An Analysis of the Differences between True-Mean-Square and Average-Magnitude-Squared Detector Circuits for Use in Campbelling Neutron Monitoring Systems (1970)

A mathematical analysis and some numerical results are presented that indicate how the ratio of the outputs from a true-mean-square and an average-magnitude-squared linear type detector in a Campbelling neutron monitoring system vary over a wide range of neutron fluxes or pulse rates for a given system output signal shape. Two types of system output pulse shapes have been considered. One type is of the form v = Vε <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-ωt</sup> corresponding to a single differentiated output pulse. The other shape has the form v = C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1ε</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-ωt</sup> + C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2ε</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-ω1t</sup> + C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> ε <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-ω</sup> 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sup> corresponding to a double differentiated and single integrated output pulse. C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> , C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , and C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> are constants depending upon the system characteristics. For the single differentiated pulse shape, the analysis verifies that the output signal ratio begins to deviate from the constant value 0.637 when the input pulse rate decreases below the single low cut-off frequency, <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ω</sub> , of the system. As for the double differentiated, single integrated pulse shape, all three time constants influence the results. For the specific case where the integrating time constant, 1/ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ω2</sub> , is much smaller than either differentiating time constant, 1/ω or 1/ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ω1</sub> , and these last two time constants are made equal, the output signal ratio also deviates from the constant value of 0.637 when the input pulse rate decreases below the low cut-off frequencies. Some measurements of the two types of output signals, |v⊽| <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> and v <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , obtained from actual Campbelling systems, show excellent agreement with the numerical results for both types of pulse shape considered.