Re: Magnifier system

To: tesla-at-pupman-dot-com
Subject: Re: Magnifier system
From: Bert Hickman <bert.hickman-at-aquila-dot-com>
Date: Wed, 20 Nov 1996 22:54:56 -0800
Tesla List wrote:
> 
> >From MALCOLM-at-directorate.wnp.ac.nzTue Nov 19 22:02:42 1996
> Date: Wed, 20 Nov 1996 10:29:29 +1200
> From: Malcolm Watts <MALCOLM-at-directorate.wnp.ac.nz>
> To: tesla-at-pupman-dot-com
> Subject: Re: Magnifier system
> 
> Bert,
>        I think the point you make about this explains something i've
> been wondering about quite well.......
> 
> <lottsa snip>
> > The Corums' open-circuit helical resonator model probably comes closest
> > to modelling actual behavior. An unloaded helical resonator behaves very
> > much like an open-circuit high-impedance transmission line driven at its
> > 1/4 wave frequency. The amplitude of the voltage as we progress up the
> > coil should increase approximately as the sine of the phase distance
> > from the bottom, rising to a maximum at the top (90 degrees). Fully 50%
> > of the output voltage is reached only 1/3 of the way up the coil! This
> > certainly agrees with your statement that the maximum volts/turn
> > gradient is at the base of the resonator. Similarly, the current
> > amplitude should vary approximately as the cosine, with the maximum at
> > the bottom, decreasing to 0 at the very top. However, fully 50% of the
> > coil base current would still be present 2/3 of the way up the coil.
> <oodles more snip>
> 
> It _is_ a distributed resonator (being << 1 wavelength long) and what
> you suggest makes sense of that! Would I be correct in thinking that
> the V.I product (phase angles accounted for) at any point is the same
> for any other point? If so, the observation about 0.5I being present
> 2/3 of the way up makes sense and also supports Greg's view that the
> M in the structure doesn't really count! So much for my turn-turn
> induction idea :(
> 
> Malcolm

Malcolm,

I think so. In an ideal 1/4 wave helical resonator (or a lossless
transmission line) with no breakout and no top termination, V and I will
be 90 degrees out of phase at _all_ points. The instantaneous real power
at any point is the same - zero - since the power dissipated at the far
end is zero (open circuit). Zero real power is at the base as well,
except this end looks like a short circuit. In a low loss resonator with
a non-zero, but relatively small wire resistance, V and I will still
have nearly the same 90 degree relationship, but a small amount of real
power is now lost in the resonator itself. 

-- Bert --