A BRAUN TUBE HYSTERESIGRAPII 



297 



This voltage e is applied to the first stage of the amplifier, resulting 

 in a voltage ei at the output of this stage which is then applied to 

 the second stage, and so on. Fig. 4 represents the first stage of the 



wmn^ 



Fig 4 — Equivalent circuit of one stage of the amplifier. 



amplifier, pi being the internal resistance of the vacuum tube whose 

 amplification constant is /^i, Vi the external plate resistance, Ri the 

 grid leak resistance for the next tube, Ci the coupling capacity having 

 the effective leak resistance r/'. Solving for ei by the same method 

 that was used for e and omitting negligible terms gives the result 



e\ = 



NS 



Bix^R^Vx 



RC {Ri + ri)(pi + ri) - rr 



cos wt 



' +^ + 



r'C 



RCc 



1 2 



~^—^ — + ^ I sin wt 



(8) 



Similarly, the output from 5 stages of the amplifier is 



5 + 1 





where 



n^is 



M,= 



cos w/ 



r'Ccjo RsCso: Z 



I sin w/ , 



(9) 



IJi.R.r, 



fs 



{Rs + rs){ps + rs) — Ts- ' ps + r. 



The product from 1 to 5 contains only amplifier constants, while the 

 summation from to 5 means that the values for the integrator are 

 included. 



According to equation (9) the circuit introduces errors which at 

 low fields makes the spot describe an ellipse instead of a straight line 

 with positive slope. This ellipse is traced in the clockwise direction, 

 the opposite direction to that in which the apparatus traces hysteresis 

 loops. Since in all practical cases the hysteresis loop at low frequencies 

 approaches an ellipse traced in the counter-clockwise direction, the 

 eflFect of finite time constants and condenser resistance is to make 

 the figure traced by the apparatus narrower than it ought to be. 



20 



