Clifton Laboratories 7236 Clifton Road  Clifton VA 20124 tel: (703) 830 0368 fax: (703) 830 0711

E-mail: Jack.Smith@cliftonlaboratories.com
 

Revision History
Original: 08 April 2010
11 April 2010. Added Steward data sheet extract for 40T0501 cores.

I've occasionally wondered how repeatable inductors are when wound according to instructions along the line of "wind 20 turns on an FT-50-75 core." So far, none of Clifton Laboratories kits require accurate inductance from similar instructions, but the question still bothered me.

Two aspects of inductor winding are at play here:

• Effective inductance is related to the percentage of core perimeter covered by the winding; and
• Sample-to-sample variation in the permeability of the core material.

The first point may be due to a combination of distributed capacitance and leakage inductance. In any event, I will leave it for later study. For a view on distributed capacitance in a toroid inductor see http://g3ynh.info/zdocs/magnetics/appendix/Toroid_selfC.html

I examined the second point today, by measuring the inductance of a reasonable sample size of two ferrite  toroid cores:

1. Fair-Rite 5975001101 (sample size = 61, all from one manufacturing lot)
2. Steward 40T0501 (sample size = 57, from unknown number of mixed lots)

Both cores are similar size, approximately 0.5 inches (12.7mm) diameter. The Fair-Rite core is more commonly known in amateur radio circles by the notation FT50-75, although this is not the core's part number.

I measured the inductance of the 118 sample cores using a one-turn loop winding through the core. The measurement was made with an HP4192A LF Impedance meter and 16047A test fixture, at 1.000 MHz, and an applied test voltage of 1.0 volts. The inductance value is parallel inductance, Lp. Both the 75-mix and 40-mix cores have low Q (1 or less) at 1 MHz and accordingly the series and parallel inductance values will differ significantly.
 

The plots below show the distribution of measured inductance values for the two sets of core samples. The difference in mean inductance is a consequence of the difference relative permeability of the two core types. Stewart 40 material has a relative permeability of 10,000, whilst Fair-Rite 75 mix has a relative permeability of 5,000.

I mentioned in the bullet points that the Fair-Rite cores are all from the same manufacturing lot, whilst the Steward cores are not. The Steward cores came from the stock I use in various Clifton Laboratories kits, and were purchased from DigiKey. I don't keep track of lot numbers for the Steward cores and I don't believe lot numbers are provided by DigiKey for these parts. The Fair-Rite cores were purchased from Kreger Components in Salem, VA and came with a manufacturer's lot ID.

The manufacturing lot provenance of the cores is important because it is reasonable to expect that cores manufactured at the same time, from the same batch of ferrite material, will demonstrate greater similarity than cores from different batches. The data supports this supposition, although of course other mechanisms may explain the greater variance of the 40T cores.

The plot below places both sample sets on the same axis, along with a fitted Gaussian distribution.

Looking at the 40T material, the data could support an analysis that the cores are mostly from two lots. One with a permeability yielding around 9 uH inductance, and a second lot, around 6.5 uH inductance. This explanation fits with how I order cores; when my stock runs low, I buy another batch and put the new ones on top of the older cores in the storage box. Hence, the bottom strata of cores represents an older buy than those on upper layers.

The final plot normalizes the measured inductance values, setting the mean inductance as 1.000. This provides a better view of the dispersion of the measured inductance.

The table below provides statistics on the normalized  values.

Steward 40 material specifications below.

If (a major assumption) the same tolerance applies to the mean of the measured inductance, then the maximum and minimum expected values match the measured values for 75 material reasonably well. Steward's 40 material cores are within the maximum and minimum inductance generally, with a few cores outside the maximum 1 turn inductance of 9.5uH. However, the data sheet states inductance at 100 KHz, and I measured the cores at 1 MHz. The relative permeability of 40 material drops between 100 KHz and 1 MHz..

Please don't take this analysis as meaning that Steward cores have greater variability than Fair-Rite, when all samples are drawn from the same manufactured lots. That hypothesis was not tested as the Steward cores are random lots.

It does, however, suggest that with respect to the two core types measured, the inductance obtained from "wind X turns of wire" instructions will have roughly a ±20% spread, just from variance in relative permeability for these  two core types.

Powdered iron cores and other types of ferrite may have a different inductance spread, but appropriate caution should be exercised in expecting repeatable results based purely upon the number of turns.