Re: Difference between 1/2 wave and 1/4 wave resonance ? ? ?

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

Original poster: "Robert Jones" <alwynj48-at-earthlink-dot-net> 

Hi Dan,

 > Tesla list wrote:
 >  >
 >  > Original poster: "Mccauley, Daniel H" <daniel.h.mccauley-at-lmco-dot-com>
 >  >
 >  > Does anyone have how to calculate from an RLC circuit, both the 1/2
wave
 >  > and 1/4 wave resonant frequency?
 >  >
 >  > A simple parallel resonant circuit Fres = 1/SQRT (L*C).  Now is this
 >  > technically a 1/2 wave resonant frequency of
 >  > this parallel resonant circuit?
 >  >
 >  > Any help appreciated in this confusing matter.
 >  >
 >  > Thanks
 >  > Dan
 >
I am not certain what your question is. Perhaps the following will help.

The equation you gave is missing a 2xpi term on the bottom assuming the
frequency is in Hz and L (H) and C (F) and your refering to lumped
components. With lumped components the resonance is frequently referred to
as simply harmonic.

Systems with distributed parameters such as transmission lines and secondary
coils exhibit wave propagation  effects and can have standing waves
(resonances) at a series of frequencies under certain conditions. In
transmission lines the two fundamental resonance modes are called 1/4 wave
and 1/2 wave.

You should not refer to resonance in lumped LCR components as 1/4 or 1/2
wave as the resonances are not wave effects.

However it is common to use a lumped LCR equivalent circuit as an
approximation of  1/4 and 1/2 (or higher order) wave resonance in
transmission lines and secondary coils. (Perhaps this has caused your
confusion)

Parallel or series is dependent on where and what the equivalent circuit is
intended to approximate. For example the impedance into a length of
transmission line that is shorted at the opposite end or looking in to the
top end of a secondary can be approximated by a parallel tunes circuit up to
about 1.5 times the first resonant frequency. Where as the impedance looking
into the shorted end of a transmission line or the grounded end  of a
secondary can be approximated by a series tuned circuit.

Hope this helps. For more information do a web search for "1/4 wave
resonance" or "impedance 1/4" or "standing waves".  As you have probably
noted opinions differ as to the relevance of waves in Tesla coils and you
can probaly find long threads on the subject in the Tesla list archives.

Bob