@ieales
Hi Ian,
I’m afraid I have to question or disagree with several things in your analysis:
1)I’ll start with the least significant of the issues that I see. What length are you assuming in your calculation that resulted in 0.05 ohms at 1 kHz? Plugging the numbers for the particular cable into your methodology I find that the result at 1 kHz is almost completely dominated by resistance, with the result therefore being not much different than the cable’s resistance spec of 0.00098 ohms per foot (x2 conductors, presumably, although that isn’t made clear in the table).
2)Your equation "Z=1/(1/(ZL+ZR)+1/ZC) * Length" would reflect the parallel combination of (ZL + ZR) and (ZC), yet as you correctly state L and R are in series, while C is in parallel.
3)Related to that, specifically to the fact that L and R are in series, I don’t see the basis for your statement that "this impedance is in parallel with the amp and speaker." Certainly the amp is not being loaded with 0.05 ohms!
4)Most significantly, I believe you are conflating "impedance," derived as a combination of the individual impedances of R, L, and C at a given frequency, with "characteristic impedance," which is not the same thing.
I recognize that the two terms are sometimes used interchangeably, but that is incorrect and potentially confusing. (Even the heading in the Goertz table that I referred to makes that mistake, although the writeup above the table makes clear that they are referring to characteristic impedance). For example, a 75 ohm coaxial cable has a "characteristic impedance" of 75 ohms, but at most frequencies certainly does not have a 75 ohm "impedance" based on any series and/or parallel combination of the individual impedances of R, L, and C at each frequency.
"Characteristic impedance" is essentially independent of frequency, assuming, as I alluded to earlier, that conductor resistance per unit length and dielectric conductance per unit length would not affect a calculation based on the square root of (L/C) significantly. See the Wikipedia writeup on
"Characteristic Impedance," which is consistent with my understanding of the matter.
Best regards,
-- Al