446 BELL SYSTEM TECHNICAL JOURNAL 



During this interval the secondary circuit is practically isolated from 

 the primary. The switching process is sustained by the alternations of 

 the sinusoidal primary current and is periodic, as we have seen, since 

 similar conditions exist at the start of each pulse. The times at which 

 switching occurs are those at which the current through the coil passes 

 through the critical values (dz /o) where the inductance changes. 



Since the narrow discharge pulse provides the principal contribution 

 to the higher harmonics in which we are interested, and since this 

 discharge takes place in the secondary independently of the primary, the 

 elements of the secondary mesh during discharge determine the form of 

 the output spectrum. From this viewpoint we may regard the con- 

 denser as the source of energy for these harmonics and hence as a 

 possible location for equivalent harmonic generator e.m.f.'s. In this 

 light, the discharge circuit becomes a half-section of low-pass filter 

 terminated in resistance i?2, with L2s as the series element and C2 as the 

 shunt element. 



IV. Quantitative Results of Analysis 



To connect the three solutions which hold for the three linear regions 

 of the B-H characteristic, conditions at the junctions are introduced 

 which lead to transcendental equations. These may be solved graph- 

 ically when definite values are assigned to the circuit parameters. 

 From these may be obtained the maximum value Qm of charge on C2 

 which is reached at the end of the charging stage. 



By plotting a representative group of these final charges over a range 

 of parameters ordinarily encountered, an empirical equation has been 

 deduced for Qm as follows : 



C„ = V2f(f»)"-(,c*)..»(f;)- C) 



For the usual operating conditions the narrow peaked discharge part 

 of the current pulse is most important in the determination of the 

 higher harmonics (say beyond the 9th) with which we are concerned 

 here. The charging interval then may be neglected in calculating the 

 higher harmonics. The form of the discharge pulses is determined by 

 the parameters PC2R2 and k, where 



k = UsjRi^Ci. 



The familiar criterion for oscillation in a series circuit containing 

 inductance, capacity and resistance may be expressed in terms of k. 

 If ^ > I, the discharge is an exponentially decaying oscillation; if 



