# Principle of switching power supply and design of parallel switching power supply for Energy Storage inductance calculation (10)

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Author: User

1-4-3. Calculation of energy storage inductance of the parallel switching power supply
Similar to the numerical method used to calculate the energy-saving inductance in the inverted series switching power supply, the energy storage inductance of the parallel switching power supply is also analyzed starting from the critical continuous current state of the current flowing through the energy storage inductance. The working principle of the energy storage inductance in the parallel switching power supply is basically the same as that in the inverted series Switching Power Supply. The back-voltage force is generated to provide energy to the load during the shutdown of the control switch K. Therefore, the current flowing through the load is only 1/4 of the current flowing through the energy storage inductance.
According to the (1-45) formula:
ILM = UI * ton/L -- instant before K shutdown (1-45)
(1-45) format can be rewritten:
4io = UI * t/2L -- instant before K shutdown (1-53)
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 (1-54)
Or:
L> UI * t/8io -- d = 0.5 (1-55)
(1-54) and (1-55) are the formulas for calculating the energy storage inductance of the parallel switching power supply. Similarly, the calculation results of the (1-54) and (1-55) formulas only show the median value or average value of the filtering inductance L for the energy storage of the parallel switching power supply, in extreme cases, we can multiply the average value by a factor greater than 1.
For the analysis of the inductance working under different values and different duty cycles, please refer to the previous section on "calculating the energy storage inductance of inverted series Switching Power Supply.
1-4-4. Calculation of the filtering capacitor of the parallel switching power supply
For the calculation of the storage filter capacitor of the parallel switch power supply, refer to the calculation method of the storage filter capacitor in the previous series-connected switch power supply or reverse series switch power supply, you can also refer to the filling and discharging process of the filter capacitor C in Figure 1-6.
Note that the parallel switching power supply is the same as the energy storage inductance in the inverted series switching power supply. Only the back-potential force is generated to provide energy to the load during the shutdown of the control switch K, even if the duty cycle D is equal to 0.5, the charging time of the energy storage filter capacitor is not the same as the discharge time. The charging time of the capacitor is less than half a working cycle, the discharge time of the capacitor is more than half a working cycle, but the charge of the capacitor charge and discharge is equal, that is, the current when the capacitor charge is greater than the current when the discharge.

From Figure 1-13, we can see that the current of the parallel switching power supply is twice smaller than that of the tandem switching power supply, the current IO that flows through the load is only 1/4 of the maximum current of the energy storage inductance ILM. When the duty cycle D is equal to 0.5, the charging time of the capacitor is 3 TB/8, and the average charging current of the capacitor is 3ilm/8, or 3io/2; the discharge time of the capacitor is 5 TB/8, and the average discharge current of the capacitor is 0.9 Io. Therefore:

In formula, △q is the charge charged by the capacitor, and the average current of Io flowing through the load. T is the working cycle. When the capacitor is charged, the voltage at both ends of the capacitor is charged from the minimum value to the maximum value (absolute value), and the corresponding Voltage Increment is 2 △uc. Thus, the corrugated voltage at both ends of the capacitor is obtained as follows:

(1-58) and (1-59) are the formulas used to calculate the filtering capacitance of the energy storage of the parallel switching power supply (D = 0.5 hours ). Formula: Io is the average value of the load current, T is the switching cycle, and △up-P is the ripple of the filtered output voltage, or the voltage ripple. Generally, the ripple voltage is the peak-peak value of the Voltage Increment. Therefore, when D = 0.5, the ripple voltage equals the Voltage Increment of the capacitor charging, that is, Delta up-P = 2 △uc.
Similarly, the calculation results of the (1-58) and (1-59) modes only show the median value or average value of the filtering capacitor C of the parallel switching power supply, in extreme cases, we can multiply the average value by a factor greater than 1.
When the switch K's duty cycle D is less than 0.5, because the current flowing through the energy storage filter inductance L will be discontinuous, the discharge time of the capacitor will be much greater than the charging time of the capacitor, the ripple of the output voltage filtered by the switch power supply will increase significantly. In addition, the load of the switching power supply is generally not fixed. When the load current increases, the ripple of the output voltage filtered by the switching power supply will also increase. Therefore, there must be sufficient balance when designing the switching power supply. In actual application, it is best to calculate the parameters of the energy storage filter capacitor by more than twice the formula (1-58.

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