Would you change your amp selection knowing...?

@almarg 

Hi Al,
good spotting. ~<|:-/

Actually, I've never seen the formula Z = ( L / C )^0.5.
Where does it originate?

1) 25 foot length as that is what was shown on the MI/AG site in Fig 4. 

3) I mistyped. Conceptually, the cable LR are in series and the C is parallel with the load. 

4) I understand characteristic impedance. A 75Ω cable is designed to be driven by 75Ω source and terminate in 75Ω load impedances. I dealt with PCB impedances for years in high speed digital and have fixed innumerable CATV issues by changing splitters or  terminating open jacks with 75Ω loads for friends and family.

Hi Ian,

Thanks for the clarifications.

While Zo (denoting characteristic impedance) = ( L / C )^0.5 is an equation that is widely used in various EE applications, I don’t recall ever seeing a **simple** derivation of it. The Wikipedia writeup I referred to on Characteristic Impedance, in conjunction with the Telegrapher’s Equations writeup it links to, provides a derivation, although it is rather complex. Another derivation is shown at this link in the first answer to someone’s question.

Note that in both derivations the bottom line equation which includes series resistance R and shunt conductance G reduces to Zo = ( L / C )^0.5 when R and G are zero, and therefore to a close approximation of that equation when R and G are small enough to be negligible (on the same per unit length basis that is used for L and C). And under those circumstances Zo becomes essentially independent of frequency. Keep in mind also, as you probably realize, that characteristic impedance is essentially independent of length.

Best regards,
-- Al