Tsys = Trx + Tant
Where:
Tsys = total system noise temperature
Trx = receiver noise temperature
Tant = antenna temperature (everything seen by the antenna)
Expanded form:
Tsys = Trx + Tspill + Tsky + Tatm + Tground
Where:
Trx = receiver + LNA + cable + feed losses
Tspill = spillover onto ground or nearby structures
Tsky = cosmic background + Galactic emission + sources
Tatm = atmospheric emission (oxygen, water vapour)
Tground = extra ground pickup via sidelobes
Another common engineering form:
Tsys = Trx + eta_sky * Tsky + eta_spill * Tground + Tloss
Where:
eta_sky = fraction of beam seeing cold sky
eta_spill = fraction seeing warm ground
Tloss = ohmic / feed / cable losses converted to temperature
Key relationship behind all of this:
P = k * T * B
Where:
P = noise power
k = Boltzmann constant
T = equivalent noise temperature
B = bandwidth
Simplifying this further into a “hydrogen line telescope budget” specifically for your 1420 MHz setup and show which term dominates in your system.
Tsys = Trx + Tsky + Tspill + Tatm
Where:
Trx = receiver noise temperature (LNA, cables, feed, SDR front-end)
Tsky = sky noise (cosmic background + Galactic emission + radio sources)
Tspill = spillover noise (ground pickup through sidelobes)
Tatm = atmospheric noise (mainly oxygen + water vapour)
Typical 1420 MHz values:
Cold sky direction: Trx = 20 to 60 K
Tsky = 3 to 10 K
Tspill= 5 to 30 K
Tatm = 2 to 5 K
So: Tsys = 30 to 100 K (typical range)
Galactic plane direction:
Trx = 20 to 60 K
Tsky = 20 to 200 K
Tspill= 5 to 30 K
Tatm = 2 to 5 K
So: Tsys = 50 to 300+ K
Key point:
- Trx dominates good receivers
- Tspill dominates poor antenna design
- Tsky dominates when pointing into the Milky Way
- Tatm is usually small but always present