Principle of switching power supply and Design of series-connected Switching Power Supply for Energy Storage filtering inductance (III)

1-2-3. Calculation of energy storage filter inductance of tandem Switching Power Supply
From the above analysis, we can see that the output voltage of the tandem switch power supply is related to the duty cycle D of the control switch and the energy storage inductance L, because the energy storage inductance L determines the current rise rate (DI/dt), that is, the output current size. Therefore, it is important to correctly select the parameters of the energy storage inductor.

It is recommended that the tandem Switching Power Supply Work in the critical continuous current state or continuous current state. When the tandem switching power supply works in the critical continuous current state, the Filtered Output Voltage uo is the average UA of the filtered input voltage uo. At this time, the output voltage adjustment rate of the switching power supply is the best, and the output voltage of UO is not big. Therefore, we can analyze the critical continuous current state. Let's first look at the (1-6) formula:

ILM = (ui-uo)/L * ton + I (0) -- instant before K shutdown (1-6)

When the tandem switching power supply is in the critical continuous current state, that is, when D = 0.5, I (0) = 0, ILM = 2 Io, therefore, (1-6) format can be rewritten:

2io = uo/2L * t -- instant before K shutdown (1-12)
In the formula, Io is the current (average current) flowing through the load. When d = 0.5, its size is exactly equal to 1/2 of the maximum current flowing through the energy storage inductance l ilm; T is the working cycle of the switch power supply, and T is exactly equal to 2 times ton.
The following result is obtained:
L = uo/4io * t -- d = 0.5 (1-13)
Or:
L> uo/4io * t = UI/2io * t -- d = 0.5 (1-14)

(1-13) and (1-14) are the formulas used to calculate the inductance L of the tandem switching power supply (D = 0.5 hours ). The calculation results of the (1-13) and (1-14) modes only show the median or average value of the inductance L used to calculate the energy storage of the tandem switching power supply, in extreme cases, we can multiply the average value by a factor greater than 1.
If the electrical inductance of the energy storage filter inductance L is increased, the output voltage of the filter will be less than the average UA of the input voltage uo. Therefore, when the output voltage of the filter is a fixed value, it is necessary to increase the duty cycle D of the control switch K to ensure the stability of the output voltage uo; while the duty cycle D of the control switch K increases, it will shorten the time for the current il discontinuous flowing through the energy storage filter inductor L, or change from the current discontinuous to the current continuous, thus, the voltage of the output voltage uo will be further reduced, and the output voltage will be more stable.
If the L value of the energy storage filter inductance is less than the (1-13) value, the output voltage of the series-connected switching power supply will be greater than the average UA of the input voltage of the filter, when the Filtered Output Voltage uo is a fixed value, the duty cycle D of the control switch K is reduced to keep the output voltage uo value unchanged. The duty cycle D of the control switch K is reduced, this will cause the current il flowing through the filter inductance L to be discontinuous, so that the voltage of the output voltage uo will be increased by Delta up-P, resulting in unstable output voltage.
From this we can see that adjusting the output voltage of the series-connected switching power supply to the output voltage uo is actually adjusting the flow through the filter inductance L and the control switch K duty cycle D at the same time.
Figure 1-4 shows that when the duty cycle D of the control switch K is less than 0.5, the current il flowing through the filter inductor L is discontinuous, the output current IO is less than 1/2 of the maximum current (ILM) flowing through the filter inductor. The voltage Delta-P of the output voltage will increase significantly. Therefore, it is recommended that the series-connected Switching Power Supply do not work in the current discontinuous state of Figure 1-4, but it is best to work in the critical continuous current and continuous current state shown in Figure 1-3 and figure 1-5.
The Tandem switching power supply works in the critical continuous current state. The output voltage uo is equal to 1/2 of the input voltage UI and the average UA of the filtered input voltage uo; and the output current IO is equal to 1/2 of the maximum current of the filtering inductance l ilm.
The Tandem switching power supply operates in the continuous current state. The output voltage uo is greater than 1/2 of the input voltage UI and greater than the average UA of the filtered input voltage uo; the output current IO is also greater than 1/2 of the maximum current (ILM) flowing through the filter inductor L.