66 INSTRUMENTATION IN SCIENTIFIC RESEARCH [Chap. 1 



systems; the phase angle between the. two voltages increases with 

 the torsion of the axis. 



1-23. Capacitive Transducers 



The general form of a capacitive displacement transducer is shown 

 in Fig. (1-2)50. The capacitance between the terminals (neglecting 

 fringe effects) is C = kea/d, or numerically, 



a 

 C^ F = 0.0885e - linear dimensions, cm 



(1) 

 or C M/xV = 0.225e - linear dimensions, in. 



where e is the dielectric constant of the medium between the plates 

 P, a the area formed by the projection of the plates upon each other 

 (overlapping area), and d the distance between the plates. 



The fringe effect (stray capacitance at the edges of the plates) 



cannot always be neglected. In a 

 capacitor formed by two circular 

 plates in which the ratio of plate 

 radius to plate separation is 50 and 

 -I C^c m which the plate thickness is 

 equal to the separation, the capac- 

 itance is actually 6 per cent 

 greater than the value computed 



Xl\ 



d a 



P\ 



Pz 



T7 ,1 inta /-. -4.- i- i * from Eq. (1). The fringe effect 



Fig. (1-2)50. Capacitive displacement n \ / o 



transducer, schematic diagram. contributes less than 1 per cent if 



the ratio of radius to separation is 

 greater than 200. (For formulas for the computation of the fringe 

 effects see Thickness Transducers, 1-13.) 



The capacitance can be varied in response to a physical displace- 

 ment in three ways: (1) by varying d, i.e., by changing the plate 

 separation; (2) by varying a, i.e., moving one plate in the direction y, 

 Fig. (1-2)50; and (3) by varying e, e.g., by moving a body with a 

 dielectric constant higher than air into the gap between the plates. 

 The latter method is seldom used. 



a. Change-of -distance Systems; Two -plate Capacitor. This type of 

 capacitive transducer is most frequently used. The response charac- 

 teristic, C —f(d), is hyperbolic, Eq. (1), and only approximately 

 linear over a small range of displacement. Brookes-Smith and Colls, 1 

 have improved the linearity of the transducer by inserting in the gap 



1 C. H. W. Brookes-Smith and J. A. Colls, J. Sci. Instr., 16, 361 (1939). 



