Principle and Design of switching power supply the calculation of the storage filter capacitor of the tandem switch power supply (IV)

1-2-4. Calculation of the filtering capacitor of the series-connected Switching Power Supply
We also started from the current flowing through the energy storage inductor as the critical continuous current state, analyzed the charge and discharge process of the energy storage filter capacitor C, and then calculated the value of the energy storage filter capacitor C.
Figure 1-6 shows the voltage and current waveforms of each point in the tandem switching power supply circuit when the tandem switching power supply is in critical continuous current state. In Figure 1-6, UI is the input voltage of the power supply, UO is the output voltage of the control switch K, UO is the output voltage filtered by the power supply, and IL is the inductor current flowing through the energy storage filter, io is the current that flows through the load. Figure 1-6-A) is the waveform for controlling the output voltage of the switch K; Figure 1-6-B) is the charge and discharge curve of the energy storage filter capacitor C; Figure 1-6-C) is the waveform flowing through the energy storage filter inductance current Il. When the tandem switching power supply is in the critical continuous current state, the duty cycle D of the control switch K is equal to 0.5, and the current IO flowing through the load is equal to 1/2 of the maximum current ILM flowing through the energy storage filter inductor.

 

During the ton period, the control switch K is connected, and the input voltage UI controls the output voltage uo of the switch K. Under the output voltage uo, the current flowing through the energy storage filter inductance L begins to increase. When the time t is greater than 1/2 ton, the current il flowing through the energy storage filter inductor L is greater than the current IO flowing through the load, therefore, some of the current il flowing through the energy storage filter inductor L starts charging the energy storage filter capacitor C, and the voltage at both ends of the energy storage filter capacitor C starts to rise.
When T is equal to ton, the current il flowing through the energy storage filter inductance L is the largest, but the voltage at both ends of the energy storage filter capacitor C does not reach the maximum, the voltage at both ends of the energy storage filter capacitor C is still rising, because the current il flowing through the energy storage filter inductance L is greater than the current IO flowing through the load; when the time t is equal to 1/2 toff, the current il flowing through the energy storage filter inductor L is exactly equal to the load current IO, the voltage at both ends of the energy storage filter capacitor C reaches the maximum value, the capacitor stops charging, and starts from charging to discharging.
It can be proved that when the energy storage filter capacitor is charged, the voltage at both ends of the capacitor changes at the speed of the sine curve. When the energy storage filter capacitor is discharged, the voltage at both ends of the capacitor changes at the rate of the exponential curve. For more information, see the detailed analysis in Figure 1-23, Figure 1-24, and Figure 1-25.

 

 

 

 

 

In Figure 1-6, the charge and discharge curves at both ends of the capacitor intentionally enlarge the curvature of the capacitor. In fact, their varying curvature is not that large. Because the time constant composed of the energy storage filter inductance L and the energy storage filter capacitor is very large compared with the switch ON or OFF time (sine curve cycle:

(1-17) and (1-18) are the formulas used to calculate the filter capacitance of the tandem switching power supply. (D = 0.5 hours ). Type: Io is the current flowing through the load, T is the cycle of the control switch K, and delta up-P is the ripple of the output voltage. Voltage ripple Delta up-P generally take the peak-peak value, so the voltage ripple is exactly equal to the voltage increment when the capacitor is charging or discharging, that is: Delta up-P = 2 △uc.
By the way, because people are used to taking the average output voltage as a horizontal line, the electric ripple is divided into two parts: positive and negative, therefore, the voltage increment during capacitor charging or discharging is also divided into two parts, namely, 2 △uc.
Similarly, the calculation results of the (1-17) and (1-18) formulas only provide the median value or average value for calculating the C of the series-connected Switching Power Supply's Energy Storage filter capacitor, in extreme cases, we can multiply the average value by a factor greater than 1.
When the value of the energy storage filter capacitor is smaller than the value of (1-17), the voltage of the output voltage of the series-connected switching power supply will increase by Delta up-P, when the duty cycle of the switch K is less than 0.5, the current il flowing through the energy storage filter inductance L is discontinuous, and the discharge time of the capacitor is greater than the charging time of the capacitor, when the output voltage of the switch power supply is filtered, the voltage of the power supply will increase significantly. Therefore, it is better to select the parameters of the energy storage filter capacitor by more than twice the calculation result of the formula (1-17.