Principle and Design of Switching Power Supply (Part 10) Calculation of Energy Storage Inductance of Parallel Switching Power Supply

1-4-3. Calculation of energy storage inductance of parallel switching power supply

The calculation of the energy storage inductor in the parallel switching power supply is basically the same as the numerical method for calculating the energy storage inductor in the reverse series switching power supply. The calculation of the energy storage inductor in the parallel switching power supply is also based on the analysis of the current flowing through the energy storage inductor as a critical continuous current state. The energy storage inductor in the parallel switching power supply and the energy storage inductor in the reverse series switching power supply have basically the same working principle. Both generate 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 only one-fourth of the current flowing through the energy storage inductor.

According to formula (1-45):
iLm =Ui*Ton/L —— K is turned off at the moment (1-45)
Formula (1-45) can be rewritten as:
4Io =Ui*T/2L —— K is turned off at the moment (1-53)
Where Io is the current flowing through the load. When D = 0.5, its magnitude is equal to one-fourth of the maximum current iLm; T is the working cycle of the switching power supply, which is exactly equal to 2 times Ton.
From this, we can obtain:
L =Ui*T/8Io —— D = 0.5 (1-54)
or:
L >Ui*T/8Io —— D = 0.5 (1-55)

Formulas (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 formulas (1-54) and (1-55) only give the intermediate value or average value of the energy storage filter inductance L of the parallel switching power supply. For extreme cases, the average value can be multiplied by a coefficient greater than 1.
For the analysis of the situation where the inductance takes different values ​​and works under different duty cycle conditions, please refer to the previous discussion on "Calculation of energy storage inductance of reverse series switching power supply".

1-4-4． Calculation of energy storage filter capacitors for parallel switching power supplies

The calculation of the energy storage filter capacitor of the parallel switching power supply can refer to the calculation method of the energy storage filter capacitor in the previous series switching power supply or reverse series switching power supply. You can also refer to the charging and discharging process of the energy storage filter capacitor C in Figure 1-6.

It should be noted here that the energy storage inductor in the parallel switching power supply is the same as that in the reversing series switching power supply. Back electromotive force is generated to provide energy to the load only during the period when the control switch K is turned off. Therefore, even when the duty cycle D is equal to 0.5, the charging time and discharging time of the energy storage filter capacitor are not equal. The charging time of the capacitor is less than half a working cycle, while the discharging time of the capacitor is greater than half a working cycle. However, the charge and discharge of the capacitor are equal, that is, the current when the capacitor is charging is greater than the current when it is discharging.

As can be seen from Figure 1-13, the current flowing through the load of the parallel switching power supply is half that of the series switching power supply, and the current flowing through the load Io is only one-fourth of the maximum current iLm flowing through the energy storage inductor. When the duty cycle D is equal to 0.5, the capacitor charging time is 3T/8, and the average value of the capacitor charging current is 3iLm/8, or 3io/2; while the capacitor discharge time is 5T/8, and the average value of the capacitor discharge current is 0.9 Io. Therefore:

Where ΔQ is the charge of the capacitor, Io is the average current flowing through the load, and T is the working cycle. When the capacitor is charged, the voltage across the capacitor is charged from the minimum value to the maximum value (absolute value), and the corresponding voltage increment is 2ΔUc. The ripple voltage ΔUP-P across the capacitor is obtained as follows:

Formulas (1-58) and (1-59) are the formulas for calculating the energy storage filter capacitor of the parallel switching power supply (when D = 0.5). Where: Io is the average value of the current flowing through the load, T is the switching duty cycle, and ΔUP-P is the ripple of the filtered output voltage, or voltage ripple. Generally, the ripple voltage is the peak-to-peak value of the voltage increment. Therefore, when D = 0.5, the ripple voltage is equal to the voltage increment of the capacitor charge, that is: ΔUP-P = 2ΔUc.

Similarly, the calculation results of equations (1-58) and (1-59) only give the intermediate value or average value of the energy storage filter capacitor C of the parallel switching power supply. For extreme cases, the average value can be multiplied by a coefficient greater than 1.

When the switch K working duty cycle D is less than 0.5, the current flowing through the energy storage filter inductor L will be discontinuous, and the capacitor discharge time will be much longer than the capacitor charging time. Therefore, the ripple of the switching power supply filter output voltage 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 switching power supply filter output voltage will also increase. Therefore, when designing the switching power supply, sufficient margin should be left. In practical applications, it is best to calculate the parameters of the energy storage filter capacitor by more than twice the calculation result of formula (1-58).