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Re: Medhurst now empirical formulas
"Bryan writes: "Has anyone found the physical basis for the data?"
Terman is speaking specifically about the inductance equations but I
think
the statements
also apply to the empirical capacitance equations as well. Terman
writes:
"Skilled mathematicians have derived formulas that give the inductance
of all
the
commonly used types of coils with non-magnetic cores in terms of the
coil
dimensions.
These formulas are usually both complicated and hard to derive because
of the
difficulty
encountered in calculating the magnetic flux produced by the current
flowing
in the coil.
In order to make such formulas of practical value, they are always
simplified
by the use of coefficients.""
The inductance formulae for solenoidal inductors were worked out almost
100 years ago. They involve the difference between two series of
elliptic integrals, as I recall, and are very very messy to work out
exactly. Japanese gentlemen named Nagaoka published a lot on this, anbd
much has been published since. Perhaps the best collection of
inductance formulae is in the long-out-of-print Bureau of Standards
Circular 74. which also has some interesting stuff on spark excitation
and coupled circuits. More recently Dover did a reprint of a book
"Inductance Formulas and Working Tables" (or was it tables and
formulas?) which has a lot on inductance and mutual inductance, but
nothing on capacitance.
Not sure that anyone has tried really hard to work out the distributed
capacitance for a solenoid, and don't know how hard it would be.
Someone here mentioned doing it, I seem to remember. Note that even
Wheeler's approximations are plenty good enough for most any TC work.
Many more complex expressions exist, most of which will give results
whose errors are determined mostly by uncertainty in the input
parameters.
Ed