In Maths σ is standard deviation1.- standard deviation
σ stands for standard deviation.
Defition of standard deviation :
https://www.math.net/standard-deviation#:~:text=Standard%20deviation%20Standard%20deviation%20is%20a%20statistical%20measure,values%20tend%20to%20be%20close%20to%20the%20mean.
2.- Signals with null DC
In Communications, wireless modulated signals, radiated received by antennas, over-the-air sinals, as well as spectral noise have nullnull DC values.
Radiated Electromagnetic fields do not have DC.
Indeed noise and signals can and are often biased, on circuit boards there are plenty of examples to be found.
These are conducted, not radiated, signals.
3.- dB dBm clarification
In the context of this question, since the question originator starts equating squared σ and η to dBm and dB values, such practice is often found in literature for signals and noise with null DC component.
σdBm and dB are often the short for dBmW and dBW that it's assumed this way there's no way to confuse them with dBmV and dBV.
Experts advise, in case of any doubt, when mixing power W and Volts V in same text, to use the whole expressions dBmW instead of dBm and dBW instead of dBW when referring to signal power and the equivalent with Volts when signal amplitude levels referred.
4.- Signal to Power
So σ is usuallycommonly assigned to signal deviation and η forη to noise deviation.
BothSo when both signal s and noise n have null mean valuevalues, but when you takethen taking the absolute value,values abs(s) abs(n) both variables are most of the time, statistically speaking, constrained below certain levels.
This is, most of the times one measures thems and n the readings of s and n below certain abs() level, now equivalently to power level.
5.- Power measurements require known impedance(s)
Circuit imedances are measured in Ohms = Ω (Omega, last character of Greek alphabet, as in Rev22:13).
RF and microwave systems are mostly built with standard impedances of 70 Ohmthe following impedances: (VHF75Ω for VHF some UHF), and 50 OHm50Ω system impedances, alothough there are plenty of 50Ω for UHF systems.
So the averaged poweraveraged power, in a wide sense (rms? avg? another question),
is squared amplitude over impedance.squared amplitude over impedance
However, accademia often obviate system impedances and tacitally assume 1 Ohm,1Ω allowing a lot more theory to be conveyed in the same text.
When you readone reads -95dBm-95dBm for a sigma square probably means a weak signal, because dBm is another short for dBmWdBmW.
30dBmW = 0 dBW means 1mW = 1e-3W30dBmW = 0 dBW means 1mW = 1e-3W
There are books that use η6.- Disambiguation circuit impedance and wave impedance
The above explanation is for electromagneticsignals.
Signals impedances in general, are often referred as
Z = R +1j*X,
R resistance and X reactance
Z (waveΩ) impedancedirectly relates Voltage (OhmVolts), and Current (Amperes).
Then there are books that use η in a particular way as electromagnetic wave impedance also in Ω Ohm :
wave impedance is the ratio between |E| electric field and |H| magnetic field
electric field units [V/m]
mangetic field units [A/m]
B is not magnetic field, but magnetic flux.
magnetic flux as H * A , A : area, square feet, square meters . B is not H/A
https://www.vedantu.com/physics/magnetic-flux
B units : Tesla [T]
1 T = 1Wb/sqm =1N/(C * (m/s)) = 1N/(A * m)
Weber [Wb] : 1 Wb = 1 V·s = 1 T·m2 = 1 J/A = 10e8 Mx
Maxwell [Mx]
sqm square meter, same as m2
That for air is the impedance that for instance mobile phonesphone signals encounter when crossingpropagating through atmosphere, about 377 Ohm butZ0 = 377Ω but it varies with weather and other factors. But it doesn't seem the case here
η as wave impedance is often also found in literature as Z0.
If you supply more details aboutwhen Z0 values depart from standard values as the context then more details could be addedones shown above it may referred with variable names like Z1 Z2 .. for instance in impedance transformers.
