Topband: Calculating Saturation of Ferrite Cores

[K8LV1 at aol.com]

The postings on this subject give the false impression that this issue is too 
complicated for the average person to handle himself, and suggests that those 
who need the correct information consult the self-appointed experts. In fact, 
the required calculations are trivial and I will show how to do it quickly 
and easily.

The crux of the problem is to avoid DC biasing the core far enough up on its 
BH curve to approach flux saturation, at which point the (incremental) 
permeability rapidly decreases. At this point and beyond your inductor becomes a 
resistor!  The objective is to keep the values of B/H well below this point.

For the ferrites commonly used in RF work, the BH curves are very narrow and 
almost rectangular. The onset of saturation is very close to "clipping", and 
for the most popular materials (44,73,77,43) this point may be taken as 1 Oe 
(call that Hmax). For HF above 10MHZ, type 61 is usually more preferable and its 
Hmax is 3Oe. This Hmax is the 'magic' number for this issue, and it is always 
clearly stated in mfr. data.

Given Hmax, which will be 1Oe. almost always, the calculation of the maximum 
DC bias current is simple:  I=.8 x Hmax x length(cm). The last quantity is 
simply the magnetic path length, which for a toroid is equal to the mean 
diameter. It is always given in mfrs. specs for most geometries. So, for a .5" toroid 
(length=3cm) and 1Oe. the maximum current is simply .8 x 1 x 3=2.4A. (a/k/a 
ampere-turns).

The parameters of magnetic materials are not precision quantities and are all 
quite temperature/aging and process dependent compared to other materials. 
Hence, it is foolish to attempt to make highly-precision calculations based on 
them. In particular, the 'Hmax' value should be regarded as a (good) 
approximation and one should not try to push the limit (e.g. aim for Hmax=.95Oe. by 
using as many turns of wire as possible.) A good practical rule used by me and 
many that I know, is to stay below 50% of Hmax. This would be .5Oe for the noted 
materials. This will guarantee that your choke or coil will always be on the 
lower portion of the BH curve where losses are lowest. Hence, the working rule 
is simply: Imax=.5 x length(cm) A. or IOW 500ma. per cm. (For 61 material this 
would be 1.5 amps/cm). 

The value of length can be easily measured by eye if you don't have data 
sheets. Just measure the mean diameter (half-way between the center hole and the 
OD) and calculate: length=PI x diameter. Mfrs. of binocular cores typically 
don't give this number, but you can easily estimate it by visualizing the core as 
two side-by-side toroids with a little fill-in material. (This type of core 
has no real benefit for ordinary chokes of this type and I recommend ordinary 
toroids or pot-cores, but if you have 'em laying around, why not use 'em.)

The very highest frequency materials (e.g. 67 and 68) have loops that are not 
nearly so rectangular, so it is not as feasible to summarize them with a 
single, basic number (Hmax) as done above. For these materials, which are VERY 
important at 30MHZ and above, you should consult the data sheet for each case.

73 and happy winding,
Eric von Valtier K8LV