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Implementing Flyback Transformer Design for Continuous Mode

Jun 1, 2003 12:00 PM
By Keith Billings, DKB Power
Inc., Ontario, Canada

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For the PDF version of this article, click here.

In last
month's Power Design column, we examined the functional principles of
continuous mode (or incomplete energy transfer mode) of a flyback
transformer. In this issue, let's apply the same design principles learned
earlier in a transformer design example and look at the function of an air
gap in a ferrite core.

Transformer Design Example

Fig. 1 shows a typical flyback converter as used for single
output application. Fig. 2 shows typical waveforms found in
continuous mode operation. In this mode, energy is stored in the magnetic
field of the core and air gap during the ON period of Q1. However, not all
the stored energy is transferred to the secondary when Q1 turns OFF We
have a variable (top) part of the waveform, and an effective dc component,
(as there would be in an output smoothing choke in a forward converter).
Fig. 3 shows the B/H characteristic.

For this transformer design example, we'll assume an output power
requirement of 100W. The input voltage is 100V. The secondary voltage is
20V at a mean current of 5A. The frequency is to be 50 kHz, with a 50% ON
period for Q1 (10µs). A gapped ferrite core with a pole area of
100mm2 is to be used. The example assumes 100%
efficiency and zero diode drop.

The first step is to decide the load current range over which the
continuous mode of operation is to be maintained. The larger the load
range, the more turns and inductance are required on the primary and the
greater will be the copper loss. We'll assume a 75% load range providing
1.25A to 5A output. This choice results in a ripple current of half the
mean value at maximum load. The waveforms in Figs. 2 and 3
show this condition. We must choose the maximum flux density swing ΔB.
The smaller the flux swing the lower the core loss, but the turns will be
greater increasing the copper loss. The optimum choice is where total
copper loss equals the core loss. This is an iterative process and can't
be fully established at this stage. It must be checked in the final
design, making required adjustments. For this example, let's assume a ΔB
of 0.16 Tesla (about ½ of the saturating flux density). This provides a
50% flux margin for the dc polarizing force shown as Bdc on the
vertical B scale in Fig. 3.

Further
Flyback Transformer Reading:

·
Designing Flyback Transformer for Discontinuous Mode

·
Choosing Core for Flyback Transformer and Choke Designs

·
Improving the Performance of Flyback Power Supplies

Full
Flyback Transformer Spotlight

We can now calculate the minimum primary turns Np; (See
Equations)

Vp = 100V, t (the ON period of Q1) is 10µs, B max is 0.166 Tesla and Ae
(the area of the core) is 100 mm2

Hence the primary turns (Np) will be 60 turns.

The primary inductance can be calculated as follows; Assuming 100%
efficiency at a power of 100W and an input voltage of 100V the time
averaged input current will be 1A. Hence, the mean current during the 50%
“on” period of Q1 must be 2A. We have chosen to make the ripple current
50% (or 1A in this example). From inspection of the top part of Fig.
2, the primary current change is from 1.5A to 2.5A, a ΔI of 1A. The ON
period is 10µs, and we can now calculate the primary inductance required
to produce this result.

The primary inductance

This will be 1000 µH. (See Equations)

While the OFF (flyback) period of Q1 is also 10µs, the secondary volts
per turn during the flyback period will be the same as the primary volts
per turn during the ON period of Q1. Thus, for 20V output, 12 turns will
be required. The 50% duty ratio is a special case. If the duty ratio is
not 50%, then this transformer like ratio won't apply, and you must obtain
the secondary turns from the calculated secondary inductance, in the same
way as it was in the discontinuous mode example in the April article.
Also, we've provided no adjustment for rectifier diode drop.

The secondary current ratio follows the turns ratio, since the primary
ampere turns product must be maintained. Thus, Is = Ip × 60/12. As shown
in Figs. 2 and 3, the secondary waveform starts at 12.5A and
falls to 7.5A at the end of the OFF period. A mean value of 10A for the
half period giving 5A average at 20V and power equality is maintained.

The “transformer” is now wound using a wire size for the 60 turns
primary that will use less than 50% of the bobbin area to allow for
insulation. The remaining space is used for the secondaries. To minimize
skin effect, several parallel strands of a smaller wire size would
normally be used. Although there's no direct transformer action (because
the primary and secondary aren't conducting at the same time), the leakage
inductance should still be minimized. As Q1 turns OFF, the primary
current must be commutated from the primary winding to the secondary
winding. Any leakage inductance opposes this commutation and will produce
a voltage overshoot on the primary when Q1 turns OFF. Hence, the windings
would normally be interleaved — ½ primary, secondary and then ½ primary.
(See reference.) At this stage, you normally fit the core, and adjust the
gap to get the required primary inductance. However, it can also be
calculated. (See Equations.)

The main advantage of the continuous mode is reduced ripple current.
The disadvantages are that the “transformer” must support a dc current
component, the output diodes are conducting when Q1 turns ON (presenting
diode reverse recovery problems), more turns are required, and there's a
“right half plane zero” in the transfer function leading to poor transient
response. However, the reduced ripple current, makes this mode more
suitable for higher power applications.

The mode of operation was defined by adjusting the inductance, (by
using a smaller air gap). Low inductance (large air gap) leads to the
discontinuous mode, while large inductance leads to the continuous mode.
The inductance may be adjusted by changing the turns, core material, or
the size of the air gap, or a combination of these.

For multiple outputs, sum the total output power and use this value in
the equations when calculating the primary and secondary inductance of the
main controlled output. The secondary currents will adjust depending on
the loading applied to each output.

Although we've ignored the transformer action, as it's not a design
parameter, it still exists. The flyback voltage is reflected back to the
primary winding during the OFF period of Q1. Hence, reducing the secondary
turns increases secondary peak currents and increases voltage stress on
Q1.

The following equations are dimensionally modified to yield convenient
answers.

Equations

Primary Turns

Where:

NP = Primary Turns

VP = Primary Voltage

t = Q1 ON time (µs)

ΔB = Peak flux density (tesla)

Ae = effective area of center pole (mm2)

Primary Inductance Where:

LP =Primary inductance (µH)

Δt = Q1 ON time (µs)

ΔIP = Current change I1 to
I2 (A)

Inductance Factor

Where:

AL = Inductance of a single turn (µH)

Secondary Inductance LS =
NS2 ×
AL

Where:

LS = Secondary inductance (µH)

NS = Secondary turns

Secondary Turns

Air Gap Length

Where:

Air gap = (mm)

µo = 4 π × 10-7

NP = Primary turns

Ae = Area of core(mm2)

LP = Primary inductance (mH)

α = Air Gap (mm)

ac Flux Density

dc Flux Density

where α = Air Gap (mm)

In the next Power Design column, we'll cover a transformer design for a
forward converter, including alternative core materials.

Keith Billings is president of DKB Power Inc. ([email-masked]) and author of the Switchmode Power
Supply Handbook published by McGraw Hill ISBN 0-07-006719-8. He also
presents the late Abe Pressman's three-day “Modern Switching Power Design
Course.” For more information visit http://www.apressman.com/.

References

Switchmode Power Supply Handbook. Keith Billings, Published by
McGraw Hill ISBN 0-07-006719-8.

Switching Power Supply Design. Abe Pressman, Published by McGraw
Hill ISBN 0-07-052236-7.

For more information on this article, CIRCLE 339 on Reader Service
Card

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2007 Penton Media, Inc.

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Discrete Semis
Bipolar
Transistors
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Modules
Power
MOSFETs
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Power Management
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Power Control
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Drivers
Lighting
Power Management
Motor
Power Management
Power
ICs
PWM
Controllers
Regulator
ICs

Portable Power
Management
Batteries
Battery
Charger ICs
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Gauges Controllers
and Regulators
Micro
Fuel Cells

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Topic Pages
Wind
Power
Flyback
Transformers

Thermal Management
Fans
Heatpipes
& Spreaders
Heatsinks
Liquid
Cooling
Thermal
Interface Materials
Thermal
Management Simulation

Power Systems
DC-DC
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