46 INSTRUMENTATION IN SCIENTIFIC RESEARCH [Chap. 1 



and will vary with cp by 2 M sin cp. If the two coils are connected in 

 parallel, the inductance will be 



L t L 2 - M* 



L 1 +L 2 ± 2M 



Similarly, the system Bl can be converted into a mutual-induction 

 system by disconnecting contacts B and C. 



single output versus differential output. In general the 

 inductance variations AL or AJf of a transducer will be small com- 

 pared with the inductance L or the mutual inductance M of the 

 system. If the succeeding stage responds to the total inductance 

 L + AL rather than to the inductance variation, the sensitivity of 

 such simple systems will be only moderate. Higher sensitivity and 

 higher accuracy can be obtained with systems in which the input 

 magnitude (force or displacement) simultaneously causes an increase 

 of one inductance and a decrease of another, so that the subsequent 

 stage measures either the difference or the ratio of two inductances 

 (differential, push-pull, balanced, or ratio output). Each inductive 

 transducer system within a basic group can be designed either with 

 single output (vertical columns A, B, C), or with differential (ratio) 

 output (columns D, E, F). The transformation from single to dif- 

 ferential output is frequently only a matter of circuitry (see, for in- 

 stance, Al and D\ or A2 and D2). 



Inductive displacement transducers with differential or ratio out- 

 put offer, in general, advantages besides that mentioned above. Their 

 output is less influenced by external magnetic fields and by tem- 

 perature changes and variations of the supply voltage and frequency. 



air- versus iron-core coils. An inductive displacement trans- 

 ducer system can be further modified by designing it either with coils 

 in air (horizontal columns 1 and 3) or with cores of high permeable 

 materials. Air-coil systems can be operated at a high carrier fre- 

 quency so that they are applicable to the conversion of mechanical 

 movement over a wide frequency range. A practical advantage of 

 iron-core systems is that they are less likely to cause an extended 

 magnetic stray field and they are also not affected as much by ex- 

 ternal magnetic fields, as are air coils. A disadvantage of iron-core 

 transducers is that their inductance is likely to vary with the current 

 passing through the coil. The frequency of the supply voltage used 

 for the measurement of the inductance should not exceed 20,000 cps 

 for iron-core transducers. Line voltage (60 or 400 cps) is frequently 

 used. 



