454 THK BELL SYSTEM TEf'HXirAL JOURXAL, MARCH 1957 



the last step being obtained with tlie aid of (4). Equation (12) is plotted 

 in Fig. 4. From the symmetry of the graph it is obvious that for a given 

 ^'8AVR, the signal will be the same for the overcoupled and undercoupled 

 case. However, as we will see later from the standpoint of noise the 2 

 cases are not necessarily identical. 



2. Detector Output Proportional to Input Voltage 



Let r be the reflection coefficient, then T'refl from the cavity is 



2^'s^v 



Khefl - ^2 ^ " V2 VvswrTT/ " V2 



1 - 



+ ij 



\SWR 



With the aid of (10) and (11) this gives for the undercoupled case: 



_ JL( "^r \ 



and the overcoupled case 



^ ^^^ " V2 V Tim' + r) 

 We are interested only in the change of output voltage which is: 



A7rk.. = ^^ Ar = ± V2 FAr ^-^4^ (15) 



dr [Ron- + r)2 



The two signs corresponding to the undercoupled or overcoupled case, 

 respectively. In order to find the optimum coupling 



d(AV) 



d{Ron') 



= Ron - r = 



rW_ ^ ^ 



r 

 Putting this value into (15) we get the max. value 



^Z552 = ± ^' ^_: = T ^ ^» = T 5^ 4.x",<3. (16) 

 V 4 ;• 4i Qo 4 



(15) is again plotted in Fig. 4. From this graph we see that for maximum 

 sensitivity we want to work near match. However, one should not work 

 so close to match that the absorption signal will carry the cavity through 

 the matching condition while .sweeping through a resonance fine. This 

 would result (due to the sign reversal of the signal at match) in a dis- 

 torted line. Incidentally, the sign of the signal may be conveniently used 



