Sec. 1-2] 



MFJ'IIAMCAL IX ITT THAXSDrCERS 



67 



JL 



'^1 



, 



-■ 



~M 



C,E, 



a material with high dielectric constant (mica) which partially fills 

 the gap. The correct thickness to obtain linearity is found by 

 methodical experimentation. 



Example: In a capacitor with flat circular plates of \ in. diameter 

 separated by a parallel gap of 0.001 in., a mica disk approximately 

 0.00075 in. was inserted. This caused a linear characteristic over a 

 range of displacement of about 0.0001 in. in which the capacitance 

 varied by 20 jujuF. 



The sensitivity of the capacitive transducer with variable separa- 

 tion is 



AC ea 



''Ad ~J* 



i.e., the sensitivity is proportional to the area of the plates and 

 inversely proportional to the square of the separation of the plates. 

 Theoretically, the sensitivity of the 

 transducer can be increased to any 

 desired degree by making the distance 

 d increasingly smaller, but a practical 

 limit is reached when the electric field 

 strength in the air gap exceeds the 

 voltage-breakdown limit. 1 



Frequently the output from a capac- 

 itive transducer is applied to a modi- 

 fier system which responds to the 

 fractional capacitance variation ACjC rather than to the absolute 

 variation AC. In this case the sensitivity is 



S' = — = - x 



" C Ad' d 



i.e., the sensitivity S' increases in inverse proportion to the separa- 

 tion d and is independent of the other dimensions of the capacitor. 

 The response characteristic AC/C versus Adjd is linear. 



differential capacitor. The capacitor shown in Fig. (1-2)51 has 

 three plates; two fixed plates P 1 and P 2 and a plate 31 which to- 

 gether form the two capacitors C x and C 2 . In the center position the 

 distance between M and either plate is d; the capacitors C x and C 2 are 

 equal. If the middle plate is moved by an amount x in response to an 

 applied mechanical signal, the magnitude of the two output capaci- 

 tors will be 



CzE 2 



Fig. (1-2)51. Differential-capac- 

 itor displacement transducer. 



G 1 



€Cl 



and 



°'"2 



€Cl 



d + x a - - x 



1 The breakdown strength in air at atmospheric pressure is 30 kV/cm. 



