G/T from first principles: what makes a good amateur ground station

One number for the station#

In the downlink budget of a small satellite, everything on the ground collapses into one term[1]:

$$\frac{C}{N_0}=\mathrm{EIRP}-L_{\mathrm{path}}+\frac{G}{T}-k$$

$G$ is the gain of the receiving antenna and $T$ the system noise temperature referred to its terminals; $k=-228.6$ dBW/(K·Hz) is Boltzmann’s constant. Every decibel of G/T is a decibel of margin, or 26% more data rate at the same energy per bit. For a spacecraft that cannot raise its transmit power, as a PocketQube cannot, G/T is the main lever left, and it is cheap to improve.

Gain is the easy part: a crossed Yagi of moderate size reaches about 13 dBi at 437 MHz, a turnstile or quadrifilar helix about 2 dBi. The noise temperature takes more thought.

Where the noise comes from#

The antenna delivers noise from everything its pattern sees. At UHF the cold sky contributes a few tens of kelvin and the galactic plane more; the warm ground at about 290 K enters through side and back lobes, and man-made noise from power lines, switching supplies and electronics adds to both. ITU-R P.372 tabulates median levels of galactic, atmospheric and man-made noise by frequency and environment[2]; in towns, man-made noise can dominate the system temperature of a good receiver. In this note we assume 150 K for a Yagi looking up at a pass and 300 K for an omnidirectional antenna, which sees the ground over half of its pattern.

The cable attenuates the signal by its loss factor $L$ and, being at the physical temperature $T_0\approx 290$ K, adds noise of its own, $(L-1)T_0$. Ahead of any amplifier, each 0.1 dB of loss costs 7–9 K, and one decibel 75 K.

The receiver is characterized by its noise figure $F$, with noise temperature $T=T_0(F-1)$. A low-cost software-defined radio with a noise figure of 6 dB has about 865 K. A good low-noise amplifier (LNA) with 0.5 dB has 35 K.

The cascade#

Friis showed how the noise of a chain of stages adds up when referred to its input[3]:

$$T_{\mathrm{sys}}=T_{\mathrm{ant}}+T_1+\frac{T_2}{G_1}+\frac{T_3}{G_1{G}_2}+\dots$$

Each stage’s noise is divided by the gain of everything ahead of it. The first stage therefore sets the system temperature, provided its gain is high. For the three arrangements of a Yagi, a 1.8 dB cable, an LNA with 20 dB of gain and the SDR:

$$\begin{array}{rl}\text{LNA at the mast:}& T_{\mathrm{sys}}=T_{\mathrm{ant}}+T_{\mathrm{LNA}}+\frac{(L-1)T_0}{G}+\frac{L{T}_{\mathrm{rx}}}{G}\\ \text{LNA after the cable:}& T_{\mathrm{sys}}=T_{\mathrm{ant}}+(L-1)T_0+L{T}_{\mathrm{LNA}}+\frac{L{T}_{\mathrm{rx}}}{G}\\ \text{No LNA:}& T_{\mathrm{sys}}=T_{\mathrm{ant}}+(L-1)T_0+L{T}_{\mathrm{rx}}\end{array}$$

The table makes the rule visible. With the amplifier at the antenna, the cable and the SDR almost vanish behind 20 dB of gain, and the system is as quiet as the antenna allows. Behind the cable, the amplifier still hides the SDR, but the cable’s own noise is already in. Without an amplifier, the SDR’s noise, multiplied by the cable loss, dominates everything.

What G/T buys: Grizu-263A#

The PocketQube review evaluated the downlink of Grizu-263A, 20 dBm of EIRP from a 0 dBi monopole at 4800 Bd, against a directional station of 13 dBic and 350 K and an omnidirectional one of 2 dBic and 500 K[4]. Replacing those two stations by the five receive chains of this note:

Receive chain	Gain (dBi)	System temperature (K)	G/T (dB/K)	Margin at 30° (dB)	Lowest usable elevation
Crossed Yagi, LNA at the mast, 20 m of low-loss cable	13	200	−10.0	+7.1(positive margin)	5°
Crossed Yagi, LNA indoors after the same cable	13	366	−12.6	+4.5(positive margin)	13°
Crossed Yagi, no LNA	13	1,607	−19.1	−2.0(link does not close)	42°
Omnidirectional (QFH or turnstile), LNA at the antenna	2	370	−23.7	−6.6(link does not close)	Never
Omnidirectional, no LNA	2	1,463	−29.7	−12.5(link does not close)	Never

Friis cascade with assumed antenna temperatures of 150 K (Yagi looking at the sky) and 300 K (omnidirectional antenna that also sees the warm ground), LNA noise figures of 0.5–0.8 dB with 20 dB gain, and a 6 dB noise figure for a low-cost SDR.

The directional station of the review, at −12.4 dB/K, sits between the first two rows; its threshold of about 12° matches the observation that early recordings often lacked the signal-to-noise ratio needed for decoding. With the amplifier at the mast the same antenna decodes from 5°; without any amplifier it needs 42°. No omnidirectional chain closes at 4800 Bd. At 2400 Bd, 3 dB easier, an omnidirectional antenna with an LNA reaches the link only above about 55°, near zenith, as the review found.

The thresholds turn into contact time. For a station at 41.45° N, the latitude of the station in Zonguldak that operated the mission, and the 525 km Sun-synchronous orbit:

Moving one amplifier from the shack to the mast doubles the usable contact; leaving it out leaves about two minutes a day. Requiring 3 dB of margin instead of zero raises every threshold, but not the ranking. The pass geometry article explains why the low elevations hold so many of the minutes.

Antenna gain or noise temperature?#

A larger antenna raises G and narrows the beam, which then needs a better rotator and tracks less forgivingly. Lowering T costs an amplifier and some weatherproofing. At 437 MHz the second is almost always the cheaper decibel. A rough comparison for the Yagi of this note:

• Doubling the antenna, from 13 to 16 dBi: +3 dB.
• Moving the LNA from the shack to the mast: +2.6 dB.
• Adding an LNA at the mast to a station that had none: +9.1 dB.

The two levers interact: a higher-gain antenna sees less ground and less man-made noise, so its antenna temperature tends to fall as its gain rises, but no antenna gets below the temperature of the sky it looks at.

A checklist for building a station#

1. Put the LNA at the antenna, with as little cable and as few connectors ahead of it as possible.
2. Protect it, then accept the price. A band-pass filter ahead of the LNA guards against strong out-of-band transmitters, but its loss adds to the system temperature exactly as cable loss does; use the lowest-loss filter the site allows.
3. Use circular polarization on the ground. A tumbling spacecraft with a linear antenna and Faraday rotation in the ionosphere make the received polarization unpredictable; a circular ground antenna costs a fixed 3 dB instead of deep fades.
4. Choose and measure the site. Compare the noise with the antenna pointed at the cold sky and at the warm ground or an absorber: the ratio of the two noise powers, the Y-factor, gives the noise temperature of the receiving chain. Man-made noise shows up the same way.
5. Think in networks. A single excellent station still sees the satellite for half an hour a day; many modest stations spread over latitudes and longitudes, as in SatNOGS, multiply that time[5].

The ground segment entry covers station hardware and operations, and the UHF link budget article derives the rest of the budget into which G/T enters.