Re: [Phys-l] Reference needed

[Jack Uretsky <jlu@hep.anl.gov>]

Hi all-
	Thanks, Brian, for your comments.  This is all new to me, and I'm 
working through some of this for the first time.
	My understanding essentially agrees, I think, with Brian's 
comments.  Terminating the transmission line with a sqrt(L/C) resistor 
makes the line "look" infinite, as Feynman points out in his "lumped" 
model.  I found the exercise as problem 1, Chapter IX of Slater & Frank's
old book <Electricity and Magnetism>.  The problem asks for a proof that 
for the infinitely long case the ratio of applied voltage to current is 
just the quoted termination value, independent of frequency.  The ratio 
would therefore hold in the DC case.  Here L and C are the inductance and 
capacitance per unit length.
	In the lumped case, with proper termination, the impedence is that 
of a low-pass filter.  At frequencies below cut-off the impedance is just
sqrt(L/C) with a frequency dependant phase that ranges from 0 to pi/2.
This can all be worked out from the discussion in Feynman's book.
				Regards,
					Jack




On Sat, 19 Aug 2006, Brian Whatcott wrote:

> At 10:50 AM 8/19/2006, you wrote:
> > .... the
> > correct matching termination for a lossless transmission circuit is a
> > resistance with value \sqrt{L/C}.  Feynman derives this result in a model
> > of lumped L-C circuit elements (II-22-12), although he doesn't tell us
> > that he's really modeling a transmission line circuit.  I'm looking for
> > the classical derivation of this result.
> >         I will be discussing Feynman's derivation, which has generated
> > some unnecessary controversy at the Feynman Festival at U. Md, starting on
> > 8/25.  The controversy arises from disbelief that a circuit of purely
> > reactive elements can look resistive at low frequencies.  The DC
> > resistance of the circuit is just the termination value referred to above.
> >         It doesn't seem to be in Jackson's or Schwinger's texts.  If
> > someone has a text on transmission lines, it might be there.
> >                                         Regards,
> >                                                 Jack
>
> Although not responsive to Jack's question, I want to assert that
> a circuit of purely reactive elements does not look resistive at
>  low frequencies. It is certainly true that a long transmission line
> has a ratio of voltage to current at intermediate points which
> behaves like a resistance of that value  (called the characteristic
>  impedance) for a time period equal to the transmission time
> for traversing that line both ways. After that time - i.e. in the
>  low frequency limit, the line can look capacitive, inductive or
>  resistive at the near end, depending on the value of the
> terminating resistor at the far end, if any.
>
>
>
> Brian Whatcott    Altus OK    Eureka!
>
>
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