A BRAUN TUBE HYSTERESIGRAPH 

 through zero, it may be represented by the Fourier series 



4- JU 1 



5 = 5,„-i:(-i)«-i- 



X 1 



COS m wt, 



299 



(11) 



where Bm is the saturation value, n = 1, 2, 3, etc., and m = 2n — I. 

 It is assumed that the magnetizing field has the constant fundamental 

 frequency w/lir, but it need not be sinusoidal. Each- term of this 

 series can be treated as was the single term in the expression of B 

 for the small fields. When this is done for the integrator and amplifier 

 and the terms are again summed, the output voltage is given by 



KL IT 



U^^s 



E 



(- 1)"-^ 



cos m (Jit 



m 



1 -sp 1 \ sin m (xit 5 + 1 sin m cot 



Z 



m 



NS 

 RC 



Br, 



\lM. 



1 



z 



1 



r'Cu) RsCsOi 





(12) 



where 



= 1 from cct = 





1 from w/ = — to 3 - ; (Fig. 6) 



TT TV 



j3 = cot from o^t = — — to + — ; 



TV TV 



^ = {it — wt) from co/ = — to 3 — ; (Fig. 7) 



4 -^ , ^ X , sin m wt 

 TT 1 m 



m = 2n — \. 



(Fig. 8) 



rr 



2 



-1 



n 3n 



3n 



2 

 I 



Ujt 



Fig. 6 — The value of a during one cycle. 



