MAGNETIC GENERATION OF A GROUP OF HARMONICS 447 



k — \, the discharge is an exponentially decaying pulse. This last 

 condition is the one assumed in the description of operation given 

 above. 



If the discharge is oscillatory, and if further the second peak is large 

 enough, the current through the coil may become less than 7o during 

 the discharge interval. Thus L^ will return to its larger value, and 

 recharging of the condenser will result. This process may lead to large 

 and undesired variations in the amplitudes of the harmonics. To 

 maintain the frequency distribution as uniform as possible over the 

 frequency range of interest, the circuit parameters are usually adjusted 

 so that recharging does not occur. 



Harmonic analysis shows that the nth harmonic amplitude under the 

 above assumptions is given by 



I{n) = ^^Z"^^^- , (2) 



VI + (1 - 2k){npC2R2Y + k^npC^R^Y 



where n is odd. This expression neglects the contributions due to the 

 charging stage, which are usually small for harmonics higher than 

 the ninth. 



The corresponding harmonic power output is 



^IWR,^ W, 



2 1 + (1 - 2k)inpC2R2y + k\npC2R2Y' 



where Wo is a convenient parameter which does not vary with n and 

 hence serves as an indication of the power of the output spectrum. It 

 is related to W, the total power delivered to the load resistance, by 

 the equation, 



Wo=-pC2R2W. 



IT 



For purposes of calculation. Wo may be found from (1) and (2) to be 

 Wo = ^' pBrAdH, ( f-° ) "' {pC2R2y-' ( ^ ) "■' watts, (4) 



where 



1-20 = ^ ' -^1 = ^-^Nlild, 



and N is the number of turns wound on the toroidal core of diameter d 

 cm. and cross-sectional area A cm.} 



