Principle of switching power supply and Design of invert series Switching Power Supply)

1-4-1. operating principle of the parallel switching power supply
Figure 1-11-A is the simplest working principle of the parallel switching power supply, and Figure 1-11-B is the waveform of the output voltage of the parallel switching power supply. In Figure 1-11-A, the UI is the operating voltage of the switching power supply, L is the energy storage inductance, k is the control switch, and r is the load. In Figure 1-11-B, the UI is the input voltage of the switch power supply, the uo is the output voltage of the switch power supply, the up is the peak voltage of the switch power supply output, and the UA is the average voltage of the switch power supply output.
 

When the control switch K is connected, the input power supply UI starts to power on the energy storage inductance L, the current flowing through the energy storage inductance L begins to increase, and the current also produces a magnetic field in the energy storage inductance; when the control switch K is switched from power-on to power-off, the energy storage inductance will generate a back-to-potential. The back-to-force current will generate the same direction as the original current. Therefore, high voltage is generated on the load.
During the ton period, the control switch K is switched on, and the voltage El at both ends of the energy storage filter inductance L is exactly the same as the input voltage UI, that is:
El = LDI/dt = UI -- k connection period (1-35)
By integrating the above formula, the current flowing through the energy storage inductance L can be obtained as follows:

In formula, Il is the instantaneous value flowing through the energy storage inductance L current, t is the time variable, and I (0) is the initial current flowing through the energy storage inductance, that is: the current that flows through the energy storage inductor instantly before the switch K is switched on. Generally, when the duty cycle D is less than or equal to 0.5, I (0) = 0. Therefore, the maximum current (ILM) flowing through the energy storage inductance L can be obtained as follows:
ILM = UI * ton/L -- k connection period (D = 0.5) (1-37)
In the formula, Ton is the time when the switch K is switched on. When the control switch K in Figure 1-11-A is suddenly switched from the on state to the off state, the energy storage inductance L will release its stored energy (magnetic energy) through the back-to-force, the back-EMR generated by the energy storage inductance L is:

Negative signs in the formula indicate that the polarity of El is opposite to that of El in the (1-35) formula, that is, the polarity of the Back-EMR of the inductance is exactly the opposite when K is switched on and off. The solutions for (1-38) Order Differential Equations are as follows:

C is a constant in the formula, and the initial condition is substituted into the formula, it is easy to find C, because the control switch K is suddenly switched from the on state to the off state, the current il flowing through the energy storage inductor L cannot change. Therefore, I (ton +) is exactly the same as the maximum current ILM flowing through the energy storage inductor L, so the (1-39) formula can be written:

When T is very large, the output voltage value of the parallel switch power supply will be close to the input voltage UI, but this usually does not happen because the shutdown time of the control switch K cannot be so long.
From the (1-42) type, we can see that when the load R of the parallel switching power supply is large or open, the output pulse voltage range will be very high. Therefore, the parallel switching power supply is often used in high voltage pulse circuit.