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BELL SYSTEM TECHNICAL JOURNAL 



As n becomes large the second term under the radical becomes small and 

 (13) becomes 



hn = 



A(1 + t) 



nir 



for odd harmonics 



(14) 



Equations (12) and (14) are identical with (10) and (11) showing that in 

 harmonic generators of this type the harmonic content of the output wave 

 is primarily a function of the initial and final values of the current rather 

 than of the shape of the decay curve. 



All of the foregoing curves show that the amplitudes of the higher har- 

 monics are quite small so that in many applications some method of in- 

 creasing their amplitudes may be required. This can be accomplished by 

 the use of tuned^ amplifiers. An alternative method is to modulate a 

 standard frequency wave with a lower derived frequency. 



mf 



FREQUENCY 



Fig. 6 — Frequency spectrum of wave of frequency mf modulated by a series of pulses of 



frequency f 



Assume a standard frequency of the form 



A cos moot 



This wave is completely modulated by a rectangular wave of frequency 

 co/Itt and pulse width b. The modulated wave will then be of the form 



/ = ^[1 -f KfiO] cos mcot (15) 



As shown previously the modulating wave is of the form 



/(/) = ;r- + XI — sin — cos nut 



ZTT n=l WX Z 



(16) 



For 100 per cent modulation K = 1. Since 



cos (muit) + cos {ntot) = | cos (m + n) ut -\- ^ cos {m — n) coi (17) 

 the modulated wave is 



Ab ^ A . nb r , \ , 



tp = — cos moit -+- 2^ — sm -— cos [m -\- n) ut 



ZTT n=l WTT 2 



A 



nb 



(18) 



+ zl — sin — cos {m — n) cat 

 n=i rnr 2 



