Re: Lumped parameters

To: tesla-at-pupman-dot-com
Subject: Re: Lumped parameters
From: "Antonio Carlos M. de Queiroz" <acmq-at-compuland-dot-com.br> (by way of Terry Fritz <twftesla-at-uswest-dot-net>)
Date: Fri, 10 Dec 1999 16:38:16 -0700
Approved: twftesla-at-uswest-dot-net
Delivered-To: fixup-tesla-at-pupman-dot-com-at-fixme

Finn Hammer wrote:

> I have always wondered, what is _exactly_ meant by the term "lumped" as
> opposed to for example transmissionline, when a tesla coil system model
> is being discussed.
> Transmission line vs. lumped parameter model seems to be the phrases
> used.

"Lumped elements" are elements without significant physical size, so
there are no significant distributed electrical effects in them.
In a lumped resistor, capacitor, or inductor, the current entering
one terminal is exactly the current exiting through the other terminal.
Or, "lumped elements" are precisely the usual elements, and the
modeling through "lumped parameters" is the usual modeling, with
elements interacting only through voltages and currents at their
terminals (and magnetic couplings).
In Tesla coiling, the secondary coil and the toroidal terminal can
be, approximately, modeled as a lumped inductor (with coupling to
the primary inductor) in parallel with a grounded lumped capacitor,
that represents the effects of the distributed capacitance of the
coil and of the terminal.
Transmission lines are one step ahead in the modeling, because
the physical dimensions of the elements in relation the the wavelength
of the signals in them determine their properties. A long wire above
ground, a long coaxial cable, a waveguide, or a long coil of wire 
above ground are examples of transmission lines. All can behave as
different associations of lumped elements at different frequencies,
and show multiple resonances.

Antonio Carlos M. de Queiroz