Further to Amidon's method of rating ferrite inductors and transformers, this article discusses some interesting measurements of ferrite toroids by Manfred Mornhinweg (Mornhinweg 2019).

Mornhinweg ferrite core measurements – #31 discussed his measurements of a #31 suppression sleeve.

Above are his measurements of a FB-61-6873 sleeve. Essentially there are two measurements at each frequency, and the expected flux density B is in the ratio of approximately 2:1. He has fitted a straight line on a log/log graph to the measurements at each frequency. The similarity of the slopes is not unexpected, and is a tribute to his experiment design, execution and calculations.

The first thing to consider is the slope of the the fitted line.

If the material was linear in its characteristic, we might expect the core heating to increase as the square of B. The blue line has such a slope and can be used to compare the slope of the red lines. By eye, the measurements show slightly higher slope, and no conclusions can be drawn about linearity as there are only two points for each frequency.

Lets estimate the core loss of a 2 turn inductor (ignoring conductor loss) using complex permeability from the datasheet.

We should keep in mind that suppression sleeves are not controlled principally for permeability in manufacture (they are controlled for Z at some frequency, see Using complex permeability to design with Fair-rite suppression products), so predictions based on published permeability curves have additional uncertainty.

Above is a plot of calculated core loss vs frequency, and Mornhinweg's measurements at 21V impressed. The nature of the responses are somewhat similar, importantly the dip around 7MHz exists in both measured and calculated responses.

Though #61 is a low loss material at 1MHz, the loss turns upwards at the low end in the above plot simply because there is not much magnetising impedance Zm, and so magnetising current Im is high, and Im^2R grows quickly with decreasing frequency.

Above is a chart comparing calculated core loss for 2t and 4t on the core, it can be seen that increased Zm leads to lower core loss. The 4t case has 50% the volts/turn, 50% the flux density, 25% of the loss.

The matter of control of suppression product parameters has been mentioned and could be one of the factors giving rise to a difference to the datasheet.

However, there are other issues with #61 operated at high power.

Above is the B-H curve for the material, and at 100° saturation is above 1000gauss (100mT). The measurements at 21V have B ranging from 11mT @ 1.8MHz to 0.4mT @ 50MHz, it is always well under saturation.

Whilst we might then think that small signal analysis applies, lets look at the temperature sensitivity of the material.

We can see from the chart above that the loss increases with core temperature, more so at the lower frequency / higher B range. The DUT temperature varied from 21.5 to 29.4° @ 1.8MHz, not a very great range but enough to cause a 10% increase in loss at the end of the test. This issue is more relevant to the final application where the core might well operate at higher temperatures.

Another factor is that of conductor loss which is captured in the measurements. Though we might dismiss conductor loss out of hand, at the lowest frequency the real component of Zm (ie the equivalent core loss resistance) is very low and wire RF resistance may be significant.

## References

- Mornhinweg, M. 2019. Ferrite core loss in HF power applications.

- Ferrite permeability interpolations
- Inductance of RF cored inductors and transformers
- Calculate ferrite cored inductor – rectangular cross section
- Calculate ferrite cored inductor – circular cross section
- Calculate ferrite cored inductor (from Al)
- Calculate ferrite cored inductor – ΣA/l or Σl/A
- Ferrite permeability interpolations