Principle and design of switching power supply (Part 8) Working principle of parallel switching power supply

1-4-1. Working principle of parallel switching power supply

Figure 1-11-a is the simplest working principle diagram 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, Ui is the working voltage of the switching power supply, L is the energy storage inductor, K is the control switch, and R is the load. In Figure 1-11-b, Ui is the input voltage of the switching power supply, Uo is the output voltage of the switching power supply, Up is the peak voltage of the switching power supply output, and Ua is the average voltage of the switching power supply output.

When the control switch K is turned on, the input power supply Ui starts to energize the energy storage inductor L, and the current flowing through the energy storage inductor L starts to increase. At the same time, the current also generates a magnetic field in the energy storage inductor. When the control switch K turns from on to off, the energy storage inductor will generate a back electromotive force. The direction of the current generated by the back electromotive force is the same as the direction of the original current. Therefore, a very high voltage will be generated on the load.

During the Ton period, the control switch K is turned on, and the voltage eL across the energy storage filter inductor L is exactly equal to the input voltage Ui, that is:
eL = Ldi/dt = Ui —— K is turned on (1-35)

By integrating the above formula, the current flowing through the energy storage inductor L can be obtained as:

Where iL is the instantaneous value of the current flowing through the energy storage inductor L, t is the time variable, and i(0) is the initial current flowing through the energy storage inductor, that is, the current flowing through the energy storage inductor immediately before the switch K is turned on. Generally, when the duty cycle D is less than or equal to 0.5, i(0) = 0, from which the maximum current ILm flowing through the energy storage inductor L can be obtained as:

ILm =Ui*Ton/L —— K on-time (D = 0.5) (1-37)

Where Ton is the time when the control switch K is turned on. When the control switch K in Figure 1-11-a suddenly turns off from the on state, the energy storage inductor L will release its stored energy (magnetic energy) through the back electromotive force. The back electromotive force generated by the energy storage inductor L is:

The negative sign in the formula indicates that the polarity of the back electromotive force eL is opposite to that in formula (1-35), that is, the polarity of the back electromotive force of the inductor is exactly opposite when K is turned on and off. Solving the differential equation of formula (1-38) yields:

Where C is a constant. Substituting the initial conditions into the above formula, it is easy to find C. Since the current iL flowing through the energy storage inductor L cannot change suddenly when the control switch K suddenly turns from the on state to the off state, i(Ton+) is exactly equal to the maximum current ILm flowing through the energy storage inductor L, so (1-39) can be written as:

When t is very large, the output voltage of the parallel switching power supply will be close to the input voltage Ui, but this situation generally does not happen because the turn-off time of the control switch K cannot be that long.

From equation (1-42), it can be seen that when the load R of the parallel switching power supply is large or open circuit, the amplitude of the output pulse voltage will be very high. Therefore, parallel switching power supplies are often used in high-voltage pulse generating circuits.