*Most of the Isolated Offline Power Supplies less than 100W are flybacks. These converters have many advantages over other topologies. It is the least expensive isolated topology because it uses the fewest number of components. The transformer behaves as a coupled inductor, which stores the energy in the gap. This eliminates the need for a separate LC filter on each output. *

*By Florian Mueller, Texas Instruments*

Most of the Isolated Offline Power Supplies less than 100W are flybacks. These converters have many advantages over other topologies. It is the least expensive isolated topology because it uses the fewest number of components. The transformer behaves as a coupled inductor, which stores the energy in the gap. This eliminates the need for a separate LC filter on each output.

The transformer is the most important component that determines the performance of an offline design. Specifying the transformer of a quasi resonant flyback (QR Flyback) is quite complex and needs a lot of experience. The primary inductance turns ratio between the primary and the secondary windings, which defines the operating mode of the controller. The transformer will determine if the controller works in transition mode or deep in discontinuous mode for fixed input voltage and full load. Incorrect calculated primary inductance can decrease the efficiency or can make it impossible to deliver the full output power. This article shows an easy way to optimise the transformer. Typically this approach leads to higher efficiency for full load.

### Quasi Resonant Flyback Controller

There are two kinds of QR flyback controllers. The first only modulates the switching frequency (like UCC28610), the second modulates the switching frequency and the primary peak current (e. g. UCC28600, LM5023). This article only describes the more complicated controller which modulates the switching frequency and the primary peak current at the same time.

### Frequency and current modulated QR Controller

Figure 2 shows the relationship between the switching frequency and the output power of the QR Flyback Controller LM5023 from Texas Instruments.

The controller operates at a defined switching frequency for full load. As the output power decreases the switching frequency increases up to a maximum switching frequency clamp of usually 130kHz. For loads that are lower than approximately 30% full rated power (dashed line), the LM5023 works in frequency foldback mode (FFM), where the peak switch current is constant and modulating the switching frequency regulates the output voltage.

The operating mode for full load is called quasi resonant mode (QR mode), where the frequency varies in order to have the switching event happen on the first resonant valley that occurs after the demagnetising of the transformer. After the secondary side current has ramped down to zero (core is completely demagnetised) there will be a resonant ringing, caused by the primary inductance and the energy stored in the parasitic capacitances. The controller detects the valley of the resonant ringing and turns on the mosfet. Why does the frequency decrease with increasing load during QR mode? Higher output power means that more energy must be stored and thus a longer on time is needed. A longer on-time leads to a higher primary current and because of the fixed transformers turns ratio also to a higher secondary current. The demagnetising time is longer because the higher secondary currents needs more time to ramp down to zero. The longer on-time and the longer demagnetising time results in a lower switching frequency for higher output power. In opposite decreasing the load means increasing the switching frequency as long as the controller is operating in QR mode.

### Turns ratio

The turns ratio N_{turns} between the primary and secondary winding defines the flyback voltage. The higher the flyback voltage, the lower the voltage of the valley of the resonant ringing. Therefore, switching losses will be reduced. Zero voltage switching can be achieved if the flyback voltage is equal to the input voltage. The disadvantage of a high flyback voltage is the high voltage stress of the mosfet. The maximum voltage seen by the mosfet is the input voltage, plus the flyback voltage, plus the voltage spike due to the leakage inductance. A good tradeoff is to choose a flyback voltage a bit lower than the minimum input voltage.

### Primary Inductance

The primary inductance should be calculated carefully, because it defines the operating mode and the switching frequency. For maximum output power and minimum input voltage the operating frequency must be higher than the minimum switching frequency clamp of the controller. If the operating frequency is too low the controller will skip pulses and may get unstable. If the operating frequency is too high the controller will work deep in discontinuous conduction mode over most of the input voltage range, resulting in lower efficiency. A good starting point is to set the switching frequency for low line at least 20kHz above the minimum switching frequency clamp. This will give enough margin during large transients on the output.

Unfortunately, the equation to calculate the primary current for a controller who modulates both the switching frequency and the primary peak current is very complicated.

Using the energy balance and ideal components makes it possible to derive a simple formula for the primary inductance.

Derivation of the primary inductance:

V

_{in}= minimum input voltage

V

_{out}= output voltage

P

_{out}= output power

N

_{turns}= primary to secondary turns ratio

L

_{pri}= maximum allowed primary inductance

This equation gives an acceptable result even though all components are supposed to be ideal and the time it takes to hit the first valley after the demagnetising is not considered. Taken into account real components the resulting recommended primary inductance will be approximately 5 to 10% lower.

### A 16W QR Flyback Design example:

Input voltage = 90VAC – 265VAC

Output voltage = 24V

Output current = 0.7A

Output power = 16.8W

Allowing an input ripple of 30% the minimum input voltage will be 89.1V (90VAC x root (2) x 0.7). Therefore, a flyback voltage of about 80V is chosen. The calculated turns ratio is 3.3. The efficiency is estimated by 85%. Assuming a minimum switching frequency clamp of 30kHz (data can be taken from datasheet), the switching frequency for full load and low line will be set to 50KHz to get 20kHz of frequency margin.

The calculated primary inductance is 890uH.

Considering a deviation of maximum 10% for real components, the maximum recommend inductance value will be 800uH. The primary inductance should be equal or lower to keep the minimum switching frequency above 50kHz.

A test report of the fully tested and working design can be found at: http://www.ti.com/tool/pmp8655

**Conclusion **

The transformer is the “heart” of the flyback. An optimal turns ratio and a carefully chosen primary inductance pushes the efficiency to its achievable maximum. Unfortunately, the equations to estimate the behaviour of the system can be quite complicated. For example, solving a cubic equation is necessary to determine the peak primary current. The derived equation provides a very fast way to get a good starting point for the primary inductance. Nevertheless, a good understanding of the QR operation is essential to achieve optimal performance. Texas Instruments datasheets of QR flyback controllers (see references) provides useful information about this popular topology.

**References**

[1] “Datasheet UCC28600”, Texas Instruments, http://www.ti.com/product/ucc28600

[2] “Datasheet UCC28610”, Texas Instruments, http://www.ti.com/product/ucc28610

[3] “Datasheet UCC28700”, Texas Instruments, http://www.ti.com/product/ucc28700

[4] “Datasheet LM5023”, Texas Instruments, http://www.ti.com/product/lm5023

[5] “Reference Design PMP8655”, Florian Mueller, Texas Instruments,http://www.ti.com/tool/pmp8655