Stochastic dynamics in first-order thermal Sigma-Delta modulation

Abstract

The objective of this paper is the analysis of stochastic drifts in first-order thermal Sigma-Delta modulation due to the presence of noise at the input of the comparator. This type of temperature controls has been extensively used in constant temperature anemometry in three missions to Mars. It will be shown that the presence of additive zero-mean noise at the input of the comparator generates non-zero mean drifts on the controlled temperatures. These drifts may increase the response time of sensors working under Constant Temperature Operation (CTO). The case of the MEDA wind sensor in Mars2020 is analyzed, showing that even though this phenomenon slightly increases the response time above the expected thermal dynamics under perfect CTO, it is still below the 0.5 s requirement for the 90% response time. A comparison is presented between the modeled dynamics and measurements made in wind tunnel.

This work has been partially funded by MICINN, Spain, grant nos. PID2021-126719OB-C41, PID2021-126719OB-C42, PID2021-126719OB-C43 by the Spain Ministry of Science, Innovation/State Agency of Research MCIN/AEI/ 10.13039/501100011033, by “ERDF A way of making Europe” TED2021-131442B-C32 and PDC2023-145889-C22; AGAUR, Spain, grant no. 56 30142 2021 2A, CPP2021-008740 and CPP2023-010559. Part of this work was carried out at the Jet Propulsion Laboratory/California Institute of Technology, United States under a NASA-STMD grant, and under a contract with the National Aeronautics and Space Administration, United States (80NM0018D0004).

Peer Reviewed

Postprint (published version)