Sec. 1-2] 



MECHANICAL INPUT TRANS DICF. US 



69 



The output varies in a nonlinear fashion with the displacement x, as 

 shown in Fig. (1-2)52. Only for very small displacements, when 

 x < d, does 



N = l +^ 

 a 



For xjd = |, the deviation from linearity is about 20 per cent. 



Moving plate 





-0.8 -0.6 -0.4 -0.2 0.2 0.4 0.6 0.E 

 Displacement of the middle plate, x /d 



(6) 



Fig. (1-2)52. Transfer characteristic 

 C\IC 2 versus displacement of the 

 middle electrode of a differential- 

 capacitor transducer. 



Fig. (1-2)53. Capacitive displacement 

 transducer: (a) schematic diagram; (b) 

 transfer characteristic. 



b. Change-of-area Systems. Figure (1-2) 53a shows an example of 

 this system and Fig. (1-2)536 a transfer function of a capacitive trans- 

 ducer where a longitudinal displacement of one plate causes a varia- 

 tion of the area a and, thus, of the capacitance. In the middle part of 

 the characteristic, the capacitance can be expressed by 



C = 



Iw 

 ~d 



where I is the length and w the width of the overlapping part of the 

 two plates. The sensitivity is 



AC ew 

 ~d 



S = 



M 



and the sensitivity for a fractional capacitance variation AC/C is 



AC 1 

 CAZ ~~l 



S' 



