Would you change your amp selection knowing...?

@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

Given that a speaker cable can't be hurt to have a CI matching that of the speaker, its reasonable to expect that the amp should be stable with such a speaker cable. That's why I say that designers have to accept that.

@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