Switching power supply principle and design (Part 2) Series switching power supply output voltage filter circuit

1-2-2. Series switching power supply output voltage filter circuit

Most switching power supplies output a DC voltage, so the output circuit of a general switching power supply is equipped with a rectifier and filter circuit. Figure 1-2 is a working principle diagram of a series switching power supply with a rectifier and filter function.

Figure 1-2 is based on the circuit of Figure 1-1-a, with a rectifier diode and an LC filter circuit added. Among them, L is the energy storage filter inductor, which is used to limit the large current during the period Ton when the control switch K is turned on, to prevent the input voltage Ui from being directly added to the load R, and to cause voltage shock to the load R. At the same time, it converts the current iL flowing through the inductor into magnetic energy for energy storage, and then converts the magnetic energy into current iL during the period Toff when the control switch K is turned off to continue to provide energy output to the load R; C is the energy storage filter capacitor, which is used to convert part of the current flowing through the energy storage inductor L during the period Ton when the control switch K is turned on to store charges, and then converts the charges into current during the period Toff when the control switch K is turned off to continue to provide energy output to the load R; D is the rectifier diode, whose main function is the freewheeling effect, so it is called the freewheeling diode, and its function is to provide a current path for the energy storage filter inductor L to release energy during the period Toff when the control switch is turned off.

During the control switch off period Toff, the energy storage inductor L will generate a back electromotive force, and the current iL flowing through the energy storage inductor L flows out from the positive electrode of the back electromotive force eL, passes through the load R, passes through the positive electrode of the freewheeling diode D, and then flows out from the negative electrode of the freewheeling diode D, and finally returns to the negative electrode of the back electromotive force eL.
For Figure 1-2, if the control switch K and the input voltage Ui are ignored, it is a typical inverse г type filter circuit, which is used to output the average value of the pulsating DC voltage through smoothing filtering.

Figures 1-3, 1-4, and 1-5 are the voltage and current waveforms of several key points in the circuit of Figure 1-2 when the duty cycle D of the control switch K is equal to 0.5, < 0.5, and > 0.5, respectively. Figures 1-3-a), 1-4-a), and 1-5-a) are the waveforms of the output voltage uo of the control switch K, respectively; Figures 1-3-b), 1-4-b), and 1-5-b) are the waveforms of the voltage uc across the energy storage filter capacitor, respectively; Figures 1-3-c), 1-4-c), and 1-5-c) are the waveforms of the current iL flowing through the energy storage inductor L, respectively.

During the Ton period, the control switch K is turned on, the input voltage Ui is output as voltage uo through the control switch K, and then added to the filter circuit composed of the energy storage filter inductor L and the energy storage filter capacitor C. During this period, the voltage eL across the energy storage filter inductor L is:

eL = Ldi/dt = Ui – Uo —— K on-time (1-4)

Where: Ui is the input voltage, Uo is the DC output voltage, that is: the average value of the voltage uc across the capacitor.

By the way, since the voltage change ΔU across the capacitor is very small relative to the output voltage Uo, for simplicity, we treat Uo as a constant. In some cases, if it is necessary to analyze the initial charge and discharge process of the capacitor, it is necessary to establish a differential equation and solve it. Because it takes a certain amount of time to establish the output voltage Uo, the result obtained by accurate calculation generally contains exponential function terms. When the time variable is equal to infinity, that is, when the circuit enters a steady state, the average value of the relevant parameters is taken, and the result is basically equal to (1-4).

Integrating equation (1-4) yields: where i(0) is the switching instant of the control switch K (t = 0), that is, the current flowing through the inductor L at the moment when the control switch K is just turned on, or the initial current flowing through the inductor L. When the control switch K suddenly switches from the on period Ton to the off period Toff, the current iL flowing through the inductor L reaches its maximum value:

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 (1-8) is iLm in formula (1-6), that is:

The above calculations are based on the assumption that the output voltage Uo remains basically unchanged. This is also the case in actual application circuits. The voltage ripple of the output voltage Uo is very small, only a few percent of the output voltage, and can be completely ignored in engineering calculations.

From equations (1-4) to (1-11) and Figures 1-3, 1-4, and 1-5, it can be seen that:
when the switching power supply operates in the critical continuous current or continuous current state, during the entire cycle of K being turned on and off, there is current flowing out of the energy storage inductor L, but the rate of increase (absolute value) of the current flowing through the energy storage inductor L during the period when K is turned on and during the period when K is turned off is generally different. During the period when K is turned on, the rate of increase of the current flowing through the energy storage inductor L is Ui-Uo/L: ; during the period when K is turned off, the rate of increase of the current flowing through the energy storage inductor L is: -Uo/L
Therefore:

(1) When Ui = 2Uo, that is, when the filter output voltage Uo is equal to half of the power input voltage Ui, or when the duty cycle D of the control switch K is one-half, the current rise rate flowing through the energy storage inductor L is completely equal in absolute value during the period when K is turned on and during the period when K is turned off, that is, the speed at which the inductor stores energy is completely equal to the speed at which it releases energy. At this time, i(0) in (1-5) and iLX in (1-11) are both equal to 0. In this case, the current iL flowing through the energy storage inductor L is the critical continuous current, and the filter output voltage Uo is equal to the average value Ua of the filter input voltage uo. See Figure 1-3.

(2) When Ui > 2Uo, that is, when the filter output voltage Uo is less than half of the power supply input voltage Ui, or when the duty cycle of the control switch K is less than one-half: Although the current rise rate (absolute value) flowing through the energy storage inductor L during the K on period is greater than the current rise rate (absolute value) flowing through the energy storage inductor L during the K off period; but because i (0) in (1-5) is equal to 0, and Ton is less than Toff, at this time, iLX in (1-11) will have a negative value, that is, the output voltage will charge the inductor in turn, but due to the existence of the rectifier diode D, this is impossible, which means that the current flowing through the energy storage inductor L passes through 0 in advance, that is, there is a current interruption. In this case, the current iL flowing through the energy storage inductor L is not a continuous current, and the switching power supply operates in a discontinuous current state. Therefore, the ripple of the output voltage Uo is relatively large, and the filter output voltage Uo is less than the average value Ua of the filter input voltage uo. See Figure 1-4.

(3) When Ui < 2Uo, that is, when the filter output voltage Uo is greater than half of the power supply input voltage Ui, or when the duty cycle of the control switch K is greater than one-half: during the period when K is turned on, although the current rise rate (absolute value) flowing through the energy storage inductor L is less than the current rise rate (absolute value) flowing through the energy storage inductor L during the period when K is turned off. However, since Ton is greater than Toff, i (0) in (1-5) and iLX in (1-11) are both greater than 0, that is, the energy stored in the inductor cannot be fully released each time. In this case, the current iL flowing through the energy storage inductor L is a continuous current, the switching power supply operates in a continuous current state, the ripple of the output voltage Uo is relatively small, and the filter output voltage Uo is greater than the average value Ua of the filter input voltage uo. See Figure 1-5.