Learn power supply technology from power supply expert Tao Xianfang (Part 2): The influence of leakage inductance and distributed capacitance on output waveform (Part 2)

When the switch tube starts to turn off, the external circuit adds a negative voltage (or low voltage) to the gate. Through electrostatic induction, the carriers (electrons) in the depletion layer of the switch tube will be redistributed under the action of the electric field, which is equivalent to the external circuit extracting carriers from the depletion layer. The concentration of carriers in the depletion layer will decrease exponentially, and the thickness of the depletion layer will also decrease with time. As a result, the resistance of the depletion layer will change from small to large over time. This process is very similar to the current flowing through the capacitor from large to small when the capacitor is charged; therefore, when the switch tube is just turned on, the switch tube can be equivalent to an ideal switch in parallel with a capacitor. This capacitor is the distributed capacitance Cds between the drain and the source. Figure 5 is a working principle diagram of the flyback switching power supply when the switch tube is turned off.

According to the above analysis, the gate capacitance Cgs has a greater impact on the conduction of the switch tube. The larger the capacitance, the longer the conduction rise time of the switch tube. The drain capacitance Cds has a greater impact on the turn-off of the switch tube. The larger the capacitance, the longer the turn-off storage time of the switch tube. Capacitors Cgs and Cds are also called diffusion capacitors. They have the properties of both resistance and capacitor charging and discharging. This property is mainly related to the change in carrier concentration in the depletion layer.

When the power switch is a transistor, Cgs and Cds correspond to Cbe and Cce respectively, and the working principle is basically the same or similar to that of the field effect tube. However, the increase or decrease of the density of carriers participating in the conduction in the base region is not due to the effect of electrostatic induction, but to the injection of base current.

Since the nature and function of the distributed parameters of the switch tube change during the on or off period, it is very difficult to accurately calculate the current loop composed of the distributed inductance Ls and distributed capacitance Cs, as well as Cgs and Cds in Figures 1 to 5. Below, we will analyze and calculate the above circuit in a long article.

In FIG4 , the distributed inductance Ls and the distributed capacitance Cs can be regarded as a series oscillation circuit. When the switch tube Q1 starts to turn on, the rising rate of the input pulse voltage is much greater than the rising rate of the voltage of the distributed capacitance Cs charged by the input voltage through the distributed inductance Ls. At this time, the series oscillation circuit starts to absorb energy, the input voltage charges Cs through Lds and Ls, and the current flowing through Ls and Cs increases according to a sine curve. When the switch tube Q1 is fully turned on, the value of Lds is equal to 0. At this time, the input pulse enters the flat-top stage, which is equivalent to the rising rate of the input pulse voltage being 0. Since the rising rate of the input pulse voltage is much smaller than the rising rate of the voltage when the distributed inductance Ls and the distributed capacitance Cs are charged and discharged, the oscillation circuit starts to release energy and the oscillation circuit will produce damped oscillation.

Since the time constants of the distributed inductance Ls and the distributed capacitance Cs are relatively small relative to the excitation inductance, the process of the distributed inductance Ls and the distributed capacitance Cs generating damped oscillation mainly occurs at the moment when the switch tube Q1 is turned on and off. Shortly after the switch tube Q1 is turned on or off, the damped oscillation will stop soon. When the input voltage fully charges the distributed capacitance Cs, the input voltage is fully applied to both ends of the excitation inductance. If it is a flyback switching power supply, the current flowing through the excitation inductance will increase linearly from 0 over time; if it is a forward switching power supply, the current flowing through the excitation inductance will increase according to a trapezoidal wave curve over time.

During the conduction period of the switch tube Q1, the distributed capacitance Cds is basically ineffective because the conduction internal resistance of the switch tube is very small. When the switch tube Q1 is switched from the on state to the off state, the distributed capacitance Cds between the drain and source of the switch tube will be connected to the circuit, and the distributed inductance Ls and the excitation inductance will simultaneously generate back electromotive force, and charge and discharge the distributed capacitance Cds and Cs respectively. In the process of alternating energy exchange between the capacitor and the inductor, series and parallel oscillations will be generated.

However, since the time constant of the excitation inductance is much larger than that of Ls, Cs and Cds, in the process of generating oscillation, Ls, Cs and Cds are the main factors that play a role. In addition, during the period when the switch tube starts to turn off, since Cds is actually a variable resistor with an impedance that changes from small to large, its impedance change process is similar to that of a capacitor charging. It only absorbs energy but does not release energy. Therefore, in the process of generating oscillation, it only affects the rising rate of the charging curve, but not the falling rate of the discharge curve.

FIG6 is a diagram showing the voltage waveform at both ends of the distributed capacitor Cs when the switch tube is turned on (FIG. 4) and the input voltage ui charges the distributed capacitor Cs through the leakage inductance Ls of the switching transformer, causing the leakage inductance Ls and the distributed capacitor Cs to produce impact oscillation in the circuits of FIG4 and FIG5; and the waveform at both ends of the D and S poles of the power switch tube when the input voltage ui, the leakage inductance Ls of the switching transformer and the distributed capacitors Cs and Cds produce charging and discharging when the switch tube is turned off (FIG. 5).

In Figure 6, Figure 6-a is the voltage waveform of the input voltage ui applied to both ends of the primary coil of the switching transformer when the power switch tube Q1 is turned on; Figure 6-b is the voltage waveform across the distributed capacitor Cs; Figure 6-c is the voltage waveform between the drain D and source S of the power switch tube Q1.

At t0, the power switch Q1 starts to conduct, and the input voltage ui is applied to both ends of the switch transformer. The input voltage ui first charges the distributed capacitance Cs through the distributed inductance Ls. At this time, since the rising rate of the input voltage ui is greater than the voltage rising rate of the current charging the distributed capacitance Cs through the distributed inductance Ls, the distributed inductance and distributed capacitance both absorb energy from the input voltage. When the input voltage ui is charging the distributed inductance Ls and the distributed capacitance Cs, the voltage across the distributed capacitance Cs rises according to the sine curve; and when discharging, the voltage across the distributed capacitance Cs drops according to the cosine curve.

At time t1, the current flowing through Ls reaches its maximum value, and the voltage across the distributed capacitor Cs is equal to the input voltage ui (or equal to the half-wave average value Upa of the forward output of the primary coil of the transformer). At this time, the rising rate of the input voltage ui is 0, and the rising rate of the input voltage ui is less than the rising rate of the voltage uc charged by the distributed inductance Ls to the distributed capacitor Cs. Therefore, the distributed inductance Ls begins to release energy to continue to charge the distributed capacitor Cs. At this time, Ls is releasing energy, while the input voltage ui and the distributed capacitor Cs are absorbing energy, and the voltage uc across the distributed capacitor Cs continues to rise according to the sine curve.

At time t2, the current flowing through Ls is equal to 0 (the energy stored in Ls is completely released), and the back electromotive force generated by the distributed inductance finishes charging the distributed capacitance Cs. At this time, the voltage across Cs also reaches the maximum value, and then Cs begins to discharge Ls and the input voltage ui according to the cosine curve. The current flowing through Ls begins to reverse, and Ls begins to store magnetic energy in the reverse direction.

At time t3, the voltage across Cs is equal to the input voltage ui again, and the capacitor stops discharging. At this time, the magnetic energy stored in Ls will be converted into back electromotive force es to reverse charge the capacitor Cs, making the voltage across Cs lower than the input voltage ui.

At time t4, the reverse current flowing through Ls is equal to 0, the voltage across Cs reaches the minimum value, and then the input voltage starts to charge Cs through Ls. At this point, the first charge and discharge cycle of the distributed inductance Ls and the distributed capacitance Cs ends.

After time t4, the process of input voltage ui charging the distributed inductance Ls and distributed capacitance Cs, and the process of distributed inductance Ls and distributed capacitance Cs charging each other, are basically the same as those from time t0 to t4. However, since the input voltage rise rate is equal to 0 during this period, the input voltage no longer provides energy to the distributed inductance Ls and distributed capacitance Cs. Therefore, the amplitude of the free oscillation generated by the distributed inductance Ls and distributed capacitance Cs decays with time, and its decay rate is related to the size of the equivalent resistance.

At time t10, the amplitude of the damped free oscillation generated by the distributed inductance Ls and the distributed capacitance Cs is attenuated to almost zero. At this time, the voltage across the distributed capacitance Cs is equal to the half-wave average value Upa of the forward output of the primary coil of the transformer. For the calculation method and definition of the half-wave average values ​​Upa and Upa-, please refer to equations (1-70) and (1-71) and their explanations in Chapter 1.

In Figure 6-b, Upa is the half-wave average value of the forward output voltage of the transformer primary coil, which is equal to the input voltage; Upa- is the half-wave average value of the flyback output voltage of the transformer primary coil, which is related to the duty cycle; when the duty cycle is equal to 0.5, Upa- is equal to the input voltage in value, but has opposite signs.

At time t11, the power switch tube Q1 begins to turn off. Since the current path flowing through the distributed inductance Ls and the excitation inductance is suddenly cut off, it will inevitably generate back electromotive force and, these two back electromotive forces will be connected in series with the input voltage ui to charge the distributed capacitors Cs and Cds. However, since the voltage across Cs is basically equal to the voltage, the voltage used to charge the distributed capacitor Cds is exactly the sum of the input voltage ui and the back electromotive force voltage and.

At time t12, the power switch tube Q1 has been completely turned off, but the back electromotive force and the input voltage ui continue to charge the distributed capacitances Cs and Cds. However, at this time, the capacity of Cds has become very small, because it represents the diffuse capacitance inside the switch tube, which is a resistor. When the switch tube is completely turned off, the resistance is infinite.

Until the moment t13, the magnetic energy stored in the distributed inductor Ls is basically released, and the two back electromotive forces and stop charging the distributed capacitors Cs and Cds; at this time, the voltages at both ends of the distributed capacitors Cs and Cds reach the maximum value, that is, the voltage added to the drain of the power switch tube Q1 reaches the maximum value; then, the distributed capacitor Cs discharges the original charging loop and generates free oscillation, but because the impedance of the power switch tube Q1 is invalid after it is turned off, its discharge loop can only be carried out through the equivalent R and the excitation inductance, so the amplitude quickly decays to 0. Figure 3-c shows the waveforms at both ends of the power switch tubes D and S.

In Figure 6-c, Uda is the half-wave average value of the voltage between the D and S poles during the period when the switch tube Q1 is turned off. Uda is equal to the sum of the input voltage ui (ui=U) and the half-wave average value Upa- of the flyback output voltage generated by the primary coil of the transformer; Udp is the peak value of the voltage between the D and S poles during the period when the switch tube is turned off. The values ​​of Udp and Uda are both related to the duty cycle. When the duty cycle is equal to 0.5, Uda is approximately equal to 2 times the input voltage ui (ui=U), while Udp is greater than 2 times the input voltage. The value of Udp is also related to the value of the leakage inductance Ls. The larger the value of Ls, the larger the value of Udp.

By the way, it is difficult to measure the waveform in Figure 6-b, because the process of free oscillation of the distributed inductance Ls and the distributed capacitance Cs is basically carried out between the distributed inductance and distributed capacitance inside the transformer, and it is difficult to measure it directly with an instrument; but by measuring the waveform of the secondary coil of the transformer, the amplitude of the waveform in Figure 6-b can also be indirectly measured; and the waveform in Figure 6-c can be measured directly, and the amplitudes of both are related to the numerical value of the distributed inductance Ls and the resistance value of the equivalent resistance R. The larger the numerical value of the distributed inductance Ls, the larger the amplitude, and the larger the resistance value of the equivalent resistance R, the larger the amplitude.

When the free oscillation is very strong, it will cause EMI interference to the surrounding circuits or electronic devices in the form of electromagnetic radiation. This point must be paid attention to when designing the switching transformer, and the value of the distributed inductance Ls should be minimized.