Principle and Design of switching power supply circuit transition process (20)

1-7-2. Transition Process of switching power supply circuit
We have analyzed all the switching power supply circuits and seldom mentioned the concept of circuit transition. In fact, in the switching power supply circuit, the changes of current and voltage in the circuit are all in the circuit transition process. However, to make the analysis simple, the circuit transition process is basically ignored. If you carefully analyze the switching power supply circuit, the current in the output circuit is generally not linear or jagged; the output voltage is not a rectangular or jagged wave, we treat them as rectangular or jagged waves, the change rate or value is treated as an average value within a specific condition or range.
In a circuit with inductance, capacitance, and resistance, the voltage and current during the circuit transition are generally changed according to the curve of the exponential function, and the sine or cosine function is a special case of the exponential function. In a circuit with a transitional process, we cannot simply use the calculation method of the sine wave circuit for analysis, and it is difficult to analyze accurate results by using the method of Fu's transformation. It is the best method to analyze the circuit transition process by using differential equations.
During the circuit transition process, the initial values of voltage or current must be considered. Only when the initial value is basically 0 or tends to be a fixed value can the circuit transition process be considered to have entered a stable State, but strictly speaking, this situation does not exist in the switching power supply circuit. Because the active switch in the switch power supply is always switching back and forth between the active state of the switch on and off, and the duty cycle D is changing, it is impossible to have a stable value. However, we can treat the switching power supply as a special case, or repeat the initial values of voltage or current in the switching power supply circuit, it can be considered that the switching power supply has been working in a stable State.
For example, when the switching power supply is switched on or off within one or two working cycles, the initial values of the voltage or current of a circuit are basically equal or very close, we can think that the switching power supply has entered a stable working state.
When the switching power supply enters the stable state, for simplicity, we generally use the average or half-wave average of voltage or current for circuit calculation or analysis. For example, when calculating the current flowing through the load, we generally use the average value of the output voltage (UO) for calculation, and seldom consider the impact of the output voltage ripple on the load, the result of calculating the load current is the average Io that flows through the load current.
However, in the design of the switching power supply, the transition process of the switching power supply at the start time cannot be ignored, because the storage charge of the energy storage filter capacitor is 0, which requires a lot of work cycles, only when the energy storage filter capacitor is fully powered can the voltage at both ends be basically stable, and the switching power supply can enter a stable working state. Next, we will analyze in detail the transition process of the switching power supply at the start time.
 

In Figure 1-19, when the active switch is switched from power-on to power-off, the back-EMR generated by the secondary Coils of the switching power supply transformer is:
 
In formula, Q is the charge volume stored by the capacitor, c1 and c2 are the undetermined coefficient, ω =, is the angle frequency, that is, the charge rate of the capacitor. To simplify the process, we often save the subscript of inductance L and capacitor C in the case of no confusion.

 

When T = 0 and q = 0, C1 = 0 is obtained. When T = toff, due to the large capacity of the capacitor, A capacitor is generally not fully charged within a working cycle. It takes more than a dozen cycles to fully fill the capacitor. When the capacitor is fully charged, the voltage at both ends of the capacitor can reach the peak of the power supply voltage, that is, q = UPC. Therefore, C2 = UPC is obtained, so (1-112) the time t in the (1-112), (1-113), and (1-114) types is not continuous for capacitor charging, it is superimposed on a sine curve segment and segment, 23.
 

Figure 1-23-a) shows the pulse waveform of the transformer secondary coil output voltage. The dotted line is the output waveform of the transformer secondary coil before the rectification (half-wave average), and the solid line is the actual output waveform, due to the limiting effect of the diode, the actual output voltage is much lower than normal operation. The output voltage of the transformer secondary coil is charged by the rectifying diode during the switching from power-on to power-off of each Working switch, the voltage at both ends of the energy storage filter capacitor is increased step by step, and the output voltage is also increased step by step.
Figure 1-23 B) is the voltage waveform of the energy storage filter capacitor for charging. It requires multiple working cycles before it can fully charge the energy storage filter capacitor. Therefore, the voltage at both ends of the energy storage filter capacitor is in a sine curve. The voltage at the two ends of the energy storage filter capacitor is increased like a stair-up until the voltage at both ends of the energy storage filter capacitor reaches the maximum value.
Figure 1-23-c) is the current waveform of the first and second coils of the transformer. In the figure, I1 is the current flowing through the primary coil of the transformer, and I2 is the current flowing through the secondary coil of the transformer (dotted line shows ). In fact, the current I2 in the transformer coil does not decrease linearly, but changes according to the cosine or exponential curve. However, because of its small curvature change, we regard it as a straight line in an approximate way, or use the average value of the change rate to correspond to the output voltage waveform (Rectangular Wave.