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1. INTRODUCTION
Because the flyback converter transformer combines so many functions (energy storage, galvanic isolation, current-limiting inductance), and also because it is often required to support a considerable DC current component, it can be rather more difficult to design than the more straightforward push-pull transformer. For this reason, the following section is entirely devoted to the design of such transformers.
To satisfy the design requirement, many engineers prefer to use an entirely mathematical technique. This is fine for the experienced engineer. However, because it is difficult to get a good working feel for the design by using this approach, it will not be used here.
In the following transformer design example, the chosen process will use an iterative technique. No matter where the design is started, a number of approximations must be made initially. The problem for the inexperienced designer is to get a good feel for the controlling factors. In particular, the selection of core size, the primary inductance, the function of the air gap, the selection of primary turns, and the interaction of the ac and DC current (flux) components within the core are often areas of much confusion in flyback transformer design.
To give the designer a better feel for the controlling factors, the following design approach starts with an examination of the properties of the core material and the effect of an air gap. This is followed by an examination of the ac and DC core polarization conditions. Finally, a full design example for a 100-W transformer is given.
2. CORE PARAMETERS AND THE EFFECT OF AN AIR GAP
FIG.1a shows a typical B/H (hysteresis) loop for a transformer-grade ferrite core, with and without an air gap.
FIG. 1 (a) Total magnetization loops for a ferrite transformer, with and
without an air gap. (b) First-quadrant magnetization loops for a typical ferrite
core in a single ended flyback converter when large and no air gaps are used.
Notice the increased transferred energy delta H when a large air gap is used.
It should be noted that although the permeability (slope) of the B/H loop changes with the length of the air gap, the saturation flux density of the combined core and gap remains the same. Further, the magnetic field intensity H is much larger, and the residual flux density Br much lower, in the gapped case. These changes are very useful for flyback transformers.
FIG.1b shows only the first quadrant of the hysteresis loop, the quadrant used for flyback converter transformers. It also shows the effect of introducing an air gap in the core. Finally, this diagram demonstrates the difference between the effects of the ac and DC polarizing conditions.
2.1 AC Polarization
From Faraday's law of induction, emf = [(N d phi) / dt]
& It is clear that the flux density in the core must change at a rate and amplitude such that the induced (back) emf in the winding is equal to the applied emf (losses are assumed to be negligible).
Hence, to support the ac voltage applied to the primary (more correctly, the applied volt seconds), a change in flux density delta Bac is required. (This is shown on the vertical axis in Fig. 1b.) The amplitude of delta Bac is therefore proportional to the applied voltage and the "on" period of the switching transistor Q1; hence Bac is defined by the externally applied ac conditions, not by the transformer air gap.
Therefore, the applied ac conditions may be considered as acting on the vertical B axis of the B/H loop, giving rise to a change in magnetizing current delta Hac. Hence H may be considered the dependent variable.
2.2 The Effect of an Air Gap on the AC Conditions
It is clear from Fig. 1b that increasing the core gap results in a decrease in the slope of the B/H characteristic but does not change the required delta Bac. Hence there is an increase in the magnetizing current delta Hac. This corresponds to an effective reduction in the permeability of the core and a reduced primary inductance. Hence, a core gap does not change the ac flux density requirements or otherwise improve the ac performance of the core.
A common misconception is to assume that a core that is saturating as a result of insufficient primary turns, excessive applied ac voltages, or a low operating frequency (that is, excessive applied volt-seconds delta Bac) can be corrected by introducing an air gap. From Fig. 1b, this is clearly not true; the saturated flux density Bsat remains the same, with or without an air gap. However, introducing an air gap will reduce the residual flux density Br and increase the working range for delta Bac, which may help in the discontinuous mode.
2.3 The Effect of an Air Gap on the DC Conditions
A DC current component in the windings gives rise to a DC magnetizing force HDC on the horizontal H axis of the B/H loop. (HDC is proportional to the mean DC ampere-turns.) For a defined secondary current loading, the value of HDC 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, HDC2, 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 continuous mode, a considerable DC current component is present, and an air gap must be used.
FIG.1b shows the flux density excursion delta Bac (which is required to support the applied ac voltage) applied to the mean flux density Bdc developed by the DC component HDC for the nongapped and gapped example. For the nongapped core, a small DC polarization of HDC1 will develop the flux density Bdc. For the gapped core, a much larger DC current (HDC2) is required to produce the same flux density Bdc. 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. 1b shows that the change in flux density delta Bac 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 Bdc (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 saturate.
Remember, the applied volt-seconds, turns, and core area define the required ac change in flux density delta Bac applied to the vertical B axis, while the mean DC current, turns, and magnetic path length set the value of HDC on the horizontal axis. Sufficient turns and core area must be provided to support the applied ac conditions, and sufficient air gap must be provided in the core to prevent saturation and support the DC current component.
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 transformer 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 following design approach will give the maximum inductance consistent with minimum transformer 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 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 "saturation 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, Section. 4.
4. DESIGN EXAMPLE FOR A 110-W FLYBACK TRANSFORMER
Assume that a transformer is required for the 110-W flyback converter specified in Part 2, Sec. 1.11.
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 rating. 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 temperatures. High permeability is not an important factor for flyback converters, as an air gap will always be used with ferrite materials.
FIG. 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. 2.3.
FIG. 2 Nomogram of transmissible power P as a function of core size (volume),
with converter type as a parameter. (Siemens AG.)
FIG. 3 Static magnetization curves for Siemens N27 ferrite material. (Siemens
AG.)
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 designs.) Example 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.
Calculate the DC voltage Vcc 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, Section. 6 provides methods of establishing the DC voltage.
For this example, a fair approximation of the working value of Vcc 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.)
Example
At a line input of 90 V rms, the DC voltage Vcc will be approximately 90 × 1.3 × 1.9 = 222 V.
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 copper loss.
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. Hence, for this example the maximum peak-to-peak ac flux density Bac 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.
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:
Nmin =Vt/ delta Bac Ae
where Nmin = minimum primary turns
V = Vcc (the applied DC voltage)
t = "on" time, Ms
delta Bac = maximum ac flux density, T
Ae = minimum cross-sectional area of core, mm2
Example
For minimum line voltage (90 V rms) and maximum pulse width of 16us
Hence…
Np(min) = 89 turns
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.
Example At this point, it is more convenient to convert to volts per turn.
Primary V/turn=Vcc/ N p = 222/89=2.5 V/N
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
Ns= Vs/[V/N] = 2.48 turns
… where Vs = secondary voltage
Ns = secondary turns
V/N= volts per turn
For low-voltage, high-current secondaries, half turns are to be avoided unless special techniques 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, Section. 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 completely 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 (½LI 2 ). Hence, the system becomes self power limiting, 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.
Hence:
Ns = 3 turns
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
[…]
The mark space ratio must change in the same proportion to maintain volt-seconds equality:
[…]
The remaining secondary turns may then be calculated to the nearest half turn.
Example
For 12-V outputs,
…where Vs =13 V for the 12-V output (allowing 1 V for the wiring and rectifier drop) Vfb /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.
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.)
4.8 Step 8, Establishing Core Gap Size
General Considerations
FIG.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 Br is much lower, giving a larger usable working range for the core flux density, delta B. However, the permeability is lower, resulting in a smaller inductance per turn (smaller AL value) and lower inductance.
With existing ferrite core topologies and materials, it will be found that an air gap is invariably required on flyback units operating above 20 kHz.
In this design, the choice between complete 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. FIG.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 Br is much lower in the gapped case, giving a larger working range delta 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 operation. FIG.4 shows three possible modes.
FIG.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 I^2 R (copper) losses within the transformer itself.
FIG.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. FIG.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.
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 characteristic, and adjust the air gap to get the required slope.
FIG. 4 Primary current waveforms in flyback converters. (a) Complete energy
transfer mode; (b) incomplete energy transfer mode (maximum primary inductance);
(c) incomplete energy transfer mode (optimum primary inductance).
This gives a very quick method of obtaining a suitable gap that does not require Hanna curves. Even when gaps are calculated by other methods, some adjustment similar to the preceding will probably be required. This check is recommended as a standard procedure, as many supplies have failed at high temperature or under transient conditions because the transformer did not perform as intended.
4.10 Calculating the Air Gap
Using Fig. 4, the primary inductance may be established from the slope of the current waveform (delta i/delta t) as follows:
[…]
(In some cases the area of the outer limbs is not equal to the area of the center post, in which case an adjustment must be made for this.)
4.11 Step 10, Check Core Flux Density and Saturation Margin
It is now necessary to check the maximum flux density in the core, to ensure that an adequate margin between the maximum working value and saturation is provided. It is essential to prevent core saturation under any conditions, including transient load and high temperature. This may be checked in two ways: by measurement in the converter, or by calculation.
Core Saturation Margin by Measurement
Note: It is recommended that this check be carried out no matter what design approach was used, as it finally proves all is as intended.
1. Set the input voltage to the minimum value at which control is still maintained-in this example, 85 V.
2. Set output loads to the maximum power limited value.
3. With a current probe in series with the primary winding P1, reduce the operating frequency until the beginning of saturation is observed (indicated by an upturn of current at the end of the current pulse). The percentage increase in the "on" time under these conditions compared with the normal "on" time gives the percentage flux density margin in normal operation. This margin should allow for the reduction in flux level at high temperatures, and an extra 10% should be allowed for variations among cores, gap sizes, and transient requirements. If the margin is insufficient, increase the air gap.
Core Saturation Margin by Calculation
1. Calculate the peak AC flux contribution B ac, using the volt-seconds equation, and calculate or measure the values of "on" time and applied voltage, with the power supply at maximum load and minimum input voltage, as follows:
B Vt NA pe ac _ where V _ Vcc, V
t = "on" time, Ms
Np = primary turns
Ae _= area of core, mm2
Bac = peak flux density change, T
Note: Bac is the change in flux density required to sustain the applied voltage pulse and does not include any DC component. It is therefore independent of gap size.
2. Calculate the contribution from the DC component BDC, using the solenoid equation and the effective DC component IDC indicated by the amplitude of the current at the beginning of an "on" period.
By assuming that the total reluctance of the core will be concentrated in the air gap, a conservative result showing an apparently higher DC flux density will be obtained.
This approximation allows a simple solenoid equation to be used.
[…]
The sum of the ac and DC flux density gives the peak value for the core. Check the margin against the core material characteristics at 100°C.
5. FLYBACK TRANSFORMER SATURATION AND TRANSIENT EFFECTS
Note: The core flux level has been chosen for minimum input voltage and maximum pulse width conditions. It can be seen that this leaves a vulnerability to core saturation at high input voltages. However, under high-voltage conditions, the pulse width required for the transmitted power will be proportionately narrower, and the transformer will not be saturated.
Under transient load conditions, when the power supply has been operating at light loads with a high input voltage, if a sudden increase in load is demanded, the control amplifier will immediately widen the drive pulses to supply this extra power. A short period will now ensue during which both input voltage and pulse width will be maximum and the transformer could saturate, causing failure.
The following options should be considered to prevent this condition.
1. The transformer may be designed for the higher-voltage maximum-pulse-width condition. This will require a lower flux density and more primary turns. This has the disadvantage of reducing the efficiency of the transformer.
2. The control circuit can be made to recognize the high-stress condition and maintain the pulse width at a safe value during the transient condition. This is also somewhat undesirable, since the response time to the applied current demand will be relatively slow.
3. A third option is to provide a pulse-by-pulse current limit on the drive transistor Q1.
This current-limiting circuit will recognize the onset of core saturation resulting from the sudden increase in primary current and will prevent any further increase in pulse width. This approach will give the fastest response time and is the recommended technique. Current-mode control automatically provides this limiting action.
6. CONCLUSIONS
The preceding sections gave a fast and practical method for flyback transformer design.
Many examples have shown that the results obtained by this simple approach are often close to the optimum design. The approach quickly provides a working prototype transformer for further development and evaluation of the supply.
In this design example, no attempt has been made to specify wire sizes, wire shapes, or winding topology. It is absolutely essential that these be considered, and the designer should refer to Part 3, Section. 4, where these factors are discussed in more detail. It is important to realize that just filling the available bobbin area with the largest gauge of wire that will fit simply will not do for these high-frequency transformers. Because of proximity and skin effects (see App. 4.B), the copper losses obtained in this way can quite easily exceed the optimum design values by a factor of 10 or more.
7. PROBLEMS
1. Calculate the minimum number of primary turns required on a complete energy transfer (discontinuous-mode) flyback transformer if the optimum flux density swing is to be 200 mT. (The core area is 150 mm, the primary DC voltage is 300 V, and the maximum "on" period is 20 Ms.)
2. For the conditions in Prob. 1, calculate the secondary turns required to give an output voltage of 12 V if the flyback voltage is not to exceed 500 V (neglecting any overshoot). Assume the rectifier diode drop is 0.8 V.
3. Calculate the maximum operating frequency if complete energy transfer (discontinuous mode) operation is to be maintained.
4. Calculate the required primary inductance, and hence the air gap length, if the transferred power is to be 60 W. (Assume maximum operating frequency, complete energy transfer, and no transformer loss. A transformer-grade ferrite core is used, and all reluctance is concentrated in the air gap.)
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