How large a core is needed to handle a certain amount of power? This is a question often asked, but unfortunately there is no simple answer.
There are several factors involved such as: cross sectional area of the core, core material, turns count, and of course the variables of applied voltage and operating frequency.
Overheating of the coil will usually take place long before saturation in most applications above 100 KHz. Now the question becomes "How large a core must I have to prevent overheating at a given frequency and power level? "
Overheating can be caused by both wire and core material losses. Wire heating is affected by both DC and AC currents, while core heating is affected only by the AC content of the signal. With a normal sine wave signal above 100 KHz, both the Iron Powder and Ferrite type cores will first be affected by overheating caused by core losses, rather than by saturation.
The extrapolated AC flux density limits (see table below) can be used for BOTH Iron Powder and Ferrite type cores as a guideline to avoid excessive heating. These figures may vary slightly according to material being used.
Operating frequency is one of the most important factors concerning power capability above 100 KHz. A core that works well at 2 MHz. may very well burn up at 30 MHz. with the same amount of drive.
Core saturation, a secondary cause of coil failure, is affected by both AC and DC signals. Saturation will decrease the permeability of the core causing it to have impaired performance or to become inoperative. The safe operating total flux density level for most Ferrite materials is typically 2000 gauss, while Iron Powder materials can tolerate up to 5000 gauss without significant saturation effects.
Iron Powder cores (low permeability) are superior to the Ferrite material cores for high power inductors for this reason: Fewer turns will be required by the Ferrite type core for a given inductance. When the same voltage drop is applied across a decreased number of turns, the flux density will increase accordingly. In order to prevent the flux density from increasing when fewer turns are used, the flux drive will have to be decreased.
Either core material can be used for transformer applications but both will have 'trade-offs'. Ferrite type cores will require fewer turns, will give more impedance per turn and will couple better, whereas the Iron Powder cores will require more turns, will give less impedance per turn, will not couple as well but will tolerate more power and are more stable.
The equation for determining the maximum flux density of a given toroidal core is as follows:
The safety factor may be increased by using the peak AC voltage in the equation. This is a standard practice among many RF engineers who design broadband RF power transformers.
The above equation may be changed as shown below to make is more convenient during calculations of Bmax at radio frequencies.
The sample calculation below is based on a frequency of 7 MHz, a peak voltage of 25 volts and a primary winding of 15 turns. The cross-sectional area of the sample core is 0.1333 cm2. From previous guidelines we know that the maximum flux density at 7 MHz should be not more than 57 gauss.
This hypothetical toroid core will have a flux density of 40 gauss according to the above formula and when operated under the above conditions. This is well within the guidelines as suggested above.
Temperature can be the result of using an undersized wire gage for the amount of current involved as well as magnetic action within the core. Both will contribute to the overall temperature of the transformer. This can be calculated with the following equation:
If the operating temperature (ambient temperature + temperature rise) is more than 100° C when used intermittently, or more than 75° C if used continuously, a larger size core and/or a heavier gauge wire should be selected.
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