"Jeff Liebermann" wrote in message
...
On Sun, 20 Sep 2009 17:48:51 +0200, "Antonio Vernucci"
wrote:

I wonder whether you could indicate us a reference where all those
trade-offs
are mathematically discussed.

This should help:
http://www.microwaves101.com/encyclopedia/why50ohms.cfm


--
Jeff Liebermann
150 Felker St #D http://www.LearnByDestroying.com
Santa Cruz CA 95060 http://802.11junk.com
Skype: JeffLiebermann AE6KS 831-336-2558


Thanks Jeff, that reference does help but it gets a bit confused over
matters of relative permittivity, Er.

Some time ago (2005), in my work, I derived the whole lot from almost first
principles. It turns out that the series conductor loss (as opposed to the
shunt dielectric loss) is proportional to (1+p)/ln(p), where p is the ratio
of the inside diameter of the outer conductor (D) to the outside diameter of
the inner conductor, and to SQRT(Er). The minimum value of this loss is
found by differentiating the function of p with respect to p and that's what
gives the 76.7 ohms value for Er = 1 (it also involves a constant for copper
conductors, the root frequency and 1/D). The result scales with SQRT(Er)
for polythene.

I should have stated the _peak_ power handling because the 30 ohms (air)
value results from combination of the expression for the electric field
strength and the expression for the characteristic impedance (along the
lines of P = V^2/R). Minimising the field strength gives the greatest
resistance to dielectric breakdown, but a different value of p results when
the impedance is taken into account at the same time. Again, the result
scales with SQRT(Er).

The application for all this was analogue to digital terrestrial television
switch over - the digital signals have much greater peak-to-mean ratios than
the analogue ones, so flashover in air-spaced feeders is a potential power
limitation.

Chris