Explore the key principles of transformer switching power supply

During Toff, the control switch K is turned off, and the current flowing through the primary coil of the transformer suddenly becomes 0. Since the current in the primary coil loop of the transformer changes suddenly, and the magnetic flux in the iron core of the transformer cannot change suddenly, the current flowing through the secondary coil loop of the transformer must also change suddenly to offset the influence of the sudden change in the primary coil current of the transformer. Otherwise, a very high back electromotive force voltage will appear in the primary coil loop of the transformer, breaking down the control switch or the transformer.

If the magnetic flux ф in the transformer core changes suddenly, the primary and secondary coils of the transformer will generate infinitely high back electromotive force, which in turn will generate infinitely large current. The magnetic lines of force generated by the current in the coil will resist the change of magnetic flux. Therefore, the change of magnetic flux in the transformer core will ultimately be constrained by the current in the primary and secondary coils of the transformer.

Therefore, during the Toff period when the control switch K is turned off, the magnetic flux in the transformer core is mainly determined by the current in the transformer secondary coil loop, that is:

e2 =-N2*dф/dt =-L2*di2/dt = i2R —— K off period (1-64)

The negative sign in the formula indicates the polarity of the back electromotive force e2, that is, the polarity of the induced electromotive force generated by the secondary coil of the transformer when K is turned on and off is exactly opposite. Solving the differential equation of formula (1-64) yields:

In the formula, C is a constant. Substituting the initial conditions into the above formula, it is easy to find C. When the control switch K suddenly turns from the on state to the off state, the current in the transformer primary coil circuit suddenly becomes 0, and the magnetic flux in the transformer core cannot change suddenly. Therefore, the current i2 in the transformer secondary coil circuit must be exactly equal to the current i2 (Ton+) during the period when the control switch K is on, and the sum of the excitation current in the transformer primary coil circuit converted to the transformer secondary coil circuit current. Therefore, formula (1-65) can be written as:

In formula (1-66), the first term in the brackets represents the current in the secondary coil circuit of the transformer , and the second term represents the current obtained by converting the excitation current in the primary coil circuit of the transformer to the secondary coil circuit of the transformer.

The output voltage uo of the single-excitation transformer switching power supply is equal to:

Up- in (1-68) is the peak value of the counter-attack output voltage, or the maximum output voltage. It can be seen that at the moment when the control switch K is turned off, when the load of the transformer secondary coil loop is open, the transformer secondary coil loop will generate a very high back electromotive force. Theoretically, it takes time t equal to infinity for the output voltage of the transformer secondary coil loop to be 0, but this situation generally does not happen because the control switch K cannot be turned off for that long.

It can be seen from formula (1-67) that the working principle of the switching power supply transformer is different from that of an ordinary transformer. When the switching power supply works in forward mode, the working principle of the switching power supply transformer is basically the same as that of an ordinary transformer; when the switching power supply works in flyback mode, the working principle of the switching power supply transformer is equivalent to an energy storage inductor. If we represent the positive and negative half-waves of the output voltage uo with the average values ​​Upa and Upa- respectively, we have:

Integrate equations (1-71) and (1-72) respectively to obtain:

From this we can find that the area of ​​the positive half-wave of the output voltage of the single-excitation transformer switching power supply is exactly equal to the area of ​​the negative half-wave, that is:

Formula (1-75) is used to calculate the half-wave average values ​​Upa and Upa- of the output voltage of the single-excitation transformer switching power supply. In the above formulas (1-73), (1-74), and (1-75), Upa and Upa- are defined as the positive half-wave average value and the negative half-wave average value, respectively, referred to as the half-wave average value, and Ua and Ua- are called the weekly average values.

The half-wave average values ​​Upa and Upa-, as well as the one-week average values ​​Ua and Ua-, are very important concepts for analyzing the working principle of the switching power supply. They are often used below, so be sure to remember them clearly here.

In a switching power supply , the forward voltage and the flyback voltage exist at the same time, but in a single-excitation switching power supply, generally only one voltage can be used for power output. This is because single-excitation switching power supplies generally require that the output voltage is adjustable, that is, the magnitude of the switching power supply output voltage is adjusted by changing the duty cycle of the control switch. For example, in a forward switching power supply, only the Upa voltage on the left side of the equal sign in equation (1-75) provides power output to the load, and by changing the duty cycle of the control switch, the average value of its output voltage can be changed; in a flyback switching power supply, only the Upa- voltage on the right side of the equal sign in equation (1-75) provides power output to the load, and by changing the duty cycle of the control switch, the half-wave average value of its output voltage can be changed.

In formula (1-75), if Upa on the left side of the equal sign is regarded as the forward voltage, then Upa- on the right side of the equal sign can be regarded as the flyback voltage, and vice versa. In a forward switching power supply, since only the forward voltage Upa provides power output to the load, the flyback voltage Upa- is equivalent to an auxiliary product that needs to be recycled separately; in a flyback switching power supply, since only the flyback voltage Upa- provides power output to the load, the forward voltage Upa is equivalent to storing energy to provide energy output to the flyback voltage Upa-.

If there is no current output in the forward voltage in (1-75), the forward voltage cannot be regarded as a forward output voltage. We should regard it as a process of the flyback output voltage, that is, storing energy for the flyback output voltage. Although this definition is a bit forced, its main purpose is to enhance our understanding of the working principle of the switching power supply.

This is because, in equation (1-75), both the forward voltage Upa and the reverse voltage Upa- are generated by the magnetic flux generated by the excitation current flowing through the primary coil of the transformer, which is generated by the mutual inductance. However, the magnetic flux generated by the excitation current does not directly provide energy output to the forward voltage Upa, because the magnetic flux in equations (1-71), (1-72), (1-73), and (1-74) is not generated by the forward voltage, but by the excitation current. Although the magnetic flux ф generated by the excitation current will generate a forward voltage through electromagnetic induction, it does not generate a forward current output, that is, the excitation current does not provide power output for the forward output voltage. Regardless of the forward output power or current, the change in the excitation current or magnetic flux in the primary coil of the transformer is only related to the input voltage and the primary inductance of the transformer, and has nothing to do with the forward output power or current.

This is because we divide the magnetic flux ф in the transformer core into two parts, namely: the magnetic flux generated by the excitation current and the magnetic flux generated by the forward current for analysis. The magnetic flux generated by the forward output current and the magnetic flux generated by the current flowing through the primary coil of the transformer are opposite in direction and can cancel each other out, and the remaining magnetic flux is exactly what is generated by the excitation current; therefore, only the magnetic flux generated by the excitation current will generate the flyback output voltage and current. The forward output voltage is only related to the input voltage of the transformer and the turns ratio of the primary and secondary coils of the transformer. The two voltage output mechanisms are not exactly the same. In the transformer switching power supply, the calculation of the forward output voltage is relatively simple, while the calculation of the flyback output voltage is relatively complicated. Therefore, if it is not absolutely necessary, it is best to use the concept of half-wave average value and formula (1-75) to calculate the half-wave average value of the forward voltage to deduce the half-wave average value of the flyback output voltage. Therefore, formula (1-75) is mainly used to calculate the half-wave average value of the flyback output voltage.

In addition, special attention should be paid to the following: In formula (1-75), the amplitude or half-wave average value of the forward voltage will not change with the change of the on-time Ton or the duty cycle D of the control switch; while the amplitude or half-wave average value of the flyback voltage will change with the change of the on-time Ton or the duty cycle D of the control switch. The larger the duty cycle D, the higher the amplitude or half-wave average value of the flyback voltage. The difference between the forward switching power supply and the flyback switching power supply is not only the difference in the polarity of the output voltage, but more importantly, the different parameter requirements of the transformer; in the forward switching power supply, the energy of the flyback output voltage is generally smaller than that of the forward output voltage, and sometimes it can even be ignored.

The output voltage of the forward switching power supply is:

From equations (1-76), (1-77), (1-78) and (1-79), we can see that:

When the switching power supply works in the forward output state, changing the duty cycle D of the control switch K can only change the average value Ua of the output voltage, while the amplitude Up of the output voltage remains unchanged; when the switching power supply works in the flyback output state, changing the duty cycle D of the control switch K can not only change the amplitude Up- of the output voltage uo, but also change the average value Ua- of the output voltage.

It should also be noted here that in the formula (1-78) that determines the output voltage of the flyback switching power supply, the concept of the maximum or peak value Up- of the flyback output voltage is not used, and the Up used in the formula is exactly the peak value of the forward-strike output voltage. This is because the maximum or peak value Up- of the flyback output voltage is more complicated to calculate (formula (1-68)), and the amplitude of the peak value Up- is unstable, and it will change with the change of the output load size; while the peak value Up of the forward-strike output voltage will not change with the change of the output load size.