Basic Principle and Circuit Design of Discontinuous Mode Flyback Converter

1. Introduction
　　The flyback converter topology is widely used in low-power applications ranging from 5W to 150W. The important advantage of this topology is that no filter inductor is required at the output of the converter, which saves cost and reduces size. In the description of some previous Chinese reference materials, since both the circuit and magnetic circuit design are involved, it is easy to cause confusion in the design process, and some characteristics of the flyback converter circuit itself are not properly reflected. In the literature [1], the basic working principle of the flyback converter is introduced, and the design process of the discontinuous mode flyback converter and the relationship between various parameters are described concisely and accurately. Since the circuit design and magnetic circuit design are introduced separately, it is very helpful for readers to master the design of the flyback converter. The magnetic circuit design is not involved in this article, and can be referred to in relevant literature.

2. Basic principle of discontinuous mode flyback converter
　　When the switch tube of the flyback converter is on, the transformer stores energy and the load current is provided by the output filter capacitor. When the switch tube is off, the energy stored in the transformer is converted to the load to provide load current, while charging the output filter capacitor and compensating for the energy lost during the switch tube on period.
　　Figure 1a is the basic topology of the flyback converter. There are two output circuits in the figure, a master output and a slave output. The negative feedback closed loop samples the master output voltage Vom. The sampled value of Vom is compared with the reference value, and the output error signal amplification signal controls the on-time pulse of Q1, so that the sampled value of Vom is equal to the reference voltage when the grid and load change, thereby stabilizing the output voltage. The slave output follows the master output and is adjusted accordingly.
　　The working process of the circuit is as follows: When Q1 is turned on, the same-name end (with ·) of all coils is negative relative to the non-same-name end (without ·). The output rectifier diodes D1 and D2 are reverse biased, and the output load current is provided by the output filter capacitors C1 and C2.
　　During the conduction period of Q1, a fixed voltage (Vdc-1) is applied to Np (here it is assumed that the on-state voltage drop of the switch tube is 1V), and a current with a linear increase of slope dI/dt=(Vdc-1)Lp flows through, where Lp is the magnetizing inductance of the primary side. At the end of the on-time, the primary current rises to Ip=(Vdc-1)Ton/Lp. This current represents the energy stored in the inductor.

Here E is in joules, Lp is in henry, and Ip is in amperes.
　　When Q1 is turned off, the current in the magnetic inductor forces the polarity of all coils to reverse. Assume that there is no secondary winding at this time, only the primary and secondary windings. Since the current in the inductor cannot change instantaneously, at the moment of shutdown, the primary current is transferred to the secondary with an amplitude of Is = Ip (Np/Nm).
　　After several cycles, the secondary DC voltage Vom has been established. As Q1 is turned off, the same-name terminal on Nm is positive polarity, and the current flows out of the same-name terminal and decreases linearly (Figure 1c), with a slope of dIs/dt=Vom/Ls, where Ls is the secondary inductance. If the secondary current drops to 0 before the next conduction time, the energy stored in the primary inductance is completely released to the load, and the circuit is said to operate in discontinuous mode. The input power is expressed as the energy E released during a conduction time T of Q1, then at the end of this cycle, the power absorbed from Vdc is

　　In addition, since Ip=(Vdc-1)Ton/Lp, then

　　It can be seen from equation (2b) that as long as the product of VdcTon is kept constant, the feedback loop keeps the output voltage constant.

3. Relationship between output voltage, input voltage, on-time and load
　　If the converter efficiency is 80%, then

　　From (2b), we can see that the maximum on-time

Occurs at minimum supply voltage,so

So,

Right now

　　In this way, when Vdc or Ro increases, the feedback loop will adjust the output by reducing Ton. When Vdc or Ro decreases, Ton increases.

4. Circuit design process and the relationship between various parameters

4.1 Determine the primary/secondary turns ratio
　　In the correct design process, there are many parameters that need to be determined. The first is to select the primary/primary-secondary turns ratio Np/Nsm. This parameter determines the maximum turn-off voltage stress on the power switch tube.

(Leakage inductance spikes are not considered). Ignoring leakage inductance spikes, at maximum DC inputand 1V rectifier dropout, the maximum switch voltage stress is

　　Assuming the leakage inductance peak is 0.3Vdc, under the condition that the maximum rated value of the switch tube related parameters (Vceo, Vcer or Vcev) has a safety margin greater than 30%,

The choice should be as low as possible.

4.2 Ensure that the core is not saturated and the circuit remains in discontinuous mode
　　In order to ensure that the core does not deviate from the hysteresis loop, the conduction volt-second product (A1 in Figure 1d) must be equal to the reset volt-second product (A2 in Figure 1d). Assuming that the conduction voltage drop of Q1 and the forward conduction voltage drop of D2 are both 1V,

Here Tr is the reset time, which is also the time required for the secondary current to return to 0, see Figure 1c.
　　In order to ensure that the circuit operates in discontinuous mode, the dead time (Tdt in Figure 1c) is set so that the maximum on time

(Occurs when Vdc is minimum) plus the reset time Tr, it is only 80% of the entire cycle. A margin of 0.2T is left to cope with unexpected decreases in Ro, because according to formula (3), if Ro decreases, the feedback loop will increase Ton to keep Vo constant.
　　Since the error amplifier is designed to keep the loop stable when discontinuous, if the circuit intermittently enters continuous mode, oscillation will occur. The process of oscillation is as follows: an increase in DC load current or a decrease in Vdc causes the error amplifier to increase Ton to keep Vo constant, see formula (3). The increase in Ton causes a decrease in the dead time Tdt, and even the secondary current does not drop to 0 before the next conduction time of Q1 begins. This is the beginning of the continuous mode. If the error amplifier does not have a very low bandwidth to cope with this situation, the circuit will oscillate. To ensure that the circuit remains in discontinuous mode, the maximum conduction time must satisfy the following relationship

Right now

　　When Np/Nsm has been determined by formula (4)

When calculated, there are only two unknowns in (5) and (6), so we can get from these two equations

4.3 Primary inductance determined by minimum output resistance and minimum DC input voltage
　　From (3), the primary inductance is

4.4 Switching peak current, maximum voltage stress
　　If it is a bipolar transistor, when the peak current is

There should be acceptably high gain when

is certain. (9)                               

and                （6）

         (3)

             (2b) (2a)