SE541896C2 - An apparatus for measuring electric field vectors - Google Patents

Abstract

The present invention relates to an apparatus for determining electric field vectors of an external electric field in multiple dimensions. The apparatus comprising at least one sensor arrangement, each sensor arrangement comprising: a sensor element with at least two sections and a shutter configured to rotate around a fixed axis, a motor assembly configured to rotate the shutter at a controllable rotation rate thereby alternatively exposing each of the at least two stationary sections to the external field; and a circuitry coupled to the sections for measuring the electric flux impinging on each section by the external electric field and responsively generating respective current signals. The circuitry further comprises a data processor configured to calculate the electric field vectors of the external electric field in at least two dimensions based on the difference between electric flux impinging on two alternatively exposed section.

Description

AN APPARATUS FOR MEASURING ELECTRIC FIELD VECTORS TECHNICAL FIELD The present invention relates to an apparatus for measuring electric field vectors of an external electric field.

BACKGROUND By knowing how much static charge there is in an atmosphere, on the moon, Mars or on Earth, it is possible to prevent the problems that arise from strong static discharge. The problems can be, like here on earth, a discharge in an airplane that could risk electronics. Or high-rise equipment starts charging, which may be dangerous to those who work with the equipment or equipment in-house.

Measured static charge can be used to build a warning system for greater static charge. It is also possible to use the information to obtain an understanding of how charged particles, dust in high-tech industry, for example, move in a space.

There are two established technologies to measure static charge, one is a flat field mill, as illustrated in figure 1, and a cylindrical field mill as illustrated in figure 2. A flat field mill can only measure a single component in x, y or z, and a cylindrical field mill rotate 90 degrees against the electric field and may also only measure one component.

Figure 1 discloses a shutter type electric field mill 10, wherein a sensor electrode 11 is periodically exposed and shielded from an external electric field E by a grounded rotating shutter 12 using a motor 13. Shutter-type field mills are grounded and distort the electric fields in their vicinity. The charge qsinduced by ambient electric fields in its sensing electrode 11 at any time instant t, as well as the induced current is, between the ground and the sensing electrode 11 is alternatively exposed and shielded as the shutter rotates. The charge and the current are proportional to the amplitude of the component of the local electric field E perpendicular to the shutter surface. The signal of the charge, and therefore the direction of the current, depends on the polarity of the field. A drawback with prior art shutter-type field mills is that the signals from all electrodes form a single channel. A field direction cannot be calculated from just a single channel of data. Furthermore, it has a rather small field-of view, which means that the field mill only can determine the charge directly above the sensor and not in the environment around the field mill.

Figure 2 discloses a cylindrical field mill 20 that measures the electric field by measuring the amplitude and phase of the current flowing between the two half-cylinder electrodes 21 rotating with constant angular velocity ?, and connected to each other by a low-impedance measuring circuit.

The shutter-type field mill in figure 1 and the cylindrical field mill in figure 2 have rotating components that produce a measurable AC signal based on the DC external or ambient electric field E. Rather than a sensing surface that is alternatively shielded and unshielded by grounded elements, the cylindrical field mill contains a fixed volume enclosed by a conductive surface. A fixed volume covered by a conducting surface shorts the external or ambient electric field, and therefore experiences a redistribution of surface charge that cancels any internal electric field, which means that no calibration is needed.

US 8,536,879 by Renno et al. discloses a cylindrical field mill configured to only measure planar direction of an electric field.

Thus there is a need for an improved apparatus for measuring electric field vectors in multiple dimensions.

SUMMARY It is an object of some embodiments to solve or mitigate, alleviate, or eliminate at least some of the above or other disadvantages.

According to one aspect, this is achieved by an apparatus for determining electric field vectors of an external electric field in multiple dimensions. The apparatus comprises at least one sensor arrangement, each sensor arrangement comprising: a planar sensor element with at least three sections and a shutter configured to rotate around a fixed axis; a motor assembly configured to rotate the shutter at a controllable rotation rate thereby alternatively exposing each of the at least three sections to the external field; and a circuitry coupled to the sections for measuring the electric flux impinging on each section by the external electric field and responsively generating respective current signals. The circuitry further comprises a data processor configured to calculate the electric field vectors of the external electric field in three dimensions based on the difference between electric flux impinging on the at least three alternatively exposed sections.

An advantage with the present invention is that a less complex apparatus for measuring electric field vectors is achieved compared to prior art field mills.

Another advantage is that an apparatus with a single motor may be used to determine the electric field vectors in multiple dimensions compared to prior art field mills.

BRIEF DESCRIPTION OF THE DRAWINGS Further objects, features and advantages will appear from the following detailed description of embodiments, with reference being made to the accompanying drawings. The drawings are not necessarily to scale, emphasis instead being placed upon illustrating the example embodiments.

Figure 1 illustrates an apparatus for measuring electric field vectors with a rotating shutter according to prior art.

Figure 2 illustrates an apparatus for measuring electric field vectors with a rotating cylinder according to prior art.

Figures 3a - 3b illustrate a first set of configurations for a sensor arrangement adapted to measure electric field vectors in multiple dimensions.

Figures 4a and 4b illustrate a second set of configurations a sensor arrangement adapted to measure electric field vectors in multiple dimensions.

Figures 5a and 5b illustrate a third set of configurations a sensor arrangement adapted to measure electric field vectors in multiple dimensions.

Figure 6 illustrates a first embodiment of a system for measuring electric field vectors of an external electric field having three sensors working in tandem.

Figure 7 illustrates a second embodiment of a system for measuring electric field vectors of an external electric field having two sensors working in tandem.

Figure 8 illustrates one embodiment of an apparatus for determining electric field vectors having two sensors working in tandem.

Figure 9 is a flow chart illustrating the process to determining the electric field using an inverse of the field correlation matrix.

Figure 10 is a flow chart illustrating the process to obtain an inverse of the field correlation matrix.

Figure 11 illustrates how an electric field illuminates the electrodes in a field mill according to figure 4a.

DETAILED DESCRIPTION It should be emphasized that the term "comprises/comprising" when used in this specification is taken to specify the presence of stated features, integers, steps, or components, but does not preclude the presence or addition of one or more other features, integers, steps, components, or groups thereof. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise.

Embodiments of the present disclosure will be described and exemplified more fully hereinafter with reference to the accompanying drawings. The solutions disclosed herein can, however, be realized in many different forms and should not be construed as being limited to the embodiments set forth herein.

In electromagnetism, electric flux is the measure of flow of the electric field through a given area. Electric flux is proportional to the number of electric field lines going through a normally perpendicular surface. If the electric field is uniform, the electric flux passing through a surface of vector areas S is (?E=E·S=EScos?, ?E=E·S=EScos?, where E is the electric field (having units of V/m), E is its magnitude, S is the area of the surface, and ? is the angle between the electric field lines and the normal (perpendicular) to S.

Electrical flux ?? has SI units of volt meters (Vm), or, equivalently, newton meters squared per coulomb (N m2 C-1). Thus, the SI base units of electric flux are kg-m3-s-3-A-1.

This disclosure contains example embodiments of a field mill designed to measure the electric field in two or three dimensions at the same time. Current technology requires several prior art field mills according to figure 1 or 2, one in each direction, to determine the electric field in two or three dimensions.

The field mills disclosed reduces the complexity of the systems as well as the cost of purchasing, operation, etc. In addition, prior art field mills are very limited in the area they can measure, and the field mill according to the invention has a much wider field of view compared to prior art field mills, when taking the direction of the field lines into consideration. Thus, it is possible to "see" more of the area above at once. In addition, with at least two sensors working in tandem, as described in connection with figures 6, 7 and 8, it is possible to triangulate the largest charge density, the direction in which the charges are moving and whether they are growing or decreasing.

Figures 3a - 3b illustrate a first set of configurations of a sensor arrangement adapted to measure electric field vectors in multiple dimensions.

Figure 3a is a schematic illustration of a configuration of a sensor arrangement 30 for measuring electric field vectors in two dimensions, e.g. X and Z direction. The sensor arrangement 30 comprises a shutter 31 with an opening arranged to be rotated around a fixed axis 32 using a motor assembly (not shown), and a sensor element with two sections 33-A and 33-B. The opening of the shutter preferably corresponds to the size of one section.

Connections 34-A and 34-B (representing two channels) that are provided for connecting a circuitry (not shown) to the section 33-A and 33-B, respectively, for measuring a change in electric flux impinging on each section by an external electric field and responsively generating respective current signals.

When the motor assembly rotates the shutter 31, at a controllable rotation rate, the sections 33-A and 33-B are alternatively exposed to the electric field through the opening of the shutter 31 and the respective current signals are used in a data processor (not shown) to calculate the electric field vectors of the external electric field in two dimensions based on the difference between electric flux impinging on the two alternatively exposed sections 33-A and 33-B.

Figure 3b is a schematic illustration of a configuration of a sensor arrangement 35 for measuring electric field vectors in three dimensions, in this example X, Y and Z direction. The sensor arrangement 35 comprises a shutter 36 with an opening arranged to be rotated around a fixed axis 37 using a motor assembly (not shown), and a sensor element with three sections 38-A, 38-B and 38-C. The opening of the shutter corresponds to the size of one section, thereby exposing only one section at the time for the electric field when the shutter rotates. Connections 39-A, 39-B and 39-C (representing three channels) are provided for connecting a circuitry (not shown) to the section 38-A, 38-B and 38-C, respectively, for measuring an electric flux impinging on each section by an external electric field and responsively generating respective current signals.

When the motor assembly rotates the shutter 36, at a controllable rotation rate, the sections 38-A, 38-B and 38-C are alternatively exposed to the electric field and the respective current signals are used in a data processor (not shown) to calculate the electric field vectors of the external electric field in two dimensions based on the difference between electric flux impinging on the three alternatively exposed sections 38-A, 38-B and 38-C.

Figures 4a - 4b illustrate a second set of configurations of a sensor arrangement adapted to measure electric field vectors in multiple dimensions, which is more balanced compared to the configurations illustrated in connection with figures 3a and 3b.

Figure 4a is a schematic illustration of a configuration of a sensor arrangement 40 for measuring electric field vectors in three dimensions, e.g. X, Y and Z direction. The sensor arrangement 40 comprises a shutter 41 with two openings, preferably having the same size, arranged to be rotated around a fixed axis 42 using a motor assembly (not shown), and a sensor element with four sections 43-A to 43-D. The openings of the shutter are separated and each opening corresponds to the size of one section in order to only expose one section at the time for the electric filed when the shutter rotates. Connections 44-A to 44-D (representing four channels) are provided for connecting a circuitry (not shown) to the section 43-A to 43-D, respectively, for measuring an electric flux impinging on each section by an external electric field and responsively generating respective current signals.

When the motor assembly rotates the shutter 41, at a controllable rotation rate, the sections 43-A to 43-D are alternatively exposed to the electric field through the openings of the shutter 41 and the respective current signals are used in a data processor (not shown) to calculate the electric field vectors of the external electric field in three dimensions based on the difference between electric flux impinging on the four alternatively exposed sections 43-A to 43-D. In this example sections 43-A and 43-C are exposed to the electric field at the same time while sections 43-B and 43-D are not exposed, and vice versa.

Figure 4b is a schematic illustration of a configuration of a sensor arrangement 45 for measuring electric field vectors in three dimensions, in this example X, Y and Z direction. The sensor arrangement 45 comprises a shutter 46 with three openings, preferably having the same size, arranged to be rotated around a fixed axis 47 using a motor assembly (not shown), and a sensor element with six sections 48-A to 48-F. The openings of the shutter are separated and each opening corresponds to the size of one section, in order to expose only one section at the time for the electric field when the shutter rotates. Connections 49-A to 49-F (representing six channels) are provided for connecting a circuitry (not shown) to the section 48-A to 48-F, respectively, for measuring an electric flux impinging on each section by an external electric field and responsively generating respective current signals.

When the motor assembly rotates the shutter 46, at a controllable rotation rate, the sections 48-A to 48-F are alternatively exposed to the electric field through the openings of the shutter and the respective current signals are used in a data processor (not shown) to calculate the electric field vectors of the external electric field in three dimensions based on the difference between electric flux impinging on the six alternatively exposed sections 48-A to 48-F. In this example sections 48-A, 48-C and 48-E are exposed to the electric field at the same time while sections 48-B, 48-D and 48-F are not exposed, and vice versa.

The number of channels, i.e. separate measurement of electric flux impinging on the alternatively exposed sections, represents the rank of the sensor arrangement. A rank two (as illustrated in figure 3a) may determine the electric field vectors in two dimensions, and a rank three (as illustrated in figure 3b) may determine the electric field vectors in three dimensions.

Sensor arrangements having a rank three, as illustrated in figure 4a and 4b, have a more stable and balanced functionality compared to lower rank configurations.

Figures 5a and 5b illustrate a second set of configurations of a sensor arrangement adapted to measure electric field vectors in multiple dimensions.

Figure 5a is a schematic illustration of a configuration of a sensor arrangement 50 for measuring electric field vectors in two dimension, similar to the configuration described in figures 3a and 4a. However, the sensor arrangement in figure 5a represents the simplest configuration with a balanced rotor and rank three. More sensors will provide better performance and redundancy in the system, as described below in figure 5b. The sensor arrangement 50 comprises a shutter 41 with two openings, preferably having the same size, arranged to be rotated around a fixed axis 42 using a motor assembly (not shown), and a sensor element with four sections 43-A to 43-D. The openings of the shutter are separated and each opening corresponds to the size of one section in order to only expose one section at the time for the electric filed when the shutter rotates. Four connections are provided for connecting a circuitry to sections 43-A to 43-D. The circuitry comprises two difference amplifiers 52 and 53, each configured to generate an output signal 51-1 and 51-2 (representing two channels) indicative of the difference between electric flux impinging on two alternatively exposed sections. A first difference amplifier 52 is connected to sections 43-A and 43-B and a second difference amplifier 53 is connected to sections 43-C and 43-D.

When the motor assembly rotates the shutter 41, at a controllable rotation rate, the sections 43-A to 43-D are alternatively exposed to the electric field through the openings of the shutter 41 and the respective current signals are used in a data processor (not shown) to calculate the electric field vectors of the external electric field in two dimensions based on the difference between electric flux impinging on the four alternatively exposed sections 43-A to 43-D. In this example sections 43-A and 43-C are exposed to the electric field at the same time while sections 43-B and 43-D are not exposed, and vice versa.

Differential measurement is not required, but has the advantage to reduce disturbances, such as 50Hz from mains AC voltages, ELF transmissions and other fields that lie within the pass band of the signal chain.

Figure 5b is a schematic illustration of a configuration of a sensor arrangement 55 for measuring electric field vectors in three dimension, similar to the configuration described in figures 3b and 4b. The sensor arrangement 55 comprises a shutter 46 with two openings, preferably having the same size, arranged to be rotated around a fixed axis 47 using a motor assembly (not shown), and a sensor element with six sections 48-A to 48-F. The openings of the shutter are separated and each opening corresponds to the size of one section in order to only expose one section at the time for the electric filed when the shutter rotates. Six connections are provided for connecting a circuitry to sections 48-A to 48-F. The circuitry comprises three difference amplifiers 57, 58 and 59 each configured to generate an output signal 56-1, 56-2 and 56-3 (representing three channels) indicative of the difference between electric flux impinging on two alternatively exposed sections. A first difference amplifier 57 is connected to sections 48-A and 48-B, a second difference amplifier 58 is connected to sections 48-C and 48-D, and a third difference amplifier 59 is connected to sections 48-E and 48-F.

When the motor assembly rotates the shutter 46, at a controllable rotation rate, the sections 48-A to 48-F are alternatively exposed to the electric field through the openings of the shutter 46 and the respective current signals are used in a data processor (not shown) to calculate the electric field vectors of the external electric field in three dimensions based on the difference between electric flux impinging on the six alternatively exposed sections 48-A to 48-F. In this example sections 48-A, 48-C and 48-E are exposed to the electric field at the same time while sections 48-B, 48-D and 48-F are not exposed, and vice versa.

Figure 6 illustrates a first embodiment of a system 60 for measuring electric field vectors of an external electric field having at least two sensor arrangements, in this example three sensor arrangements 55-1 to 55-3, arranged on a supporting structure 61 working in tandem. In this example the supporting structure 61 is a cube, but other geometric shapes may be used to obtain redundancy in the measurements, and the sensor arrangements are arranged in a U-shape. In this example the sensor arrangements are non-parallel, wherein the orientation of the fixed axis of the shutter of each of the at least two (in this example three) non-parallel sensor arrangements differs.

Figure 7 illustrates a second embodiment of a system 70 for measuring electric field vectors of an external electric field having two sensors arrangements, a first is a planar sensor arrangement and the second is a cylindrical sensor arrangement, working in tandem. The system 70 comprises a shutter 71 in the shape of an upside down barrel having four openings on a planar side 72-p and four openings on the cylindrical wall 72-c. The shutter is configured to be rotated around a fixed axis 73 using a motor assembly (not shown). The system 70 further comprises a sensor element 74 with eight sections, each denoted 75-p, on a planar side and eight sections, each denoted 75-c, on a cylindrical side.

The openings on the planar side 72-p on the shutter 71 and the sections 75-p on the sensor element 74 constitute the first sensor arrangement, and the openings on the cylindrical side 72-c on the shutter 71 and the sections 75-c on the sensor element 74 constitute the second sensor arrangement. The sensor arrangements are non-parallel to each other although the orientation of the fixed axis 73 of the shutter 71 for each of the at least two non-parallel sensor arrangements coincides. It should be noted that other configuration, such as a spherical configuration may be used.

Figure 8 illustrates one embodiment of an apparatus 80 for determining electric field vectors having at least one sensor arrangement 55. Each sensor arrangement is connected to a circuitry for measuring the electric flux impinging on each section by the external electric field and responsively generating respective current signals. The circuitry comprises in this example, difference amplifiers 57, 58, 59 (as described in connection with figure 5b), amplifiers 82 and analogue-to-digital converters, ADC, 83 before the signal is fed into a data processor 84. Other configurations having the same functionality may be used, such as using transimpedance amplifiers (simple RC anti-aliasing filters and differential ADCs with built-in difference amplifiers). The apparatus further comprises a tachometer 85 configured to detect the rotation rate and phase/angle when rotating each shutter, wherein the data processor 84 is further configured to calculate the electric field vectors of the external electric field based on the detected rotation rate.

The sensor arrangement, difference amplifiers, amplifiers, ADCs and tachometer are integrated in a sub-system 81-1 connected to the data processor 84. More subsystems 81-2, as indicated by the dashed lines, may be connected to the same data processor 84. The data processor 84 is configured to calculate the electric field vectors of the external electric field in at least two dimensions based on the difference between electric flux impinging on two alternatively exposed sections, in this example the data processor is configured to calculate the electric field vectors based on the signal from each difference amplifier.

Figure 9 is a flow chart illustrating the process to determining the electric field using an inverse of the field correlation matrix. The flow starts in step 510, and in step Sll, the electric flux impinging on each sensor plate, i.e. each sector on sensor element, is measured. The result may be represented as a vector f. In an optional step S12, the result is stored.

In step S13, the electric field e is calculated using a precalculated Cinv, which is an inverse of the field correlation matrix, as described in more detail in connection with figure 10. The result is obtained through the following equation: e = Cinv* f (1) In the optional step S14, the result is output to the user and the flow ends in step S15.

Figure 10 is a flow chart illustrating the process to obtain an inverse of the field correlation matrix, CinvThe flow starts in S20, and in step S21 a decision is made regarding how to obtain the CinvIs FEM (Finite Element Method) or real measurements going to be used? If real measurement is going to be used, the flow continues to step S22 and the apparatus is mated with the calibration jig before continuing to step S24. If the decision in step S21 is to use FEM instead, the flow continues to step S23 where the geometry is constructed and tessellated. Necessary modelling for applying known external E-fields in X/Y/Z directions is added, and necessary modelling for applying a voltage to the apparatus relative to ground is added before continuing to step S24.

In step S24, an E-field with known strength Exin X-direction is applied. The electric flux impinging on each sensor plate (section) is measured. The fluxes are normalized by dividing them by Ex. Normalized fluxes are collected in column vector cx.

In step S25, an E-field with known strength ??in Y-direction is applied. The electric flux impinging on each sensor plate (section) is measured. The fluxes are normalized by dividing them by ??. Normalized fluxes are collected in column vector CY.

In step S26, an E-field with known strength Ezin Z-direction is applied. The electric flux impinging on each sensor plate (section) is measured. The fluxes are normalized by dividing them by Ez. Normalized fluxes are collected in column vector cz.

In step 527, a known Voltage VQis applied to the apparatus relative to ground. The electric flux impinging on each sensor plate (section) is measured. The fluxes are normalized by dividing them by VQ. Normalized fluxes are collected in column vector CQ.

In step S28, field correlation matric C is constructed from column vectors cx, CY, CZand CQ, and thereafter calculate the (pseudo-) inverse of the field correlation matrix Cinv, step S29, which is used in flowchart illustrated in figure 9. Flow ends in step S30.

Figure 11 illustrates how an electric field illuminates the electrodes in a field mill according to figure 4a, wherein the field mill has four channels which means that the electric field may be determined in three dimensions, which is illustrated with the graphs for Z, X and Y. The direction of X and Y are indicated by arrows in the field mill and the Z-direction is perpendicular to X and Y and is indicated by a circle with a cross (direction through the paper).

This configuration can measure the electric field in three dimension as illustrated in the graphs having the induced current I in ampere. A positive signal represents a downward electric flux through a section (indicated by a sign) and a negative signal represents an upward electric flux through a section (indicated by a - sign). The curves in the graphs indicate the detection of electric flux in Z direction when curve A is equal to curve C, and curve B is equal to curve D. Electric flux in the X direction is detected when curve A is equal to curve D, and curve B is equal to curve C. Electric flux in the Y direction is detected when curve A is equal to curve B, and curve C is equal to curve D.

If an electric field of 1 V/m has been used in all directions, i.e. X, Y and Z, the electric flux impinging on each sensor plate is measured as described in connection with step 27 above. The fluxes are normalized by dividing them with 1 V/M. Therefore the column vector CQmay be omitted from the field correlation matrix. The fluxes are measured in pico Ampheres, pA, and the field correlation matrix C is in this example: Image available on "Original document" Thus (pseudo-) inverse of the field correlation matrix is: Image available on "Original document" The electric field may then be calculated using equation (1): Image available on "Original document"

Claims (9)

1. An apparatus (80) for determining electric field vectors of an external electric field in multiple dimensions, the apparatus comprising at least one sensor arrangement (35; 40; 45; 55), each sensor arrangement comprising: - a planar sensor element with at least three sections (38-A, 38-B, 38-C; 43-A, 43-B, 43-C, 43-D; 48-A, 48-B, 48-C, 48-D, 48-E, 48-F) and a shutter (36; 41; 46) configured to rotate around a fixed axis (37; 42; 47); a motor assembly configured to rotate the shutter at a controllable rotation rate thereby alternatively exposing each of the at least three sections to the electric field; and a circuitry (57, 58, 59, 82, 83) coupled to the sections for measuring the electric flux impinging on each section by the external electric field and responsively generating respective current signals; wherein the circuitry further comprises: - a data processor (84) configured to calculate the electric field vectors of the external electric field in three dimensions based on the difference between electric flux impinging on the at least three alternatively exposed sections.

2. The apparatus according to claim 1, wherein the circuitry further comprises at least one difference amplifier (57, 58, 59), each configured to generate a signal indicative of the difference between electric flux impinging on two alternatively exposed sections, and the data processor (84) is further configured to calculate the electric field vectors based on the signal from the difference amplifier.

3. The apparatus according to claim 2, wherein the signal of each difference amplifier (57, 58, 59) is indicative of the difference between electric flux impinging on adjacent sections.

4. The apparatus according to any of claims 2 or 3, wherein the signal of each difference amplifier (57, 58, 59) is indicative of the difference between electric flux impinging on nonadjacent sections.

5. The apparatus according to any of claims 1-4, comprising at least two non-parallel sensor arrangements, wherein the orientation of the fixed axis of the shutter for each of the at least two non-parallel sensor arrangements coincides.

6. The apparatus according to any of claims 1-4, comprising at least two non-parallel sensor arrangements, wherein the orientation of the fixed axis of the shutter of each of the at least two non-parallel sensor arrangements differs.

7. The apparatus according to any of claims 1-6, further comprising a tachometer (85) configured to detect the rotation rate when rotating each shutter, wherein the data processor is further configured to calculate the electric field vectors of the external electric field based on the detected rotation rate.

8. The apparatus according to any of claims 1-7, wherein at least one sensor arrangement comprises at least four sections.

9. The apparatus according to any of claims 1-7, wherein at least one sensor arrangement comprises at least six sections.