series switching power supply. For extreme cases, the average value can be multiplied by a coefficient greater than 1.

When the value of the energy storage inductor L is less than the value of formula (1-29), the rate of rise of the current flowing through the filter inductor L will increase. If the current iL flowing through the filter inductor L is a continuous current, the output voltage Uo will increase. If the filter output voltage Uo is to be maintained unchanged, the duty cycle D of the control switch K must be reduced. However, the reduction in the duty cycle D will cause the current iL flowing through the energy storage inductor to become discontinuous, thereby increasing the voltage ripple of the filter output voltage Uo.

如果流过滤波电感L的电流iL不是连续电流，储能电感L的减小，将会使流过储能电感的电流iL不连续的时间变长，电源滤波输出电压Uo不但不会升高，反而会使反转式串联开关电源滤波输出电压Uo的电压纹波显著增大。

当储能滤波电感L的值大于(1-29)式的值时，流过储能电感L的电流上升率将减小，输出电压Uo将降低，但滤波输出电压Uo的电压纹波显著减小;如果为了维持电源滤波输出电压Uo不变，控制开关K必须要把占空比D增大，而占空比D的增大又会使流过储能电感的电流iL不连续的时间缩短，或由电流不连续变成电流连续，从而使电源滤波输出电压Uo的电压纹波降低。