Electric Field Measurement Techniques And Their Practical Applications

Static, quasi-static and low frequency electric fields are being used in many fields of science and engineering. They are utilized in research studies of fundamental properties of materials, exploration of high-energy physics, in biology and medicine, etc., but also in a multitude of practical applications such as precipitation, painting, xerography, to name a few. In all these endeavors it is a good practice to find out what the electric fields are in terms of value, direction, and temporal and spatial distribution. This information can be crucial for making the application successful. Electric fields are also being created by many naturally occurring and man-made phenomena. The aim of this paper is to present different options for electric field evaluation and measurement. Aside from traditional approaches, new concepts using machine learning in electric field assessment and interpretation are discussed. As technologies progress, electric field detection methods become a part of sensor fusion realm by providing additional capabilities in process, environmental and situational awareness monitoring. They can provide unique information enhancing our knowledge and understanding. Examples of such sensor integrations are shown and explained.


Introduction
Electric fields accompany a multitude of phenomena found in nature and in man-made applications.They are omnipresent, and carry a wealth of information.Unfortunately extracting and interpreting the specific set of data related to the process of interest can be a very complex endeavor.When working with constant and low frequency electric fields, scientists and engineers resort to selection of field sensors frequently called "electrostatic".Such statement can be misleading, because in reality researchers would like to have a representation of a phenomenon or an event captured within its full frequency spectrum, if possible.After all, the definition of electrostatics adopted by the Electrostatic Society of America [1] states that "Electrostatics is the class of phenomena recognized by the presence of electrical charges, either stationary or moving, and the interaction of these charges...", which implies that the involved effects are not necessarily static, and the resulting electric fields accompanying electrostatic events can be changing very fast.This fact represents a technical challenge for the data acquisition systems, especially if longer monitoring times and high spatial and temporal resolutions are required to capture the relevant information.In consequence, the electric field measurement technique has to be tuned to the application.This manuscript focuses on electric fields that are static, quasistatic and of low frequency, which suggests that the frequencies of interest are limited from DC (0 Hz) to low (several kHz) upper frequency limit.However, please keep in mind that this range is superficial.In order to make the electric field determination successful, a typical approach involves use of: • a sufficiently sensitive electric field sensor, • a signal conditioning process, • a data display or a decision-making method.
In this review a brief overview of the available electric field sensing techniques is presented along with selected set of applications.The main focus, however, is on efforts that can bring electric field sensing and monitoring into the mainstream applications comparable to widespread use of acoustic, magnetic, infrared technologies.

Electric field sensors
The most common approach in electrostatic sensing relies on a charge induction, or electrostatic induction effect.Origins of this technique are dated back to Lord Kelvin work published in 1898 [2].Electric charge induced on a conductor in presence of electric field is proportional to the field magnitude.The conductor serves a sensor's electrode.The electrostatic induction sensor is frequently represented as a capacitor in which one of the electrodes is exposed to the electric field and the other electrode is grounded, as shown in Figure 1.The sensor's capacitance C G and the charge Q determine the electric potential V C : This potential, which can be easily converted to the electric field value can be measured, the difficulty of that measurement is in the fact that any contact made to the conductor will remove the induced charge.This is illustrated by the internal resistance R M and capacitance C M of the Figure 1: A capacitive electric field sensor arrangement [3].
measuring device in Figure 1.To capture the original value of V C the resistance of the meter has to be very high and the capacitance very small.At this point the researcher has a number of options to consider, which lead to a different front-end preamplifier circuits.

Measuring electric fields by sensing current or charge.
The first approach is to discharge the conductor, and measure the electric current that flows from the charged conductor to ground through a preamplifier circuit.That measurement can be done using an operational amplifier with a shunt resistor R S at the input (Figure 2a), or using the transimpedance topology shown in Figure 2b.In the first case we have a classic noninverting voltage amplifier, where the output voltage V out is representing the input current I in by amplifying the voltage drop across resistor R S : The op-amp used in this circuit needs to have high input impedance and low input bias current.
An inverting op-amp topology can also be utilized as a shunt circuit.
The second, more popular circuit utilizes a low input impedance op-amp topology (a.k.a transimpedance or transresistance op-amp) in which the incoming current is converted to the output voltage, represented as: by monitoring the discharge current and with the knowledge of the feedback resistance R F the original value of the charge Q can be computed.In both circuits the input current I in is related  to the sensor potential V C by the following equation: To recover the voltage value of V C , the current I in can be integrated over its discharge duration to determine the original charge Q (see Equation 1).From the practical point of view these circuits require careful calibration as the capacitance C G is not always easy to determine, and can change depending on the sensor placement and geometry of the measurement setup.Once the conductor is discharged, the current stops flowing, even when the conductor is still present in the external electric field, and the output voltage for both circuits is zero.In order for the measurement to continue the current needs to keep flowing, therefore the voltage V C needs to change in time, as implied by Equation 4.
An alternative approach to the induced charge and potential measurement is utilizing a circuit shown in Figure 3a, with an op-amp exhibiting a very high input impedance (a.k.a."charge amplifier"'), where the charge induced on the conductor is charging the known input capacitance of a preamplifier and converted to voltage using well known dependence  An option can be added where the feedback resistor R F is present, which provides a voltage gain to the output signal (Figure 3b).Induction sensors configurations can be enhanced with additional circuitry and special sensor geometries (guarding) that minimize influence of measurement errors arising from leakage, thermal noise, bias currents of the op-amp, microphonics, tribo-and piezoelectric effects, electrochemical phenomena and dielectric absorption in the connecting cables [4,5].The induction probe instruments cannot be used for extended continuous monitoring -the current sensing circuit require a varying potential at the sensing conductor, so they are not feasible for DC fields or slow changing variable fields measurements at their sensitivity is low.A very high input impedance of the charge amplifier causes the input voltage drift, therefore the input has to be periodically zeroed, thus removing the induced charge from the conductor.Charge amplifiers are also susceptible to accidental charging, for example by ionized air [6,7].An extensive overview of the induction current and charge sensor applications is given by Yan et al [8].They are best fitted for detection of varying electric fields created by moving charged objects.

Measuring electric fields using contacting ultra-high input impedance preamplifiers
Voltage of the charged conductor can be measured directly with an ultra-high input impedance circuits.One of the commercial examples is Trek Infinitron contacting hand-held electrostatic voltmeter, which utilizes a concept of input bias current cancellation.The input bias current value is recorded and stored.Another circuit produces an output current equal in magnitude to the value of this bias current but opposite in polarity.This current is applied to the input of the amplifier to cancel the bias current [9,10].Proper nullification of the input bias current of the preamplifier circuit along with independent bootstrapping of the amplifier power supply allows for increase of the input resistance to the range of 30 TΩ and lowering of the input capacitance to 5.3 fF.This impedance is still allowing the conductor to discharge, therefore the instrument's use in electric field sensing is not practical.

Measuring electric fields with non-contacting methods
Since making contact with a conductor on which the electric field induced charge is present removes the charge, many applications resort to non-contacting methods of making the electric field measurement.In that case the electric field sensor is placed in proximity of the conductor to measure its potential.In this case an induction probe principle can still be used, following the principle of Equation 4, which requires the electric field to vary over time.This approach is used, for example, in ARL "D-dot" sensors [11], EPIC sensor by Plessey Semiconductors (unfortunately discontinued) [12], or in designs reported in literature by Chi [13] or Spinelli [14] for biopotential monitoring.Preamplifiers of these devices utilize variations of the input bias current cancellation and bootstrapping along with MOS circuitry to achieve the high input impedance and drift immunity.A classic approach to non-contacting measurements of electric fields and potentials ventures back to the original Kelvin design [2].The principle of the Kelvin's probe operation has its origin in the very basic equation defining capacitance of a capacitor: as illustrated in Figure 4. where C is the capacitance, Q is the electric charge accumulated by the capacitor, U is the voltage between electrodes of the capacitor.The "Object under test" is our charged conductor from Figure 1.Let's assume, for the sake of discussion, that we have a simple parallel plate electrodes capacitor, like the one shown in Figure 4.At this point, any change of the distance D between electrodes during the time interval dt requires certain amount of electric charge dQ to be delivered to or taken away from the capacitor in order for the voltage U to remain constant: Since dQ/dt is an electric current, measurement of that current allows for measurement of the voltage if the capacitance variation is known.This approach allows for measurements of DC and AC voltages, however the bandwidth is limited by the frequency of the sensor's motion.
In fieldmeters and electrostatic voltmeters the capacitance C is formed by the instrument's sensor and the object that is being measured.In 1932 Zisman [15] introduced the vibrating Kelvin probe.The sensor moved sinusoidally in the direction perpendicular to the tested object, and the current flowing to and from the sensor changed proportionally to the amplitude and frequency of that vibration.This technique became a base for contemporary Kelvin probe techniques, including Kelvin force microscopes (KFMs) [16,17], fieldmeters and electrostatic voltmeters [18].The mechanical motion of the sensor needs to be precisely controlled, to assure proper measurement accuracy of the meters.The fieldmeters with mechanically vibrating sensors and rotating vane fieldmeters [3,19] [20], atmospheric research [21], etc. Fieldmeters are not very sensitive and their bandwidth is limited by the velocity of the rotating vane or the vibration frequency of the sensor.Electrostatic voltmeters (ESVM), such as those manufactured by Advanced Energy (formerly Trek and Monroe) are much more sensitive and precise than fieldmeters with the bandwidth of up to 3 kHz.Their construction, however, is relatively expensive and complicated, since they utilize a field -nullification approach where the electric potential is applied to the vibrating sensor to cancel out the external electric field [18].Non-contacting vibrating electric field sensors can be miniaturized and are implemented as microelectromechanical (MEMS) devices [22,23,24,25].Instead of changing the circuit capacitance C mechanically, this process can be handled electronically.There are several electronic devices that can have their capacitances controlled that way: a varactor (a.k.a.varicap), a MOS (metal-oxide-semiconductor) or a MIS (metalinsulator-semiconductor) structure.The idea of using varactors for direct/contacting low current measurements was introduced in 1979 by Herscovici [26] and commercialized by Hewlett Packard in their 4140B pA Meter/DC Voltage Source [27].With minimal modifications the same technique can be utilized in non-contacting electric potential and field measurements [28,29].Other types of electric field sensors encompass the range of electrooptic devices based on Pockels and Kerr effect [7,30].

Signal processing/conditioning
Raw signals produced by sensors need to be collected and interpreted.Depending on application, we may want to report electric field magnitude or RMS value, or detect the peak values of the fields and potentials.In charge flow monitoring application one may want to track the signals with multiple sensors to provide redundancy and improve reliability of the collected information [8].This approach has been used in object/people tracking, e.g.[31,32], power line condition sensing [33,34], industrial processes monitoring [8], etc.The signal processing algorithms depend on the application, and most frequently involve filtering and feature extraction.

Conclusions
Multi-sensor applications along with machine learning based processing are becoming popular and widespread in the industry and science.Electrostatic sensors are bound to follow that route.In the era of multi-nodal sensing and sensor fusion they are good candidates for implementation in sensing networks with other types of sensors due to their relative simplicity.

Figure 2 :
Figure 2: Typical circuits used in electric field sensors.
(a) Charge amplifier (b) Charge amplifier with gain.
, are used in broad range of applications, for example in semiconductor and other industries for assessment of the electrostatic discharge (ESD) threats