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Re: Bogus proof?
At 11:26 PM 2/11/97 -0700, you wrote:
>Subscriber: jd231825-at-engr.colostate.edu Tue Feb 11 23:07:41 1997
>Date: Tue, 11 Feb 1997 16:11:13 -0700
>From: Jeff Detweiler <jd231825-at-engr.colostate.edu>
>To: tesla-at-pupman-dot-com
>Subject: Bogus proof?
>
>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
>
>
Jeff,
The typical 1/4 wavelength antenna is as you have shown not resonant in and
of its self. It is actually only 1/2 of the antenna. That is why a ground is
so important in a TC or any other 1/4 wave resonant system. Ground is the
other 1/2 of the antenna. Like a mirror the ground or counterpoise presents
what is effectively the other 1/4 wave length of wire.
George...
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