Transparent Induction Based D-Dot Electric Field Sensors

Description (excerpt)

RELATED APPLICATION DATA This application claims benefit to U.S. Provisional Patent Application No. 63/646,4362 of the same title filed on May 13, 2024. The disclosure thereof is incorporated by reference herein its entirety for all purposes. GOVERNMENT INTEREST The invention described herein may be manufactured, used and licensed by or for the U.S. Government. FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT Some research underlying this invention was made with government support under W911NF-20-2-0199, W911NF-15-2-0086 and W911NF-04-2-0005 awarded by the Army Research Laboratory. TECHNICAL FIELD The present disclosure relates to sensors, and in particular to electric-field sensors. BACKGROUND Electric-field (E-field) sensors are often built in one of two main types. The first type, potential gradiometers, sense a voltage between two electrodes connected to a high-impedance voltage preamplifier. In resistive media like soil or water, it is a relatively simple matter to make the sensor's input impedance (typically measured in MΩ) higher than the source impedance (typically measured in kΩ). These sensors are used in soil resistivity sensors, including “Meggers” and resistivity imaging systems, including those made by AGI SuperSting and Geometrics OhmMapper. For high-impedance sources like E-fields in air due to power lines, the source impedance is typically GΩ, so the sensor's input impedance must be much higher, up to TΩ. Such sensors have been built by Plessey and Quasar. Differential pairs of sensors can be used to measure the ambient electric field along the axis defined by the pair of sensors. One electrode can be grounded, or both electrodes can be electrically floating to create a “free body” sensor. Three such pairs of floating electrodes can be used to measure an ambient 3-D electric field. The second main type of E-field sensors use electrode pairs with an input impedance that is low relative to the source impedance. The sensor effectively shorts the source E-field between the electrodes with a transconductance preamplifier. These sensors are sometimes called charge induction sensors or “D-dot” sensors because they measure the time-rate-of-change (dot) of the induced charge q, where q= ρ s = D. The induced charge q is the induced charge density ρ s integrated over the electrode area. The induced charge density on the (quasi-conducting) electrode surface is equal to the electric flux D. The output of the D-dot electrode is proportional to the induced current, i, flowing between the electrodes in response to a time-varying electric field: i = dq dt = kA ⁢ D . , ( 1 ) where k is a geometric factor that accounts for field distortions like fringing and also variations in the flux density over the electrode surfac