Re: Series resonance/Was: Waveguide TC

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Paul Nicholson by way of Terry Fritz <twftesla-at-qwest-dot-net>" <paul-at-abelian.demon.co.uk>

Jolyon Vater Cox wrote:

 > There is a common belief (incorrect?) that the secondary of a TC
 > is a series-resonant circuit

Let me clarify.  Look into the base of the secondary and it appears
like a series resonance at some frequencies (the odd quarter-wave
modes) and like a parallel resonance at some other frequencies,
(the even quarter-wave modes).  Look at the impedance into the top
of the coil and the situation is reversed: odd modes are parallel,
even modes are series.

 > would this not presume a 90 degree phase shift between input and
 > output

The forward and reflected waves each suffer some number of degrees
of phase shift, not necessarily 90, (usually less because the topload
C makes up the rest), in accordance with the finite travel time of
signals along the winding.  However, with total reflection from the
top and bottom, the two waves combine to form a standing wave with
zero phase shift along the coil, ie all the voltages waggle up and
down in unison, and ditto all the currents, with the two unisons 90
degrees apart.

The TC secondary can be analysed successfully either as a lumped
network, or a continuous transmission line. The two are equivalent,
with the lumped model being an approximation to the more detailed
transmission line model, which in turn is an approximation to the
full EM solution.  You choose which level of detail you wish to work
with.  None are considered 'wrong'.

The familiar telegraphist's equation for the t'line needs a couple of
extra terms to properly describe a solenoid, see

  http://www.abelian.demon.co.uk/tssp/pn2511.html

for a derivation.
--
Paul Nicholson,
Manchester, UK
--