1456 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1953 



Discontinuity Errors Due to Averaging 



Another effect acts to limit the sharpness of measurement when dis- 

 continuities occur. This is due to variations in successive operations of 

 the device being tested. Obviously, if the actuation time varies over a 

 range of it 0.1 milliseconds, then any device such as the present one 

 which measures by averaging many measurements, will not measure 

 accurately in the close vicinity of such a discontinuity. 



For a displacement measurement made at the average time of armature 

 impact, part of the measurements will be before impact, the others after. 

 The meter therefore will register too small a displacement. For another 

 measurement a short time earlier or later than the impact part will be 

 before and part after the average instantaneous displacement but the 

 instrument average will still be good because the function now is smooth. 

 The only displacement error then is just at impact and when the data 

 are plotted, appears as a rounding of the curve. A good correction can 

 be made merely by continuing the adjacent slopes to a sharp intersection. 



A more striking effect is observed for velocity. At the moment of 

 armature impact against core, the velocity drops suddenly from maxi- 

 mum to zero. The indication shown by the instrument then for this 

 averaging type error is just half the final velocity. Another measurement 

 made a short time earlier is good and the slope from that region can be 

 extrapolated to the instant of the half velocity indication as the plot 

 for the true velocity. 



Choice of Output Transformer Inductance 



The output transformer primary inductance is a compromise between 

 output amplifier gain limitation due to equivalent shunt capacity of the 

 inductor and the lowest desired cycle time. It was shown above that at 

 at 0.1 second cycle time only 1 volt is needed for a full scale deflection 

 whereas 5 volts is available. As the instrument current is inversely pro- 

 portional to the cycle time, 1.0-second cycle time will provide about half 

 scale. The 11. 5H chosen then, just barely covers the timing range of 

 present interest. The impedance of the equivalent shunt capacitor at 10 

 kc is approximately equal in magnitude to the transformer dc resistance, 

 and full internal gain is available over the operating frequency band. 



The delay time is not altered by a change in inductance. For instance, 

 if the inductance were halved the rate of current rise would be doubled 

 but twice the change would be necessary for the same instrument de- 

 flection. The same result can be had merely by reducing the gain by 

 one-half. 



