Theoretical modeling and experimental investigation of magnetic field multiplicative coupling of differential transformers in space inertial sensors

Abstract This paper investigates the multiplicative coupling effect of magnetic interference in transformer bridge-based capacitive sensing circuits, a key technology widely employed in space science missions such as satellite gravity measurements and gravitational wave detection. Transformer bridges typically use a carrier modulation of approximately 100 kHz to perform differential capacitance measurements. However, magnetic fields at different frequencies not only affect the measured signal through additive interference but also exhibit significant multiplicative coupling effects, resulting in complex impacts on the sensing outcomes. In this paper, we proposed a theoretical model for the multiplicative coupling between low-frequency magnetic fields and transformer bridges, and validated the model experimentally. The experimental results indicate that the amplitude of the interference signal is independent of the magnetic field frequency, with the first harmonic interference signal being directly proportional to the magnetic flux density and the second harmonic interference signal being proportional to the square of the magnetic flux density. Moreover, based on the current transformer parameter model, we have quantified the impact of magnetic interference under conditions similar to those in space gravitational wave detection applications such as laser interferometer space antenna, which is less than 4.6 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>19</mml:mn> </mml:mrow> </mml:msup> <mml:mstyle scriptlevel="0"/> <mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">m</mml:mi> <mml:mstyle scriptlevel="0"/> <mml:msup> <mml:mi mathvariant="normal">s</mml:mi> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:mstyle scriptlevel="0"/> <mml:msup> <mml:mi>Hz</mml:mi> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:mrow> </mml:mrow> </mml:math> . For practical applications, it is essential to assess the multiplicative coupled noise based on the actual test parameters of the transformer to ensure accurate and reliable measurements.