50 INSTRUMENTATION IN SCIENTIFIC RESEARCH [Chap. 1 



of higher harmonics. Frequently it can be reduced by low-pass 

 filters in the input circuit, by balancing the individual output circuits 

 with resistive and capacitive shunts, or by adequate grounding. 



The input and output of the transducer can be interchanged. The 

 normal connection, Fig. (1-2)28, produces higher output voltages, 

 while the inverted connection may be preferable for matching to low 

 impedance loads and also has the advantage of reducing the effect 

 of stray magnetic fields (see below) . 



The linear-variable differential transformer may be used for a total 

 linear range of displacements varying with the construction from 

 ^0.005 to several inches. In general, 1 per cent of the total range 

 can still be measured; with some care it is possible to measure 0.1 per 

 cent. The smallest displacement to be detected is of the order of 

 10- 5 in. 



The mechanical force requirements at the input depend upon the 

 operating conditions. The axial force which the transducer exercises 

 on the core is zero if the core is in the center position and increases 

 linearly with the core displacement, tending to move the core to- 

 ward the axial center. The force is proportional to the square of the 

 current in the primary coil. For a commercial transducer driven at 

 60 cps and for full displacement, the force is of the order of 0.3 gram 

 (300 dynes); if operated at 400 cps, it diminishes to 0.075 gram (75 

 dynes). The coil system also exercises a radial force on the core 

 which increases with the square of the primary current. This force is 

 zero when the core is in the radial center, but in this position the core 

 is in an unstable equilibrium since the radial force increases with the 

 radial displacement and tends to move the core toward the periph- 

 ery of the bore. A restraint of this sideways movement is required. 



The open-circuit output voltage for full-range displacement of the 

 core is, in practice, between a fraction of a volt and several volts. The 

 output impedance varies for different constructions between 20 and 

 several thousand ohms. The output impedance is predominantly 

 resistive, with an inductive component which varies slightly with the 

 core displacement. 



The errors of the linear-variable differential transformer amount in 

 general to about 0.5 per cent of the maximum linear output. | The 

 deviation from linearity of commercial transducers is also about 0.5 

 per cent of the specified range; it can be reduced considerably by 

 reducing the travel length of the core. The dynamic response is 

 limited mechanically by the mass of the core (smallest mass about 

 0.1 gram, in larger models up to 3 grams) and is limited electrically 

 by the frequency of the applied a-c voltage. This frequency (carrier 



