464 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 



satisfied and (31) becomes 



\ V A" 



(¥) 



5^ 



/Ron-' , tY f^ 



+ 2 -71T-T^^^ (33) 



y (^^+iy 



+ 1 -i^ + 1 (Fo _ r«) 



An inspection of (31), (32), and (33) shows that the noise voltage, enters 

 as a first order effect in 5 when tuned to %'• This is not too surprising 

 since a frequency effect is expected to affect predominantly the disper- 

 sion mode. When tuned to x" the effect becomes second order as long 

 as I To — F/j I is large. Under those conditions the 2 terms in (33) are of 

 comparable magnitude. We can easily see the origin of the second term. 

 It arises from the first order out-of-phase component of the noise volt- 

 age. Being, however, sensitive only to in-phase components it will be 

 reduced to a second order effect — as long as | To — Fs | is large, i.e., as 

 long as we have a carrier which makes us insensitive to out-of-phase com- 

 ponents.* When To — Ffl goes to zero (33) ceases to hold and the noise 

 voltage will be given by (32). 



There are two important conclusions to be drawn from (33). 



We want to keep To — T^ as large as possible. Therefore in schemes 

 (hke the superheterodyne see section VI E) where this is not feasible, 

 special care has to be taken to eliminate this noise source. 



From (15) we find that the desired signal is proportional to 



Comparing this expression with (33) we see that the signal-to-noise 

 ratio may be improved by increasing Ron^/r, i.e., overcoupling the 

 cavity until this noise source does not contribute any more. A compari- 

 son of (15) with (32) shows that overcoupling will not improve the 

 signal-to-noise ratio when tuned to x'- Ii^ this connection it should be 

 pointed out that only those frequency stabilization schemes can alleviate 

 the problem of frequency instabilities whose response time is at least of 

 the order to the inverse modulation frequency since the troublesome noise 

 components are at this frequency. Some stabilization schemes make use 

 of the cavity into which the sample is placed as the stabilizing element. 

 Although this system maj^ be excellent for the observation of x" (it is 

 the only one which can compensate for cavity microphonic), it fails in 

 the case of x'- The reason is that x' makes itself obser^'able essentially by 

 a frequency shift which in this scheme would be compensated for. 



* For a similar reason one cannot avoid an admixture of dispersion to an ab- 

 sorption signal, when investigating a saturated sample in which x'mai ^x"mai. 



