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Re: Magnifier system

Malcom explains:

>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

Malcolm,

Thanks so much for explaining this, but I have a few questions. From what I
have read, I thought the secondary coil could be electrically modelled as a
series RLC circuit in some sense because of the way it behaves when driven
at different frequencies. And to get maximum output voltage at the
terminal, we should drive it at the 1/4 wavelength frequency to produce a
voltage maximum at the terminal, but you pointed out that this is the
electrical length of the wire (not physical) when we wind up the coil. So
how exactly is electrical length mathematically determined? You mention:

>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.

How is uo multiplied? And isn't the capacitance due to the effect of the
wire or loops of the wire above ground?

And for the magnifier system, how exactly does this system multiply the
base fed input voltage to produce a higher output voltage?

Thanks for explaining,
Jeff