| Summary: | In space gravitational-wave-detection missions, inertial sensors are used as the core loads, and their acceleration noise needs to reach <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>15</mn></mrow></msup><mo> </mo><msup><mrow><mi>ms</mi></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup><mo>/</mo><msqrt><mrow><mi>Hz</mi></mrow></msqrt></mrow></semantics></math></inline-formula> at a frequency of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.1</mn><mo> </mo><mi>mHz</mi></mrow></semantics></math></inline-formula>, which corresponds to the capacitive sensing system; the capacitive sensing noise on the sensitive axis needs to reach <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo> </mo><mi>aF</mi><mo>/</mo><msqrt><mrow><mi>Hz</mi></mrow></msqrt></mrow></semantics></math></inline-formula>. Unlike traditional circuit noise evaluation, the noise in the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>mHz</mi></mrow></semantics></math></inline-formula> frequency band is dominated by the thermal noise and the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>/</mo><mi mathvariant="normal">f</mi></mrow></semantics></math></inline-formula> noise of the device, which is a challenging technical goal. In this paper, a low-frequency, high-precision resonant capacitor bridge method based on a planar transformer is used. Compared with the traditional winding transformer, the developed planar transformer has the advantages of low temperature drift and low <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>/</mo><mi mathvariant="normal">f</mi></mrow></semantics></math></inline-formula> noise. For closed-loop measurements of capacitive sensing circuits and sensitive structures, the minimum capacitive resolution in the time domain is about <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3</mn><mo> </mo><mi>aF</mi></mrow></semantics></math></inline-formula>, which is far lower than the scientific measurement resolution requirement of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>5.8</mn><mo> </mo><mi>fF</mi></mrow></semantics></math></inline-formula> for gravitational wave detection. The capacitive sensing noise is converted to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1.095</mn><mo> </mo><mi>aF</mi><mo>/</mo><msqrt><mrow><mi>Hz</mi></mrow></msqrt></mrow></semantics></math></inline-formula> in the frequency band of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>10</mn><mo> </mo><mi>mHz</mi><mo>–</mo><mn>1</mn><mo> </mo><mi>Hz</mi></mrow></semantics></math></inline-formula>. Although there is a gap between the closed-loop measurement results and the final index, the measurement environment is an experimental condition without temperature control on the ground; additionally, in China, the measurement integrity and actual measurement results of the capacitive sensing function have reached a domestic leading level. This is the realization of China’s future space gravitational wave exploration.
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