Sec. 1-2] MECHANICAL INPUT TRANSDUCERS 47 



A number of iron-core transducers have been described. 1 Most of 

 these transducers are variations of the basic system illustrated in Fig. 

 (1-2)27(7-2, which consists of a coil wound around a core of the (uni- 

 form) cross-sectional area a and the effective permeability ju (i.e., the 

 permeability at the magnetic field strength and frequency actually 

 used). The average length of the magnetic path in the iron core is I, 

 the iron core is interrupted by an air gap of the width d. (d should be 

 small compared with any dimension of a.) The inductance of the coil 



is 2 



n 2 



where 8% is the reluctance of the magnetic circuit, a magnitude anal- 

 ogous to the resistance in an electric circuit ( ^ = magnetomotive 

 force/magnetic flux; the infrequently used magnitude permeance is 

 the reciprocal of the reluctance). The reluctance varies with the 

 width of the air gap and is approximately (neglecting fringe effects 



and leakage) 



I fi 



8% = — ■ where // = 



ap' n 1 - (d/l)fi 



In most applications the reluctance is primarily that of the air gap, 

 the contribution of the iron core is small. 



Inductive displacement transducers can be used at high tempera- 

 ture. For such applications, the coil forms can be made from high- 

 temperature refractive ceramics, the armature from hollow cobalt. 

 The transducer can be enclosed in a ceramic shell sealed with refrac- 

 tory cement. The core can be made of magnetic alloys, such as 

 Hypersil or Permandur, which have a curie point above 1000°F. 



A transducer of the type illustrated in Fig. (l-2)272£-3 is described 

 by Hermann and Stiefelmeyer. 2 The transducer which is used for the 

 measurement of torque has no slip rings. The voltage is supplied to 

 a pair of coils by means of a transformer with one stationary and one 

 rotating coil; the output voltage is picked up with a similar trans- 

 former. 



Compared with the capacitive displacement transducer, the induc- 

 tive transducer requires in general higher mechanical forces at the 

 input and has a lower output impedance and a higher output power 

 level, so that sometimes the output can drive the following stage and 

 no amplification is required. 



1 See H. C. Roberts, "Mechanical Measurements by Electrical Methods," chap. 

 IV, pp. 41-97, The Instrument Publishing Company, Pittsburgh, 1951. 



2 P. Hermann and G. Stiefelmeyer, Arch. tech. Messen, V 171-4 and V 171-5, 

 March and April, 1957. 



