System Noise Temperature

Three Different Meanings of Temperature

Temperature	Meaning	Example
Physical,	Actual hardware temperature; a thermometer could measure it	290 K
Equivalent noise,	Receiver-added noise expressed as an equivalent input temperature	50 K
Reference,	The fixed convention for defining noise factor and noise figure	Always 290 K

• One receiver can have 290 K hardware, 50 K equivalent noise, and a 290 K reference
• is what noise figure is defined against

Equivalent Noise Temperature

• A useful way to describe added noise:
  1. Noise arrives: the receiver amplifies the incoming noise
  2. The receiver adds noise: the output contains both contributions
  3. Express that addition at the input: is the strength of an equivalent thermal source
• Two models, exactly the same output:
  • Actual receiver: input signal + source noise → physical receiver (gain , adds noise) → output signal + total noise
  • Equivalent calculation model: same input + equivalent added density → noiseless amplifier (same gain ) → same output signal and noise
• We relocate the added noise in the model; the hardware and its output are unchanged
• From a noise figure: (NF ↔ Tₑ)

Which Noise Contribution Matters Most?

• System noise temperature = source (antenna) noise + receiver-added noise:

Same Receiver, Two Sources

• Same receiver: NF = 0.69 dB; convert once: (Ref: JPL DESCANSO Vol. 10, Ch. 2)

Source			Larger part
Cold sky, 30 K	80 K	19.0 dB-K	Receiver noise
Room temperature, 290 K	340 K	25.3 dB-K	Source noise

• Lowering receiver noise helps most when receiver noise dominates
• Antenna noise need not be 290 K: lower antenna noise gives lower total noise with the same receiver NF

Reference Planes in the Receiving System

• 
• Plane A (antenna terminal): ,
• Plane B (receiver input): ,

WARNING

• Use signal and total equivalent noise at the same plane

Feed Loss and Noise at Two Planes

• A room-temperature feed: 1.0 dB loss, 290 K physical; linear loss
• At A (feed input): antenna noise 30 K, signal
• At B (feed output): signal dB, antenna noise
• The feed’s own thermal noise:
  • Referred to input A:
  • Delivered at output B:
  • Both terms represent the same feed noise at different planes

One System, Two Noise Ledgers

System Noise Temperature with a Lossy Feed

Lunar Link Noise Ledger

Contribution	At A: before feed	At B: after feed
Antenna	30.0 K	23.8 K
Feed emission	75.1 K	59.6 K
Receiver	63.0 K	50.0 K
	168.0 K	133.5 K
	22.3 dB-K	21.3 dB-K

• A to B: and both fall 1.0 dB, so S/N₀ stays unchanged
• The receiver term at A is ; this slide rounds it to 63.0 K, the later system-noise slide shows 62.9 K

What Attenuates Signal? What Adds Noise?

Mechanism	Signal	Noise
Free space, pointing, polarization mismatch	Less received power	No thermal emission implied by this loss
Room-temperature feed / absorbing atmosphere	Attenuated	Incoming noise attenuated; thermal emission added
Receiver amplifier	Amplified	Incoming noise amplified; receiver noise added

• The absorbing-atmosphere case: loss and emission

Lunar Link: Reference Planes

Quantity	Antenna terminals A	LNA input B
Received signal	−131.9 dBW	−132.9 dBW
Equivalent system temperature	168.0 K / 22.3 dBK	133.5 K / 21.3 dBK
Equivalent noise density	−206.3 dBW/Hz	−207.3 dBW/Hz
S/N₀	74.5 dB-Hz	74.5 dB-Hz

• Same complete system represented at two planes; B includes receiver-added noise referred to its input

WARNING

• Moving the bookkeeping plane changes nothing, but physically inserting a lossy cable still degrades the link (LNA placement)