7-3] RECEIVER NOISE FIGURE 353 



performance requirements imposed on the radar system by the tactical 

 requirements. 



Some examples of the effects that the choice of a given receiver character- 

 istic has on the overall receiver performance are indicated in Table 7-1. 



7-3 RECEIVER NOISE FIGURE 



The ultimate sensitivity of a receiver is dependent upon the inherent 

 noise generated in the receiver circuits. A useful measure of this noise is 

 the receiver noise figure which is defined as the ratio of the actual noise 

 power output of a linear receiver to the noise power output of a noiseless 

 receiver of otherwise identical characteristics. 



Noise in a receiver is made up oi thermal noise., which results from thermal 

 agitation of charge carriers in conductors, and shot noise, which results 

 from random electron motions in vacuum tubes. These noises are charac- 

 terized by a Gaussian amplitude distribution with time. Such noise sources 

 are independent and uncorrelated. The average power from the various 

 sources is additive, and it is therefore convenient to employ ratios involving 

 power in determining noise figure. 



Consider a signal generator described by a short-circuit signal current 

 source /» and an internal conductance ^s which is at an absolute temperature 

 Tg. Let the generator be connected to a load gL which is at an absolute 

 temperature Tl. Both gs and gL will generate fluctuation currents which 

 are given by^ 



TZ' = ^kT.gJj (7-1) 



and 



/;? = \kTLgLdj (7-2) 



where ins and /„l are the rms noise currents in a frequency bandwidth 

 element dj, k is Boltzmann's constant = 1.37 X 10"^^ joule /i^°. 



The available signal power from the generator is Is^ /4:gs and the available 

 thermal noise power is inJ^ l^gs = kTsdf. 



The available signal power from the circuit composed of the signal 

 generator and the load gi is 



4(^. + gL) 

 If t is defined as Tl/Ts, the available noise power is 



7^ + ^ ^ kTsdf{gs+tgL) ,^ .. 



^{g. + ^l) g.^gL ' ^ " ^ 



^J. B. Johnson, "Thermal Agitation of Electricity in Conductors," Phys. Rev. 32 (1928). 



