Position measurement using a balanced capacitance bridge

Abstract

A capacitive position sensor includes a capacitance bridge and a balanced bridge circuit. The capacitance bridge includes at least one first electrode, and at least two second electrodes. The balanced bridge circuit separately adjusts excitation of the at least two second electrodes to balance a signal at the at least one first electrode toward a desired target value, wherein a level of the excitation is used as input to calculate a position of the at least one first electrode relative to the at least two second electrodes.

Description

[0001] Position Measurement Using a Balanced Capacitance Bridge Technical Field This disclosure relates generally to measuring devices and methods and, more particularly, to measuring displacement and / or position using variable capacitance. Background In general, devices and methods for non-contact measurement of displacement and / or position of adjacent objects by capacitive means are well known. More specifically, displacement and / or position measurement applied to movable stages, especially stages made for low temperature use, are also well known. There are many methods for high precision nanoscale displacement measurements (Fleming, 2013). In a cryogenic setting, industry standard position sensors for linear and rotational bearing stages are resistive and optical based. Downsides of resistive based displacement measurement: 1. Dissipates heat into a sensor from electrical current in resistive elements of the sensor. 2. Mechanical hysteresis typically from a wiper that makes contact with resistive material. 3. Mechanical wear from contact points on resistive material. Downsides of optical based displacement measurement: 1. Dissipates heat into a system via a light source. 2. Alignment difficulty associated with typical interferometry measurements. 3. Cost is usually much higher for a quality measurement. Capacitive sensors are commonly used for displacement measurement in movable stages. It’s useful to divide capacitive sensors into two separate categories: 1. Single ended capacitance measurement of the distance from the sensor head to a target for short range displacement measurement. 2. Vernier style capacitive electrode pattern for long range displacement measurement. The first category of capacitive sensors measures displacement by forming a capacitor with an electrode that is part of a sensor head, and another electrode attached to a stationary body of a stage (or the body of the stage itself). When the stage moves, the distance between the electrodes changes and therefore the capacitance changes. According to (Fleming, 2013), these are the most common type for use in nanopositioning. The main weakness of this style of sensor is that a large sensor head is needed to effectively measure large displacements. These are typically installed on flexure stages where motion is on the order of microns. This type of displacement measurement is used in commercial stages available from (PI-USA, 2023), (Thorlabs, 2023), and many others in industry. The second category of capacitive sensors measures displacement by using an electrode pattern that causes a sensor signal to vary periodically with displacement as a stage moves. Typically, there will be overlapping electrode patterns that cause a signal to increase when they are aligned, and capacitance is high, and to decrease when they are not. While this is a great simplification of the operation, the principle is shared by this category of sensor. This category has the advantage of being able to sense over longer ranges, but usually suffers some drawbacks, such as only measuring incremental displacement instead of absolute displacement. There are instances of absolute displacement measurement, but usually at the cost of more complicated electrode arrangements, signal generation and processing (Liu, 2016) (Liu, 2018). A capacitive sensor for measuring displacement is a well-known prior invention with many embodiments over the years. One of the earliest is (US Patent No. US3312892A, 1964) that describes a contactless transducer. This prior art has descriptions of capacitance measurements where the capacitance changes with the motion of a device by varying the overlapping area of conductive plates. There are two notable separable categories of displacement sensors based on measuring capacitance, incremental and absolute. Incremental sensors have the advantage of high precision and ostensibly infinite range. In an incremental sensor, electrodes are arranged such that a measured signal varies with displacement, but the signal is not unique for a particular position. The signal will typically change periodically with displacement, so some sort of counting is needed to actively track a displacement. An example of this is seen in the Vernier caliper of (Baxter, 1997) chapter 18 where the capacitance of “comb” shaped electrodes is measured to determine displacement and a course position counter is needed to track the absolute position. Because the displacement signal is periodic, amplification of the signal can be matched to the maximum electrode overlap to maximize signal to noise ratio. On the other hand, an absolute position measurement typically can excel at short range displacement measurements, but the signal quickly saturates as displacement increases. An example of this can be seen in an accelerometer in (Baxter, 1997) chapter 15 where a high precision displacement is measured using capacitance but is limited to measurements on the order of a few microns. Another patent (US Patent No. US6492911B1, 1999) gives a comprehensive overview of the different types of rotation and displacement sensors based on capacitance measurements. It also references the differences between incremental and absolute sensors and describes the absolute category as a “course” encoder. Balanced bridge techniques have proven useful for measuring capacitance, for example, as disclosed in patent (US Patent No. US20070227253A1, 2007) for sensing a periodic process variable, including temperature or pressure, with a capacitance bridge. The capacitance bridge in turn varies periodically within specific baseband frequencies based on the process variable and there is a detector connected to the center of the bridge. The potential at each end of the bridge is controlled as a function of the detected signal by a control circuit, which also provides a process variable output at the baseband frequency range. Summary A capacitive position sensor includes a capacitance bridge and a balanced bridge circuit. The capacitance bridge includes at least one first electrode, and at least two second electrodes. The balanced bridge circuit separately adjusts excitation of the at least two second electrodes to balance a signal at the at least one first electrode toward a desired target value, wherein a level of the excitation is used as input to calculate a position of the at least one first electrode relative to the at least two second electrodes. Brief Description of the Drawings Figure 1: Basic three electrode capacitance bridge showing capacitances as variable with relative displacements of electrodes, according to the prior art. Figure 2: Two separate possible methods to interface to a movable electrode to read a signal at a center of a capacitance bridge, according to the prior art. Figure 3: A physical arrangement of a basic capacitance bridge where capacitances vary by changing overlap area of a movable electrode and stationary electrodes, according to the prior art. Figure 4: A physical arrangement of a basic capacitance bridge where capacitances vary by changing a gap between a movable electrode and stationary electrodes, according to the prior art. Figure 5: Illustration of balancing signals that can be applied to facilitate a displacement measurement, according to the present disclosure. Figure 6: An embodiment of a circuit that is able to automatically balance a capacitance bridge for a displacement measurement, according to the present disclosure. Figure 7: A second embodiment of a circuit that is able to automatically balance a capacitance bridge for a displacement measurement, according to the present disclosure. Figure 8: An embodiment of a linear bearing stage with one embodiment of electrodes installed for a displacement measurement, according to the present disclosure. Note that bearings are not illustrated to help clearly show the electrode locations. Figure 9: An embodiment of a flexure stage with one embodiment of electrodes installed for a displacement measurement, according to the present disclosure. Figure 10: An embodiment of a rotational bearing stage with one embodiment of electrodes installed for a displacement measurement, according to the present disclosure. Detailed Description The present disclosure improves upon the state of the art for measuring position using a multiple (e.g. three) electrode balanced capacitance bridge where at least one of the electrodes is an electrode movable relative to at least two fixed electrodes. An example application for this electrode arrangement is a moveable stage, where one electrode is fixed to a movable part of the stage and the other two electrodes are fixed to a stationary part of the stage. Conversely, one electrode can be fixed to the stationary part of the stage and the other two can be fixed to the movable part of the stage. Either way, the three electrodes form a capacitance bridge where separate excitations can be applied to the ends of the bridge, and the resulting signal at the middle of the bridge can be measured. The movable stage may include a linear bearing stage, a rotational bearing stage, a flexure stage, or the like. Additionally, a balanced bridge measurement circuit may be coupled to the capacitance bridge. The circuit applies separate adjustable excitations on both sides of the capacitance bridge and automatically balances the signal at the center node near zero or some other balance level. The adjustable excitations when the circuit is balanced are used to calculate the position of the movable electrode. The presently disclosed apparatus and method may provide significant benefits compared to previous approaches, especially in a low temperature or cryogenic setting because the measurement causes very little power dissipation. A balanced bridge measurement is used to achieve the benefits of an absolute measurement of the position of the movable electrode, while maintaining benefits usually ascribed to incremental encoders, such as high precision and long range encoders. The present disclosure is particularly useful in a rotational or linear bearing stage, or flexure bearing stage, and especially for cryogenic applications where high- performance displacement measurement with low heat dissipation is required. The present disclosure provides a displacement measurement that has the combined benefits of both typical absolute and incremental position capacitance-based measurements of high precision, long range, and absolute measurement. A balanced bridge has excitation on each end that is proportional to the value of each impedance in the bridge when a center value is 0. In a balanced capacitance bridge, the impedances are made up of capacitance. Figure 1 shows a bridge schematically, including excitation sources, with a measurement point labelled node 3 at a center of the bridge. Figure 2 shows the capacitance bridge connected to two of many possible amplifier arrangements to facilitate measuring the bridge. In the present disclosure, we are concerned with using capacitance to measure a position. To achieve that end, in Figures 1, 2 and 5, node 3 in each of the schematics represents a middle electrode of the bridge that is moveable relative to the electrodes at node 1 and node 2. A movable middle electrode at node 3 causes capacitance values of both a first capacitor ^^^and a second capacitor ^^ଶto vary with the location of the middle electrode relative to the electrodes at nodes 1 and 2. Therefore a measurement of both ^^^and ^^ଶis equivalent to measuring the position of the middle electrode. The three-electrode capacitor can be arranged so that movement of the center electrode changes the capacitance bridge values due to changing overlapping areas of the electrodes (Figure 2) or by changing a gap between the electrodes (Figure 3). The present disclosure uses a balanced bridge measuring method where the center node of the circuit is set to zero by separately adjusting the excitation at the ends of the capacitance bridge, labeled V1 and V2 in Figure 1, to determine the bridge capacitances, and from the measured capacitances the position of the center electrode is calculated. In principle, using a balanced bridge for calculating the position of the center electrode may have one or more of the following benefits for a position encoder or sensor. 1. Zero output current because of the balanced nature of the bridge. This is particularly applicable to cryogenic applications where even nanowatt power dissipation in the sensor and wiring is undesirable. 2. Insensitive to electrode spacing in an area variation sensor because the output current is zero [Baxter page 42-44]. 3. The adjustment factor A is proportional to ^^^ െ ^^ଶ so it can have a linear outputwith area variation sensors in a bridge configuration and a low impedance input amplifier. (This achieves something like (Baxter, 1997) equation 3.6 on page 43, but with a low impedance amplifier) The input for the amplifier is guarded by ground, unlike a high impedance amplifier in (Baxter, 1997) page 54. This is particularly applicable to cryogenic applications because a sensor is located remotely from electronics, and it greatly simplifies wiring that is required to connect to the sensor. 4. Does not require floating the exciting voltage as described in (Baxter, 1997) pages 55, 56 and 164, to get the advantages of a feedback amplifier configuration. 5. The output would normally saturate with high amplification and a small movement of the sensor. But the presently disclosed apparatus and method maintain a zero output to accommodate theoretically unlimited ranges of motion with some practical limitations. 6. The amplifier output is zero, so it is less susceptible to amplifier gain and linearity errors, or signal measurement errors downstream, such as ADC gain and linearity errors. In one embodiment of the present disclosure, the excitation on both ends of the capacitance bridge uses a common adjustment factor to balance the signal. This is shown in Figure 4 where the excitation includes adjustment factor ^^ that is common to both ends of the bridge. In these circuits there is a fixed nominal excitation level ^^ that is also common to both ends of the bridge. It can be shown for both circuits in Figure 4 that if the bridge is balanced by adjusting ^^ so that node 3 is set to 0 V, then we have ^^^ ^ ^^^^^^ ൌ ^^^ െ ^^^^^ଶ [1]And if we solve for ^^ we have ^^ െ ^^^ ൌ ^^ ^ ^ଶ[2] ^^^ ^ ^^ଶFrom this we can see that we to ^^^ െ ^^ଶ and it is in the form of a over-sum an areasuch as in Figure 2. In the present disclosure, ^^^and ^^ଶvary with the changing position the center electrode at node 3. The adjustment factor ^^ can either be measured, or assumed to be known because it is applied to the circuit and the position of the middle electrode is proportional to ^^. In another embodiment of the present disclosure, a capacitance bridge circuit has independent excitation levels for each end of the bridge, such as the circuits in Figure 1 where they are labeled ^^^and ^^ଶ. If the bridge is balanced by adjusting ^^^and ^^ଶso that node 3 is set to 0 V, then we have ^^^^^ଶ[3] ൌ ^^ଶ^^^We can see that the excitations ^^^and ^^ଶare proportional to each capacitance ^^ଶand ^^^respectively. The excitations ^^^and ^^ଶcan either be measured, or assumed to be known because they are applied to the circuit. Then the position of the center electrode can be calculated using the excitations directly. For an area variation sensor as an example, the position can be calculated as ^^^^^^^^^^^^^^^^^^ ൌ ^ െ ^^ଶ[4] ^^^ ^ ^^ଶThere are embodiments of a full circuit for performing balanced bridge capacitance measurement discussed in the following paragraphs. In a preferred embodiment of the present disclosure, the bridge excitations are generated by separate digital-to-analog converters (DACs) connected to a processing unit or controller, shown in Figure 6. The DACs are connected to the ends of the capacitance bridge, and there is an amplifier connected to the center of the bridge at node 3. As mentioned previously, node 3 in the present disclosure is movable relative to nodes 1 and 2. Then the signal at the amplifier can be used by the controller as a measurement of the state of the bridge to determine if it is balanced via an analog-to-digital converter (ADC). The controller adjusts the excitation level from the DACs until the signal from the middle electrode is near zero. In practical applications, signal levels on the order of hundreds of millivolts or less are useful and are considered to be near zero. In another preferred embodiment of the present disclosure, an excitation is generated by a single DAC connected to a controller and the excitation is passed through separate multiplying DACs. In this embodiment the excitation level at each end of the bridge is controlled by the multiplying DACs to balance the signal at the middle electrode. This configuration is shown in Figure 7. The excitation levels in Figures 6 and 7 can be measured by the controller via extra ADCs connected to the outputs of each DAC, or since the controller is controlling the DACs the setpoint of the DACs can be used directly as the excitation levels. In all the previously discussed embodiments, the controller can be a microcontroller, field programmable gate array, programmable logic controller, computer, or anything else suitable for interfacing and controlling a DAC to generate an excitation, or an ADC to measure an electrical signal. Now we will discuss embodiments of the electrodes inside movable stages that are connected to a balanced bridge measurement circuit. In one preferred embodiment of the present disclosure, the electrodes corresponding to nodes 1 through 3 in the previous Figures may be mounted in a linear bearing stage. The electrodes can be any of many possible physical forms and arrangements, but in this preferred embodiment they are flat conductive metal arranged in a capacitance bridge where the capacitance varies with overlapping area of the electrodes, shown in Figure 8 and Figure 9. Figure 8 has the bearings removed to show the electrodes better. The linear bearing stage or flexure stage has two electrodes mounted to the stationary base of the stage, and a third electrode mounted to the movable carrier of the stage. The electrodes on the stationary base correspond generally to nodes 1 and 2, and the movable electrode corresponds to node 3 in the previous circuit diagrams. Similar to the linear bearing stage, electrodes can be mounted to a rotational stage. Figure 10 shows a preferred embodiment where two electrodes are mounted to a stationary base and a third electrode is mounted to a movable carrier of the stage. The movable carrier rotates relative to the stationary base and the bridge capacitances vary according to the angle of rotation. Note that within the stage embodiments it is just as valid to switch the two electrodes to be on the movable carrier and the single electrode to be on the stationary base. It is also just as valid to arrange the electrodes such that movement of the carrier causes capacitance variation due to changing the distance between the electrodes, i.e. changing the electrode gap, instead of changing the overlapping electrode area. In all these preferred embodiments where the electrodes are mounted in movable stages, the capacitance measurements via the balanced bridge circuit are converted to a real position measurement of the middle electrode by the controller. The excitation levels at the ends of the bridge can be used directly to calculate position in the manners previously discussed. In a preferred embodiment, the controller can be interfaced to a means to automatically move the carrier, and a positioning system with the following characteristics may be achieved. 1. Absolute position (non-incremental) 2. High precision 3. High resolution 4. Low power dissipation These characteristics are especially useful in cryogenic applications where movable stages are required to have high precision and it is highly preferable to have low power dissipation with the presently disclosed apparatus and method. A capacitance measurement is capable of several orders of magnitude lower power dissipation than other position measurement techniques that involve resistive or optical measurements of a comparable performance. As used herein, the terminology “processing unit” and “controller” include any suitable device or apparatus to carry out various aspects of the presently disclosed method. In one example, the controller may receive input data and instructions from a user, a computer, another controller, or the like, process the received input in light of stored software and / or data, and transmit output signals to the balanced bridge. Conversely, in another example, the controller may receive input signals from the balanced bridge, processes the received input signals in light of stored data and software, and transmit output data to the user, a computer, another controller, or the like. The controller may include, for example, an electrical circuit, an electronic circuit or chip, and / or a computer. The controller generally may include memory, a processor coupled to the memory, one or more interfaces coupled to the processor, one or more input devices coupled to the processor, and / or one or more output devices coupled to the processor. Of course, the controller further may include any ancillary devices, for example, clocks, internal power supplies, and the like (not shown). Although not shown, the controller may be supplied with electricity by an external power supply, for example, an AC to DC transformer, one or more batteries, fuel cells, and the like. The processor may process data and execute instructions that provide at least some of the functionality for the presently disclosed apparatus. As used herein, the term instructions may include, for example, control logic, computer software and / or firmware, programmable instructions, or other suitable instructions. The processor may include, for example, one or more microprocessors, microcontrollers, discrete logic circuits having logic gates for implementing logic functions on data signals, application specific integrated circuits with suitable logic gates, programmable or complex programmable logic devices, programmable or field programmable gate arrays, and / or any other suitable type of electronic processing device(s). The memory may include any computer readable medium or media configured to provide at least temporary storage of at least some data, data structures, an operating system, application programs, program modules or data, and / or other computer software or computer-readable instructions that provide at least some of the functionality of the system and that may be executed by the processor. The data, instructions, and the like may be stored, for example, as look-up tables, formulas, algorithms, maps, models, and / or any other suitable format. The memory may be in the form of removable and / or non-removable, volatile memory and / or non- volatile memory. Illustrative volatile memory may include, for example, random access memory (RAM), static RAM (SRAM), dynamic RAM (DRAM) including synchronous or asynchronous DRAM, and / or the like, for running software and data on the processor. By way of example, and not limitation, the volatile memory may include an operating system, application programs, other memory modules, and data. Illustrative non-volatile memory may include, for example, read only memory (ROM), erasable programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), dynamic read / write memory like magnetic or optical disks or tapes, and static read / write memory like flash memory, for storing software and data. Although not separately shown, the controller may also include other removable / non-removable volatile / non-volatile data storage or media. For example, the other media may include dynamic or static external storage read / write device(s). Finally, the subject matter of this application is presently disclosed in conjunction with several explicit illustrative embodiments and modifications to those embodiments, using various terms. All terms used herein are intended to be merely descriptive, rather than necessarily limiting, and are to be interpreted and construed in accordance with their ordinary and customary meaning in the art, unless used in a context that requires a different interpretation. And for the sake of expedience, each explicit illustrative embodiment and modification is hereby incorporated by reference into one or more of the other explicit illustrative embodiments and modifications. As such, many other embodiments, modifications, and equivalents thereto, either exist now or are yet to be discovered and, thus, it is neither intended nor possible to presently describe all such subject matter, which will readily be suggested to persons of ordinary skill in the art in view of the present disclosure. Rather, the present disclosure is intended to embrace all such embodiments and modifications of the subject matter of this application, and equivalents thereto, as fall within the broad scope of the accompanying claims.

[0002] References Bai, Y. (2016). Absolute Position Sensing Based on a Robust Differential Capacitive Sensor with a Grounded Shield Window . Sensors. Bargen, D. (1967). US Patent No. US3510696A. Baxter, L. (1997). Capacitive Sensors Design and Applications. IEEE PRESS. Cagdaser, B. (2013). US Patent No. US20140266256A1. Fleming, A. (2013). A review of nanometer resolution position sensors: Operation and performance. Sensors and Actuators A: Physical, 106-126. Foley, A. (1947). A Self-Balancing Capacitance Bridge. Transactions of the American Institute of Electrical Engineers, 797 - 801. Frick, R. (1983). US Patent No. US4519253A. Gerber, J. (1978). US Patent No. US4167697A. Haritonidis, J. (1988). US Patent No. US4896098A. Kimura, A. (1980). US Patent No. US4357834A. Kleven, L. (2007). US Patent No. US20070227253A1. Knoedgen, H. (2004). US Patent No. US20050134292A1. Knoedgen, H. (2008). US Patent No. US20100097015A1. Liu, X. (2016). A New Capacitive Displacement Sensor With Nanometer Accuracy and Long Range. IEEE Sensors Journal, 2306 - 2316. Liu, X. (2018). A High Precision Capacitive Linear Displacement Sensor with Time-Grating that Provides Absolute Positioning Capability Based on a Vernier-Type Structure . Applied Sciences. Netzer, Y. (1999). US Patent No. US6492911B1. Ossart, F. (2005). US Patent No. US20080231292A1. Ossart, F. (2006). US Patent No. EP8149002B2. Parnell, J. (1970). US Patent No. US3668672A. Parnes, A. (1964). US Patent No. US3312892A. Petkov, V. (2011). US Patent No. EP2751580B1. PI-USA. (2023). Linear Piezo Stages for Nanopositioning (Flexure Guided). Retrieved from PI- USA: https: / / www.pi-usa.us / en / products / piezo-flexure-nanopositioners / x-linear-piezo- flexure-nanopositioning-stages Reddi, M. (1999). US Patent No. US6366099B1. Roziere, D. (2002). US Patent No. US20060097733A1. Ruesch, J. (1981). US Patent No. US4381677A. Sämann, R. (2011). EP Patent No. EP2697609B1. Tamura, H. (1984). US Patent No. US4644798A. Thorlabs. (2023). Linear Z-Axis Stage Driven by an Amplified Piezo Motor. Retrieved from Thorlabs: https: / / www.thorlabs.com / newgrouppage9.cfm?objectgroup_id=11246 Towner, G. (1968). US Patent No. US3522528A. Turner, R. (1967). Bridges and other Null Devices. Indianapolis: Howard W. Sams & Co., Inc. Wang, R. (2001). US Patent No. US6509746B1. Weber, J. (1998). US Patent No. US6486681B1. Wocher, B. (1991). US Patent No. EP0459118B1.

Claims

Claims1. A capacitive position sensor, comprising:a capacitance bridge including at least one first electrode, and at least two second electrodes; and a balanced bridge circuit to separately adjust excitation of the at least two second electrodes to balance a signal at the at least one first electrode toward a desired target value, wherein a level of the excitation is used as input to calculate a position of the at least one first electrode relative to the at least two second electrodes.

2. The capacitive position sensor of claim 1, wherein the balanced bridge circuitautomatically balances the signal at the at least one first electrode toward the desired target value while there is relative movement between the at least one first electrode and the at least two second electrodes.

3. The capacitive position sensor of claim 2, wherein the position of the at least one firstelectrode relative to the at least two second electrodes is used to move a bearing stage or a flexure stage to a desired position.

4. The capacitive position sensor of claim 1, wherein the desired target value is zero.

5. The capacitive position sensor of claim 1, wherein the at least one first electrode is amovable electrode and the at least two second electrodes are stationary electrodes.

6. The capacitive position sensor of claim 1, wherein the balanced bridge circuit adjusts the level of the excitation using a common adjustment factor (A) to balance the signal, wherein a fixed nominal excitation level (V) is common to both ends of the capacitance bridge, which has a first capacitance (C1) and a second capacitance (C2), wherein ^^ ^^ ^^^ െ ^^ଶand wherein A is at least one ofto be known.

7. The capacitive position sensor of claim 1, wherein each end of the capacitance bridge hasindependent excitation values ^^^and ^^ଶ, wherein the balanced bridge circuit adjusts ^^^and ^^ଶso that the signal is set to 0 V, then ^^^^^ ൌଶ^^ଶ^^^wherein the excitations ^^^and ^^ଶis of measure or assumed to be known, andwherein a position of the first calculated using the excitations directly.

8. The capacitive position sensor of claim 1, wherein the balanced bridge circuit adjusts theexcitations by separate digital-to-analog converters (DACs) connected to a controller and connected to ends of the capacitance bridge, and an amplifier connected to a center of the bridge and providing a signal used by the controller as a measurement of a state of the bridge to determine if the bridge is balanced via an analog-to-digital converter (ADC), wherein the controller adjusts the level of the excitation from the DACs until the signal from the center of the bridge is zero or about zero.

9. The capacitive position sensor of claim 1, wherein the balanced bridge circuit adjusts the excitations by a single DAC connected to a controller, wherein the excitations are passed through separate multiplying DACs, wherein the levels of the excitation at each end of the capacitance bridge are controlled by the multiplying DACs to balance the signal at a center of the bridge.

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