Pujpin — Resonance Analysis of Alternating Currents. 379 



Art. LIII. — Resonance Analysis of Alternating Currents /* 

 by M. I. Pupin, Ph.D., Columbia College. 



I. Introduction. 



The presence of upper harmonics in an alternating current 

 wave is a fact which deserves careful consideration both on 

 account of the purely scientific interest which is attached to it, 

 and also on account of the technical bearing of electrical reso- 

 nance upon the construction of conductors possessing apprecia- 

 ble distributed capacity. 



That alternating current and electromotive force waves of a 

 very great variety of forms can be produced by properly design- 

 ing the pole-pieces of the field magnet, and the iron core of the 

 armature of an alternator is a fact nearly as old as the discov- 

 ery of electromagnetic induction. Fully as old is also the 

 knowledge that a great variety of alternating current and elec- 

 tromotive force waves can be obtained by the induction of an 

 intermittent current. 



A careful investigation of these waves was first made more 

 than forty years ago by Lenzf and Koosen,^ who employed 

 alternators with iron in the armature. They plotted these 

 waves from the instantaneous values of current and electromo- 

 tive force obtained by means of the now well-known revolving 

 sliding contact. Employing the same method of investigation 

 Joubert§ showed in 1880 that the electromotive force wave 

 obtained from an eight pole Siemens alternator without iron in 

 the armature is very nearly a sine wave. The method is now 

 known as Jouberfs method of the sliding contact. The name 

 " indicator diagram" has been applied to the wave curves of 

 current and electromotive force obtained by Joubert's method, 

 and very properly, I think, because they do very clearly indi- 

 cate the action of alternating current apparatus. 



Our knowledge of the action of alternating current apparatus 

 has been extended cpiite considerably by these indicator dia- 

 grams. 



Although much must be said in favor of the sliding contact 

 method of obtaining indicator diagrams, yet it must be also 

 acknowledged that the method is a very laborious and uninter- 

 esting process of investigation. Many attempts have been 

 made to devise some optical or some automatic method, but 



* Read before the Annual Meeting of the American Institute of Electrical Engi- 

 neers at Philadelphia, May 17th, 1894. 



fPogg. Ann. lxxvi, p. 494. 1849; xcii, p. 128. 1854. 



$ Ibid., lxxxvii, p. 386, 1852. 



§ Comptes Rendus, vol. xci, p. 161, 1880; Ann. de l'ecole super. 10, p. 131, 

 1881. 



