Principle and design of switching power supply (serial 9) parallel switching power supply output voltage filter circuit

1-4-2. Parallel switching power supply output voltage filter circuit

As we know above, when the parallel switching power supply does not have an output voltage filter circuit, the amplitude of the output pulse voltage will be very high. However, in applications, the output voltage of most parallel switching power supplies is still a DC voltage after rectification and filtering. Therefore, the output circuit of a general switching power supply is equipped with a rectifier and filter circuit.

Figure 1-12 is a working principle diagram of a parallel switching power supply with rectification and filtering functions. In Figure 1-12, Ui is the operating voltage of the switching power supply, L is the energy storage inductor, eL is the back electromotive force generated by the current iL at both ends of the energy storage inductor, K is the control switch, and R is the load. Figures 1-13, 1-14, and 1-15 are the voltage and current waveforms of each point in the circuit of Figure 1-12 when the control switch K of the parallel switching power supply works at a duty cycle of 0.5, < 0.5, and > 0.5. In Figures 1-13, 1-14, and 1-15, Ui is the input voltage of the switching power supply, uo is the output voltage at both ends of the control switch K, uc is the output voltage at both ends of the filter capacitor, Up is the peak voltage output by the switching power supply, Uo is the output voltage (average value) of the switching power supply, Ua is the average voltage output by the switching power supply, iL is the current flowing through the energy storage inductor L, iLm is the maximum value of the current flowing through the energy storage inductor L, and Io is the current flowing through the load R (average value).

When the control switch K is turned on, the input power supply Ui starts to energize the energy storage inductor L, and the current iL flowing through the energy storage inductor L starts to increase. At the same time, the current also generates a back electromotive force eL in the energy storage inductor; when the control switch K is turned from on to off, the energy storage inductor will also generate a back electromotive force eL. The direction of the eL back electromotive force is opposite to the direction before the switch K is turned off, but the same as the direction of the current. Therefore, the output voltage uo at both ends of the control switch K is equal to the sum of the input voltage Ui and the back electromotive force eL.
Therefore, during the Ton period:

eL = Ldi/dt = Ui —— K on-time (1-43)

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

(1-44) In the formula, iL is the instantaneous value of the current flowing through the energy storage inductor L, t is the time variable; i(0) is the initial current, that is, the current flowing through the energy storage inductor L before the control switch K is turned on. When the switching power supply operates in the critical continuous current state, i(0) = 0, from which the maximum current flowing through the energy storage inductor L can be obtained as:

iLm =Ui*Ton/L —— the moment before K is turned off (1-45)

During the switch off period Toff, the control switch K is turned off, and the energy storage inductor L converts the current iLm into a back electromotive force, which is superimposed in series with the input voltage Ui, and continues to provide energy to the load R through the rectifier diode D. During this period, the voltage eL across the energy storage inductor L is:
eL = -Ldi/dt = Uo-Ui —— K off period (1-46)

The negative sign in the formula indicates that the polarity of the back electromotive force eL is opposite to that of formula (1-43), that is, the polarity of the back electromotive force of the inductor is exactly opposite when K is turned on and off. Integrating formula (1-46) yields:

In the formula, i(Ton+) is the current flowing through the inductor before the control switch K switches from Ton to Toff. i(Ton+) can also be written as i(Toff-), that is, the current flowing through the inductor L before and after the control switch K is turned off or on is equal. In fact, i(Ton+) in formula (1-47) is iLm in formula (1-45). Therefore, formula (1-9) can be rewritten as:

When the switching power supply operates in the critical continuous current state, the initial current i(0) flowing through the energy storage inductor is equal to 0 (see Figure 1-13), that is: In formula (1-49), the minimum value iLX of the current flowing through the energy storage inductor is equal to 0. Therefore, from formulas (1-45) and (1-49), the output voltage Uo of the inverting series switching power supply can be obtained as:

Generally, the output voltage Uo of the parallel switching power supply is taken from the amplitude Up of the output voltage uo pulse voltage. After rectification and filtering, the output voltage across the energy storage filter capacitor C is basically Up, that is:

Up = Uo —— Parallel switching power supply (1-51)

It is particularly pointed out here that although the results of equations (1-50) and (1-51) are obtained under the condition that the switching power supply operates in the critical continuous current state, they are also valid for the switching power supply operating in the continuous current state or the interruption state, because the output voltage Uo only takes its peak voltage Up, rather than its average value.
In addition, the average value Ua of the output voltage uo of the parallel switching power supply is equal to the input voltage, that is:

Ua = Ui —— Parallel switching power supply (1-52)

Since the amplitude of its output voltage uo is equal to the sum of the input voltage Ui and the back electromotive force eL generated by the energy storage inductor L, the parallel switching power supply generally takes the amplitude Up of its output voltage uo as the output (the method of extracting the voltage amplitude will be discussed in detail later). Therefore, the parallel switching power supply belongs to the boost type switching power supply. Although the amplitude of the output voltage of the parallel switching power supply can be higher than the input voltage, the average value Ua of its output voltage has nothing to do with the duty cycle D of the control switch K, that is: the average value Ua of the output voltage of the parallel switching power supply is always equal to the input voltage Ui.