Isolated DC power supplies will use a transformer to provide galvanic isolation, as well as to act as an inductive element on the primary and secondary sides of the system. Transformers respond when driven with switching waveforms, which magnetically couples power to the secondary side of the transformer followed by delivery to a load. In order to do this while providing the required power rating, the transformer must be sized properly in terms of its inductance and turns number, and sometimes that requires a custom transformer.
The easiest way to create a custom transformer is to use an off-the-shelf core and bobbin. Bobbins are like the housing that holds the core material and transformer windings on the primary and secondary sides. When designing a transformer, you can't just use any core and bobbin, the core and bobbin must be carefully selected to hit a power handling target and required inductance.
We'll go over some of the simple design formulas used to determine if a particular core and bobbin will work in a power supply design.
Selecting a Core for Inductance
A good place to start determining whether a core and bobbin will be suitable for a transformer are its coil inductance and power handling ability.
To reach the inductance target, the number of turns in the coil must be determined. If your power supply transformer has a specific inductance requirement, there is a value in the transformer core data sheet that can be used to calculate the coil inductance.
This value is specified as an inductance factor, and it will state the amount of inductance per turn of wiring in the coil. It is a value that is expressed in the following ratio:
Inductance factor formula.
The inductance factor will determine the number of turns needed to reach the desired inductance. Technically, an inductance factor can be calculated using the equivalent area covered by the windings, but transformer core datasheets may provide this value.
If it is not provided, then the inductance per wire loop can be calculated using the core’s relative permeability, wire gauge, and the core’s cross sectional area:
Once the primary turns number is known, the secondary turns number and inductance are calculated using the required turns ratio. Next, we can move to power handling the selected core and bobbin.
Coil Flux Density
The goal in determining the maximum coil flux density is to determine if the coil will saturate the core when maximum current is driven to the coil. This maximum flux will also determine the power that can be delivered to the coil. The maximum flux density in a coils is determined using the standard formula for a solenoid (D is the length of the coil):
For this portion of the calculation, it is best to use the coil that carries more current to determine the maximum flux because the two are proportional. This becomes important in the next section where the maximum power output is determined.
Power Output Calculation
The power output with the transformer can be determined using the maximum flux value from the last section and a quantity called the area product. The area product is found by multiplying the following two quantities. These quantities can be determined from the mechanical drawing for the core and bobbin:
The window area, or the open area enclosed by the coil windings
The core area, or the cross-sectional area of the core within the windings
AP = (Window area)*(core area)
The value AP is related to the power output, flux density (B), signal frequency (f), and current density in the windings (J). An approximate relation in standard metric units is:
The factor 1,000 in the numerator arises due to the topology of the transformer and its switching converter circuit, as well as due to the driving waveform shape.
Using these numbers and the input frequency, solve for the maximum power output in the above equation. If the calculated power output (P) above is less the power being drawn into the coil, then a larger transformer will be needed.
Some Limitations on the Above Process
There are some limitations in the above process that have to do with the sizing of the wiring and core material. The wiring takes up some space in the bobbin, so the bobbin will only be able to support some maximum number of turns in a coil. This maximum number of turns then depends on the wire diameter as this will limit the current in a coil.
Next, there is a limit on the flux density that a core can handle. This occurs due to magnetic saturation in the core, and particularly in ferrite cores. If the flux density calculated above is larger than the saturation flux density, then the core will have limited power output once the core saturates. To fix this problem, a physically larger transformer will be needed in order to reduce the flux density.
Larger transformers allow for lower flux density and higher area products, which then allow the transformer to be run at higher powers.
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