202 INSTRUMENTATION IN SCIENTIFIC RESEARCH [Chap. 3 



the core axis, the two cores will be magnetized in the same direction 

 by the external field and in the opposite direction by the magnetizing 

 a-c current. As shown in Fig. (3-1)26, d x and d 2 , the voltages induced 

 in the secondary coils D x and D 2 , will be phase-shifted in different 

 directions so that an output voltage containing primarily the second 

 harmonic (and higher even harmonics) of the excitation frequency 

 will appear at the output terminals, as shown in Fig. (3-l)26e. This 

 voltage can be filtered, amplified, and rectified in subsequent stages. 

 The output voltage of the second harmonic is 



^o.rms = 44 X I0- 9 WO/V r # 



where n is the number of turns of the coils C 2 and D 2 , a the cross- 

 sectional area of the ferromagnetic core in square centimeters, fi r the 

 (effective) permeability of the core, /the frequency of the a-c genera- 

 tor, and H the externally applied field. The factor h depends upon 

 the ratio of magnetizing field strength H M to the field strength H s at 

 which saturation occurs : 



4 . 2# s 

 h = - sin — -? 



77 H M 



The method can be used for very small field strengths from 5 x 10 -4 

 oersted 1 to above 10 oersteds. Adams, Dressel, and Towsley 2 de- 

 scribe an instrument for the range of 1 -3 to 1 00 oersteds . The transfer 

 function (output voltage versus external field strength) is approxi- 

 mately linear; only at high field strength does the curve flatten out, 

 and at very low field strength (at about 10~ 5 oersted) does an output 

 voltage remain which does not diminish to zero at zero oersteds. 

 Reversal of the field direction reverses the phase but not the magni- 

 tude of the output voltage. If one of the cores is inverted so that not 

 only the fundamental frequency but also the even harmonics cancel, 

 the arrangement can be used for the measurement of magnetic-field 

 differences. The response time depends upon the frequency of the 

 excitation voltage. For frequencies in the order of 1 to several kilo- 

 cycles per second, magnetic fields varying within more than 0.01 sec 

 can be measured. No errors due to residual flux are encountered. 



The sensitivity is of the order of 1 volt/oersted; the output im- 

 pedance usually several hundred ohms. A summarizing report on 

 systems of this type, including references, has been published by 

 Kuhne. 3 



1 V. Vaquier, R. F. Simons, and A. W. Hull, Rev. Sci. Instr., 18, 483 (1947). 



2 G. D. Adams, R. W. Dressel, and F. E. Towsley, Rev. Sci. Instr., 21, 69 

 (1950). 



3 R. Kuhne, Arch. tech. Messen, V 392-1, August, 1952. 



