Noise Temperature and G/T Explained for VHF, EME and Satellite
Weak-signal operators on satellites, EME and the higher VHF and UHF bands talk about their stations in a language that sounds odd at first: the system has a noise temperature of 120 kelvins, the dish has a G/T of 10 dB per kelvin, a preamplifier at the mast head “gains” a decibel. Behind this vocabulary there is a simple idea that applies to every receiving station, including your HF setup: what limits the reception of a weak signal is not the signal level alone but the level of the noise that competes with it. Noise temperature is a way to put all the sources of that noise, from the sky to the transistor in the first stage, on one scale. This guide explains the idea step by step, with numbers you can check with a calculator.
Noise Is Power, and Power Can Be a Temperature
Every resistor produces a small random voltage because its electrons are in thermal motion. This is Johnson-Nyquist noise, and the available noise power in a bandwidth B at a temperature T is simply k times T times B, where k is the Boltzmann constant. The Wikipedia article on noise temperature gives it as 1.381 times 10 to the power of minus 23 joules per kelvin and defines noise temperature as the temperature that would produce a given level of noise power in this way. The idea is useful because noise from any source, not only a warm resistor, can be described by the temperature of a resistor that would give the same noise power. A device that adds noise looks, from the outside, like a hotter resistor.
At the standard reference temperature of 290 K, kT equals about -174 dBm per hertz. To find the noise in a receiving bandwidth, add 10 times the logarithm of the bandwidth in hertz. The results are easy to remember for the usual filters:
| Bandwidth | Typical use | Noise power at 290 K |
|---|---|---|
| 500 Hz | CW | About -147 dBm |
| 2400 Hz | SSB | About -140 dBm |
| 10 kHz | AM and narrow FM | About -134 dBm |
The table shows why a narrow filter helps with weak signals: reducing the bandwidth from 2400 Hz to 500 Hz lowers the noise power by about 7 dB, and a CW signal that fits into the narrow filter loses nothing. The same reasoning explains the success of the very narrow digital modes.
Noise Figure and Noise Temperature Are the Same Thing
The better known way to describe the noise of a receiver or preamplifier is the noise figure, in decibels. The two descriptions are connected by a formula given in the Wikipedia article: the noise figure NF equals 10 times the logarithm of one plus the equivalent noise temperature Te divided by 290. In the other direction, Te = 290 × (10^(NF/10) – 1). A few values show how much the scale spreads out at the low end:
- NF 0.5 dB corresponds to about 35 K, a good low noise amplifier for VHF and UHF.
- NF 1 dB corresponds to about 75 K.
- NF 3 dB corresponds to about 289 K, which is the same as the reference temperature.
- NF 6 dB corresponds to about 865 K. The article uses a very similar example of an amplifier with a noise temperature of 870 K and a noise figure of 6 dB.
Kelvins are more useful than decibels when the numbers are small, since temperatures simply add. If a receiver adds 35 K and the antenna contributes 50 K, the total is 85 K, and if you reduce the receiver noise by 10 K, the total falls by 10 K. In decibels, the same changes are harder to see. For a compact introduction to the relationships between noise figure, sensitivity and preamplifiers in the HF range, see our article on when to use a preamplifier or attenuator.
What the Antenna Contributes
The antenna does not have a temperature of its own. The article on antenna gain-to-noise-temperature says that antenna noise temperature is not the physical temperature of the antenna but an expression of the available noise power at its terminals, and that it depends on the gain pattern and on the thermal environment in which the antenna sits. A directional antenna pointed at the cold sky collects a very low noise temperature: the article gives the night sky as roughly 4 K for the night sky as a rough value for the cosmic background. The same antenna pointed at the ground sees the temperature of the ground, around 290 K. The practical meaning is that a dish or a Yagi with its beam well above the horizon and with small side lobes has a low antenna noise temperature at the high frequencies, while the same antenna pointed at the horizon, or with large side lobes that look at the ground, gets much more noise.
At lower frequencies the story changes. Atmospheric and man-made noise rise strongly towards the lower HF bands, and the antenna temperature there can be many thousands of kelvins. The noise temperature article makes the same point when it notes that for an antenna at lower frequencies, where atmospheric noise dominates, the input source’s noise temperature is much higher, and there is little degradation of the signal-to-noise ratio from a receiver with a poor noise figure. This is why a noise figure of 10 dB on 80 metres does no harm, while 1 dB matters on 1296 MHz or on a satellite downlink.
The System Noise Temperature
The G/T article defines the system noise temperature as the sum of the antenna noise temperature and the noise temperature of the receiving chain referred to the antenna terminals. The receiving chain is a cascade of stages: the feedline, the preamplifier, the receiver. The Friis formula for the noise of a cascade, given in the same article, shows that the first stage dominates. Each later stage contributes its noise temperature divided by the gain of everything before it, so with a good preamplifier of 20 dB gain, the noise of the receiver behind it is divided by 100 and becomes almost irrelevant. The same article states the corollary that matters most in practice: an attenuator, or a lossy cable, placed before the first amplifier degrades the noise figure of the amplifier.
Feedline Loss: The Expensive Decibel
A passive loss has a noise temperature of its own, since a lossy cable at 290 K is a warm resistor. A loss of 1 dB adds about 75 K, as in the table above, to the system, and the noise of everything after it is also increased by the loss in the same ratio. Take a satellite or EME station with a sky temperature of 50 K at the antenna and a low noise amplifier of 0.5 dB (35 K). If the amplifier is at the antenna, the system noise temperature is about 85 K. If a cable with 1 dB of loss sits between the antenna and the amplifier, the system temperature becomes 50 + 75 + 1.26 × 35, which is about 169 K. The ratio is 2, or 3 dB. In other words, 1 dB of loss ahead of the amplifier costs about 3 dB of the weak-signal performance in this example, because the signal falls by 1 dB and the noise rises by almost 2 dB. That is the reason why serious VHF, UHF and microwave stations place the preamplifier at the antenna, as we discuss in the article on mast-mounted preamplifiers, and why they use low-loss cable, as in the comparison of coaxial cables for ham radio.
G/T: The Figure of Merit
The Wikipedia article on antenna gain-to-noise-temperature calls G/T a figure of merit in the characterisation of antenna performance, where G is the antenna gain in decibels at the receive frequency and T is the equivalent noise temperature of the receiving system in kelvins. Expressed in decibels, G/T = G (dBi) – 10 × log10(T). With a gain of 30 dBi and a system noise temperature of 100 K, G/T is 30 – 20 = 10 dB per kelvin. The measure combines the two things that decide the signal-to-noise ratio of a received signal, the signal captured by the antenna and the noise it has to compete with. A bigger dish raises G. A better preamplifier, a lower loss cable and a quiet pointing direction lower T. Either one improves the figure by the same number of decibels, and this lets you compare options directly. Doubling the dish area adds 3 dB of gain, and removing 1 dB of loss in front of the amplifier can be worth as much or more.
Look at our guides to EME with Q65 and the QO-100 geostationary satellite for examples of stations where G/T decides what is possible. In both cases, the signals are weak and the operators spend their effort on the same two terms: raising the gain and lowering the noise.
A Worked Comparison: Dish Size Against Preamplifier Position
To see how the two levers compare, imagine a small satellite dish with a gain of 30 dBi, first with the amplifier at the feed and a system temperature of 85 K. Its G/T is 30 minus 10 times the logarithm of 85, which is about 30 – 19.3 = 10.7 dB per kelvin. Now move the amplifier into the shack behind 1 dB of cable. The system temperature rises to about 169 K, the G/T falls to 30 – 22.3 = 7.7 dB per kelvin, and you have lost 3 dB. To recover the same 3 dB by gain alone you would need a dish with twice the area, which means a diameter larger by about 40 per cent. A short, cheap change of the amplifier position gives what a much larger and heavier dish would otherwise be needed to give. This is the kind of comparison that G/T makes possible, and it is why weak-signal operators spend a lot of time on cables, connectors and relays.
Practical Steps to Lower Your System Noise
- Put the low noise amplifier as close to the antenna as practical, before the feedline, so that the loss comes after the gain.
- Keep the loss before the amplifier minimal. Use short jumpers, good connectors and a relay or switch with low loss, since every tenth of a decibel in front of the amplifier counts.
- Point the antenna carefully and choose a design with low side lobes, so that it sees the sky and not the ground.
- Pick the amplifier on the noise figure of the first stage, with enough gain to hide the noise of the later stages.
- Beware of local noise. If the noise comes from a source in your neighbourhood, a better amplifier will not help, and the cure is to find the source.
- Do not add gain without a reason. Too much gain overloads the stages that follow. The aim is a lower noise temperature, not a louder signal.
The Bottom Line
Noise temperature puts all noise sources on one scale: the noise power is kTB, and every component, including the antenna, can be given a temperature. Noise figure and noise temperature convert by Te = 290 × (10^(NF/10) – 1), so 0.5 dB is about 35 K and 3 dB is about 289 K. The first stage of a receiver dominates the noise, and a lossy cable before the first amplifier hurts, since 1 dB of loss ahead of a good LNA can cost several decibels of G/T. G/T, the antenna gain in decibels minus 10 times the logarithm of the system temperature, shows how gain and noise trade off. On the HF bands, external noise hides these differences, but on VHF, UHF and microwaves, they decide whether the signal can be heard.
Frequently Asked Questions
What is noise temperature?
It is a way of expressing the noise power of a component or a source as the temperature of a resistor that would produce the same noise. The noise power in a bandwidth B is k times T times B.
How do I convert noise figure to noise temperature?
Use Te = 290 × (10^(NF/10) – 1). A noise figure of 1 dB is about 75 K, and 3 dB is about 289 K.
What does G/T mean?
G/T is the antenna gain in decibels minus 10 times the logarithm of the system noise temperature in kelvins. It is a figure of merit for a receiving station, in dB per kelvin.
Why does cable loss before a preamplifier matter so much?
A lossy cable weakens the signal and adds its own thermal noise. Because the amplifier comes after it, the amplifier cannot recover the lost signal-to-noise ratio, so the loss counts almost twice.
Does noise temperature matter on HF?
Much less. On the lower HF bands the external noise is so high that the receiver’s noise figure is hidden, so a preamplifier seldom helps. It matters more on VHF, UHF and above.
How cold is the sky for an antenna?
For an antenna pointed at the clear night sky at high frequencies, the contribution is small, of the order of a few kelvins for the cosmic background, but real antennas also pick up noise from the ground, the atmosphere and their own losses.