44 INSTRUMENTATION IN SCIENTIFIC RESEARCH [Chap. 1 



of the electrodes, an effect which causes nonlinearity of the voltage- 

 current characteristic. The effect can be eliminated by operation 

 with alternating current of sufficiently high frequency, but other 

 complications may arise through the capacitance between the elec- 

 trodes and between each electrode and ground. Also, the require- 

 ments for the associated equipment (oscillator, detector, shielding) 

 are considerable if the transducer is operated by alternating current. 

 The described difficulties and other technical difficulties connected 

 with most electrolytic transducers (e.g., evaporation of the solvent, 

 capillary forces between the electrolyte and the electrodes, mechani- 

 cal alterations of the rubber membranes or tubes, lack of portability) 

 are the reasons that electrolytic transducers are primarily used for 

 laboratory applications or where the accuracy requirements are 

 moderate. 



1-22. Inductive Displacement Tbansducers 



An inductive displacement transducer consists essentially of a coil 

 with the inductance L; a mechanical force or a displacement causes 

 a variation of the coil parameters and consequently a change of 

 inductance AL. A variety of inductive transducers has been designed 

 and described; a synopsis illustrating the more frequently used 

 systems is shown in Fig. (1-2)27. 



The inductance of a coil is 



L = n 2 G[x 



where n is the number of turns, G a geometric form factor, and li the 

 effective permeability of the medium in and around the coil. Since 

 either n, G, or li can be changed, there exist three basic groups of 

 inductive displacement transducers. These are described in Fig. 

 (1-2)27, vertical columns A, B, C or D, E, F. 



a. Inductance and Reluctance-variation Transducers, self-induct- 

 ance versus mutual inductance. Each transducer within a group 

 can be designed either with a single coil, in which case the input 

 magnitude changes the self-inductance of the coil, Fig. (1-2)27, hori- 

 zontal columns 1 and 2, or with multiple coils, in which case the input 

 magnitude causes a variation of the mutual inductance, i.e., the 

 magnetic coupling between the coils (columns 3 and 4). A mutual- 

 inductance system can frequently be converted into a self-inductance 

 system by series or parallel connections of the coils. For instance, if 

 in B3 the terminals B and C are connected, the total inductance 

 between the terminals A and D will be 



L s = L l +L 2 ± 2M 



