Typical flyback topology design - achieving optimal power supply

The flyback topology is the most common isolated power supply topology because it can provide multiple isolated outputs with a low-side switch transistor and a limited number of external components. However, the flyback power supply also has some peculiarities that may limit its overall performance if the designer does not fully understand and analyze them.

For this topology, this article will use a very simple mathematical method to unveil the mystery of all flyback power supply designs and guide designers to complete an optimized design.

Flyback Converter

Depending on the application, a DC-DC application (DC/DC application) may require multiple outputs and output isolation. In addition, the isolation of the input from the output may have to comply with safety standards or provide impedance matching.

Not only does an isolated power supply protect the user from potentially lethal voltages and currents, it also offers performance advantages. By interrupting the ground loop, an isolated power supply maintains instrument precision and can smoothly provide a positive regulated voltage from a negative power bus without sacrificing the benefits of the bus.

For designers, the flyback topology has historically been the first choice for power isolation converters with output power below 100 W. This topology requires only one magnetic component and one output rectifier, which has the advantages of simplicity and low cost, while it can also easily implement multiplexed outputs.

However, the disadvantages of the flyback topology are that it requires a high-value output capacitor, high current stress on the power switch and output diode, high eddy current loss in the air gap area, a large transformer core, and possible EMI problems.

The flyback converter is derived from the buck-boost topology, whose main disadvantage is that energy is collected from the source only during the on-time of the switching MOSFET. During the subsequent off-time, this energy from the primary winding is transferred from the inductor to the output. This is a characteristic of both flyback and buck-boost topologies. (Figure 1)

Figure 1: A typical flyback power supply operating in continuous conduction mode.

When the primary and secondary currents flow simultaneously, the flyback transformer does not work normally like a traditional transformer. In fact, only a small part of the energy (magnetization energy) is stored in the transformer. The flyback transformer is more like multiple inductors on the same core rather than a typical transformer. Ideally, the transformer does not store energy, and all energy is transferred from the primary side to the secondary side instantly.

The flyback transformer can be used as an energy storage device, where the energy is stored in the air gap of the iron core or in the distributed air gap of the Permalloy powder core.

The design of the inductor transformer should minimize leakage inductance, AC winding losses and core losses.

Leakage inductance is the portion of the primary inductance that is not coupled to the secondary inductance. It is important to keep the leakage inductance as low as possible because it reduces the efficiency of the transformer and can also cause spikes on the drain of the switching element. Leakage inductance can be thought of as a portion of the energy stored in the transformer that is not transferred to the secondary and the load. This energy needs to be dissipated on the primary side by an external snubber. The configuration of the snubber will be discussed later.

When the MOSFET is turned on and voltage is applied to the primary winding, the primary current increases linearly. The change in input current is determined by the input voltage, the transformer primary inductance and the on-time. During this time, energy is stored in the transformer core, the output diode D1 is reverse biased, and energy is not transferred to the output load. When the MOSFET is turned off, the magnetic field begins to decrease, reversing the polarity between the primary and secondary windings. D1 is forward biased and energy is transferred to the load.

Discontinuous Conduction Mode vs Continuous Conduction Mode:

Flyback converters, like any other topology, have two different operating modes – discontinuous conduction mode (DCM) and continuous conduction mode (CCM). When the output current increases beyond a certain value, the discontinuous mode design circuit will switch to continuous mode. In discontinuous mode, all the energy stored in the primary side during the on-time is completely transferred to the secondary side and the load before the next cycle starts; and there is a dead time between the instant when the secondary current reaches zero and the start of the next cycle. In continuous mode, when the next cycle starts, some energy will still be left in the secondary side. The flyback converter can operate in both modes, but it has different characteristics.

On the one hand, discontinuous conduction mode has a higher peak current and therefore a higher output voltage spike when switching off. On the other hand, it has a faster load transient response and a lower primary inductance, so the transformer size can be smaller. The reverse recovery time of the diode is not important because the forward current is zero before the reverse voltage is applied. In discontinuous conduction mode, the turn-on of the transistor occurs with zero collector current, which reduces the noise of conducted EMI.

Continuous conduction mode has lower peak current and thus reduces output voltage spikes. However, its control loop is more complicated because its right half plane (RHP) zero forces the overall bandwidth of the converter to be reduced. Since continuous conduction mode is the preferred mode for most applications, only this mode is analyzed in more detail above.

Determining Flyback Transformer: Winding Turns Ratio and Its Inductance

The first challenge designers have to deal with is determining the flyback transformer. Often they can choose from a catalog of standard flyback power transformers, rather than a more expensive custom transformer. Many suppliers offer a complete line of transformers for different applications and power sizes, but it is important to understand how to choose the most appropriate transformer. In addition to the power size and number of turns on the secondary winding, transformers can be classified by the primary/secondary winding turns ratio, and the primary or secondary inductance.

If the effect of the voltage drop across the switching MOSFET and the output rectifier diode is ignored, under steady-state execution conditions, the voltage*seconds during the on-time () should be equal to the voltage*seconds during the off-time ():

(1)

In the formula:

is the input voltage

is the output voltage

is the primary turns/secondary turns ratio of the flyback transformer

Then, the direct relationship between the maximum duty cycle turns ratio and the minimum input and output voltage is:

(2)

Where D is the duty cycle: / switching cycle.

In many cases, the maximum duty cycle selected is 50%, but in applications with a wide input voltage range, it is important to understand how to optimize the following relationships: maximum duty cycle, transformer turns ratio, peak current, and rated voltage.

One of the main advantages of the flyback topology is that it can operate at duty cycles greater than 50%. The increase in the maximum duty cycle reduces the peak current on the primary side of the transformer, thereby achieving a higher utilization factor of the primary copper transformer and reducing the ripple of the input source. At the same time, the increase in the maximum duty cycle increases the maximum stress voltage between the drain and source of the main switch MOSFET and increases the peak current on the secondary side.

Before starting to design a converter, it is important to understand the relationship between the maximum duty cycle, the transformer primary/secondary turns ratio (Np/Ns), the maximum voltage stress of the primary MOSFET, and the maximum current on the primary and secondary sides.

Formula (2) shows the main relationship between the output voltage Vo and the input voltage Vi (due to its simplicity, the voltage drop across Q1 and the secondary rectifier Q2 is not considered). In order to ensure the regulation of Vo over the entire input voltage range, the maximum duty cycle can be arbitrarily selected to a theoretical value of <1.

Then Np/Ns can be calculated:

(3)

Here, represents the maximum voltage between the drain and source of the main MOSFET, which can be obtained from formula (4) and formulas (5) and (6), respectively, which represent the average current on the primary and secondary sides of the transformer.

In the formula:

is the forward voltage drop of the secondary rectifier diode

is the voltage drop across the switching MOSFET during conduction

is the overall power efficiency

is the maximum output current

The optimal occupancy ratio can be obtained by maximizing the utilization coefficient U(D) function of the occupancy ratio:

The utilization factor (Ui) is obtained by dividing the output power by the sum of the total maximum stress of the secondary side switching MOSFET and the rectifier diode.

Figure 2: Utilization factor vs. duty cycle for a typical flyback converter. The duty cycle for maximum utilization is 30-40%.

The two curves in the figure show the utilization factor calculated considering only the switching MOSFET stress (blue dashed line), and the utilization factor considering the secondary-side switching MOSFET and rectifier diode (red dashed line).

To optimize the power efficiency for a rated input voltage, the primary/secondary transformer turns ratio is calculated using the duty cycle to maximize the utilization factor, which is typically between 30-40%.

The curves above consider the theoretical stress voltage on the active device. In practice it is more important to evaluate how the MOSFET maximum stress voltage and the transformer turns ratio vary with the chosen maximum duty cycle, and choose a turns ratio value that gives a 'round' turn ratio within a certain maximum breakdown voltage of the switching MOSFET.

Determine the primary inductance

There are several criteria for selecting primary and secondary inductors.

First, select a primary inductor that ensures continuous mode operation from full load to some minimum load.

Second, calculate the primary and secondary inductances by determining the maximum secondary ripple current.

Third, the primary inductance is manipulated to keep the right half plane zero (RHP) as high as possible, thereby significantly increasing the closed-loop crossover frequency.

In practice, the first criterion is only used in special cases, and the magnetizing inductance is chosen as the best compromise between transformer size, peak current and RHP zero.

In order to determine the maximum ripple current on the secondary side to calculate the primary and secondary inductances, the secondary inductance () and primary inductance () can be calculated using the following formulas:

(8)

Where is the switching frequency and is the allowable secondary ripple current, which is usually set at about 30-50% of the effective value of the output current:

(9)

Then, the equivalent primary inductance can be obtained from the following formula:

(10)

As mentioned before, the primary inductance and duty cycle affect the right half plane zero (RHP). The RHP adds phase lag to the closed loop control characteristic, forcing the maximum crossover frequency to be no more than 1/4 of the RHP frequency.

RHP is a function of duty cycle, load, and inductance, and can cause and increase loop gain while reducing loop phase margin. A common practice is to determine the worst-case RHPZ frequency and set the loop unity gain frequency below one-third of the RHPZ.

In the flyback topology, the formula for calculating RHPZ is:

(11)

The primary inductance can be selected to reduce this undesirable effect.

The curves in Figure 3 show the effect of primary inductance on primary and secondary currents and RHP zero: as the inductance increases, the ripple current decreases, so the input/output ripple voltage and capacitor size may also decrease. However, the increased inductance increases the number of transformer primary and secondary windings, while reducing the RHP zero.

Figure 3: Relationship between primary and secondary ripple current, RHP zero point and primary inductance of a typical flyback design.

It is generally recommended that the inductor should not be too large, as this affects the overall closed-loop performance and size of the entire system, as well as the losses of the flyback transformer. The above graphs and formulas are only valid for a flyback implementation in continuous conduction mode.

Select the power switch MOSFET and calculate its losses

The selection of the MOSFET is based on the maximum stress voltage, maximum peak input current, total power loss, maximum allowable operating temperature, and the current drive capability of the driver. The source-sink breakdown (Vds) of the MOSFET must be greater than:

(12)

The continuous drain current (Id) of the MOSFET must be greater than the primary peak current (Equation 15).

In addition to the maximum rated voltage and maximum rated current, the other three important parameters of MOSFET are Rds(on), gate threshold voltage and gate capacitor.

There are three types of losses in switching MOSFETs, namely conduction losses, switching losses, and gate charge losses:

The conduction losses are equal to the losses, so the total resistance between source and drain in the on-state should be as low as possible.

Switching loss is equal to: switching time * Vds * I * frequency. Switching time, rise time and fall time are functions of the MOSFET gate-drain Miller charge Qgd, the driver internal resistance and the threshold voltage. The minimum gate voltage Vgs (th) helps the current pass through the drain-source of the MOSFET.

Gate charge loss is caused by the gate capacitor charging and then discharging to ground each cycle. Gate charge loss is equal to: frequency * Qg (tot) * Vdr

Unfortunately, the components with the lowest resistance tend to have higher gate capacitance.

Switching losses are also affected by the gate capacitor. If the gate driver charges a bulk capacitor, the MOSFET needs time to ramp up in the linear region, and losses increase. The faster the rise time, the lower the switching losses. Unfortunately, this will result in high frequency noise.

The conduction loss does not depend on the frequency, it also depends on the square of the primary RMS current:

(13)

In continuous conduction mode, the primary current in flyback operation looks like a trapezoidal waveform as shown in the upper part of Figure 4.

Ib is equal to the primary side peak current:

Ia is the average current obtained from the above formula (5), minus half of the ΔIp current:

(16)

Then the RMS current of the switch tube can be obtained from the following formula:

(17)

or its rapid approach:

(18)

The switching losses () depend on the voltage and current during the transition, the switching frequency and the switching time, as shown in Figure 4.

Figure 4: Current and voltage waveforms across the MOSFET during commutation.

During the on-time, the voltage across the MOSFET is the input voltage plus the output voltage reflected on the primary side, and the current is equal to the average intermediate maximum current minus half ΔIp:

(19)

(20)

During the shutdown process, the voltage across the MOSFET is the input voltage plus the output voltage reflected in the primary winding, plus the Zener clamp voltage and absorption leakage inductance used for clamping. The switch tube cut-off current is the primary side peak current.

(twenty one)

The switching time depends on the maximum gate drive current and the total gate charge of the MOSFET. The MOSFET parasitic capacitor is the most important parameter for regulating the MOSFET switching time. The capacitors Cgs and Cgd depend on the geometric size of the component and are inversely proportional to the source voltage.

These capacitor values ​​are usually not provided directly by MOSFET manufacturers, but can be obtained from the Ciss, Coss, and Crss values.

The turn-on switching time can be estimated from the gate charge using the following formula:

(twenty two)

(twenty three)

In the formula:

Qgd is the gate drain charge

Qgs is the gate-source charge

is the on-time when the drive voltage is pulled up to the drive resistance

is the internal drive resistance when the drive voltage is pulled down to ground voltage

is the gate-source threshold voltage (the gate voltage at which the MOSFET starts to conduct)

Buffer:

The leakage inductance can be thought of as a parasitic inductance in series with the primary inductance of the transformer, where a portion of the primary inductance is not coupled to the secondary inductance. When the switching MOSFET is turned off, the energy stored in the primary inductance flows to the secondary and the load through the forward biased diode. The energy stored in the leakage inductance becomes a large voltage spike on the switch leg (MOSFET drain). The leakage inductance can be measured by shorting the secondary winding, while the primary inductance measurement is usually given by the transformer manufacturer.

A common method of dissipating the leakage inductance energy is to block the diode in series with the primary winding through a Zener diode in parallel with the primary winding, as shown in Figure 5.

(Figure 5: Zener clamp circuit)