Toroid cores come in sizes ranging from 2mm outside diameter up to 150mm o.d., with the common sizes between 6mm and 50mm o.d. The power rating of a given size core will depend upon several factors, and the calculation of this is probably the most complex consideration of all. At frequencies above 100 kHz both ferrite and iron powder materials are generally limited by temperature rise before saturation occurs. Many ferrite cores can permanently change their permeability after being subjected to relatively high power (flux) levels, whereas iron powder cores return to their original value after cooling. In circuits up to 500mW, saturation is not usually of any concern, but when we use a ferromagnetic core at levels above 1 or 2W it must be taken into account in the design. It is good practice to use the largest core (within reason) which will conveniently fit into your layout. See the core cross reference tables for some equivalents.

The following flux density limits for both ferrite and iron powder cores can be used as an initial guide when making calculations for core size.
Frequency (MHz): 0.1 1 7 14 21 28
AC Flux Density (gauss): 250 150 57 42 36 30
Note: 10000 gauss = 1 Tesla = 1000 mTesla

Operating frequency is one of the most important factors in power capability above 100 kHz. A core that works well at 2 MHz may burn up at 30 MHz with the same amount of drive. For a given inductance, iron powder cores require more turns (because of their lower permeability) than an equivalent ferrite core and will therefore be able to handle higher power since the flux density will be lower for a given applied voltage. To prevent the flux density from increasing due to fewer required turns on a ferrite core, the applied voltage must be reduced.
Either core may be used for transformer applications, but both will have compromises. Ferrite cores require fewer turns, will give more impedance per turn and will give tighter coupling. Iron powder cores will require more turns, less impedance per turn and looser coupling, but will tolerate more power.
To determine the maximum flux density (Bmax) of a core we must take into account the following factors: applied rms voltage (E), cross sectional area of the magnetic path in cm2 (Ae), number of turns (N), operating frequency in MHz (f), bias current in amps Idc, core inductance index AL. These terms are used in the following combined (ac + dc) formula for flux level (gauss):
Bmax = (E * 102) / (4.44 * f * N * Ae) + (N * Idc * AL) / 10 * Ae
(use 4.44 for sine wave, 4.0 for square wave. If no dc present neglect terms after +)
The previous data gave a guide to the maximum flux densities of cores at various rf frequencies. The formula shows that we should use the lowest operating frequency expected in our application (e.g. 3Mhz in a 3 to 30Mhz wideband transformer) and the highest value of Erms (calculated from the required rf power and winding impedance) to give a conservative design figure for flux density. Some designers actually use the peak voltage (Epk) rather than Erms to give the greatest margin against saturation. Core saturation is affected by both dc and ac signals, and decreases the permeability of the core.
Simple Design Example

Using the following data we will determine if an FT-50-43 core without DC is suitable for the power we require.
E = 25, f = 7 Mhz, N = 15, Ae = 0.133
Substituting these values in the formula for Bmax we get:
Bmax = (25 * 100) / (4.44 * 7 * 15 * 0.133) = 40.3 gauss.
From the previous table we know that the maximum flux density at 7 MHz should not exceed 57 gauss. The calculation shows this core is well below the guideline figure and is therefore suitable.

Temperature rise can be the result of using too small a size wire for the current involved as well as magnetic action within the core. The effects can be calculated using the following formula:
temp rise = (total power dissipation / surface area)0.833
where: temp rise (deg C), power dissipation (mW), surface area of core (cm2)

If the operating temperature (ambient + temp rise) is greater than 60C when used intermittently, or more than 40C if used continuously, a larger size core and/or larger gauge wire should be selected.

The following data is presented as a guide to rf power handling capabilities for wideband transformers operating in the 1.8 - 30 MHz range using impedance ratios not exceeding 4 : 1 and the maximum impedance not exceeding 300 ohms.
FT-82-( ) 50 - 75 Watts max.
FT-114-( ) 100 - 150 Watts max.
FT-140-( ) 300 - 400 Watts max.
FT-240-( ) 1000 - 1500 Watts max.

When iron powder cores are used in low pass filters, the stop frequencies are usually harmonics of the fundamental frequency and therefore at a lower level, so that relatively small cores can be used in the filter inductors. As a guide the following size cores are suitable for use in hf transmitters from 1.8 - 30 MHz when used in output low pass filters. The important thing to remember is that the cores should never get very warm.
T-37-( ) 10 Watts max.
T-50-( ) 50 Watts max.
T-68-( ) 100 Watts max.
T-106-( ) 500 Watts max.

More accurate calulations with ferrite toroid cores are to be found at Programs.