WAVE SHAPES USED IN HARMONIC PRODUCERS 



333 



is the case is shown in the curves of Fig. 1 in which the harmonic amplitudes 

 are plotted against n for pulse widths of 5°, 2° and 1°. With a 5° pulse 

 harmonics in the vicinity of the 105th and again the 150th become negligibly 

 small. For a shorter pulse width the amplitude of the lower harmonics 

 decreases but all harmonics up to beyond the 200th are present. 



The wave shown in Fig. 1 can only be considered as a first approximation 

 of the plate current in such a harmonic generator as it implicitly assumes 

 that the tube is linear to cut-oflf. More frequently sufl5cient excitation is 

 placed on the grid of the tube to saturate it and the resulting current wave 

 may better be represented by a series of rectangular pulses such as shown 



Fig. 3 — Oscillograms of the plate current of a vacuum tube showing the transition from 

 sinusoidal to rectangular pulses as excitation is increased 



(a) Excitation 6 volts 



(b) Excitation 8 volts 



(c) Excitation 10 volts 



(d) Excitation 20 volts 



in Fig. 2. This transition from sine wave pulses to rectangular pulses as 

 the grid excitation is increased is shown in the series of oscillographs in Fig. 3. 

 The analysis of a wave consisting of rectangular pulses such as the one in 

 Fig. 2 shows the amplitude of the nth harmonic to be 



, 2A . nb 

 hn = — sm - 



tlT 2 



(2) 



From this equation it is seen that certain of the harmonics are not present 

 as the expression (2) becomes equal to zero whenever 



