466 THE BELL SYSTEM TECHNICAL JOURXAL, MARCH 1957 



The method used to determine the above noise figures is similar to the 

 one described in Reference 4. The figures are expected to be several times 

 larger when a 30 me IF is used. (A factor of 2 is quoted by Hamilton, 

 et al.*) It is also worth noting that the relative noise power decreases on 

 going to higher modes. 



E. Sig7ial-to-Xoise Ratio for Specific Systems 



In this section we Anil analyze specific systems under varying condi- 

 tions. The reason why we do not present the analj^sis of one "The Best" 

 system is that sometimes a compromise between complexity and sensi- 

 tivity has to be reached and also because some systems may be superior 

 at high power whereas others at low powers. 



The expression for the noise power Pk at the output of the microwave 

 detector (X-tal or bolometer) is" 



P^ = {GXk + nMPL + t - iXkTAp) (35) 



where : 



G = conversion gain of the detector (generally smaller than one. A 

 quantity often used instead of G is the conversion loss L = 1/G). 



Xk = noise figure at the input of the detector. Usually due to random 

 ampUtude or frequencj^ fluctuations of the microwave source or the mi- 

 crowave components (see Section A^ID). 



Fampi, = noise figure of the amplifier 



t = noise temperature of the detector 



Comparing the equivalent voltage fluctuations of this noise power with 

 the signal voltage as derived in (26), we get for the minimum detectable 

 x" 



'(GNk + nMP + t - DkTAu J ^^^^ 



» _ 1 



Xniin 



QoJJTT 



2GPo 



The above relation should apply to all systems. The problem then 

 reduces to the determination of G, X^ , Famp , and t for the particular 

 detection scheme. A difficulty arises from the fact that not only are those 

 quantities a function of the RF power and modulation frequency but 

 in the case of detectors vary from unit to unit. It is probabty for this 

 reason that the values quoted in the literature are sparse and are not 

 in agreement with each other. The values used in this analysis for the 

 A'-band barretters (821) and crj'stals (1X23C) Avere obtained by us. 

 ^'alues for i^-band crj'stals can be found in References 6 and 7. It 

 should also be borne in mind that the values are time dependent and 



