Sec. 1-2] MECHANICAL INPUT TRANSDUCERS 71 



The force requirements can be extremely small, probably the 

 smallest of any transducer system, with the exception of some optical 

 systems. 



The force between two capacitor plates is 



8.85 X 10- 12 E 2 a 



F = 



2 d 2 



where E is the potential difference between the plates. Whenacapac- 

 itive transducer has two plates of an area a of 2 cm 2 which are 1 mm 

 apart and connected to a potential difference of 100 volts, the force 

 of attraction between the plates (i.e., the force required to move the 

 plates by an infinitesimal amount) is of the order of 1 dyne. 



The capacitance variations representing the output signal are 

 generalty between 10~ 3 and 10 3 ju/liF; capacitance variations of 10~ 6 

 fijuF have been observed. 1 The fractional capacitance variations are 

 of the order of 10 -6 to 1; smaller values (2 x 10~ 9 ) have been 

 observed in laboratory experiments. 2 



The magnitude of the output impedance depends upon the fre- 

 quency of the alternating current used for the determination of the 

 capacitance; for practical cases (capacitances of the order of 10 to 

 several hundred fijuF), the output impedance is in the range between 

 10 3 and 10 7 ohms. The magnitude of both the output signal and of the 

 output impedance may be changed by series and parallel capacitor 

 circuits, but such modifications are always accompanied by a reduc- 

 tion of the signal. 



The dynamic response characteristic of capacitive transducers, as 

 well as hysteresis, mechanical aftereffects, and drift, and the in- 

 fluence of the environmental temperature and pressure upon the 

 transducer performance are all determined by its mechanical con- 

 struction rather than by its electrical characteristic. The source of 

 the greatest mechanical difficulties is frequently the insulation em- 

 ployed to hold the plates in position. 



Errors may arise from humidity affecting the insulation resistance 

 and from stray electric fields inducing parasitic potentials in the not- 

 grounded plate and its connections. 



Cables connecting the transducer with other elements can also 

 cause serious errors. Any capacitance variation arising in such a 

 cable can produce a spurious signal. Further noise in such cables can 

 arise from relative motion between a conductor and the dielectric, in 



1 R. Gunn, Phil. Mag., (6) 48, 224 (1924). 



2 W. Burger, Z. Physik, 91, 679 (1934). 



