Principle and Design of switched series switching power supply (V)

Figure 1-7 is another type of tandem switch power supply, which is generally called a reverse series switch power supply. The difference between this type of reverse series Switching Power Supply and general series-connected switching power supply is that the output voltage of this type of reverse series switching power supply is negative voltage, this is exactly the opposite of the normal voltage polarity output by the common tandem switch power supply. Because the energy storage inductance L outputs current to the load only when the switch K is turned off, under the same conditions, the output current of the reverse series switching power supply is twice the output current of the series switching power supply.
In general, most of the circuits use single polarity power supply, but in some special cases, sometimes two sets of power supply are required, one of which is a negative power supply. Therefore, it is convenient to use the reverse series Switching Power Supply shown in Figure 1-7 as the negative power supply.

In Figure 1-7, the UI is the input power supply, k is the control switch, L is the energy storage inductance, D is the rectification diode, C is the energy storage filter capacitor, and r is the load resistance. When the control switch K is switched on, the input power supply UI starts to power on the energy storage inductance L, the current flowing through the energy storage inductance L begins to increase, and the current also produces a magnetic field in the energy storage inductance; when the control switch K is switched from on to off, the energy storage inductance will generate a back-potential force, so that the current continues to flow, and is rectified by the rectification Diode D, and then filtered by the capacitor energy storage, then the current output is provided to the load R. The control switch K is continuously switched on and off, and a negative voltage output can be obtained on the load R.

Figure 1-8, Figure 1-9, and Figure 1-10 respectively indicate that the duty cycle of the control switch K is d equal to 0.5, <0.5,> 0.5, figure 1-7 voltage and current waveforms of several key points in the circuit. Figure 1-8-a), fig 1-9-a), fig 1-10-a) respectively control the output voltage of the switch K uo waveform; fig 1-8-b), fig 1-9-9-b), fig 1-10-b) the waveforms of the voltage UC at both ends of the energy storage filter capacitor are shown in Figure 1-8-C, Figure 1-9-C, and Figure 1-10-C respectively. It should be noted that the current waveform in Figure 1-8-c), figure 1-9-c), and figure 1-10-c should be negative based on principle, however, when a negative value is obtained, it is difficult to compare it with Figure 1-5 and figure 1-6. Therefore, when performing a specific calculation, pay attention to the current and voltage directions.
When the switch is switched on, the control switch K is switched on, and the power supply UI starts to power the energy storage inductance L. During this period, the voltage El at both ends of the energy storage inductance L is:
El = LDI/dt = UI -- k connection period (1-19)
Perform the following points on the (1-19) formula:

In the formula, Il is the instantaneous value of the L current flowing through the energy storage inductor, t is the time variable, and the initial current of I (0), that is, before the control switch K is switched on instantly, the current flowing through the energy storage inductor L. When the switching power supply is in the critical continuous current state, I (0) = 0, so we can obtain the maximum current flowing through the energy storage inductance L:
ILM = UI/L * ton -- instant before K shutdown (1-21)
When Toff is switched off, the control switch K is switched off. The energy storage inductance L converts the current ILM into a back-EMR, and continues to provide energy to the load R through the rectification Diode D, during this period, the voltage El at both ends of the energy storage inductor L is:
El = LDI/dt =-uo -- K during Shutdown (1-22)
Negative signs before-uo in formula, indicating that the direction in which the inductance generates the EMF during K shutdown is exactly the opposite to that in which the inductance generates the EMF during K-on. Perform the following points for the (1-22) formula:

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 (1-23) is the ILM in (1-21), that is:
I (ton +) = ILM -- instant before K shutdown (1-24)
Therefore, the (1-9) format can be rewritten:
IL = (UO/L) * t + ILM -- K shutdown period (1-25)
When T = toff, il reaches the minimum value. The minimum value is:
ILX = (UO/L) * toff + ILM -- instant before K connection (1-26)
The output voltage of the reverse series switching power supply is generally the amplitude of the negative pulse. When the switching power supply is in the critical continuous current state, the initial current I (0) flowing through the energy storage inductor is equal to 0 (see Figure 1-8-A), that is: (1-26) the minimum ILX of the energy storage inductor current in the formula is 0. Therefore, from (1-21) and (1-26), the output voltage of the reverse series switching power supply can be obtained:

From the (1-27) type, we can see that the output voltage of the inverted series switching power supply is proportional to the input voltage and the switch-on time, and is inversely proportional to the switch-off time.
In addition, we can see from figure 1-8 that, due to the reverse series switching power supply, only when the control switch K is switched off, the back-EMR will be generated to provide energy to the load. Therefore, when the duty cycle is 0.5, the average output current IO is 1/4 of the maximum current flowing through the energy storage inductor; when the duty cycle is less than 0.5, the average Io of the output current is less than 1/4 of the maximum current flowing through the energy storage inductance (Figure 1-9). When the duty cycle is greater than 0.5, the average Io of the output current is greater than 1/4 of the maximum current flowing through the energy storage inductance (Figure 1-10 ).