Optimizing Flyback Design Step by Step

Flyback is the most well-known isolated power supply topology because it can provide multiple isolated outputs with a low-side switching transistor and a limited number of external components. However, there are some peculiarities of flyback power supplies that can limit their overall performance if the designer does not fully understand and analyze them.

This series of articles on this topology will demystify all flyback power supply designs with very simple mathematical methods and guide designers to complete a well-optimized design.

Flyback Converter

Depending on the application, DC-DC applications (DC/DC applications) may require multiple outputs and output isolation. In addition, the isolation of the input from the output may be required to meet safety standards or provide impedance matching.

Isolated power supplies not only protect users from potentially lethal voltages and currents, but also offer performance advantages. By interrupting ground loops, isolated power supplies can maintain instrument accuracy and easily provide a positive regulated voltage from a negative power bus without sacrificing bus benefits.

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

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

The flyback converter is derived from the buck-boost topology, and its main disadvantage is that the converter only collects energy from the source 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 unique feature of the flyback and buck-boost topologies. (Figure 1)

When the primary and secondary currents flow simultaneously, the flyback transformer does not work like a conventional transformer, and only a small portion of the energy (the magnetizing energy) is actually stored in the transformer.

The flyback transformer is more like multiple inductors on the same core than a typical transformer. Ideally, the transformer does not store energy, and all energy is transferred from the primary to the secondary in an instant.

(Figure 1: Typical flyback power supply operating in continuous conduction mode)

The flyback transformer can be used as an energy storage device, and the energy is stored in the air gap of the 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 part of the primary inductance that is not coupled to the secondary inductance. Keeping the leakage inductance as low as possible is very important because it reduces the efficiency of the transformer and can also cause spikes on the drain of the switching device. The leakage inductance can be considered as part 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 the voltage is applied to the primary winding, the primary current rises 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 drop, 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 modes of operation – discontinuous mode and continuous mode.
When the output current increases beyond a certain value, the circuit designed in discontinuous mode switches to continuous mode.

In discontinuous mode, all the energy stored in the primary during the on-time is completely transferred to the secondary and the load before the next cycle begins; there is also a dead time between the instant when the secondary current reaches zero and the start of the next cycle.
In continuous mode, some energy is still left in the secondary when the next cycle starts.
A flyback converter can operate in both modes, but it has different characteristics.

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

Continuous mode has a lower peak current and therefore a lower output voltage spike. Unfortunately, its control loop is more complex 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 the Flyback Transformer: Turns Ratio and Inductance

The first challenge that 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 turns ratio, and the primary or secondary inductance.

If the effects of the voltage drop across the switching MOSFET and the output rectifier diode are ignored, under steady-state operating conditions, the on-time ( ) volts*seconds should be equal to the off-time ( ) volts*seconds:
(1)
Where:
• is the input voltage
• is the output voltage
• is the primary turns/secondary turns ratio of the flyback transformer
The direct relationship between the maximum duty cycle turns ratio and the minimum input-to-output voltage is then:
(2)
Where D is the duty cycle: /switching period.

In many cases, the maximum duty cycle is selected to be 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%. An 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, an increase in the maximum duty cycle increases the maximum stress voltage between the drain and source of the main switching MOSFET and increases the peak current on the secondary side.

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

Equation (2) gives 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 regulation over the entire input voltage range Vo, the maximum duty cycle can be arbitrarily selected to a theoretical value <1.
Then Np/Ns can be calculated:
(3)

The maximum voltage between the drain and source of the main MOSFET is selected, and is given by formula (4) and formulas (5) and (6), which represent the average current on the primary and secondary sides of the transformer respectively.
Where:
• is the forward voltage drop of the secondary rectifier diode
• is the voltage drop of the switching MOSFET during conduction
• is the overall power supply efficiency
• is the maximum output current
The optimal duty cycle can be obtained by maximizing the duty cycle utilization coefficient U (D) function:

(7)

(4)

(5)

(6)

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

To optimize the power supply efficiency at the rated input voltage, the primary/secondary transformer turns ratio should be calculated with the duty cycle to maximize the utilization factor, with typical values ​​between 30-40%.

(Figure 2: Utilization factor vs. duty cycle for a typical flyback converter, with a duty cycle of 30-40% to maximize the utilization factor)
The above curves consider the theoretical stress voltage on the active components. In practice, it is more important to evaluate how the MOSFET maximum stress voltage and the transformer turns ratio vary with its chosen maximum duty cycle, and choose a value that gives a "round" turns ratio value within a certain maximum breakdown voltage of the switching MOSFET.

Determine the Primary Inductance:

There are several criteria for selecting the primary and secondary inductors.
First, choose 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, calculate the primary inductance to keep the right half plane zero (RHP) as high as possible, thereby maximizing the closed-loop crossover frequency.
In practice, the first criterion is only used in special cases, and the magnetizing inductance is selected as a good compromise between transformer size, peak current, and RHP zero.
To calculate the primary and secondary inductances by determining the maximum secondary ripple current, the secondary inductance ( ) and the primary inductance ( ) can be calculated using the following equations:

(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 previously, 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.

The 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 to less than one-third of the RHPZ.
In a flyback topology, the formula for calculating RHPZ is:

(11)

The primary inductance can be chosen to mitigate this undesirable effect.

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

Common sense suggests that an inductor that is too large should not be used, so as not to affect 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 flyback operation in continuous conduction mode.

(Figure 3: Primary and secondary ripple currents, RHP zero and primary inductance relationship for a typical flyback design)

Select the power switching 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-drain 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 the MOSFET are Rds(on), gate threshold voltage, and gate capacitance.
There are three types of losses in a switching MOSFET, namely conduction losses, switching losses, and gate charge losses:
• Conduction losses are equal to losses, so the total resistance between the source and drain in the on state should be as low as possible.
• Switching losses are equal to: switching time * Vds * I * frequency. The 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) facilitates current flow through the MOSFET drain-source.
• Gate charge losses are caused by the charging of the gate capacitance and the subsequent discharge to ground with each cycle. Gate charge losses are equal to: frequency * Qg(tot) * Vdr
Unfortunately, the lowest resistance devices tend to have higher gate capacitance.
Switching losses are also affected by gate capacitance. If the gate driver charges the bulk capacitance, 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 losses do not depend on frequency, they also depend on the square of the primary RMS current:
(13)
In continuous conduction mode, the primary current of a flyback operation will look like the trapezoidal waveform shown in the upper portion of Figure 4.

(Figure 4: Current and voltage waveforms across the MOSFET during commutation)
Ib is equal to the primary peak current:
(14)

(15)
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 it rapidly approaches:
(18)
The switching loss ( ) depends on the voltage and current during the transition, the switching frequency, and the switching time, as shown in Figure 4.
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 central top 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 off current is the primary peak current.

(21)
The switching time depends on the maximum gate drive current and the total gate charge of the MOSFET. The MOSFET parasitic capacitance is the most important parameter for regulating the MOSFET switching time. The capacitances Cgs and Cgd depend on the device geometry and are inversely proportional to the drain-source voltage.
Usually MOSFET manufacturers do not directly provide these capacitance values, but they can be obtained from the Ciss, Coss, and Crss values.
The turn-on switching time can be estimated using the gate charge using the following formula:

(twenty two)

(23)
Where:
• Qgd is the gate drain charge
• Qgs is the gate source charge
• is the on-time drive resistance when the drive voltage is pulled up to the drive voltage
• is the internal drive resistance when the drive voltage is pulled down to ground
• is the gate source threshold voltage (the gate voltage at which the MOSFET starts to turn on)

Buffer:

The leakage inductance can be viewed as a parasitic inductance in series with the primary inductance of the transformer, with a portion of the primary inductance not coupled to the secondary inductance. When the switching MOSFET turns off, the energy stored in the primary inductance moves to the secondary and the load through the forward biased diode. The energy stored in the leakage inductance has nowhere to go and becomes a large voltage spike on the switch pin (MOSFET drain). The leakage inductance can be measured by shorting the secondary winding, while the primary inductance is usually given by the transformer manufacturer.
A common method of dissipating the leakage inductance energy is to block the series diode with a Zener diode in parallel with the primary winding, as shown in Figure 5.

(Figure 5: Zener clamp circuit)
The leakage inductance energy must be dissipated by an external clamp buffer:

(24)
The Zener voltage should be lower than the maximum drain-source voltage of the switching MOSFET minus the maximum input voltage, but high enough to dissipate this energy in a very short time.
The maximum power loss of the Zener diode is:
(25)

Flyback Design Resources:

To support flyback designs, National Semiconductor has developed a series of PWM regulators and controllers specifically suited for flyback applications. Typical flyback reference designs, application notes, mathematical spreedsheets, and online simulation tools can be found on the company website (www.power.national.com) to guide designers in optimizing flyback power supply designs.

Figure 6 shows a typical 5W flyback power supply using an LM5000 regulator, simulated using WEBENCH®, with an input voltage range of 10 to 35V and an output voltage of 5V at 1A. The design follows the above process, with a Coilcraft transformer primary to secondary turns ratio of 3 and a primary inductor of 80μH to ensure a well-regulated output voltage, minimize the primary peak current to less than 1.3A, and keep the maximum voltage across the internal switching MOSFET less than 60V. The 80μF primary inductor

ensures that the secondary ripple current peak-to-peak is within 30% of the average current while maintaining a right half plane zero above 20kHz.

(Figure 6: Typical 5W flyback design using WEBENCH® online simulation tool)

WEBENCH® is an online design tool from National Semiconductor. It can realize a complete switching power supply design in four simple steps. Figures 7 and 8 show the Bode plots and switching waveforms obtained by using WEBENCH design.

(Figures 7-8: Bode plots and switching waveforms of output voltage and switch pins)