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Frequency dependent dielectrics
Hello all.
I realise that this may be old news for the more experienced coilers here,
but I was interested to find out that the relative permittivity e_r for
dielectric materials is frequency dependent.
It turns out that there are three basic (first order) polarisation processes:
(a) In induced or electronic polarisation, the centre of negative charge in
a molecule is displaced, relative to the centre of positive charge, when an
external field is applied.
(b) In orientational polarisation, molecules with a permanent dipole moment
tend to be aligned by an external field, the magnitude of the
susceptability being inversely proportional to the temperature.
(c) Finally, ionic polarisation occurs in ionic crystals: ions of one side
may move, with respect to ions of the other sign, when an external field is
applied.
For a given magnitude of the electric field ~E, both the magnitude and the
phase of the dipole moment ~p are functions of the frequency, first because
of the various polarisation processes that come into play as the frequency
changes, and also because of the existance of resonances. Thus, since e_r
is a function of the frequency, e_r is strictly definable only for a pure
sinusoidal wave!
Some relative permittivities of varous materials near 25^C:
Type Frequency (Hz)
100 10^6 10^10
Barium titanate 1250 1140 100
Benzene 2.28 2.28 2.28
Birch (yellow) 2.7 1.95
Butyl rubber 2.43 2.40 2.38
Carbon tetrachloride 2.17 2.17 2.17
Fused silica 3.78 3.78 3.78
Glass (soda borosilicate) 5.0 4.84 4.82
Ice 4.15 3.20
Lucite 3.20 2.63 2.57
Neoprene 6.70 6.26 4.0
Polyethylene 2.26 2.26 2.26
Polystyrene 2.56 2.56 2.54
Sodium chloride 5.90 5.90
Soil (dry loam) 2.59 2.55
Steatite 6.55 6.53 6.51
Styrofoam 1.03 1.03 1.03
Teflon 2.1 2.1 2.08
Water 81 78.2 34
Wheat (read, winter) 4.3 2.6
(Table from Electromagnetism, Principles and Applications, 2nd edition,
Paul Lorrain, Dale R. Corson, Table 6-1 p.162)
Since most consumer capacitance meters operate by applying a 1kHz sine wave
to the cap, its possible that your tank circuit (which resonates at a much
greater frequency than 1kHz) may be seeing a different capacitance to the
one you have measured. Also, the non-sinusoidal (i.e. damped) nature of the
resonant wave in the tank circuit may cause a changing relative
permativitty and hence a changing capacitance as the voltage decays.
In particular, the table above indicates that coilers using beer bottle
capacitors (with glass dielectrics) may have a 3-4% drop in capacitance
when their tank circuit resonates...this will result in an increase of a
couple of kilohertz in the resonant frequency (depending on the original
size of the capacitance). Coilers using polyethylene caps will not have
this problem.
Are list members interested in this sort of information (please reply off
list).
Safe coiling,
Gavin Hubbard
P.S. Is anyone interested in practical transformer design? I would be happy
to put together a few pages of practical design notes if anybody is
interested.