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Re: Magnifier system
Hi Jeff,
Your comment on the L and C of the resonator is an
interesting one.
> One thing I'm still confused about is, does the magnifier produce a maximum
> output at a resonant frequency where the coil's self-inductance and
> self-capacitance cancel (as with a series RLC circuit) to give minimum
> impedance? I want to clarify this since I thought the resonant frequency of
> a "standard" TC setup was determined by the 1/4 wavelength of the secondary
> coil (to produce maximum voltage at the top of the coil in a standing wave
> fashion) which is not based on the coil's capacitance and inductance. Is
> this where the Q factor comes in, in that resonant frequency is the 1/4
> wavelength for the standard setup, but that a coil built such that the L
> and the C cancel each other as much as possible is most ideal?
Tesla tried to make a distinction between the propagation time of a
signal through a circuit and the physical length of the circuit, but
in fact the electrical length of the circuit is what determines its
propagation time. In an isolated longwire, it turns out that the e.m.
properties of space (uo and eo) are such that the physical length
matches the electrical length almost exactly. In rolling up the wire
into a coil, we have considerably modified the inductance and
capacitance those properties give the structure. Mutual inductance
between turns gives uo a multiplier and the huge drop in physical
length of the coil (winding height) over the longwire considerably
reduces the capacitance of the structure, so much so in fact that
the increase in inductance is insufficient to compensate for the drop
in capacitance for the actual wirelength to resonate as though it were
an isolated longwire. It is found that extra capacitance is always
needed to make the physical length of wire 1/4 wave resonant. It can
be seen from this that basing resonator properties on the physical
length of conductor used to make them is in fact irrelevant to their
electrical behaviour.
Why 1/4 wavelength is resonant? The reason is that the reflections
that a disturbance undergoes when arriving at the ends must have a
certain phase with respect to the driving circuit or you will get
phase cancellation between driving circuit and resonator which forces
power to be contained within the driving circuit. All resonators will
exhibit the correctly phased end reflections at a number of
frequencies but the 1/4 wave frequency is (a) the fundamental
(strongest amplitude response), (b) the most efficient (lowest
frequency and hence losses), and (c) the one that produces a voltage
maximum at the open circuit end with no maxima in between. Such
responses and their relative amplitudes may be found by a Fourier
Series or something similar to it where the coefficients of the
various terms reflect the amplitudes of the different responses.
In short, any resonator of any type exhibits its strongest
response when the frequency is such that the resonator is
_electrically_ 1/4 wavelength long at that frequency. It cannot do
otherwise. IMO this historic confusion has added a great deal of
unnecessary mysticism to what is otherwise a simple structure. I guess
TCBOR being the most experienced in the art can answer your
operational questions best.
<snip>
Other opinions welcome of course,
Malcolm