## What is Receiver G/T?

The ratio of gain of receiver antenna to system noise temperature is called receiver G/T.

Receiver G/T describes the performance of receiver equipments.

This article explain the meaning of Receiver G/T and relation to derivation of C/N.

Carrier power \(C\) is given by:

\[C = P_r = \frac{P_tG_tG_r}{(4\pi d/\lambda)^2}\]

where \(P_t\) denotes output power of transmitting antenna, \(P_r\) denotes the power at the receiving antenna, \(G_t\) denotes the gain of transmitting antenna, and \(G_r\) denotes the gain of receiving antenna.

Note that only free space path loss is considered here (\(\lambda\) is wavelength and \(d\) is the distance between the antennas).

Noise power \(N\) is described as:

\[N = kT_sB\]

where \(k\) is Boltzman constant, \(T_s\) is system noise temperature, and \(B\) is bandwidth.

Thus, carrier-to-noise ratio can be obtained:

\[\frac{C}{N} = \frac{P_tG_tG_r}{kT_sB}\left(\frac{\lambda}{4\pi d}\right)^2\]

This equation can be rewritten as:

\[\frac{C}{N} = \frac{P_tG_t}{kB}\left(\frac{\lambda}{4\pi d}\right)^2\left(\frac{G_r}{T_s}\right)\]

It turns out that the portion of \(\frac{\displaystyle G_r}{\displaystyle T_s}\) denotes the performance of receiver equipments.

This is receiver G/T.

To sum up,

\[\mathrm{C/N_0} = \mathrm{EIRP}-L_{fsp}+G/T+228.6\]