34 BELL SYSTEM TECHNICAL JOURNAL 



ponents of /q. Let it be assumed that the reactances of the output 

 circuit are 300 ohms each at fundamental frequency and that sufficient 

 resistance has been inserted in the inductive branch to make the im- 

 pedance to fundamental frequency 2000 ohms resistance. This will 

 require about 45 ohms in series with the inductance. At second har- 

 monic frequency, then, the impedance of the inductive branch in com- 

 plex notation is 45 -f j600 and that of the capacity branch — jl50. 

 Without introducing much error in the result we may as well write 

 + j600 and — il50, which in parallel give — j200. At third harmonic 

 frequency we have -f j900 and — j'lOO which in parallel give — jll2.5. 

 At fourth harmonic frequency we have -f jl200 and — j75 which in 

 parallel give — j80. 



Thus the voltage produced by the fundamental will be 



ei = 0.96 X 2000 cos cot = 1920 cos cot, 



and that produced by the second harmonic will be 



e^ = 0.54 X 200 cos (2co/ - 90°) = 108 cos {2o:t - 90°), 



and that produced by the third harmonic will be 



ez = 0.14 X 112.5 cos (3co/ - 90°) = 15.75 cos (3co/ - 90°), 



and that produced by the fourth harmonic will be 



g4 = - 0.07 X 80 cos (4co/ - 90°) = 5.6 cos (4a;/ -f 90°), 



etc. Fig. 5B shows to scale the fundamental and second harmonic 

 voltages produced, and the dotted curve gives the sum. The higher 

 harmonic voltages are too small to show on the plot. The resultant 

 is seen to be very little different from a sine wave. Therefore, even 

 though the wave io departs radically from a sine wave, the voltage 

 produced across the output circuit is very nearly sinusoidal. Then 

 the output power at fundamental frequency is 



Wo-^-^, (6) 



where /i is the peak value of the fundamental component of io, and 

 Ro is the effective resistance of the tank circuit at fundamental fre- 

 quency. 



The output power may also be expressed : 



Wo = — ^p^^^^p (7) 



if /, = Kip. 



