What Is Noise Temperature?
Noise temperature T_e is an alternative way to express the noise added by a device. It is defined as the temperature of a matched resistor at the input that would produce the same noise power as the device's internal noise. The relationship to noise figure F is:
T_e = T₀ · (F − 1) [K] F = 1 + T_e / T₀ where T₀ = 290 K (IEEE standard reference temperature)
Noise Figure vs. Noise Temperature Conversion
| Noise Figure (dB) | F (linear) | T_e (K) |
|---|---|---|
| 0.1 dB | 1.023 | 6.7 K |
| 0.3 dB | 1.071 | 20.6 K |
| 0.5 dB | 1.122 | 35.4 K |
| 1.0 dB | 1.259 | 75.1 K |
| 2.0 dB | 1.585 | 170 K |
| 3.0 dB | 2.000 | 290 K |
| 10 dB | 10.00 | 2610 K |
Why Use Noise Temperature?
Noise temperature is preferred in satellite and radio astronomy applications where the system noise sources span a very wide range (antenna sky noise ≈ 3–50 K, cryogenic LNA T_e ≈ 5–50 K). Using noise figure (dB) at these very low noise levels is less intuitive and less numerically precise. Noise temperature scales linearly, making cascade calculations straightforward.
Friis Cascade in Noise Temperature Form
T_sys = T_ant + T_cable/G_ant + T_LNA/(G_ant · G_cable) + ... Or equivalently (component cascade): T_total = T₁ + T₂/G₁ + T₃/(G₁·G₂) + T₄/(G₁·G₂·G₃) + ···
Typical Noise Temperature Values
| Component | Noise Temperature | Notes |
|---|---|---|
| Antenna (cold sky) | 10–50 K | Pointing away from ground |
| Antenna (warm sky) | 50–290 K | Partially pointing at ground |
| Cryogenic LNA | 5–30 K | Cooled to 15–77 K |
| Room-temperature LNA | 50–200 K (0.5–2.5 dB NF) | GaAs or GaN HEMT |
| Coax cable (loss L) | T₀·(L−1) where L is linear loss | 1 dB cable → 75 K |
Relationship to S-Parameters
RF View reads the S-parameter files of LNAs and cables. The S21 of a cable directly gives its loss (L_linear = 1/|S21|²), which determines its noise temperature contribution. The noise figure (or T_e) of an LNA is specified in its datasheet alongside its S-parameters. Load the LNA .s2p file in RF View to verify S11 (input match) and S21 (gain) — both affect the contribution of subsequent stages to system noise temperature per the Friis formula.