For a defined secondary current loading, the value of H
is defined. Hence, for the DC
conditions, B may be considered the dependent variable.
It should be noted that the gapped core can support a much larger value of H (DC
current) without saturation. Clearly, the higher value of H, H
, would be sufficient to
saturate the ungapped core in this example (even without any ac component). Hence an
air gap is very effective in preventing core saturation that would be caused by any DC
current component in the windings. When the flyback converter operates in the continu-
ous mode, (as shown in figure 2.1,5(b)), a considerable DC current component is pres-
ent, and an air gap must be used.
Figure 2.2.1b shows the flux density excursion $B
(which is required to support the
applied ac voltage) applied to the mean flux density B
developed by the DC component
for the nongapped and gapped example. For the nongapped core, a small DC polar-
ization of H
will develop the flux density B
. For the gapped core, a much larger DC
) is required to produce the same flux density B
. Further, it is clear that in
the gapped example the core will not be saturated even when the maximum DC and ac
components are added.
In conclusion, Fig. 2.2.1b shows that the change in flux density $B
required to sup-
port the applied ac conditions does not change when an air gap is introduced into the core.
However, the mean flux density B
(which is generated by the DC current component in
the windings) will be very much less if a gap is used.
The improved tolerance to DC magnetization current becomes particularly important
when dealing with incomplete energy transfer (continuous-mode) operation. In this mode
the flux density in the core never falls to zero, and clearly the ungapped core would
Remember, the applied volt-seconds, turns, and core area define the required ac
change in flux density $B
applied to the vertical B axis, while the mean DC current,
turns, and magnetic path length set the value of H
on the horizontal axis. Sufficient
turns and core area must be provided to support the applied ac conditions, and suf-
ficient air gap must be provided in the core to prevent saturation and support the DC
2.3 GENERAL DESIGN CONSIDERATIONS
In the following design, the ac and DC conditions applied to the primary are dealt with
separately. Using this approach, it will be clear that the applied ac voltage, frequency, area
of core, and maximum flux density of the core material control the minimum primary turns,
irrespective of core permeability, gap size, DC current, or required inductance.
It should be noted that the primary inductance will not be considered as a transformer
design parameter in the initial stages. The reason for this is that the inductance controls
the mode of operation of the supply; it is not a fundamental requirement of the trans-
former design. Therefore, inductance will be considered at a later stage of the design
process. Further, when ferrite materials are used at frequencies below 60 kHz, the follow-
ing design approach will give the maximum inductance consistent with minimum trans-
former loss for the selected core size. Hence, the resulting transformer would normally
operate in an incomplete energy transfer mode as a result of its high inductance. If the
complete energy transfer mode is required, this may be obtained by the simple expedient
of increasing the core gap beyond the minimum required to support the DC polarization,
thereby reducing the inductance. This may be done without compromising the original
2. FLYBACK TRANSFORMER DESIGN
When ferrite cores are used below 30 kHz, the minimum obtainable copper loss will
normally be found to exceed the core loss. Hence maximum (but not optimum*) efficiency
will be obtained if maximum flux density is used. Making B large results in minimum
turns and minimum copper loss. Under these conditions, the design is said to be “satura-
tion limited,” At higher frequencies, or when less efficient core materials are used, the core
loss may become the predominant factor, in which case lower values of flux density and
increased turns would be used and the design is said to be “core loss limited.” In the first
case the design efficiency is limited; optimum efficiency cannot be realized, since this
requires core and copper losses to be nearly equal. Methods of calculating these losses are
shown in Part 3, Chap. 4.
2.4 DESIGN EXAMPLE FOR A 110-W FLYBACK
Assume that a transformer is required for the 110-W flyback converter specified in Part 2,
2.4.1 Step 1, Select Core Size
The required output power is 110 W. If a typical secondary efficiency of 85% is assumed
(output diode and transformer losses only), then the power transmitted by the transformer
would be 130 W.
We do not have a simple fundamental equation linking transformer size and power rat-
ing. A large number of factors must be considered when making this selection. Of major
importance will be the properties of the core material, the shape of the transformer (that
is, its ratio of surface area to volume), the emissive properties of the surface, the permitted
temperature rise, and the environment under which the transformer will operate.
Many manufacturers provide nomograms giving size recommendations for particular
core designs. These recommendations are usually for convection cooling and are based
upon typical operating frequencies and a defined temperature rise. Be sure to select a ferrite
that is designed for transformer applications. This will have high saturation flux density,
low residual flux density, low losses at the operating frequency, and high curie tempera-
tures. High permeability is not an important factor for flyback converters, as an air gap will
always be used with ferrite materials.
Figure 2.2.2 shows the recommendations for Siemens N27 Siferrit material at an operating
frequency of 20 kHz and a temperature rise of 30 K. However, most real environments will
not be free air, and the actual temperature rise may be greater where space is restricted or less
when forced-air cooling is used. Hence some allowance should be made for these effects.
Manufacturers usually provide nomograms for their own core designs and materials. For a
more general solution, use the “area-product” design approach described in Part 3, Sec. 4.5.
In this example an initial selection of core size will be made using the nomogram shown
in Fig. 2.2.2. For a flyback converter with a throughput power of 130 W, an “E 42/20” is
indicated. (The nomogram is drawn for 20-kHz operation; at 30 kHz the power rating of
the core will be higher.)
The static magnetization curves for the N27 ferrite (a typical transformer material) are
shown in Fig. 2.2.3.
*In this context, optimum means equal core and copper losses.
FIG. 2.2.2 Nomogram of transmissible power P as a function of core size (volume), with
converter type as a parameter. (Courtesy of Siemens AG.)
FIG. 2.2.3 Static magnetization curves for Siemens N27 ferrite material. (Courtesy of
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2. FLYBACK TRANSFORMER DESIGN
2.4.2 Step 2, Selecting “on” Period
The maximum “on” period for the primary power transistor Q1 will occur at minimum
input voltage and maximum load. For this example, it will be assumed that the maxi-
mum “on” period cannot exceed 50% of a total period of operation. (It will be shown
later that it is possible to exceed this, using special control circuits and transformer
Frequency 30 kHz
Period 33 Ms
Half period 16.5 Ms
Allow a margin so that control will be well maintained at minimum input voltage; hence
the usable period is, say, 16 Ms.
2.4.3 Step 3, Calculate Minimum DC Input Voltage to Converter Section
Calculate the DC voltage V
at the input of the converter when it is operating at full load
and minimum line input voltage.
For the input capacitor rectifier filter, the DC voltage cannot exceed 1.4 times the rms
input voltage, and is unlikely to be less than 1.2 times the rms input voltage. The absolute
calculation of this voltage is difficult, as it depends on a number of factors that are not well
defined—for example, the source impedance of the supply lines, the rectifier voltage drop,
the characteristics and value of the reservoir capacitors, and the load current. Part 1, Chap.
6 provides methods of establishing the DC voltage.
For this example, a fair approximation of the working value of V
at full load will be
given by using a factor of 1.3 times the rms input voltage. (This is again multiplied by 1.9
when the voltage doubling connection is used.)
At a line input of 90 V rms, the DC voltage V
will be approximately 90 × 1.3 × 1.9 222 V.
2.4.4 Step 4, Select Working Flux Density Swing
From the manufacturer’s data for the E42/20 core, the effective area of the center leg is
240 mm2. The saturation flux density is 360 mT at 100°C.
The selection of a working flux density is a compromise. It should be as high as possible
in medium-frequency flyback units to get the best utility from the core and give minimum
With typical ferrite core materials and shapes, up to operating frequencies of 30 kHz,
the copper losses will normally exceed the core losses for flyback transformers, even when
the maximum flux density is chosen; such designs are “saturation limited.” Hence, in this
example maximum flux density will be chosen; however, to ensure that the core will not
saturate under any conditions, the lowest operating frequency with maximum pulse width
will be used.
With the following design approach, it is likely that a condition of incomplete energy
transfer will exist at minimum line input and maximum load. If this occurs, there will be
some induction contribution from the effective DC component in the transformer core.
However, the following example shows that as a large air gap is required, the contribution
from the DC component is usually small; therefore, the working flux density is chosen at
220 mT to provide a good working margin. (See Fig. 2.2.3.)
Hence, for this example the maximum peak-to-peak ac flux density B
will be chosen
at 220 mT.
The total ac plus DC flux density must be checked in the final design to ensure that core
saturation will not occur at high temperatures. A second iteration at a different flux level
may be necessary.
2.4.5 Step 5, Calculate Minimum Primary Turns
The minimum primary turns may now be calculated using the volt-seconds approach for a
single “on” period, because the applied voltage is a square wave:
= minimum primary turns
(the applied DC voltage)
t “on” time, Ms
maximum ac flux density, T
minimum cross-sectional area of core, mm2
For minimum line voltage (90 V rms) and maximum pulse width of 16 Ms
2.4.6 Step 6, Calculate Secondary Turns
During the flyback phase, the energy stored in the magnetic field will be transferred to the
output capacitor and load. The time taken for this transfer is, once again, determined by the
volt-seconds equation. If the flyback voltage referred to the primary is equal to the applied
voltage, then the time taken to extract the energy will be equal to the time to input this
energy, in this case 16 Ms, and this is the criterion used for this example. Hence the voltage
seen at the collector of the switching transistor will be twice the supply voltage, neglecting
leakage inductance overshoot effects.
2. FLYBACK TRANSFORMER DESIGN
At this point, it is more convenient to convert to volts per turn.
The required output voltage for the main controlled line is 5 V. Allowing for a voltage
drop of 0.7 V in the rectifier diode and 0.5 V in interconnecting tracks and the transformer
secondary, the voltage at the secondary of the transformer should be, say, 6.2 V. Hence, the
secondary turns would be
V/N volts per turn
For low-voltage, high-current secondaries, half turns are to be avoided unless special tech-
niques are used because saturation of one leg of the E core might occur, giving poor trans-
former regulation. Hence, the turns should be rounded up to the nearest integer. (See
Part 3, Chap. 4.)
In this example the turns will be rounded up to 3 turns. Hence the volts per turn during
the flyback period will now be less than during the forward period (if the output voltage is
maintained constant). Since the volt-seconds/turn are less on the secondary, a longer time
will be required to transfer the energy to the output. Hence, to maintain equality in the
forward and reverse volt-seconds, the “on” period must now be reduced, and the control
circuitry is able to do this. Also, because the “on” period is now less than the “off” period,
the choice of complete or incomplete energy transfer is left open. Thus the decision on
operating mode can be made later by adjusting primary inductance, that is, by adjusting
the air gap.
It is interesting to note that in this example, if the secondary turns had been adjusted
downward, the volts per turn during the flyback period would always exceed the volts per
turn during the forward period. Hence, the energy stored in the core would always be com-
pletely transferred to the output capacitor during the flyback period, and the flyback current
would fall to zero before the end of a period. Therefore, if the “on” time is not permitted to
exceed 50% of the total period, the unit will operate entirely in the complete energy transfer
mode, irrespective of the primary inductance value. Further, it should be noted that if the
turns are rounded downward, thus forcing operation in the complete energy transfer mode,
the primary inductance in this example will be too large, and this results in the inability
to transfer the required power. In the complete energy transfer mode, the primary current
must always start at zero at the beginning of the energy storage period, and with a large
inductance and fixed frequency, the current at the end of the “on” period will not be large
enough to store the required energy (½LI2). Hence, the system becomes self power limit-
ing, a sometimes puzzling phenomenon. The problem can be cured by increasing the core
air gap, thus reducing the inductance. This limiting action cannot occur in the incomplete
energy transfer mode.
2.4.7 Step 7, Calculating Auxiliary Turns
In this example, with three turns on the secondary, the flyback voltage will be less than the
forward voltage, and the new flyback volts per turn V
The mark space ratio must change in the same proportion to maintain volt-seconds equality:
V N V N
33 2 06
206 2 5
“on” time of Q1
P total period, Ms
/N new secondary flyback voltage per turn
V/N primary forward voltage per turn
The remaining secondary turns may then be calculated to the nearest half turn.
For 12-V outputs,
13 V for the 12-V output (allowing 1 V for the wiring and rectifier drop)
/N adjusted secondary volts per turn
Half turns may be used for these additional auxiliary outputs provided that the current
is small and the mmf is low compared with the main output. Also, the gap in the outer
limbs will ensure that the side supporting the additional mmf will not saturate. If only
the center leg is gapped, half turns should be avoided unless special techniques are used.
(See Part 3, Sec. 4.14.)
In this example, 6 turns are used for the 12-V outputs, and the outputs will be high by 0.4 V.
(This can be corrected if required. See Part 1, Chap. 22.)
2.4.8 Step 8, Establishing Core Gap Size
General Considerations. Figure 2.2.1a shows the full hysteresis loop for a typical ferrite
material with and without an air gap. It should be noted that the gapped core requires a
much larger value of magnetizing force H to cause core saturation; hence, it will withstand
a much larger DC current component. Furthermore, the residual flux density B
lower, giving a larger usable working range for the core flux density, $B. However, the
permeability is lower, resulting in a smaller inductance per turn (smaller A
2. FLYBACK TRANSFORMER DESIGN
With existing ferrite core topologies and
materials, it will be found that an air gap is invari-
ably required on flyback units operating above
In this design, the choice between com-
plete and incomplete energy transfer has yet
to be made. This choice may now be made by
selecting the appropriate primary inductance,
which may be done by adjusting the air gap
size. Figure 2.2.1b indicates that increasing the
air gap will lower the permeability and reduce
the inductance. A second useful feature of the
air gap is that at H 0, flux density retention
is much lower in the gapped case, giving a
larger working range $B for the flux density.
Finally, the reduced permeability reduces the
flux density generated by any DC component in
the core; consequently, it reduces the tendency
to saturate the core when the incomplete energy
transfer mode is entered.
The designer now chooses the mode of oper-
ation. Figure 2.2.4 shows three possible modes.
Figure 2.2.4a is complete energy transfer. This
may be used; however, note that peak currents
are very high for the same transferred energy.
This mode of operation would result in maxi-
mum losses on the switching transistors, out-
put diodes, and capacitors and maximum I2R
(copper) losses within the transformer itself.
Figure 2.2.4b shows the result of having a
high inductance with a low current slope in the
incomplete transfer mode. Although this would
undoubtedly give the lowest losses, the large
DC magnetization component and high core
permeability would result in core saturation
for most ferrite materials. Figure 2.2.4c shows
a good working compromise, with acceptable
peak currents and an effective DC component of one-third of the peak value. This has
been found in practice to be a good compromise choice, giving good noise margin at
the start of the current pulse (important for current-mode control), good utilization of
the core with reasonable gap sizes, and reasonable overall efficiency.
2.4.9 Step 9, Core Gap Size (The Practical Way)
The following simple, practical method may be used to establish the air gap.
Insert a nominal air gap into the core, say, 0.020 in. Run up the power supply with
manual control of pulse width and a current probe in the transformer primary. Nominal
input voltage and load should be used. Progressively increase the pulse width, being careful
that the core does not saturate by watching the shape of the current characteristic, until the
required output voltage and currents are obtained. Note the slope on the current character-
istic, and adjust the air gap to get the required slope.
FIG. 2.2.4 Primary current waveforms
in flyback converters. (a) Complete
energy transfer mode; (b) incom-
plete energy transfer mode (maximum
primary inductance); (c) incomplete
energy transfer mode (optimum pri-
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