Principle and Design of switching power supply the output voltage filter circuit of the series-connected switching power supply (II)

1-2-2. Output Voltage filter circuit of the tandem switch power supply
Most of the output of the switching power supply is DC voltage. Therefore, the output circuit of the general switching power supply has a rectifying and filtering circuit. Figure 1-2 shows the working principle of the series-connected switching power supply with the rectification and filtering function.

 

Figure 1-2 adds a rectification diode and an LC filter circuit based on Figure 1-1-. Among them, l is the energy storage filter inductor. Its function is to restrict the high current of ton when the control switch K is switched on, to prevent the input voltage UI from being directly added to the load R, and to impact the load R voltage, at the same time, the current Il of the convection inductance is converted into the magnetic energy for energy storage, and then toff converts the magnetic energy into the current il during the control switch K off to continue providing energy output to the load R; C is an energy storage filter capacitor. Its function is to convert part of the current flowing through the energy storage inductance L into a charge during the control switch K-on for storage, then, when the control switch K is turned off, Toff converts the charge into the current and continues to provide the energy output to the load R. D is the rectification diode, and its main function is the continued flow function. Therefore, it is called the continued flow diode, its function is to provide the current path for the energy storage filter inductor L to release energy during the toff of the control switch.
During the toff of the control switch, the energy storage inductor L will generate a back-to-back potential. The current il flowing through the energy storage inductor L will flow out from the positive pole of the Back-to-source El by loading R, then, it passes through the positive pole of the continued Diode D, then flows out from the negative pole of the continued Diode D, and finally returns to the negative pole of the Back-EMR El.
For Figure 1-2, if you do not look at the control switch K and the input voltage UI, it is a typical inverse filter circuit, it outputs the average value of the pulsating DC voltage through smooth filtering.
Figure 1-3, Figure 1-4, and Figure 1-5 respectively indicate that the duty cycle of the control switch K is d equal to 0.5, <0.5,> 0.5, figure 1-2 voltage and current waveforms of several key points in the circuit. Figure 1-3-a), figure 1-4-A, and Figure 1-5-A are respectively the waveforms for controlling the output voltage of the switch K. Figure 1-3-B), figure 1-4-B), and Figure 1-5-B) the waveforms of the voltage UC at both ends of the energy storage filter capacitor are shown in Figure 1-3-C, Figure 1-4-C, and Figure 1-5-C respectively.
 
 

 

 

During the ton period, the control switch K is connected, and the input voltage UI outputs the voltage uo through the control switch K, and then adds it to the filter circuit consisting of the energy storage filter inductance L and the energy storage filter capacitor C, during this period, the voltage El at both ends of the energy storage filter inductor L is:
El = LDI/dt = UI-uo -- k connection period (1-4)
Formula medium: Ui input voltage. uo is the DC output voltage, that is, the average value of the voltage UC at both ends of the capacitor.
By the way, the voltage variation between the two ends of the capacitor is very small compared with the output voltage uo. For simplicity, we will treat uo as a constant here. In some cases, if you need to analyze the initial charge and discharge process of a capacitor, you must establish a differential equation and solve the problem. Because the establishment of the output voltage uo takes some time, the results of accurate calculation generally contain exponential function items. When the time variable is equal to infinity, that is, when the circuit enters the steady state, take the average value of the relevant parameter, and the result is basically equal to (1-4.
Perform the following points for the (1-4) formula:
 
In formula, I (0) is the moment when the switch K is switched (t = 0), that is, the current that the control switch K is just switched on and flows through the inductance L, it is also called the initial current flowing through inductance L.
When the control switch K is switched from ton during the connection to toff during the shutdown period, the current il flowing through the inductance L reaches the maximum value:
 
In the formula, I (ton +) is the current flowing through the inductance before the switch K is switched from ton to Toff. I (ton +) can also be written as I (toff -), that is, when the control switch K is switched off or switched on instantly, the current flowing through the inductance L is equal to that before and after. In fact, I (ton +) in (1-8) is the ILM in (1-6), that is:
 

The above calculation results are obtained based on the assumption that the output voltage is basically unchanged. This is also true in the actual application circuit. The output voltage is very small, only a few percent of the output voltage can be ignored in engineering computation.
From the formula (1-4) to (1-11) and Fig 1-3, Fig 1-4, and Fig 1-5, we can see that:
When the switching power supply is in the state of critical continuous current or continuous current, the energy storage inductance L has the current flowing out during the entire period of K-connection and shutdown, however, the rising rate (absolute value) of the current flowing through the energy storage inductor L is generally different between the K-switched period and the K-switched period. During the K-on period, the current rising rate of the energy storage inductance L is UI-uo/L:. During the K-off period, the current rising rate of the energy storage inductance L is-uo/L.
Therefore:
(1) When the UI is 2uo, that is, when the Filtered Output Voltage uo is equal to half of the power input voltage UI, or when the duty cycle of the control switch K is d 1/2, the current rise rate flowing through the energy storage inductor L is completely equal to the absolute value during the K-on-power period and the K-off period, that is, the speed at which the inductance stores energy is exactly the same as the speed at which the energy is released. In this case, ILX in I (0) and (1-11) of (1-5) is equal to 0. In this case, the current il flowing through the energy storage inductor is a critical continuous current, and the Filtered Output Voltage uo is equal to the average UA of the filtered input voltage uo. See Figure 1-3.
(2) When the UI is greater than 2uo, that is, when the filtering output voltage uo is less than half of the power input voltage UI, or when the duty cycle of the control switch K is less than 1/2: Although during K-on, the current rise rate (absolute value) flowing through the energy storage inductor L is greater than the current rise rate (absolute value) flowing through the energy storage inductor L during the K-off period) in formula I (0) is equal to 0, and ton is smaller than toff, at this time, the ILX in formula (1-11) will have a negative value, that is, the output voltage in turn needs to charge the inductance, however, due to the existence of the rectification Diode D, this is impossible. This indicates that the current flowing through the energy storage inductor L is too high, that is, there is a cut-off. In this case, the current il flowing through the energy storage inductance L is not a continuous current, and the switching power supply is working in a state of discontinuous current. Therefore, the output voltage uo has a large ripple ratio, the output voltage of the filter is less than the average UA of the output voltage of the filter. See Figure 1-4.
(3) When the UI is less than 2uo, that is, when the filtering output voltage is greater than half of the power input voltage UI, or when the duty cycle of the control switch K is greater than 1/2: During the K-on period, although the current rising rate (absolute value) flowing through the energy storage inductor L is smaller than the current rising rate (absolute value) flowing through the energy storage inductor L during the K-off period ). However, because ton is greater than toff, ILX in I (0) and (1-11) in (1-5) is greater than 0, that is, the storage energy of Inductance cannot be released each time. In this case, the current il flowing through the energy storage inductor is a continuous current, the switching power supply is working in a continuous current state, and the output voltage is smaller than the ripple ratio, the output voltage of the filter is greater than the average UA of the output voltage of the filter. See Figure 1-5.