Patent Publication Number: US-2023152346-A1

Title: Capacitance sensing method and assembly

Description:
RELATED APPLICATIONS 
     The present application claims priority from Australian provisional patent application No. 2021903674, filed Nov. 16, 2021, the content of which is hereby incorporated in its entirety by reference. 
     TECHNICAL FIELD 
     The disclosed subject matter relates to a capacitance sensing assembly for use with accelerometers gravimeters, gravity gradiometers and other instruments and appliances where it is necessary to sense a physical parameter. The disclosed subject matter also relates to methods for improving sensitivity of capacitive sensing assemblies. 
     BACKGROUND 
     Any references to methods, apparatus or documents of the prior art are not to be taken as constituting any evidence or admission that they formed, or form part of the common general knowledge. 
     A capacitor becomes a variable capacitor when one of its electrodes is free to move under external disturbances and another one is fixed. Their relative motion changes the value of the mutual capacitance acting as the measure of the external factors causing the disturbances. A capacitor can also change its value if electric charge is applied to one of the capacitor&#39;s electrodes. Such capacitors are called varactors or “varicaps”. By measuring this particular capacitance change it is possible to measure applied electric field. The change of the capacitive value should be translated into a measurable quantity—audio, RF, microwave, optical signals&#39; amplitude, or phase. Phase is more desirable quantity as the primary sensing elements (capacitance-to-phase transducers) can be incorporated into interferometric read-out where one arm of an interferometer contains the variable capacitor, and another contains a fixed one. Interferometric measurements provide the most sensitive instrumentation for the detection of ultra-small phase difference in the identical carrier signals propagating through the interferometer&#39;s arms. 
     The ability to measure minute variations of electric capacitance leads to a large number of academic and industrial applications including fundamental research and defense. 
     For example, in the paper A High Precision Method for Measuring very Small Capacitance Changes by Ashkan Ashrafi and Hossein Golnabie (Review of Scientific Instruments Vol 70, No. 8 Aug. 1999) the authors describe a method for measuring very small capacitance changes based on capacitance-to-phase angle conversion. The method involves using a conventional quadrature phase sensitive detector (PSD) that provides the cotangent of the output phase in order to arrive at a linear relationship between the input capacitance and the output of the PSD. Implementation of the method is believed to be complex, and the Authors reported instabilities in their readout system that they believed were due to jitter in the main oscillator which would require a very stable oscillator to address. 
     Not all methods and apparatus to measure minute variations of electric capacitance allow for the use of grounded variable capacitors, which is desirable for most applications of interest. Matko and Milanovic&#39; ( Temperature - compensated capacitance—frequency converter with high resolution ; Sensors and Actuators A 220 (2014) 262-269) described a temperature-compensated capacitance-to-frequency converter with a claimed resolution of +/−20 Zeptofarads (zF, 1 zF=10 −21  Farad). However, this approach uses a not-grounded variable capacitor and cannot be easily adapted for, say, ultra-precision mechanical displacement measurements. Also, a high Q resonant LC-tank can be used as a simple circuit for either amplitude or phase sensitive ultra-small capacitance variation detection ( Measurement of weak forces in physics experiments /V. B. Braginsky and A. B. Manukin; edited by David H. Douglass; Chicago: University of Chicago Press, 1977). Typically, it involves very high Q (Q&gt;&gt;100) values and represents a narrow-band detector where extremely high stability of its operation point is required. 
     Devices based on variable capacitors have been under development for many decades in such areas as precision accelerometry, gravimetry and gravity gradiometry. Precision accelerometers based on the MEMS technology have established their presence almost everywhere from smartphones and robotics to strategic defense applications and space missions. Consequently, there is a need for a capacitance sensing assembly that is relatively straightforward and thus compact to implement and which can measure capacitance variations. 
     SUMMARY 
     According to a first aspect of the disclosed subject matter, there is provided a capacitance sensing assembly comprising:
         an all-pass filter including an op-amp and a first capacitor with a first electrode of the first capacitor connected to a non-inverting input of the op-amp; and   a complex impedance circuit connected between a second electrode of the first capacitor and a ground and including a variable capacitor having a terminal connected to the ground;   wherein the complex impedance circuit is configured to increase a gradient of a phase to frequency response curve of the capacitance sensing assembly relative to that of the all-pass filter with the second electrode of the first capacitor connected to ground without the complex impedance circuit.       

     In an embodiment the complex impedance circuit comprises a resonant circuit wherein the variable capacitor comprises a capacitor of the resonant circuit. 
     In an embodiment the resonant circuit comprises an inductor-capacitor tank circuit. 
     In an embodiment the variable of the resonant circuit is implemented with a capacitance magnifier circuit to thereby simulate a larger capacitance value variable capacitor with a smaller capacitance value variable capacitor. 
     In an embodiment the complex impedance circuit comprises a negative capacitor circuit. 
     In an embodiment the negative capacitor circuit includes a second capacitor in parallel with the negative capacitor sensor. 
     According to a further aspect there is provided a capacitor sensing assembly wherein a variable capacitor thereof comprises a component of a resonant circuit. 
     In another aspect there is provided a capacitor sensing assembly wherein a variable capacitor thereof comprises a component of a capacitor multiplier circuit. 
     In a further aspect there is provided a capacitor sensing assembly wherein a variable capacitor thereof comprises a component of a negative capacitance circuit. 
     In a further aspect there is provided a method for improving sensitivity of a capacitor sensing assembly, the method comprising:
         replacing a variable capacitor (“first variable capacitor”) of the capacitor sensing assembly with a capacitor multiplier circuit, the capacitor multiplier circuit including a variable capacitor (“second variable capacitor”) wherein the second variable capacitor has a smaller capacitance than the first variable capacitor.       

     In an embodiment the capacitor multiplier circuit forms part of a resonant circuit. 
     In another aspect there is provided a method for improving sensitivity of a capacitor sensing assembly having a first capacitor, the method comprising:
         connecting a negative capacitance in series with the first capacitor to thereby produce an effective variable capacitance having a capacitance value less than the first capacitor.       

    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Preferred features, embodiments and variations the subject matter disclosed herein may be discerned from the following Detailed Description which provides sufficient information for those skilled in the art to perform the disclosed subject matter. The Detailed Description is not to be regarded as limiting the scope of the preceding Summary of the disclosed subject matter in any way. The Detailed Description will make reference to a number of drawings as follows: 
         FIG.  1    is a circuit diagram of a capacitively grounded all-pass filter. 
         FIG.  2    is a graph of the phase response of the all-pass filter of  FIG.  1    for three sets of component values. 
         FIG.  3    shows the circuit of  FIG.  2    with a complex impedance circuit block inserted between the capacitor and ground. 
         FIG.  4    shows a capacitive sensing circuit wherein the complex impedance circuit block comprises a tank circuit. 
         FIG.  5    is a phase response graph for the circuit of  FIG.  4    over a range of frequencies. 
         FIG.  6    is a gain response graph for the circuit of  FIG.  4    over the range of frequencies. 
         FIG.  7    is an oscilloscope trace of the phase response graph of the circuit of  FIG.  4    for a set of component values. 
         FIG.  8    is an oscilloscope trace of the gain response graph of the circuit of  FIG.  4    for the set of component values. 
         FIG.  9    is circuit of an exemplary capacitance magnifier. 
         FIG.  10    is a circuit that is simulated by the capacitance magnifier circuit of  FIG.  9   . 
         FIG.  11    is a capacitive sensing circuit wherein the complex impedance circuit block comprises the capacitance magnifier circuit. 
         FIG.  12    is a capacitive sensing circuit wherein the complex impedance circuit block comprises a negative capacitor. 
         FIG.  13    is a capacitive sensing circuit wherein the negative capacitor is implemented with an op-amp circuit. 
         FIG.  14    is a capacitive sensing circuit wherein the complex impedance circuit includes a bias capacitor. 
     
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
       FIG.  1    is a circuit schematic of an all-pass filter  3  which has a capacitor C connected by its electrode  7   a  to the non-inverting input  9  of the op-amp  5  and by its opposite electrode  7   b  to ground  11 . All-pass filters have no amplitude roll-off properties. That is, the magnitude of the signal at the output of an all-pass filter does not change with change in frequency of the input of the all-pass filter. 
     However, the all-pass filter exhibits phase-shift properties. 
     The transfer function of all-pass filter  3  is: 
     
       
         
           
             
               
                 
                   
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     so that the amplitude versus frequency response is flat. 
     The phase shift is: 
       φ=−2 arctan(ω R   1   C )  (2)
 
       FIG.  2    is a graph illustrating the phase difference to frequency relationship of the all-pass filter  3  for R=1Ω, C=0.01 μF and three different values of R 1 . 
     The inventor has recognized that all-pass filter  3  is suited to capacitive sensing since it makes use of a grounded capacitor, which can be implemented as a moving plate capacitor or other variable type capacitor that requires grounding. Capacitive sensing typically uses a grounded capacitor. Unfortunately, the Inventor has found that the capacitance-to-phase conversion that is exhibited is not suitable for detecting small changes in capacitance, for example due to small capacitor electrode movements. This can be understood by contemplating the phase shift relationship set out in Eqn (2) and illustrated in the graph of  FIG.  2   . In particular, a change in the size of C in Eqn (2) does not make a very significant difference to the change in phase shift. Consequently, whilst the topology of the circuit of  FIG.  1    is promising as a starting point for building a capacitive sensor, it is of insufficient sensitivity for the very fine sensing that is desired. The Inventor has striven to provide an improvement that can increase the sensitivity so that it is possible to detect very small capacitance variations and thus the physical perturbations that cause them and which it is desired to be able to measure. 
     In overview, in a first embodiment a capacitance sensing assembly  6  ( FIG.  3   ) is provided which includes a typical all-pass filter  3 . The all pass filter  3  includes an op-amp  5  and a first capacitor C with a first electrode  7   a  of the first capacitor C connected to a non-inverting input  9  of the op-amp  5 . A complex impedance circuit Z is connected between a second electrode  7   b  of the first capacitor C and ground  11 . The complex impedance circuit Z includes a variable capacitor C 0  having an electrode  13   b  connected to the ground  11 . The complex impedance circuit Z is configured to increase a gradient m of a phase-to-frequency response curve of the capacitance sensing assembly at a predetermined operating point OP. The complex impedance circuit Z increases the gradient m relative to that of the all-pass filter  3 , with the second electrode of the first capacitor C connected to ground, as shown in  FIG.  1   . 
     In an embodiment of a capacitance sensing assembly  8  that is illustrated in  FIG.  4   , the complex impedance circuit Z comprises a resonant circuit  15  and the variable capacitor C 0  comprises the capacitor C 0  of the resonant circuit  15 . 
     In the capacitive sensing circuit  8  of  FIG.  4    the resonant circuit  15  comprises an inductor-capacitor tank circuit which includes an inductor L in parallel with the variable capacitor C 0 . 
     With reference to the capacitance sensing assembly  10  of  FIG.  11   , the variable capacitor C 0  of the resonant circuit  15  (of  FIG.  4   ) may be implemented with a capacitance magnifier circuit  17  to thereby simulate a larger capacitance value variable capacitor with a smaller capacitance value variable capacitor C 00 . 
     In another embodiment, a capacitance sensing assembly  12  ( FIG.  12   ), the complex impedance circuit Z comprises a negative capacitor −C 0 . As shown in  FIG.  13   , the negative capacitor −C 0  may implemented with a negative capacitor simulating circuit  21  including an op-amp  19  and resistors, R 2 , R 3  and variable capacitor C 0 . 
     In a further embodiment illustrated in  FIG.  14   , the capacitance sensing assembly the negative capacitor circuit includes a second capacitor C 2  in parallel with the negative capacitor circuit for reducing a fixed (bias) portion of the capacitance of the variable capacitor C 0 . 
     Referring now again to  FIG.  4    circuit  8  incorporates a complex impedance circuit block Z in the form of a low-Q resonant tank circuit  15  comprising parallel inductor L and variable capacitor C 0 . 
       FIGS.  5  and  6    are circuit simulation plots showing respectively the phase shift response and the magnitude response of the capacitive sensing circuit  8  at a predetermined operating point OP for a fixed carrier frequency. 
     It will be observed that the addition of the tank circuit  15  makes the phase curve very steep in the vicinity of the fixed carrier frequency. The Inventor has found that a very small change in the value of the variable capacitor C 0 , for example as might be caused by minute change in distance between the electrodes of C 0  due to a physical parameter being sensed, causes a large change in the phase response as indicated by the very steep gradient of tangent m of the graph at OP. 
       FIGS.  7  and  8    are oscilloscope traces for the sensing circuit of  FIG.  4    where the component values are as follows:
         R=100 Ohm, R 1 =220 Ohm   C=6-30 pF tuneable airgap capacitor   L=100 μH, high quality factor inductor   C 0 ˜10-15 pF   and the RF signal carrier frequency is 2.806 MHz.       

     Referring now to  FIG.  9   , a capacitor multiplier circuit  2 , for example as is sometimes used to filter ripple in the output an AC-DC converter, is illustrated. The capacitor multiplier circuit  2  of  FIG.  9    uses an op-amp and a small capacitor C a  to simulate a much larger capacitor C b  as shown in the circuit  4  of  FIG.  10   . Capacitor multiplier circuit  2  simulates circuit  4 . The resistor Rb in circuit  2  is the same size as the resistor Rb in the circuit  4  being simulated ( FIG.  10   ), but the capacitor C a  in  FIG.  9    is only one hundredth the size of the capacitor C b  in  FIG.  10   . 
     The operation of the capacitor multiplier circuit  2  of  FIG.  9    will now be explained. Current flows from the input source through R a  to the capacitor (C a ). Since R a  is 100 times larger than R b , there is 1/100th the current through it into the capacitor C a . For a given input voltage, the rate of change in voltage in C a  is the same as in C b , because C b  has 100 times the capacitance to make up for 1/100th the current. 
     Therefore, the voltages across C a  and C b  are the same, but the currents are not. The op-amp in  FIG.  9    causes the negative input to be held at the same voltage as the voltage across C a . Consequently, R b  of  FIG.  9    has the same voltage across it as R b  of  FIG.  10   , and therefore the same current. 
       FIG.  11    depicts a capacitance sensing assembly  10  according to a further embodiment wherein the variable capacitor C 0  of the tank circuit of the capacitive sensing circuit of  FIG.  4    has been replaced with capacitor multiplier circuit  17  that uses a variable capacitor C 00  which, according to the selection of R 3  and R 2 , is a fraction of C 0 . Consequently, the capacitance sensing assembly of  FIG.  11    has improved sensitivity compared to the first embodiment 8 of  FIG.  4   . 
       FIG.  12    depicts an equivalent circuit of a further embodiment of a capacitive sensing circuit  12  where the effective capacitance is: 
     
       
         
           
             
               
                 
                   
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     If the difference between the positive and the negative capacitors, connected in series, is small, this can magnify the effective capacitance by orders of magnitude. In turn, this will magnify any change in the negative grounded capacitor by the same amount. That what we want in order to increase the effectiveness of the capacitive sensing. This will also allow for a reasonably low frequencies to be used for further signal processing, compared to that of microwave case. The power required to feed the circuit is negligible compared to the latter one. This type of sensing perfectly fits into a Mach-Zehnder interferometry and flip-flop phase detectors in which an overall sensing capacitance C s  is reduced to a value of C 1 +(−C 0 ) where −C 0  is a negative capacitance. 
     The negative capacitance is implemented using a negative capacitance op-amp circuit  21  as shown in  FIG.  13   . Negative capacitance op-amp circuits are analogous to the more widely known negative resistance circuits and are discussed for example at: https://en.wikibooks.org/wiki/Circuit_Idea/Revealing_the_Mystery_of_Negative_Impedance#Op-amp_implementation (retrieved Jul. 11, 2021). 
       FIG.  14    depicts another embodiment wherein the constant part of the variable capacitor (−CO) (its bias) is reduced by placing capacitor C 2  in parallel with the −CO circuit to highlight its variable part: −C 0 +C 2 −ΔC 0 , C 2 &lt;|C 0 | 
     The Inventor believes that various of the embodiments discussed herein provide a low cost and size capacitance sensing assembly for measuring capacitance variations in moving plate capacitors as low as &lt;10-20 Farad (0.00001 femtoFarad). Consequently, very small movements of the electrode, e.g. the grounded electrode of the variable capacitor may be sensed and so correspondingly, very small movements and accelerations of physical objects to which the grounded electrode is attached. Also, a very small electric field of much less than a microvolt per metre magnitude can be detected if the variable capacitor comprises a varicap. 
     In compliance with the statute, the subject matter disclosed herein has been described in language more or less specific to structural or methodical features. The term “comprises” and its variations, such as “comprising” and “comprised of” is used throughout in an inclusive sense and not to the exclusion of any additional features. It is to be understood that the subject matter disclosed herein is not limited to specific features shown or described since the means herein described comprises preferred forms of putting the disclosed subject matter into effect. The disclosed subject matter is, therefore, claimed in any of its forms or modifications within the proper scope of the appended claims appropriately interpreted by those skilled in the art. 
     Throughout the specification and claims (if present), unless the context requires otherwise, the term “substantially” or “about” will be understood to not be limited to the value for the range qualified by the terms. 
     Any embodiment herein is meant to be illustrative only and is not meant to be limiting. Therefore, it should be appreciated that various other changes and modifications can be made to any embodiment described without departing from the spirit and scope of the subject matter disclosed herein.