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Re: Magnifier system
On Sun, 17 Nov 1996, Tesla List wrote:
> >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.
Yes, but..
> > 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
1/4 and all odd multiples. There are some pretty interesting special
cases too. More later..
> 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:
You can use for example transmission line theory to determine the
propagation velosity and therefore the electrical length.
There is one pretty nice special case conserning magnifiers. I have not
done (yet) extensive calculations to find out weather this is of no
practical meaning.
If you take shorted transmission line it will look like impedance
Z(feed) = Z0*tan bl
Z0 being the caracteristic impedance of the line. If you like to take
the losses there too, replace tan bl by tanh yl where b=phase phactor,
y=complex propagation coeffisient, l=lenght of the line. If the
capasitance you are driving is "large" ie. reactance of much less then
the reactance of the transmission line short circuit approximation is
fairly valid.
Now, if you drive transmission line with another transmission line with
much lower caracteristic impedance an interesting case appears: you find
that the system (two lines in series) are at resonanse when
Z1/Z0 tan(b1*l1) tan(b2*l2) = 1
the physical meaning is that if Z1/Z0 is lot less that one ie. Z0>>Z1
the total lenght of the resonating line is much lower than the lenght
needed for either to be resonanse at itself. The configuration is such
that Z1 is the first line and Z0 the second line ie. low-impedance line
is used to drive a high-impedance line.
Yes, voltage multiplication etc. needs yet to be calculated and lot more.
Just threw this very interesting idea out. In best case it might even
mean that a properly designed system could be very compact for a very
low frequency.
The idea itself is not my idea. It actually came from a similar two
transmission line analysis for some planar magnetics. I instantly saw
a phenomena applied to magnifier coils! :) :)
> How is uo multiplied? And isn't the capacitance due to the effect of the
Think of a pulse bounching back and forth on a 1/4 line. You will
see the idea pretty quickly! You may even do a steady state calculation
to find out that an LRC-system will have a voltage multiplication
equal to Q of the system.
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