472 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 



variable flap* attenuator (which also introduces a phase shift) or after 

 changing the slide screw tuner the system has to be rephased again. This 

 makes saturation measurements less convenient than in the superhetero- 

 dyne sj'stem to be discussed in the next section. The obvious advantage 

 of the homodyne detection scheme is that it requires only one micro- 

 wave oscillator. 



2. Crystal detection 



A simple set-up is shown in Fig. 6. Although its microwave components 

 are identical to the ones used in the barretter scheme, the analysis of 

 this set-up is more comphcated. The reason is that not only do cr3'stal 

 characteristics vary greatly from unit to unit but they cannot be de- 

 scribed by one simple relation over the entire range of incident micro- 

 wave power. One can roughlj^ divide their characteristics into a square 

 law region where the rectified current / is proportional to Pa (holds for 

 Po < 10" Watts) and the Hnear region where / is proportional to 

 y/Wo . (holds for Po > 10~ Watts). The output noise of a crj^stal can be 

 represented in general by the relation.''' ' 



P.v = n^ + 1 kTA, t (47) 



where/ is the frequency' around which the bandwith Av is centered. This 

 relation reduces for the square law region to : 



p^ = (^lll + 1 j hTAb (48) 



and for the linear region to 



jPrf 



Pn = ( -^ + 1 ) kTAv (49) 



The average values of /3 we determined experimentally are: 



/3 ~ 5 X 10" Watt"- sec"^ and 



7 c^ lO" Watt~^ sec"^ 

 The conversion gain G of the crj^stal can be represented by 



G = 5Prf (50) 



in the square law^ region and by 



G = constant = C (51) 



* The phase shift associated with the Hewlett-Packard X-382-A attenuator is 

 quite small. 



t Values of a for if -band crystals are quoted in References 6 and 7. Thej' differ 

 however from each other bj^ appro.ximatelj^ 3 orders of magnitude. 



