Equivalent Noise Temperature

With terrestrial microwave systems, the noise introduced in a receiver or a component within a receiver was commonly specified by the parameter noise figure. In satellite communications systems, it is often necessary to differentiate or measure noise in increments as small as a tenth or a hundredth of a decibel. Noise figure, in its standard form, is inadequate for such precise calculations. Consequently, it is common to use environmental temperature (T) and equivalent noise temperature (T,) when evaluating the performance of a satellite system. In Chapter 7 total noise power was ex­pressed mathematically as

N=KTB

Rearranging and solving for T gives us

where      

N = total noise power (W)

K = Boltzmann's constant (J/K)

B = bandwidth (Hz)

T = temperature of the environment (K)

Noise figure equation

where

T_e = equivalent noise temperature (K)

NF = noise figure (absolute value)

T = temperature of the environment (K)

Rearranging noise figure equation , we have

T_e =T(NF-1)

Typically, equivalent noise temperatures of the receivers used in satellite transponders are about 1000 K. For earth station receivers T, values are between 20 and 1000 K. Equivalent noise temperature is generally more useful when expressed logarithmically with the unit of dBK, as follows:

T_e (dBK) = 10 log T_e

 For an equivalent noise temperature of 100 K. T_e (dBK) is

T_e (dBK) = 10 log 100 or 20 dBK

Equivalent noise temperature is a hypothetical value that can be calculated but cannot be measured. Equivalent noise temperature is often used rather than noise figure because it is a more accurate method of expressing the noise contributed by a device or a receiver when evaluating its performance. Essentially, equivalent noise temperature (T_e) is the noise present at the input to a device or amplifier plus the noise added internally by that device. This allows us to analyze the noise characteristic: of a device by simply evaluating an equivalent input noise temperature. As you will

see in subsequent  discussions, T_e is a very useful parameter when evaluating the performance of a satellite system.