# Noise Temperature and G/T of Ground Terminal (Receiving System) in SATCOM

We have presented link budget calculations for SATCOM downlink in a previous post, where we described mathematical equation to calculate input SNR of ground terminal (receiving system). For details, read here: Link budget calculations for SATCOM – Downlink.

The SNR equations involves a parameter called as **G/T of the terminal** where G is the gain of terminal antenna and T is the noise temperature of the receiving system including antenna itself, RF chain, and LNB with the assumption that LNB has sufficient gain to make any noise contributions after the LNB negligible. Mathematical equation of Terminal gain has been presented in a separate post, where we defined gain in terms of peak gain, scan angle and cosine roll-off. For details, read here: Antenna Gain of ESA Terminal (Ground Station) in SATCOM

The purpose of this post is to explain the Noise Temperature of ground terminal (receiving system) and then define terminal G/T in terms of gain and noise temperature.

There are mainly three noise contributors that define terminal noise temperature (or noise figure):

- Noise from Antenna itself (Antenna noise temperature)
- Noise from passive components such as diplexer
- Noise from Low-noise down-convertor block (LNB) with the assumption that LNB has sufficient gain to make any noise contributions after the LNB negligible.

**Antenna Noise Temperature** is quite difficult to measure and is usually provided by the manufacturer. Lets assume that we have an ESA with noise temperature of 160K

**Passive Components’ Noise Temperature **is directly related to the insertion loss of the components. This is because the noise figure of passive components is equal to their insertion loss (almost) and we all know that noise temperature is directly related to noise figure as follows:

T_{N }= T_{A} (F – 1) = T_{A} (10^{NF/10} – 1), where

T_{N }= is the noise temperature

T_{A }= is the ambient temperature (good assumption is 290 K)

F = is the insertion loss of passive component (or the noise factor)

NF = is the noise figure of passive component in dB [NF= 10.log10(Noise factor)]

Generally, we have a diplexer between antenna and LNB of SATCOM ground terminal and so, the insertion loss of diplexer defines this component of overall terminal noise temperature. Lets assume that we have a diplexer with 1 dB insertion loss, which means its noise figure is also 1 dB. So, its noise temperature becomes:

T_{N }= 290. (10^{1/10} – 1) = 75.1 K

**LNB Noise Temperature **can also be directly calculated from its Noise Figure as mentioned above. Lets assume we have a down-convertor block with 2 dB noise figure, so its noise temperature comes out to be:

T_{N }= 290. (10^{2/10} – 1) = 169.62 K

**Terminal overall Noise Temperature **is calculated as a sum of individual noise temperatures:

Terminal Noise Temp. T= Antenna Nosie Temp. + Diplexer Noise Temp. + LNB Noise Temp. = 160K + 75.1K + 169.62K = 404.72 K

**Terminal G/T **is then finally calculated in terms of terminal Gain (dBi) and noise temperature as follows:

G/T (dB/K) = Gain (dBi) – 10.log_{10}(T), where Gain (dBi) is calculated from peak gain, scan angle, and cosine roll-off.

Note that Gain (dBi) is associated with the antenna (only) of the terminal, whereas Noise temperature (T) captures the noise contribution from entire terminal including antenna itself, RF chain and LNB with the assumption that LNB has sufficient gain to make any noise contributions after the LNB (for instance, modem) negligible.

Tag:G/T, Noise Temperature