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Mind The Gap And Improve Your Low-Power Flyback Transformer Design

The low-power (milliwatt) flyback transformer used in a switched-mode power supply (SMPS) needs to be designed with a gap in the magnetic path for maximum power delivery over temperature. Transformers built on ferrite structures are typically gapped for higher-power storage capability or for large dc currents.

In low-power or low-dc-current applications, where a machined gap isn’t needed for power or current handling, there still needs to be a gap to stabilize the ferrite’s temperature variation characteristics and provide improved power delivery to the load.

The flyback transformer is very different from a signal transformer, and not making the distinction can lead to poor performance. Actually, the flyback transformer is a coupled inductor and not a transformer in the true sense.

In the signal transformer, current flows in the primary and secondary windings at the same time, inversely proportional to the turns ratio of the windings. In a flyback transformer, current flow is restricted to one winding at a time.

Designing a flyback transformer using a ferrite core that doesn’t have a gap might seem appealing for low-power (milliwatt range), low-current applications. But don’t fall into this trap because it will cause poor performance. The power delivery of the SMPS using this ungapped transformer will be limited.

This limitation is not apparent at room temperature, normal input voltages, or normal load demand. But it will become obvious at high temperature with low input voltage or increased load demand. Thus, an important aspect of flyback transformer design is to “mind the gap.”

Figure 1 shows a simplified typical SMPS converter using a flyback transformer. A source voltage is switched on and off, by means of a transistor (MOSFET), drawing current through the flyback transformer’s primary.

When the transistor is on (tON), the current through the primary windings ramps up in proportion to the applied voltage and inversely to the value of the primary inductance. Because of the blocking diode and the polarity of the secondary winding, there is no current flow in the secondary winding at this time.

When the transistor opens (tOFF), the primary winding current drops to zero, causing the voltages on all of the windings to reverse in polarity. With the secondary polarity reversed, the secondary current can now flow through the forward biased diode. The energy stored in the core transfers to the secondary windings and into a charging output capacitor and the load.

For the SMPS circuit in Figure 1, a typical current through the primary winding is expressed via a well-known electrical engineering formula using the inductance, voltage, and current relationship:

The voltage (V) across an inductor winding produces a ramping current (di/dt) with respect to the inductance value (L). Figure 2 shows some typical waveforms from a flyback SMPS circuit (such as the one shown in Figure 1).

Peak current in the primary winding is the magnitude that the current reaches at the end of the transistor time on (tON). Figure 2 shows this as the maximum value of current (ILp) (after ramping up at the slope value of di/dt) as expressed by Equation 1.

When a constant value of voltage is applied across an inductor winding, the current ramping will be steeper (ramps faster) for a lower value of inductance and flatter (ramps slower) for a higher value of inductance. Inductance value and ramping current are inversely proportional.

High values of di/dt (low inductance) result in added ripple currents that need to be compensated for or filtered out. However, low values of di/dt (high inductance) result in less energy stored and transferred to the load (since energy is directly related to the square of the current). These dynamic situations can be compensated for with feedback to alter the pulse width to the switching transistor, but there is a limit due to the switching frequency.

In pulse-width mode (PWM), the (tON) period is manipulated by a pulse-width controller device, which sends a signal to the gate of the MOSFET in Figure 1, based on feedback circuitry from the load. In pulse-frequency mode (PFM), the frequency of the switching is altered to accommodate changes in load demand. The feedback to the control circuit is from load voltage or current sensing devices.

These control circuits are designed around the assumption that the inductance of the flyback transformer is within specified values. When the inductance value varies beyond the specified limit, the power delivering capability of the SMPS suffers.

A standard practice for designing a flyback transformer is to evaluate the energy needs of the SMPS and, using information from the ferrite manufacturer, choose a ferrite platform that will accommodate these needs. Ferrite cores offer self-shielded shapes with bobbins that are easily wound, an alternative to powder iron toroids or E cores. When the inductance value is calculated by the power-supply designer and the maximum current is then known, the stored energy is calculated by:

In many SMPS applications, energy and power are significant, and large ferrite shapes with gaps machined into the magnetic path must be used. But in today’s world of portable, low-power devices, the energy requirements can be minimal and small ferrite shapes (i.e., EP7) are used for the flyback transformer design. In some instances, the requirements are so low, a gap is not needed for energy purposes.

For example, a 300-µH inductance value that must allow 100 mA of average current has an I2L power requirement of 3 × 10–5 joules. Using a ferrite manufacturer’s data on energy versus gap size, such as the tabulated data from a Ferroxcube graph in Table 1, an EP7 ferrite size with a gap of less than 0.1 mm is specified. This gap size is the lowest value listed, essentially a non-gapped value. Unless the ferrite mating surfaces are polished, this gap distance is the average physical distance due to uneven surfaces of non-gapped cores.

Specifying a ferrite core without a gap has its advantages in the design of many magnetic components. But the flyback SMPS power capability will suffer if an ungapped ferrite core is used. For non-flyback, non-inductor applications, one advantage of an ungapped magnetic path is that it allows a minimum number of turns of copper wire to achieve a specific value of inductance.

When a gap is introduced into the ferrite core’s magnetic path, the overall ferrite structure’s ability to produce a specific inductance using a minimum number of wire turns (also called the AL value) is changed significantly. If one machines a gap in the core, the needed turns will increase, and this would increase the winding resistance.

These two characteristics, machining a gap (more cost) and adding resistance (more losses), are typically unattractive to transformer manufacturers. So to the novice designer, eager to produce a low-cost, seemingly efficient flyback transformer, the use of an ungapped ferrite is at first appealing. However, the lowpower ferrite flyback transformer should in almost all applications be designed using a gapped ferrite shape.

Ungapped ferrites for low-power flyback transformers aren’t a good choice mainly because of the fluctuation in inductance over temperature. Figure 3 illustrates typical AL values (inductance producing capabilities per turn squared) of gapped and non-gapped ferrite cores over temperature, based on the data in Table 2. Notice the large variations in the ungapped ferrite as compared to the almost constant response of the gapped ferrite.

A flyback transformer, using an ungapped ferrite with an inductance value of 300 µH at room temperature, would have an inductance value of 170 µH at –40°C and 570 µH at 120°C. With a gap, the values of inductance are 285 µH at –40°C and 311 µH at 120°C. This is within a 10% tolerance over the extended temperature range with a gapped ferrite versus about a 200% variation with an ungapped ferrite.

At high temperatures, the inductance of a non-gapped flyback transformer increases significantly. An increase in the inductance has the same effect as a drop in the input voltage, as seen in Equation 1. Much has been written about minimum input voltage for SMPS design, as it is a critical value. Minimum input voltage (or high flyback transformer inductance) and maximum output load increase the power demand on the SMPS.

These conditions cause the ON time (duty cycle) of the switching to increase, as the circuit works to feed more current and power to the load. Most SMPS designers use minimum input voltage, minimum output impedance (maximum load), desired efficiency, and maximum duty cycle time to calculate the inductance value of the flyback transformer. A transformer may be designed to meet this value at room temperature. But without a gap, trouble arises when the temperature increases.

The discontinuous mode flyback SMPS has a maximum duty cycle. Once that limit is reached, the SMPS cannot produce any further power from a constant input voltage. The ungapped flyback transformer will reach this limitation when subjected to high temperature, low input voltage, or increased power demand.

In discontinuous mode, all of the energy stored in the primary is allowed to disperse into the secondary before a new cycle starts. Figure 2 shows this “dead” time as a period where there is no current flow in either the primary or the secondary.

Continuous-mode design allows a new cycle to start while there is still energy in the transformer. Additional circuitry can be employed to create a flyback SMPS that will transition from discontinuous into continuous mode, but this adds cost. Figure 4 compares the gapped flyback transformer waveforms to the non-gapped flyback transformer at high temperatures. Both the gapped and non-gapped flyback transformers had the same primary inductance at room temperature.

The current waveform for the gapped flyback transformer reaches a higher peak value in less time, indicative of its lower inductance value and higher di/dt slope value. There is a dead time of zero current before the next cycle starts keeping it well within the discontinuous mode. The waveform for the ungapped flyback transformer does not reach the needed peak current, because at higher temperature its inductance has increased, lowering its di/dt slope value.

To remain in the discontinuous mode, the time ON has to be restricted so all the energy stored can be dissipated into the load (secondary). The ungapped flyback transformer SMPS is unable to provide the same amount of power as the gapped flyback transformer SMPS when temperature increases.

Remember that flyback transformers aren’t truly transformers, but coupled inductors that need stable inductance at high temperatures to deliver maximum power. Trying to save 10% to 20% of the cost of a gapped ferrite by leaving it ungapped can lead to poor power delivery performance at high temperatures, low input voltage, and high power demand. The ferrite flyback transformer needs to have a gap. When it comes to ferrite flyback transformer design, be sure to “mind the gap.”

1. Pressman, Abraham, Switching Power Supply Design 2nd Edition, Chapters 1 and 4, McGraw-Hill Inc., 1998.

2. Lenk, John, Simplified Design of Switching Power Supplies, Chapters 1 and 3, Butterworth-Heinemann, 1995.

3. Joshi, Rahal, “Control Technique Cuts Flyback Input Capacitance,” Power Electronics Technology, April 2007.

4. Billings, Keith, “Designing Flyback Transformer for Discontinuous Mode,” Power Electronics Technology, April 2003.

5. “Soft Ferrites and Accessories.” Ferroxcube, 2009.

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