# Noise Figure

Electrical noise is unwanted alterations to a signal of random amplitude, frequency and phase. Since RADAR is typically done at microwaves frequencies, the noise contribution of most RADAR receivers is highest at the first stages. This is mostly thermal noise (Johnson noise). Each component of a receiver has its own Noise Figure (dB) which is typically kept low through the use of a LNA (Low Noise amplifier). It is important to know that all conductors generate thermal noise when above absolute zero (0K).

Noise Power

Noise Power is the product of Boltzman’s constant, temperature in Kelvin and receiver bandwidth (k*t0*B). This is typically also expressed in dBm. This value is -174 dBm at room temperature  for a 1 Hz bandwidth. If a different receiver bandwidth is present, you can simply add the decibel equivalent of the bandwidth to this value. For example, at a 1MHz bandwidth, the bandwidth ratio is 60 dB (10*log(10^6) = 60). This value can be added to the standard 1Hz bandwidth to arrive at -114 dBm. For a real receiver, this number is scaled by the Noise Figure.

The Noise Figure is defined as 10*log(Na/Ni) where Na is the noise output of an actual receiver and Ni is the noise output of an ideal receiver. Alternatively these can be converted to dB and subtracted. It can also be defined as the rate at which SNR degrades. For systems on earth, Noise Figure is quite useful as temperature tends to stay around 290K (room temperature). However, for satellite communication, the antenna temperature tends to be colder than 290K and therefore effective noise temperature would be used instead.

Noise Factor is the linear equivalent of Noise Figure. For cascaded systems, the noise factor gradually decreases and decreases as shown. This explains why in a receiver chain, the initial components have a much higher effect on the Noise Figure.

Noise Figure is a very important Figure of Merit for detection systems where the input signal strength is unknown. For example, it is necessary to decrease the Noise Figure in the electromagnetic components of a submarine in order to detect communication and RADAR signals.