A couple years ago when contemplating kit versions of the high
performance band reject, high pass and low pass filters I sell, I
measured the inductance of 32 toroid cores I wound according to
instructions similar to those found in the Elecraft manual, i.e., with a
certain type core and magnet wire of AWG X, wind Y turns with spacing
according to the photograph.
16 of the inductors had a target inductance of 2.209 uH and 16 had a
target inductance of 8.943 uH (I do build precision filters after all,
and these values are measured with an HP 4192A impedance meter and
should be good to ±0.2% at the target resonance frequency for the filter
dipole element.) Both values were wound on T50-7 (white) powdered iron
cores, 22 turns and 46 turns respectively. And yes a larger core should
have been used, such as a T68-7, for the 8.9 uH inductor but a physical
size constraint forced the 0.5" diameter core to be used in this
particular product.
The results (in percent from target value):
2.209uH
Mean -2.85%
Sdev 3.12%
Max 0.91%
Min -7.92%
8.943uH
Mean -1.47%
Sdev 2.65%
Max 1.88%
Min -5.87%
I've wound a lot of toroids and since all 32 of these samples were wound
at one sitting, I probably made them more uniformly than would be the
case for a kit builder working with his first Elecraft kit requiring
toroids to be wound. Also, the cores were likely from the same
manufacturing lot, although I don't keep track of lot IDs in my small
business.
Applying some guestimate factor, I would say that ±10% from nominal
value would be the worst case and there's an excellent chance that a kit
builder of reasonable skill will bring the parts in at ±5% of the
target value.
As far as changes in inductance with frequency, one must distinguish
powdered iron and ferrite cores and also consider changes in "true"
versus "apparent" inductance.
My measured data shows relatively small changes in measured inductance
of typical amateur radio value inductors wound powdered iron cores over
a frequency ratio of 8:1 or so. Hence, an inductor designed to be used
at, say 7 MHz, will not show much change in measured value between 2 and
15 MHz. By "not much" I mean a couple percent or so.
At the upper end of the range, parasitic capacitance enters into the
picture, and causes the measured inductance (and Q, for that matter) to
change. Other effects also can cause inductance change with frequency,
such as change in current distribution resulting from proximity effects.
And, there is some change in core permeability with frequency, although
not a great deal with powdered iron over the useful frequency range.
With ferrite cores, the relative permeability can have dramatic changes
and the frequency of use and frequency of measurement require careful
consideration. (Q also is subject to similar drastic changes.)
In theory, the excitation level also will have to be considered as the
B-H curve of magnetic materials is non-linear to some degree or other,
and hence how hard the H field drives B can cause a shift in inductance.
Perhaps more importantly for designers is the effect upon incremental
inductance caused by DC current in the magnetic material, as the smaller
(generally speaking) AC field operates over a portion of the B-H curve
dictated by the static DC superimposed field.
Happily for most of us, the designer has considered these factors and if
the instructions are followed, good results ensue.
I should add that even high quality lab equipment found in the ham
workshop (such as a HP 4342A Q-meter or the older Boonton 260A Q-meter)
have a surprisingly high error budget. ±3% is the quoted accuracy for
inductance measurement with a Boonton 260A where Cresonating > 100 pF
and the 4342A Q-meter has the same ±3% specification. It is possible, of
course, to improve the accuracy of these instruments with an external
frequency counter and individual calibration of the tuning and vernier
capacitor, and adjustments for instrument strays and residuals.
Jack K8ZOA
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