Bogus proof?

• To: tesla-at-pupman-dot-com
• Subject: Bogus proof?
• From: Jeff Detweiler <jd231825-at-engr.colostate.edu>
• Date: Tue, 11 Feb 1997 16:11:13 -0700
• Subscriber: jd231825-at-engr.colostate.edu Tue Feb 11 23:07:41 1997

Hi all,

I was doing some reading up on transmission line theory and I don't
understand what the 1/4 wavelength principle of the secondary has to do
with resonance. Consider this proof:

Velocity of a wave travelling down a transmission line is:

v = l/sqrt(LC)         l = length of transmission line
                       C = capacitance of the length "l" transmission line
                       L = inductance " " " "

And we know the resonant frequency of a secondary coil is:

f = 1/(2*pi*sqrt(LC))        eq. 2

also, since

v = f*lamda    lambda = wavelength
               f = frequency

then:

l/sqrt(LC) = f*lamda         eq. 3

substituting resonant eq. 2 into eq. 3 for "f":

l/sqrt(LC) = lambda/(2*pi*sqrt(LC))

cancelling terms and solving for "l" the length of the transmission line:

l = lambda/(2*pi)

Thus at resonance, the actual physical length of the wire should be 1/2pi
of the wavelength, and not 1/4. So where is this proof bogus? What exactly
does the 1/4 wavelength frequency have to do with resonance? I thought
resonance is only a function of the L and C of the coil. I hope Fr. McGahee
will include this in the Guide.

Thanks,
Jeff Detweiler

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