Receive chain

Everything makes noise

Every resistor makes noise because its electrons move with the heat. The power it delivers is k · T · B: Boltzmann constant times temperature times bandwidth. At 290 K, the usual reference temperature T0, that is −174 dBm in 1 Hz and −140.2 dBm in 2.4 kHz. At room temperature you cannot get less noise than this floor, and every amplifier adds a bit more.

Noise figure

The noise figure NF tells you by how many dB a stage degrades the signal-to-noise ratio when exactly the 290 K floor is present at its input. A receiver with 8 dB turns 20 dB S/N into 12 dB. For good preamps the number is awkward: 0.3 dB, 0.5 dB, 0.7 dB all look like next to nothing.

Noise temperature

That is why you work with the noise temperature Te = 290 K · (F − 1), F = 10^(NF/10). It tells you how hot a resistor at the input would have to be to make as much noise as the stage itself. 0.5 dB is 35 K, 1 dB 75 K, 3 dB 289 K, 8 dB 1540 K. Temperatures simply add up, noise figures do not.

Cable and filter

Anything that attenuates also makes noise. A cable at room temperature with 3 dB loss has exactly 3 dB noise figure, so 289 K. It swallows half the signal and adds noise at its own temperature. In the cable and filter blocks you can set the temperature: a cable up the mast in winter makes slightly less noise.

What the antenna sees

The antenna brings noise along too, its antenna temperature. A dish for 10 GHz sees cold sky and, through the side lobes, a little ground, 30 to 60 K together. On 2 m the Milky Way makes noise, several hundred K depending on direction. On HF the band noise comes on top: thunderstorms, the galaxy and above all power supplies, lines and appliances in the neighbourhood. The page works it out after ITU recommendation P.372 as Fa in dB above the floor. Rural on 20 m that is a good 35 dB, so almost a million K. Any receiver disappears against that.

The sum of antenna temperature and the noise temperature of the chain is the system temperature. It gives the noise every signal has to stand up against.

The Friis formula

With several stages in a row, each counts only divided by the gain of all stages before it:

Te = Te1 + Te2 / G1 + Te3 / (G1 · G2) + …

A preamp with 1 dB (75 K) and 20 dB gain in front of a receiver with 8 dB (1540 K): 75 K + 1540 K / 100 = 90.5 K, that is a noise figure of 1.18 dB. The receiver alone would have 8 dB. The first stage decides almost everything as soon as it has enough gain.

Cable before or after

The same 3 dB of cable costs very different amounts depending on where it sits. After the preamp: 75 + 289 / 100 + 1540 / 50 = 108.8 K, so 1.38 dB. In front of the preamp the cable counts in full, and everything after it twice: 289 + 75 · 2 + 1540 / 50 ≈ 469 K, so 4.18 dB. That is why the preamp belongs at the antenna, not in the shack. The preset “2 m, preamp in the shack” shows it: drag the preamp in front of the cable and the S/N rises by 3.6 dB.

Even more so with satellites

With QO-100 the LNB sits right at the focus. 20 m of H155 cost around 27 dB at 10.5 GHz, but only 5 dB at the 740 MHz intermediate frequency, and behind 55 dB of gain even those no longer matter. In the preset, put the cable in front of the LNB: the S/N drops by 32 dB.

When the band is louder

On HF it is the other way round. Rural on 20 m the antenna brings almost a million K, the whole chain has around 1000 K. With or without preamp, the S/N changes by 0.0 dB. A preamp lifts signal and band noise by the same amount. On 160 m this goes so far that a receive antenna with 1 % efficiency hears just as well as a full-size one: it loses 20 dB of signal, but also 20 dB of band noise, and that is still far above the receiver.

Rule of thumb: the receiver noise should sit 6 to 10 dB below the band noise, more brings nothing. You can check it on the rig: unplug the antenna. If the noise in the speaker drops clearly, you are hearing the band, not the receiver, and a preamp only makes overload more likely.

Signal against noise

The noise in bandwidth B is k · Tsys · B, in dBW: −228.6 + 10 log Tsys + 10 log B. The S/N is the signal level at the antenna minus this noise. Wider filters let more noise through: going from 2.4 kHz to 50 Hz gains you 16.8 dB, which is why EME works in CW or with narrow digital modes.

G/T

G/T sums up how good a receiving system is: antenna gain in dBi minus 10 log Tsys. More gain or less noise help equally. The 80 cm dish of the QO-100 preset has 36.7 dBi at 101 K system temperature, so 16.7 dB/K. The four Yagis of the EME preset reach −4.5 dB/K with 19 dBi and 224 K.

The path

What arrives depends on the transmitter and the path. The page knows three paths: a level in dBm right at the antenna, the flux density in dBW/m² (as satellite operators state it) and a transmitter with EIRP over a free-space path or via the moon. Free-space path loss is 20 log (4π · d / λ). Out to QO-100 at 38,000 km that is 204.5 dB on 10,489.75 MHz.

Via the moon the page uses the radar equation: the moon reflects about 6.5 % of what hits it, at a distance of 384,400 km, there and back. On 144 MHz that costs 252.1 dB compared with two isotropic antennas, and it rises by 20 dB per decade with frequency.

Two examples

QO-100: 13 dBW EIRP − 204.5 dB + 16.7 dB/K + 228.6 = 53.8 dB-Hz, that is the carrier-to-noise ratio in 1 Hz. In 2.4 kHz (33.8 dB) that leaves 20.0 dB S/N.

2 m EME: 50 dBW EIRP − 252.1 dB − 4.5 dB/K + 228.6 = 22.0 dB-Hz. In 50 Hz (17.0 dB) that leaves 5.0 dB, easy to hear in CW. In 2.4 kHz it would be −11.8 dB, lost in the noise.