[Elecraft] Re: I^2*R Losses and Coax Impedance (Was Random Wire)

[Bill Coleman]

On 1/11/03 12:51 AM, Kevin Luxford at kevinluxford@optushome.com.au wrote:

>I have just purchased Kraus Antennas and Kraus Electromagnetics and have not
>got far with them as yet, however, I question Stuart's assertion that with
>respect to coax feeders, "... the higher the impedance the lower the I
>squared R losses of a feeder."

I'm afraid such a blanket assertion is slightly erroneous. 

If we keep the center conductor constant (and hence a fixed resistive 
loss R), and increase the impedance of the coax, then,  yes, the matched 
condition of the coax leads to much lower losses. 

Ignoring for the moment such a coax will be larger than it's 
lower-impedance counterpart, the key is that the current required to 
carry the same amount of power is much lower, hence the I^2 part of 
equation is reduced greatly. (The current is lower because we assume the 
coax is fed in a matched condition)

However, typical higher-impedance coax is usually the same outer diameter 
of lower-impedance counterparts, so the resistive component of the center 
conductor tends to rise as much or more than the reduction in current.

>Surely the I^2*R losses have to do with the resistive losses of  the copper
>conductor and the parallel conductance of the dielectric.  At low
>frequencies these are practically negligible unless you have a very long
>cable and are running high powers.  A coax cable would still have a
>characteristic impedance even if the conductors had zero resistance.

While a coax cable would still have a characteristic impedance if made 
from superconductors, at HF, most of the losses in coaxial cable are 
resistive in nature.



Bill Coleman, AA4LR, PP-ASEL        Mail: aa4lr@arrl.net
Quote: "Not within a thousand years will man ever fly!"
            -- Wilbur Wright, 1901