Sec. 1-2] MECHANICAL INPUT TRANSDUCERS 53 



c. Eddy-current Displacement Transducers. The basic eddy-cur- 

 rent transducer is shown, schematically, in Fig. (1-2)32. A current 

 supplied by an rf generator passes through a coil C and creates a 

 magnetic field. This field produces circular and coaxial eddy currents 

 in a conductive plate A which is separated from the coil by a variable 

 distance d. The eddy currents in turn cause a magnetic field which is 

 opposed to that produced by the coil. The superimposition of the two 

 fields reduces the effective inductance of the coil and causes a varia- 

 tion of the magnitude and phase of the current. The variation with 

 separation d of the current appears as a change of E at the output 

 terminals. 



Figure (1-2)33 shows a modification of this setup. An rf magnetic 

 field is produced by a primary coil P. The voltage induced in the 

 secondary coil 8 is 



E o = E 12 — ^12 (1) 



or E -- -- 2tt// 1 ( M 12 - - M' 12 ) = 2-rrf^M (2) 



where E 12 is the voltage induced in S by the primary coil, E' 12 that 

 induced through the effect of the eddy current, /the frequency of the 

 applied current /, M 12 the mutual inductance between the primary 

 and the secondary coil, and M[ 2 the mutual inductance between the 

 image of the primary coil at the distance d + b behind the surface of 

 the plate and the secondary coil. 



A typical calibration curve of the transducer is shown in Fig. 

 (1-2)34. 



The sensitivity of the transducer is 



s= dEo = (oI dM 



dx dx 



Values for the effective inductance M for different geometric con- 

 ditions, and for the derivative of the inductance with respect to the 

 displacement x, have been computed by Joseph and Newman 1 and 

 are reproduced in Figs. (1-2)35 and (1-2)36. They permit the com- 

 putation of the sensitivity and the determination of the linear range 

 of eddy-current transducers for different values of the radius r p of the 

 primary coil, the radius r s of the secondary coil, and the separation x 

 between the image of the primary coil and the secondary coil. In 

 Fig. (1-2)33, x = 2d +6. The sensitivity can be found from 



S = wln^i,,!— X [ordinate of Fig. (1-2)36] 



n x and n 2 are the number of turns of the primary and the secondary 

 1 H. M. Joseph and N. Newman, Natl. Bur. Standards Rept. 2558, June, 1953. 



