WAVE SHAPES USED IN HARMONIC PRODUCERS 337 



width must be based on the type of service to which it is to be put. If only 

 a few harmonics are required, a considerable gain in the amplitudes of the 

 harmonics can be obtained by using a wider pulse width. When a wide 

 range of harmonics is required, the band width must be greatly reduced to 

 avoid blank intervals in the frequency spectrum. 



A second type of harmonic generator is the multivibrator. The output 

 wave of such a harmonic generator has a shape similar to that shown in 

 Fig. 5. The current pulse lasts for a complete 180° rising abruptly to the 

 peak value, then falling more or less exponentially to a lower value and 

 finally breaking abruptly to zero. Assuming an exponential decay this 

 wave will be found to contain the following harmonics 



hn = — for even harmonics (8) 



\/«^7r2+ (hiT)2 



hn = — , for odd harmonics (9) 



\^n^'K^+ (lnT)2 



Except for small values of n, the (In rY term is negligible and these equa- 

 tions can be written 



hn = — for even harmonics (10) 



rnr 



hn = — for odd harmonics (11) 



nir 



In all of the above equations t = B/A, the ratio of the amplitude at the 

 end to the amplitude at the beginning of the pulse. 



The curves in Fig. 5 show the harmonic content of such a wave for t = ^ 

 and T = Y^. In the first case the amplitudes of the odd and even harmonics 

 differ by approximately 9.5 db while in the second case the amplitudes are 

 not greatly different. The dotted curve shows the limiting condition which 

 all harmonics approach as t approaches zero, that is as the current at the 

 end of the pulse approaches zero. 



The analysis of such a pulse except assuming a linear rather than ex- 

 ponential decay yields the following equations 



hn = for even harmonics (12) 



flT 



h„ = — i/(l 4- t)2 + ^^^ 7J -^- for odd harmonics (13) 



fiT y fi^ir 



