Capacitive sensor and electronic circuit for non-contact distance measurement
BACKGROUND OF THE INVENTION 
     This invention relates generally to electronic non-contact distance measuring systems and the electronic circuitry employed therewith. More particularly, this invention relates to a novel electronic capacitive gap measuring transducer and a novel circuit termed a twin tee synthetic resonance circuit which may be used in conjunction with the measuring transducer. 
     There has been a continuing need for efficient and accurate devices capable of measuring gap widths or clearances without contact between spaced boundaries of a gap. For example, the difficulties of measuring the clearance gap between two plates has long plagued the art of metrology. The simple and known technique of inserting the &#34;just fits&#34; stacks of calibrated &#34;feeler&#34; shims has the disadvantage of contact inaccuracies as well as being a time consuming, non-electrical output measurement. Thus, the problem of verifying alignment of an automobile door often still requires a caliper measurement of clay daubs which have been squashed in the gap. 
     Prior art electronic devices are known to accomplish such contactless gap measurements. In these prior measurement systems, electromagnetic induction phenomena has often been employed to sense proximity or distance changes between a transducer and a metal object. Such measurement systems are useful in a wide variety of applications particularly where it is impossible or undesirable that there be physical contact with the object defining the distance to be measured. Other applications include pressure transducers, accelerometers, electronic micrometers, dimension comparators, bore gages, limit gages and liquid metal level detectors. 
     Previous electromagnetic induction measuring systems have not achieved the degree of accuracy and stability necessary for concise and accurate distance measurements. Certain limitations have restricted the development of these prior art systems, such as the difficulty in obtaining sufficient sensitivity and resolution over the effective measurement range of the system. This limitation results from the failure of the prior art systems to distinguish between the magnetic properties of the object and to compensate for these properties. Another limitation has been error caused temperature variations. Temperature changes cause impedance changes in the object and in the inductive distance measuring components of the system, and these impedance changes are reflected as a change in distance when in reality no such change may have occurred. A further problem with prior art systems has been that of non-linearity. 
     U.S. Pat. No. 4,160,204, which is assigned to the assignee hereof and incorporated herein by reference, relates to an improved non-contact measuring distance system which exhibits high sensitivity and resolution over the effective measurement range of the system, is virtually insensitive to variations in temperature and provides a high degree of linear relationship between the output provided and the distance to be measured. The measuring system of Patent No. 4,160,204 generally comprises a high frequency signal source, an inductive transducer and a reference impedance (both connected in a signal phase network and to the source), and a means for comparing the signals from the transducer and the reference impedance to provide an output related to the distance between the transducer and the object. A circuit element such as a capacitor is connected in parallel with the transducer for the purpose of enhancing the sensitivity and resolution of the system, for significantly reducing or effectively eliminating errors caused by temperature variations in the transducer or in the object measured, and for providing a high degree of linear relation between the output provided and the distance measured. 
     While well suited for its intended purposes, the inductance sensor measuring system of Patent 4,160,204 does suffer from the drawback that its measurement can be effected by the particular material which define the gap boundaries. This sensitivity to gap boundary composition may adversely affect the accuracy of the measurement system. Also, because the system is based on inductive measurement, the prior art system of Patent 4,160,204 cannot measure gaps where the boundary are not metallic (e.g. such as plastic materials). 
     SUMMARY OF THE INVENTION 
     The above-discussed and other drawbacks of the prior art are overcome or alleviated by the contactless distance measuring apparatus of the present invention. In contrast to the inductive measuring system of Patent 4,160,204, the present invention utilizes capacitance to measure the gap between two boundaries. As a result, the distance measurement provided by this invention can be independent of the gap boundary materials; and can therefore be used to measure gaps in non-metals such as plastics. 
     An important feature of the present invention is a novel thin, three-terminal capacitive transducer which is positioned in the clearance gap to be measured. This transducer comprises an insulated assembly having three parallel conductive planes with the first and second plane each containing a single electrode and the third plane containing a pair of spaced electrodes. Preferably, each electrode is composed of a thin layer of copper mounted on an insulated substrate such as an epoxy-glass composite. An air space is provided between each of the pair of electrodes in the third plane and the single electrode in the second plane. 
     Another important feature of the present invention is a novel electronic circuit for use in conjunction with the novel three terminal capacitive transducer. This circuit provides a means of &#34;synthetic resonance&#34; whereby a small capacitance (such as the three-terminal capacitive sensor of this invention) functions as if it were at or near series resonance with a synthesized large inductance. This is achieved by using a synthesized network (which is a variation of a known twin-tee circuit) in the feedback path of a high gain amplifier, thereby inverting the normal rejection notch into a resonance-like peak at a frequency determined by the equation: ##EQU1## where C input arm capacitance of first &#34;tee&#34; branch 
     C 2  =input arm capacitance of second &#34;tee&#34; branch 
     C 3  =output arm capacitance of second &#34;tee&#34; branch 
     L middle leg inductance of second &#34;tee&#34; branch 
     The novel synthetic resonance circuit of this invention may be used in conjunction with instrumentation other than capacitive measurement devices. For example, the synthetic resonance circuit of this invention may be used with inductive sensors of the type disclosed in Patent 4,160,204. 
    
    
     The above-discussed and other features and advantages of the present invention will be appreciated and understood by those of ordinary skill in the art from the following detailed description and drawing. 
     BRIEF DESCRIPTION OF THE DRAWINGS: 
     Referring now to the drawings, wherein like elements are numbered alike in the several FIGURES: 
     FIGS. 1A and 1B are diagrammatic views showing the dielectric field of a capacitive transducer in accordance with the prior art and the present invention, respectively; 
     FIG. 2A is a perspective view of the capacitive transducer of the present invention; 
     FIG. 2B is an electrical schematic diagram of the transducer of FIG. 2A; 
     FIG. 3 is another electrical schematic diagram of the transducer of FIG. 2A; 
     FIG. 4 is a graph depicting capacitance verse distance for the transducer of FIG. 2A; 
     FIG. 5 is an electrical schematic of a known RLC circuit; 
     FIG. 6 is a graph depicting natural series resonance for the RLC circuit of FIG. 5; 
     FIG. 7 is an electrical schematic of a known inductive twin-tee circuit; 
     FIG. 8 is an electrical schematic of a known twin tee bridge circuit; 
     FIG. 9 is an electrical schematic of a twin tee circuit incorporated into the feedback path of a high gain amplifier; 
     FIG. 10 is an electrical schematic of the synthetic resonance circuit of the present invention; 
     FIG. 11 is a graph depicting synthetic resonance for the circuit of FIG. 10; 
     FIG. 12 is an electrical schematic of the inductive leg network; and 
     FIG. 13 is a graph of Lpeq and Rpeq versus temperature. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT 
     Capacitive sensors are known and depend upon the change in dielectric field between electrodes of different potential. Typical prior art capacitive sensors utilize the parallel plate geometry depicted in FIG. 1A at 10. However, in accordance with an important feature of the present invention shown in FIG. 1B, the geometry of the sensor of this invention includes a pair of capacitor plates 12 and 14 which are spaced apart in the same plane to form an arching electrical field 16. It has been found that the electrode configuration of FIG. 1B will maximize the change in dielectric field between the electrodes for more accurate and reliable measurements. 
     Turning now to FIGS. 2A and 2B, the novel capacitive sensor or transducer of the present invention is shown generally at 18. Sensor 18 comprises a pair of spaced electrodes 12 and 14, both of which reside in the same plane. A coupling plate 20 is spaced back from electrodes 12, 14 in a Plane parallel to the electrodes. Suitable members 22 of an insulating dielectric material such as an epoxy-glass composite is positioned between coupling plate 20 and electrodes 14, 16 to define air spaces 24 and 26; and a central channel 28. In addition, a layer of insulating dielectric material 30 is attached to the side of plate 20 which is opposite electrodes 12 and 14. The structure comprising electrodes 14, 16, coupling plate 20 and insulating layers 22 and 30 define an insulating/coupling structure which is attached to a flat zero potential ground plate 32. It will be appreciated that during use, ground plate 32 is placed under the insulating/coupling structure to provide a physical contact reference to one side or boundary of the gap to be measured. Finally, a pair of coaxial cables 34 and 36 are respectively connected to ground plate 32 and electrode 12; and to ground plate 32 and electrode 14. Thus, a capacitive &#34;tee&#34; network is formed which has the &#34;pi&#34; network equivalent of a 3-terminal capacitor and which has the equation: ##EQU2## 
     The above equation (1) is reflected in FIG. 3 which is an equivalent electrical schematic of the sensor of FIGS. 2A and 2B. 
     The capacitive sensor of FIGS. 2A, 2B and 3 provides several significant features and advantages as a result of the novel insulated coupling structure of coupling plate 20 and electrodes 12 and 14. For example, in accordance with the present invention, sensor geometry can be scaled without changing sensor capacitance (Ceq). This is because the relative position of the coupling plate 20 between electrodes 12, 14 and ground plate 32 (together with type and proportion of insulating material selected) control the ratio of C B  to C A . 
     Still another important feature of the capacitive sensor of this invention is that the temperature coefficient of the sensor capacitance (Ceq) can be made zero, even though the dielectric constant of the insulating material 22 has a positive (or a negative) temperature coefficient. Depending upon the ratio of C B  to C A , their relative rates of change with temperature can be adjusted to maintain Ceq constant. This is most easily accomplished by lowering the temperature coefficient of C A  by proportioning the area of air-gap 24, 26 to insulation 22. 
     In a preferred embodiment of the present invention, the sensor coax cables 34 and 36 are connected to the &#34;3 terminal&#34; inputs of a known capacitance bridge (such as the Model 2500 1 kHz Automatic Capacitance Bridge manufactured by Andeen-Hagerling of Chagrin Falls, Ohio); or preferably to the novel &#34;synthetic resonance&#34; circuit described below with reference to FIG. 10. Both of these circuits effectively ignore shunt capacitances (and cable capacitance) to ground and measure only the value of Ceq. 
     Sensor 18 is preferably fabricated from copper-clad epoxy glass circuit board material, dimensioned such that C B  equals 15 pf and C A  is 5 pf. Using these dimensions, Sensor capacitance, Ceq, is then 1 pf. If C A  is proportioned to have the proper area of air-gap to epoxy glass, the high positive temperature coefficient of C B  (denominator) can be ratioed to unity by the lower coefficient of C A . 
     Referring now to FIG. 4, the capacitance change is shown for sensor 18 as the gap to a grounded metal plate varies. The 1 pf sensor capacitance is shown to decrease as the metal plate approaches, effectively reducing the arching dielectric field between electrodes (reducing both C A  &#39;s). 
     It will be appreciated that while FIG. 2A depicts a single pair of coplanar electrodes 12 and 14, the present invention also contemplates the use of multiple coplanar pairs of electrodes having an interleaved configuration. 
     Turning now to FIGS. 5-13, the novel synthetic resonance circuit of the present invention will now be described. As discussed above, this novel circuit is the preferred electronic circuit to be used with the novel capacitive sensor of FIG. 2A. However, it will be appreciated that the synthetic resonance circuit of this invention may also be used in a variety of additional applications. 
     In FIGS. 5 and 6, a simple known RLC network is shown which offers powerful instrumentation development potential for a broad range of physical measurement requirements. If a physical quantity causes one or more of these electrical proportionality constants to vary, the series resonant network provides extremely attractive transduction possibilities. If either L or C is the variable, a very sensitive change in the phase of E o  is detectable (this sensitivity being controlled by R). If R is the variable, the amplitude of E o  is the detectable change. Thus, it is capable of creating either amplitude or phase modulation from the three basic electrical parameters. The limits of application of this relatively simple network usually arise from an inability to combine practical values to satisfy the resonance equations: ##EQU3## If L or C is necessarily small due to the nature of the physical measurement, f may become impractically large or more often, R may become too large (or thermally unstable) to allow a stable sensitivity. 
     A means for overcoming the natural limitations of component values required in the simple network of FIGS. 5 and 6 is therefore highly desirable. A successful approach has been to synthesize a network with electrical behavior equivalent to that of a series resonant circuit but using simple low cost components to generate the properties impossible to obtain from an actual inductor and small capacitor. Instrumentation literature in the 1940&#39;s described a twin-tee network employing a small inductive leg and capable of balancing to a sharp null. The mathematical analysis showed that at null, the network was equivalent to a very large inductor in parallel with a small capacitor. In effect, the actual small shunt inductor had equivalent electrical behavior to a several hundred thousand times larger inductance. Unfortunately, at null no usable signal voltage remains for detection or further processing. However, if this null network is incorporated into the negative feedback path of a high gain amplifier, the signal null can be inverted into a signal peak (removal of negative feedback). The transfer function of this signal &#34;selective&#34; circuit can be shown to be equivalent to that of a natural series resonant network (which would require an impossible inductor). ##EQU4## where φ=phase angle between voltages E o  and E i   
     w=2 πf 
     The traditional inductive twin-tee network (also known as inductive parallel tee network) was configured (as shown in FIG. 7) with two variable capacitors C 1 , and C o  to achieve a zero voltage transfer. As can be seen in FIG. 8, by mathematical conversion of the parallel &#34;tees&#34; to equivalent &#34;pi&#34; networks, the significant characteristics for creating synthetic resonance are more apparent. 
     The equivalent &#34;Pi&#34; transformation include: 
     
         X.sub.L =2πfL ##EQU5## At balance, the actual C is parallel with an equivalent resonating inductance equal to the actual L multiplied by the large ratio: ##EQU6## 
    
     However, it will be appreciated that several aspects of this twin-tee must be reconfigured in order to achieve a practical synthetic resonant circuit. First, the null has to be inverted into an amplitude peak. Referring to FIG. 9, it is noted that if a twin tee network is incorporated into the feedback path of a high gain amplifier, the network&#39;s transfer function will be inverted by the feedback equation. Whereas the twin-tee is normally operated with the null balanced to zero, an infinite resonant peak is neither possible nor desirable. For the twin-tee to function as a feedback network, the null is degraded to approximately -80 db and adjusted to a slightly lower frequency than the desired resonance. Since the null equations are only exact at true balance, they are used as approximations in the resonant loop, with &#34;Q&#34; and the resonant phase angle of -90° determined in practice by providing at least two adjustable twin-tee components. The closed loop transfer function for the feedback equation of FIG. 9 is: ##EQU7## 
     Second, the classical twin-tee must be modified to provide stability against oscillations. Not only must the transfer function be adjusted to provide a +90° phase angle at null, the phase lead at higher frequencies must remain less than +180° in order to avoid regenerative feedback. (A preferred embodiment example with a 1 picofarad capacitive sensor is shown in FIG. 10). Note that R 3  (5 ohm) and Rp (35 ohm) have been incorporated to reduce the Q of the physical inductor L and its coil resistance, R i . Otherwise C 2  and L would form a high Q series resonance at 360 KHZ, resulting in excessive positive phase angle and possible parasitic oscillation. Total loop gain will be a function of all resistors (R 2  /R 1 , R 4  /R 3 , R p , R s , R i , R) and C 1 . Therefore, a convenient adjustment for Q at resonance is potentiometer R. Resonance frequency will be a function primarily of C, L, C 2  and C 3  (with some interaction from the gain determining variables). Rp and Rs also play an important function in the temperature compensation of L&#39;s coil resistance, R i . FIG. 12 shows the inductive leg network and the equivalent Lpeq and Rpeq. FIG. 13 is a graph of the behavior of Lpeq and Rpeq as R i  varies with temperature. Since Lpeq is a resonant frequency variable, its value and rate of change can be controlled by the proportion of temperature stable R s  to R i . Also R p  is selected such that the rate of change of Rpeq will adjust loop gain sufficiently to hold resonant frequency constant as temperature varies. 
     The example of FIGS. 10 and 11 show that a 1 picofarad sensor (such as the type shown in FIG. 2A) will have the equivalent transfer function of 30 KHZ series resonance with a 27.9H synthetic inductor (or approximately 600,000 times the actual inductance). In this case, the sensor has 0.1 (10%) change of capacitor over its displacement range (which results in a 10° phase angle change). In the Example shown in the FIGS. 10 and 11: 
     
         X.sub.L =2πFL=9.1 ohm ##EQU8## 
    
     Although it has been shown that the synthetic resonance circuit of the present invention can be very sensitive to small capacitance change, it should be noted that a similar configuration is of advantage for use with inductive (eddy current) sensors. Thus, when operating with an inductive sensor as the L leg of the twin-tee, the equivalent series inductance is typically a million times L; thereby functioning as a resonant network at a far lower frequency than would normally be possible with such small C and L values. Also, by employing a varactor for C 3  and a phase detector, the twin-tee can be phase-locked (or forced to balance) at resonance; thereby creating a control loop output voltage with the advantages that a closed loop system has over an open-loop transducer. 
     While preferred embodiments have been shown and described, various modifications and substitutions may be made thereto without departing from the spirit and scope of the invention. Accordingly, it is to be understood that the present invention has been described by way of illustrations and not limitation.