Principle and Design of switching power supply circuit transition process (21)

Figure 1-24 refers to the voltage waveform of the energy storage filter capacitor charging according to the sine curve when all the charging time of the energy storage filter capacitor is combined. We can regard Figure 1-24 as an energy storage filter capacitor and charge the voltage to the maximum value after six working cycles, where T1, T2 ,... T6 represents toff1, toff2 ,... Toff6. Toff1 indicates the first shutdown time of the active switch, and so on. After the energy storage filter capacitor is fully charged, due to the action of the rectification diode, it is impossible to discharge the secondary coil of the transformer. Therefore, the sine curve after T6 cannot continue.

It must be pointed out that the voltage waveform shown in Figure 1-24 does not exist in reality, because the voltage waveform shown in Figure 1-24 is not continuous in the timeline, just for convenience of analysis, compress the working switch on time ton.
In practical application, it is impossible for an energy storage filter capacitor to charge the voltage to the maximum value in six working cycles. Generally, after more than a dozen cycles, the voltage at both ends of the energy storage filter capacitor can be charged to the maximum value. For example, if the electrical inductance of the transformer secondary coil is 10-1000, and the capacity of the energy storage filter capacitor is 10000-1592, the following formula can be obtained: ω =, or F = Hz, T = 628 microseconds, 1/4 cycle is 157 microseconds; set the switching power supply to 40 kHz, D = 0.5, which can be obtained, t = 25 microseconds, the half cycle is 12.5 microseconds. Finally, we can find that the energy storage filtering capacitor can be fully charged only after 12.56 cycles, that is, 314 microseconds.
The above results have not considered the impact of load current on the charging of the energy storage filter capacitor. Because the load current will generate shunt for the energy storage filter capacitor charging, the capacitor charging speed slows down. In addition, the duty cycle of the Reverse type switching power supply is generally less than 0.5, this will cause the output current of the transformer secondary coil to flow out. If all these factors are taken into account, the time required for the energy storage filter capacitor to fully power is several times larger than the above calculation result.
In addition, the duty cycle of the anti-exciting switching power supply is constantly changed according to the output voltage. When designing the switch power supply circuit, you must note that when the switch power supply is just switched on, the energy storage filter capacitor is just starting to charge because the switch power supply is just starting to work, the circuit will generate a transitional process. When the input power supply is just connected, the voltage at both ends of the energy storage filter capacitor is very low, and the output voltage is also very low, it may make the duty cycle of the working switch very high, so that the Transformer Core is saturated, and the power switch is damaged due to over-current or over-voltage.
For simple analysis, the effects of load current are not taken into account in figures 1-23 and 1-24. If the effects of load current are taken into account, the voltage increase rate will decrease when the capacitor is charged, at the same time, when the switch is on, because the capacitor is to discharge to the load, the voltage at both ends of the capacitor will also decrease. When the energy storage filter capacitor is charged, the voltage at both ends of the capacitor changes at the speed of the sine curve. When the energy storage filter capacitor is discharged, the voltage at both ends of the capacitor changes at the rate of the exponential curve.
To verify that the voltage at both ends of the capacitor changes at the rate of the exponential curve, we further analyze the charging and discharging process of the capacitor in Figure 1-19. When the switch is switched on and off, due to the opposite polarity of the output voltage of the transformer secondary coil, the reverse bias of the rectifier diode ends. The energy storage filtering capacitor starts to discharge the load, and the discharge current of the capacitor is determined by the following formula:
 
Where a is an Arbitrary Constant. When T = 0, the voltage at both ends of the capacitor is UC:
 
The formula (1-115) is used to calculate the formula for capacitor discharge. μ c is the voltage at both ends of the capacitor, UC is the initial voltage when the capacitor is just discharged, and RC is the time constant, the time constant is generally expressed by σ, that is, σ = RC.
 
Figure 1-25 shows the voltage variation during capacitor discharge. When the capacitor is discharged, the voltage starts to decrease from the maximum value. When the discharge time is σ, the voltage at both ends of the capacitor is only 37%. When the discharge time is 2.3 ≈, the voltage at both ends of the capacitor is only 10%. When the discharge time is infinite, the voltage at both ends of the capacitor is 0. However, in practical application, the operating frequency of the switching power supply is usually very high, that is, the discharge and electrical time of the capacitor are very short. Therefore, the voltage of each discharge of the capacitor is relatively small, the voltage ripple is only a few percent relative to the output voltage, because the storage capacity of the filter capacitor is usually large.
By the way, it is pointed out that the charge and discharge time constants of the filter capacitors of the switching power supply are usually large, dozens of times the Switching Power Supply frequency period, or even hundreds of times. Therefore, the energy storage filter capacitor can be charged according to the sine curve or discharge according to the exponential law. We can regard it as charging and discharging according to the linear (straight line) law. This is because the curvature of the sine or exponent curve changes very little in the initial phase. Therefore, when analyzing the circuit parameters of the switching power supply, the average value is basically used for analysis, and the waveforms are basically drawn as square waves (rectangles) or sawing shapes.
The average value method is used to analyze complex problems, which can simplify complex problems. This is very simple for engineering design or calculation, the analysis or calculation results are accurate enough for engineering applications. Therefore, this simple method is mainly used later.