Is the propagation velocity slow down at low audio frequency?

[yungman]

I uploaded the paper from Belden cable company. It said the velocity slows down to 5EE6 m/sec from 1EE8 m/sec at RF speed. I don't remember I ever read this before, I thought velocity = 1/sqrt( μ/ε).

Please give me a link on the reason if this is true.

Thanks

Alan

 

[trurle]

Apart from goods promotions (which are mostly insignificant) in the paper you linked, the phenomenon of increased characteristic impedance of cables at very low frequency is true. The impedance transition frequency is the frequency where skin depth is comparable with the thickness of conductors. At lower frequency, fields are no longer effectively confined to dielectric and simplified formula involving only parameters of dielectric no longer works.

 

[yungman]

Thanks for the reply, I don't think rise of impedance is of importance. I mainly want to confirm the velocity of propagation really slow down to 5EE6m/s and 20Hz. I always work in RF, never even thought of 20Hz and never seen any book talk about at this low frequency.

I did a quick calculation, even if I accept the 5EE6m/s, at 20Hz, I calculated the propagation is about 1.44deg going through a 1m long cable. That's not much of a phase shift. Usually interconnect cables are less than 1m long ( I won't use longer than that if I can help it.) as the capacitance of the cable do go up. It's about 30pF/ft, the longer the cable, the more the shunt capacitance. For old tube equipment, output impedance is higher, it might affect the high frequency response ( again, that's also a stretch).

 

[yungman]

Also, more importantly, even if it is true the velocity slow down to 5EE6m/s and phase delay is 1.44deg/m for 20Hz. This is compare to a PERFECT situation where the velocity of propagation is the same at all frequency.

BUT, this is a cable comparison, meaning it is compare one cable to another, not comparing a cable to perfect condition of equal velocity. The question remains how much one can improve the velocity on the best cable material compare to the average cable. Say, if the best of the best cable only improved to say 1deg/m, that improvement is so minor that it won't matter in all do respect.

 

[trurle]

Also, more importantly, even if it is true the velocity slow down to 5EE6m/s and phase delay is 1.44deg/m for 20Hz. This is compare to a PERFECT situation where the velocity of propagation is the same as all frequency.

BUT, this is a cable comparison, meaning it is compare one cable to another, not comparing a cable to perfect condition. The question remains how much one can improve the velocity on the best cable material. Say, if the best of the best cable only improved to say 1deg/m, that improvement is so minor that it won't matter in all do respect.

Yes, you catch the idea. In worst case, velocity is proportional to square root of frequency, while phase advance is linearly proportional to frequency. Therefore, at very low frequencies phase advance and phase dispersion are not significant. You should watch out for phase dispersion at around transition frequency of cable though.