Noise Figure

The Component Specification

• Any component adds noise and degrades the input SNR
• Noise factor measures that degradation (linear):
• Noise figure expresses it in dB:
• Lower NF means less added noise under the same conditions
• Component noise figure and gain describe each receiver stage (e.g. a LNA datasheet)

The 290 K convention

• NF is defined with a source at and the same noise bandwidth at input and output
• is a reference, not the actual hardware or antenna temperature (three meanings of temperature)

Noise Figure and Equivalent Noise Temperature

Equivalent Noise Temperature from NF

NF = 0.69 dB

• This 50 K receiver is used throughout the lunar link

Receiver Cascade: Where Each Stage Adds Noise

• Source (signal + per Hz) → LNA (gain , ) → later receiver (gain , )
• Source noise passes through both stages; each stage also adds its own noise
• The LNA boosts the signal before later stages add their noise → later-stage noise matters less relative to the signal
• Input referral expresses all added noise at one common reference plane

The Friis Noise Equations

Friis Noise Equation

1. Convert catalog values to linear: ,

2. Combine the stages using their linear factors:

3. Return to dB:

• The first stage enters directly; early gain reduces the later terms

How Much Early Gain Helps

LNA Gain of 10, 20, and 30 dB

• LNA NF = 0.68 dB; following receiver NF = 6.48 dB; keep both NFs fixed as the LNA gain changes
• , :

LNA gain
10 dB	10	≈ 1.8 dB
20 dB	100	≈ 0.80 dB
30 dB	1000	≈ 0.69 dB

• Each extra 10 dB helps less; the limit as LNA gain grows is the first LNA’s own NF ≈ 0.68 dB

From Component NF to the Link Budget

• LNA (gain 30 dB, NF 0.68 dB) → following receiver (NF 6.48 dB): cascade NF ≈ 0.69 dB
• Convert once for G/T:
• NF is the component figure of merit; kelvins are what combine receiver and antenna noise (System Noise Temperature)

Clarifications From October 5

• Noise factor is linear; noise figure is in dB
• is a common reference near room temperature
  • It makes component NF values comparable
  • It is not the actual antenna or hardware temperature
• Another reference would change the reported NF, but a consistent gives the same physical noise

Why the 290 K Reference Cancels

Chosen reference	Reported noise factor	Recovered receiver
290 K	2.0 (NF = 3.0 dB)
Hypothetical 580 K	1.5 (NF = 1.8 dB)

• Same hardware, different reporting convention
• Actual output noise is unchanged by the reference choice:
• Reference: Keysight, Noise Figure application help (thermal noise and the 290 K reference)