We calculate noise temperature for the entire receiver chain of devices at a particular point normally at the input to the first device. calculate the S/N ratio we use the transmitter power, path loss (including antenna gain and polarization efficiency), and the gains (losses) of any devices for signal to the location in the receiver chain where noise temperature is being calculated. We characterize a given antenna by the ratio G/T, a measure independent of transmitter power and path loss, but including the receiver noise characteristics. Using the input of the first device as the noise reference point, we calculate the input noise temperature from component noise temperatures and gains:
 (1)Equation (1) merely states that noise temperatures are powers that decrease when we pass backward through a device with gain G. Each noise term is referred to the input of the device, and we pass backward to all previous devices and reduce noise temperature by 1/G. If we decided to locate the noise reference point at the input to the second device, the noise initially referred to the chain input would increase by the gain of the first device. The system noise temperature becomes :
The signal also passes through the first device and the new gain at the input to the second device becomes . The gain and the noise temperature change by the same factor and produce a constant ratio. By extending these operations to any location in the receiver chain, we show that G/T is constant through the receiver device chain.
It is easiest to illustrate G/T noise calculations with an example. A ground station has a 5-m-diameter paraboloid reflector with 60% aperture efficiency with the system operating at .  We compute antenna directivity using the physical area and aperture efficiency:
The reflector feed loss is 0.2 dB and it has a VSWR of 1.5 : 1. The cable between the feed and the first amplifier (LNA) has a 0.5-dB loss. These are elements under control of the antenna designer. We calculate the noise temperature of these by using Eq. (3) when we use a physical antenna temperature of  .
The gains of these devices are  , 0.959 (reflected power loss for 1.5 : 1 VSWR), and . The antenna sees the environment that generates noise due to blackbody radiation from the sky and ground. A typical value for the antenna pointed at elevation is 50 K. This is not a physical temperature but represents an equivalent received power. Remember that the 60% aperture efficiency has no noise or loss contribution, because it only represents the loss of potential gain, since no random electrons are generated. |
