460 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 



the latter sj'stem maj' be improved b}' microwave bucking, it still re- 

 mains very much inferior to the field modulation system to be described 

 presently.) A system commonly used in which the requirements on the 

 constancy' of the microwave level is less stringent, makes use of a small 

 external magnetic field modulation of angular frequency w.u super- 

 imposed on the sloAvly ^-arying dc magnetic field. Thus in the absence of 

 a resonance line the output is zero except for some small Fourier com- 

 ponents of the random fluctuations at the frequency aj.v . If the ampli- 

 tude of the field modulation A//_m is small in comparison to the line 

 width \H this method will sweep out the derivative of the line, i.e., the 

 signal will not be proportional to x" as previously assumed but to 

 dx" /dH (AH m). In order to preserve the line shape one should sweep 

 onlj' over a fraction of the line ^^idth. The sensitivity will thereby be 

 reduced by roughly the same fraction. It should be noted, however, that 

 even if one overmodulates the line (in order to increase the sensitivity) 

 the resonance condition (i.e., place of zero signal, corresponding to new 

 slope in the absorption) will not shift for a S3nnmetrical line and the 

 correct gr- value may be obtained. Also from the knowledge of the ampli- 

 tude of the modulating field the increase in line width may be corrected 

 for. For those reasons we will not be concerned with the reduction in sen- 

 sitivity due to this field modulation scheme. 



2. Choice of Frequency 

 Referring to (26) 



mm- 



and the minimum total number of electrons N', 



iV.,„ = x.r, cc (Z-A (^) -^ (27) 



Assuming that we are dealing with the same type of cavity mode at 

 different frequencies, the same power, and that the line width Aw is 



constant, we have ^c °^ -^ , Qo °^ -^ 



CO"* 0}' 



.-. iN^znin « -1 (28) 



w"- 



Equation 28 shows that in order to see the smallest number of spins 

 we want to go to as high as frequency as possible. The upper limit is 

 given by the availabilit}" of components in the millimeter region, by the 

 difficulty of handling them and by the maximum available power. The 

 most commonly used setups operate at a wavelength of 1 cm and 3 cm. 



