For HF and higher frequencies, L >> R and C >> G are generally good assumptions. We can then simplify the general expressions for complex characteristic impedance and complex propagation constant to:
Zo = sqrt(L / C) ohms
gamma = j * omega * sqrt(L * C) radians per unit length
Because the power dissipating elements R and G are assumed to be zero, the real part of gamma, the attention constant, is zero. Note that if we increase L, we increase the number of radians of wavelength that occupy each unit of length. We can therefore delay propagation by increasing L and that has been done with coax by using a spiral center conductor.
Voice frequency telephone cables pairs are often inductively loaded by placing load coils at intervals. The most popular scheme in the Bell System was 88 mH every 6000 feet, but there are other schemes. The velocity of propagation is pretty low for such loaded cables, although the reasons for loading are to reduce the attenuation and make it relatively constant below a cutoff frequency.
I don't know anything in particular about the special cables for tunnels. I would assume that the "leaked" energy would show up as an increase in attenuation, but maybe someone here knows more about those lines.
73,
Maynard
W6PAP
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On 6/30/23 20:47, Fran?ois wrote:
Thank you very much for your explanations.
1/ We found in old spectrum analyzers for RADAR (1960) delay lines made of a coaxial cable with losses. Our teacher had told us that it allowed to have a lower speed of propagation. I guess we can say that it is a lossy coaxial therefore presenting a complex characteristic impedance (true or false?). If we use a nanaoVNA, what will be the consequences?
2/ More recently I have seen the use of radiating coaxial cable to retransmit radios in the tunnels. This is a cable where the outer conductor is split. This type of cable also has a complex characteristic impedance. Also, what would be the consequence with a nanoVNA?
