Cold Sky
Understanding Cold Sky
The cosmic microwave background provides the most stable and well-characterized low-temperature reference available for microwave radiometry. Its brightness temperature of 2.725 ± 0.001 K is uniform across the sky to one part in 100,000 (excluding dipole anisotropy from Earth's motion), making it an ideal calibration standard. Radio astronomers and antenna engineers exploit this by pointing the system under test toward a "cold" patch of sky and measuring the output power, then comparing it to the output when viewing an ambient-temperature absorber load. The ratio of these two power levels, combined with the known reference temperatures, yields the system noise temperature.
In practice, the antenna does not see 2.725 K. The atmosphere contributes emission that raises the effective temperature by 2 to 10 K at frequencies below 15 GHz, increasing rapidly above 22 GHz (water vapor line) and 60 GHz (oxygen complex). Galactic synchrotron radiation adds 1 to 50 K below 2 GHz depending on the pointing direction relative to the galactic plane. Ground spillover through antenna sidelobes can add 10 to 50 K if the antenna's rear lobes intercept terrain at 290 K. For precise calibration, each contribution must be calculated and subtracted. The standard procedure uses tipping curves (measuring sky temperature at multiple elevation angles) to separate atmospheric and cosmic components.
Y-Factor and Noise Temperature
Y = Phot / Pcold
Receiver Noise Temperature:
Trx = (Thot − Y × Tcold) / (Y − 1)
Noise Figure:
NF = 10 log10(1 + Trx / 290)
Where Phot, Pcold = output power with hot/cold reference, Thot ≈ 290 K (ambient absorber), Tcold ≈ 5 to 8 K (cold sky at zenith). For Trx = 50 K: NF = 0.71 dB, Y = 5.6 dB.
Cold Sky Temperature Contributors
| Source | Temperature at 10 GHz | Temperature at 30 GHz | Frequency Dependence | Mitigation |
|---|---|---|---|---|
| CMB | 2.725 K | 2.725 K | Constant (Planck correction <1%) | None needed |
| Atmosphere (zenith) | 2 to 3 K | 5 to 12 K | Increases with frequency | Tipping curve |
| Galactic emission | 0.5 to 2 K | <0.1 K | Decreases as f-2.7 | Point away from plane |
| Ground spillover | 5 to 50 K | 5 to 50 K | Depends on sidelobe pattern | Low-sidelobe antenna |
| Total effective | 5 to 8 K | 10 to 20 K | Sum of above | Calculate and subtract |
Frequently Asked Questions
What temperature does cold sky provide as a calibration reference?
The CMB provides 2.725 K, but the effective cold sky temperature at the antenna is higher due to atmospheric emission (2 to 10 K at frequencies below 15 GHz), galactic emission (1 to 50 K below 2 GHz depending on direction), and ground spillover through sidelobes. At the optimal calibration range of 5 to 15 GHz pointed near zenith away from the galactic plane, the total cold sky temperature is approximately 5 to 8 K.
How is cold sky used in Y-factor noise figure measurement?
The Y-factor method compares receiver output power when viewing a hot reference (~290 K ambient absorber) versus cold sky (~5 to 8 K). Y = Phot/Pcold, then Trx = (Thot − Y × Tcold)/(Y − 1). The large 40:1 temperature ratio provides much higher measurement accuracy than two ambient-temperature loads, especially for low-noise receivers below 100 K noise temperature.
What conditions are required for accurate cold sky calibration?
Requirements include clear weather (clouds add 5 to 50 K), pointing at least 30 degrees from the galactic plane, avoiding the Sun and Moon, elevation above 30 degrees (atmospheric path length increases as cosecant of elevation), and stable atmospheric conditions. The atmospheric contribution must be calculated from radiosonde data or ITU-R P.676 atmospheric models and subtracted from the measured value.