Note
that I have used the ITU best case Quiet Rural noise curves as the
basis for comparison. In this case it is noticeable when the loop
sensitivity is worse than the natural noise floor over most of the
frequency range, even when using a very 'Fat' loop with a low value of
inductance.
However in an urban environment, where a
loop is being used to try and mitigate the effects of local noise
sources, which could easily be 20 or 30dB higher than the rural noise
floor, then the loop sensitivity may be adequate.
I
believe these calculations and graphs to be accurate, and my
measurements and tests on many different types of broadband loops seem
to confirm the theoretical values I have obtained. However my maths have
never been top grade, and although I have a reasonable level of
confidence in the results, I would be more than happy for someone else
to do the same work and prove, or disprove, my findings.
Loop inductance can be reduced by connecting multiple loops in parallel, or by making the conductor larger.
WRT tuned loops, even passive tuned loops can produce better results than broadband amplified loops, and for a similar size are capable of sufficient sensitivity to be able to hear the natural noise floor. However they are not quite so convenient to use if you are interested in observing large swathes of spectrum.
Reducing the loop inductance can help move the self-resonance higher in frequency, which means that a larger diameter loop a can be used on the higher frequency bands, which in turn will provide additional improvement in gain on the lower frequency bands.
I have a small tuned loop that I use to locate interference sources and it is capable of very good sensitivity on receive.
The construction details are about 2/3 down this webpage.
https://www.g8jnj.net/hfloopantennas.htm