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university:tools:m2k:alice:users-guide-m2k [10 Nov 2017 20:07] – [Background:] Doug Merceruniversity:tools:m2k:alice:users-guide-m2k [16 Dec 2017 17:08] – [Background:] Doug Mercer
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 Using the law of cosines and referring to figure 23 the magnitude of VI can be calculated as: Using the law of cosines and referring to figure 23 the magnitude of VI can be calculated as:
  
-<m>VI = sqrt(VA/\2 + VZ/\2 – 2*VA*VZ*cos(Φ))</m>+<m>VI = sqrt({VA/2{VZ/2– 2*VA*VZ*cos(Φ))</m>
  
 The angle Φ is the measured relative phase between channel 2 (VZ) and channel 1 (VA). The law of cosines is used to calculate the cosine of the angle, Θ. The angle Φ is the measured relative phase between channel 2 (VZ) and channel 1 (VA). The law of cosines is used to calculate the cosine of the angle, Θ.
  
-<m>cos(Θ) = (VA/\2 + VI/\2 – VZ/\2)/ (2 * VA * VI)</m>+<m>cos(Θ) = ({VA/2{VI/2– {VZ/2})/ (2 * VA * VI)</m>
  
 The magnitude of the total impedance (including R<sub>EXT</sub>) can be calculated as: The magnitude of the total impedance (including R<sub>EXT</sub>) can be calculated as:
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 The magnitude of the unknown reactance can be calculated as: The magnitude of the unknown reactance can be calculated as:
  
-<m>X_X = sqrt(Z_X/\2 – R_X/\2)</m>+<m>X_X = sqrt({Z_X/2– {R_X/2})</m>
  
 Again taking possible measurement errors into account it is possible that the square root of a negative number might occur. If that happens then X<sub>X</sub> should be set to zero. Again taking possible measurement errors into account it is possible that the square root of a negative number might occur. If that happens then X<sub>X</sub> should be set to zero.
university/tools/m2k/alice/users-guide-m2k.txt · Last modified: 10 Mar 2021 19:25 by Doug Mercer