Hysteresis Loops and Lissajous 3 Figures. 



419 



But the current will not be capable of being expressed in 

 any such simple fashion *. It has also long been known 

 how these curves of magnetizing current are related to the 

 hysteresis loop. If the form of the hysteresis loop is known, 

 then the form of the magnetizing current can be deduced 

 graphically. An example will be found in Kapp's ' Trans- 

 formers ' (1908), fig. 56, p. 106. Assuming that the flux- 

 density follows the equation given above, let it be plotted as 

 a curve, with maximum ordinate equal to that of the hys- 

 teresis loop. Consider any point on this curve, or the point 

 on the loop having the same ordinate ; then the ordinate at 

 the same instant on the current curve will be (on some scale) 

 proportionate to the abscissa of the same point of the 

 hysteresis loop ; whence it follows that the current curve can 

 be constructed, point by point, through the entire cycle. 

 This process is followed here, save that for convenience the 

 hysteresis loop is turned over through a right angle, so that 

 the values of 13 are taken as abscissa}, and those of & as 

 ordinates. In fig. 1 the hysteresis loop ABODEF 

 selected, has been taken from Ewing's classical memoir of 

 1885. 



Fiff. 1. 









._.#f^.l/ 



\ \^ F 









\Tp 



/ ^7 \ 

 w v J \ 



/""n 'it 

 1 f l 



ZTL 





1 



N / 





\ F 







1 



\1 ■!/-' 









\ A"A 



Relation of Current Curve to Hysteresis. 



Assuming a closed "magnetic circuit, and an impressed 

 voltage of a pure sine form, marked V, the flux-density curve 

 is a sine-curve lagging 90° behind the voltage-curve. Then 

 the current curve is derived by taking any point P on the 



* For a good example of a current curve, see Fleming's ' Alternate 

 Current Transformer,' fig. 186, vol. i. p. 543 (edition of 1898). These 

 irregular current curves seem to have been first observed by Ryan ; see 

 ' Transactions of the American Institute of Electrical Engineers,' vol. iii. 

 Jan. 10, 1890. See also the 'Electrician/ vol. xxiv. p. 239, and p. 263, 

 January 1890, and vol. xxv. p. 312, July 25, 1890. 



2 F 2 



