Principle of switching power supply and Design of inverted series Switching Power Supply for Energy Storage inductance calculation (6)

1-3-2. Calculation of energy storage inductance of inverted series Switching Power Supply
The calculation method of the energy storage inductance of the inverted series switching power supply is basically the same as that of the previous "calculation of the energy storage filter inductance of the tandem Switching Power Supply". The value of the energy storage inductance in the inverted series switching power supply is calculated, it also analyzes the critical continuous current state from the current flowing through the energy storage inductor. However, it is worth special attention that the energy storage inductance in the inverted series switching power supply only generates the back-EMR to provide energy to the load during the control switch K shutdown. Therefore, the current flowing through the load is twice as small as the current flowing through the tandem switching power supply, that is, when the duty cycle is less than 0.5, the current IO of the reverse series Switching Power Supply flows through the load R only 1/4 of the energy storage inductance L maximum current ILM.
According to the (1-21) formula:
ILM = UI * ton/L -- instant before K shutdown (1-21)
(1-21) can be rewritten:
4io = UI * t/2L -- instant before K shutdown (1-28)
In the formula, Io is the current flowing through the load. When d = 0.5, its size is equal to 1/4 of the maximum current ILM; t is the working cycle of the switching power supply, and T is exactly equal to 2 times ton.
The following result is obtained:
L = UI * t/8io -- d = 0.5 (1-29)
Or:
L> UI * t/8io -- d = 0.5 (1-30)
(1-29) and (1-30) are the formulas used to calculate the energy storage inductance in the inverted series switching power supply. Similarly, the calculation results of the (1-29) and (1-30) modes only show the median value or average value of the filtering inductance L of the inverted series switching power supply, in extreme cases, we can multiply the average value by a factor greater than 1.
When the energy storage inductance L value is smaller than (1-29), the current rising rate of the filtered inductor L will increase. If the current il flowing through the filtered inductor L is a continuous current, the output voltage uo will increase. If the output voltage uo remains unchanged, the duty cycle D of the control switch K must be reduced, however, the reduction of duty cycle D will lead to the discontinuous current il flowing through the energy storage inductance, thus increasing the voltage ripple of the output voltage uo.
If the current il flowing through the filter inductor L is not a continuous current, the reduction of the energy storage inductor L will lead to a longer time for the current il flowing through the energy storage inductor, and the power supply filtered output voltage uo will not increase, on the contrary, it will significantly increase the voltage ripple of the output voltage of the invert series switch power supply.
When the value of the energy storage filter inductance L is greater than (1-29), the current rising rate flowing through the energy storage inductance L will decrease, and the output voltage uo will decrease, however, the voltage field of the output voltage is significantly reduced. To keep the output voltage of the power supply remain unchanged, the duty cycle D of the control switch K must be increased, the increase of duty cycle D will shorten the time for the current il discontinuous flowing through the energy storage inductance, or change from the current discontinuous to the current continuous, so that the power supply filters the output voltage of UO to reduce the voltage ripple.
(This article from the world of Electronic Engineering: http://www.bbs.eeworld.com.cn/dygl/2011/0227/article_4702.html)