^2 BELL SYSTEM TECHNICAL JOURNAL 



designated by the symbol Po- Of this power, a certain fraction 5o is dis- 

 sipated as losses in the cavity itself where 



6o = ^ . (3) 



Vo 



The symbol Qo with the subscript is further defined as the intrinsic Q, 

 that is, the Q without external loading, to differentiate it from the more 

 general Qi which is the measured Q when the cavity is loaded down by 

 external coupling. It should be noted that this definition of 5 differs from 

 the logarithmic decrement by a factor t. 



When coupled to the external circuits the loaded 8 is increased. On the 

 assumption that the loading effects of the input and output irises are in- 

 dependent we can write 



5l = 6o + 5i + 52 (4) 



where 5^ is the loaded 5, and 8i and 82 are respectively the input and output 

 loadings. Physically the assumption underlying this expression is that the 

 distribution of electromagnetic fields within the cavity is not seriously al- 

 tered by the input and output coupling devices. This assumption should 

 certainly be valid as long as the absolute values of the 6's are very small 

 compared to unity. Since the 5's usually encountered are of the order of 

 10~^ or less, the assumption seems to be justified. 

 Equation (4) may be written 



l = i + *. + .. (5) 



The values of 81 and 62 evidently depend upon the ratio of the apparent 

 series resistance which the external coupling introduces into the resonant 

 cavity to the effective reactance of the cavity, that is, 



8, = *^' (6) 



where ki is the transformation ratio of the input coupUng device, Ri is the 

 resistance of the input circuit and X is the cavity reactance. Similarly 



h = *-^' . (7) 



The values of the 5's may be equally well considered as the ratios of the 

 coupled conductance to the shunt susceptance of the cavity considered as a 

 shunt resonant circuit so that equations (6) and (7) become 



