Electronic – Is it sensible to always use larger diameter conductors for carrying smaller signals

This question as originally written sounds a little bit insane: it was originally asked to me by a colleague as a joke. I am an experimental NMR physicist. I frequently want to perform physical experiments which ultimately boil down to measuring small AC voltages (~µV) at about 100-300 MHz, and draw the smallest current possible. We do this with resonant cavities and impedance-matched (50 Ω) coaxial conductors. Because we sometimes want to blast our samples with a kW of RF, these conductors are often quite "beefy" — 10 mm diameter coax with high quality N-type connectors and a low low insertion loss at the frequency of interest.

However, I think this question is of interest, for the reasons I'll outline below. The DC resistance of modern coax conductor assemblies is frequently measured in ~1 Ω/km, and can be neglected for the 2 m of cable I typically use. At 300 MHz, however, the cable has a skin depth given by

$$
\delta=\sqrt{{2\rho }\over{\omega\mu}}
$$

of about four microns. If one assumes that the centre of my coax a solid wire (and therefore neglects proximity effects), the total AC resistance is effectively

$$
R_\text{AC}\approx\frac{L\rho}{\pi D\delta},
$$

where D is the total diameter of the cable. For my system, this is about 0.2 Ω. However, holding everything else constant, this naïve approximation implies that your AC losses scale as 1/D, which would tend to imply that one would want conductors as large as possible.

However, the above discussion completely neglects noise. I understand that there are at least three main sources of noise I should consider: (1) thermal (Johnson-Nyquist) noise, induced in the conductor itself and in the matching capacitors in my network, (2) induced noise arising from RF radiation elsewhere in the universe, and (3) shot noise and 1/f noise arising from fundamental sources. I am not sure how the interaction of these three sources (and any I may have missed!) will change the conclusion reached above.

In particular, the expression for the expected Johnson noise voltage,

$$
v_n=\sqrt{4 k_B T R \Delta f},
$$

is essentially independent of the mass of the conductor, which I naïvely find rather odd — one may expect that the larger thermal mass of a real material would provide more opportunity for (at least transiently) induced noise currents. Additionally, everything I work with is RF shielded, but I can't help but think that the shielding (and the rest of the room) will radiate as a black body at 300 K…and therefore emit some RF that it is otherwise designed to stop.

At some point, my gut feeling is that these noise processes would conspire to make any increase in the diameter of the conductor used pointless, or down right deleterious. Naïvely, I think that this has clearly got to be true, or labs would be filled with absolutely huge cables to be used with sensitive experiments. Am I right?

What is the optimum coaxial conductor diameter to use when carrying information consisting of a potential difference of some small magnitude v at an AC frequency f? Is everything so dominated by the limitations of the (GaAs FET) preamplifier that this question is entirely pointless?