Fred McKenzie wrote:
In article
,
phaedrus wrote:

Hi again,

Well I have read your informative replies on the problems with making
a low Zo twin feed with much interest. Clearly it's not really a
practical proposition. Shame.

So the obvious question is: why are transmitters normalised to 50 ohms
when clearly 450 ohms would enable us to enjoy cheaper, do-it-
yourself, lower loss feeders? Was this some oversight at the time, or
good practice for some obscure reason that I simply cannot think of?

As others mentioned, the origin is probably based on military standards.

It is my understanding that the lowest loss air dielectric Co-Ax would
have an impedance of around 75 Ohms.

loss, at constant frequency, is proportional to
1/Z * (1/b + 1/a)
b= diameter of outer , a = diam of inner

This reflects the fact that at lowish frequencies (HF), the loss is
ohmic, so it's the series combination of the resistivity of the center
and outer conductors (the 1/b+1/a term), and the current flowing (the
1/Z term.. higher Z means lower current, so less IR loss)



Z is proportional to log(b/a)
so
loss = k/log(b/a)*(1/b+1/a)

Run the numbers and you see that a ratio of 1:3.6 gets you 50 ohms with
epsilon=2.3 and a ratio of 1:6.7 gets you about 75 ohms.

At 10 MHz loss is about 0.028 dB/meter for the 50 ohm, and 0.017
dB/meter for the 75 ohm.

but you can go higher in Z...and the loss keeps going down, but even at
1:20 diameter ratio, the impedance is 118 ohms, and the loss is 0.010
dB/meter. So 75 isn't a "lowest loss" frequency. More likely, 75 ohms
happens to be close to 72 ohms, which is the characteristic impedance of
a dipole in free space, or, more usefully, 1/4 of the 300 ohm impedance
of a folded dipole.

In air, the dimensions and loss a
50 ohm 1:2.3 0.033 dB/meter
75 ohm 1:3.5 0.019 dB/meter

If you use the same mechanical
dimensions but with a polyethylene dielectric, the impedance becomes 52
Ohms.


I think that is just coincidence:

Z = 138/sqrt(epsilon)* log (b/a)

air has epsilon=1 (or very close)
polyethylene has 1/sqrt(epsilon) about 0.66, so, in fact, it happens to
work out (e.g. 50/75 = 0.66)