456 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 



In the case of the transmission cavity we have two coupling coefficients 

 whose optimum value we have to determine. 



d(ni'Ro) d(:n,^Ro) (20) 



.*. ?ii 7?o = 712 Ro = r 



which means that the input and output coupling should be identical. 

 Relation 20 looks superficially like a matching condition. However, it 

 should be noted that the input impedance to the cavity contains besides 

 the cavit}^ impedance the load impedance. Hence, the "\"SWR is 



Rou^ + r 

 Ron^ 



which represents an undercoupled case. One never can overcouple a 

 transmission cavit}^ with equal input and output couplings. Putting 

 condition (20) into (19) we get: 



APl 8 Ar 8 AQo / 8 " 



Po 27 /• 27 Qo V27, 



2. Detector Output ProportioJial to In-put Voltage 

 The voltage across the load 



47rx"r?Qo (21) 



^» 



^j. _ Vnin-iRo 



V L — 



Roni" + r + i^o^h' 

 Again for max. sensitivity both couplings should be the same 



AVr 



AV, 

 V 



(22) 

 (23) 

 (24) 



Fig. 4 is a plot of (12), (15), (19), and (22). It should be noted that 

 the sensitivities of the reflection cavity are normalized to the input of 

 the magic T (in Fig. 1) and not to the input of the cavity as in the trans- 

 mission cases. This results in a 3-db decrease in output and causes the 

 power sensitivity of the transmission cavity to look relatively higher. 

 However this is somewhat arbitrary since a balanced transmission type 

 scheme would also require a magic T with an accompanying reduction 

 in usable power. 



