Capacitive Pick-Off Circuit

The invention relates to capacitive pick-off circuits; that is, circuits that are used to determine the capacitance or the gap between plates of a capacitor.

In prior art capacitive pick-off systems, such as described in the copending application of Holdren et al Ser. No. 702,389, filed on July 6, 1976, assigned to the assignee of this application, capacitance is measured by applying a time varying voltage such as a triangular or saw-tooth waveform to the capacitor plates. The resulting current through the capacitor is then used as a measure of the capacitance or the gap between the plates of the capacitor. However, due to the fact that the capacitance of the capacitor varies in an inverse relationship with the distance or gap between the plates, a change in this gap will result in nonlinearities in the output current which can, under some circumstances and in certain applications of capacitive pick-off circuits, lead to significant errors. For example, a ten percent change in the gap will give rise to over a one percent nonlinearity, a twenty percent gap change will give rise to over a four percent nonlinearity and a fifty percent gap change will result in a thirty percent nonlinearity. Also, since the output current of the capacitor increases substantially as the plate gap becomes very small, significant stability problems can appear when the capacitor is used as a position sensing element in a servoed device. Capacitive pick-off circuits are used in a large number instrumentation type applications such as transducers and accelerometers and for some highly sensitive instruments such as servoed accelerometers and transducers where nonlinearities due to significant changes in the capacitor plate gap can be a significant source of error.

It is therefore an object of the invention to provide a capacitive pick-off circuit which will tend to eliminate nonlinearities due to changes in the gap or distance between pick-off capacitor plates wherein a pick-off capacitor forms a portion of a feedback circuit of an operational amplifier and wherein the gain of the operational amplifier is directly related to the capacitance of the pick-off capacitor. A source of time varying voltage is applied to the operational amplifier and the resulting output voltage of the operational amplifier provides a measure of the pick-off capacitor capacitance.

It is an additional object of the invention to provide a differential capacitive pick-off circuit which will eliminate nonlinearities due to the varying distance between the plates in the pick-off capacitors wherein the circuit includes a pair of operational amplifiers having feedback circuits that include the pick-off capacitors. Each pick-off capacitor is effective to control the gain of one of the operational amplifiers and a time varying voltage applied to the inputs of the operational amplifiers results in output voltages for each of the operational amplifiers which in turn are applied to a differential amplifier that produces an output voltage representative of the difference in capacitance of the pick-off capacitors.

FIG. 1 is a schematic diagram of a differential pick-off circuit according to the invention.

Illustrated in FIG. 1 is a schematic diagram of the preferred embodiment of the invention which is a differential capacitive pick-off circuit including a pair of pick-off capacitors C.sub.P1 and C.sub.P2. Pick-off capacitors such as C.sub.P1 and C.sub.P2 are typically used as position detecting elements in various types of instrumentation including transducers, accelerometers and the like. As shown in FIG. 1, a source of time varying voltage 10 applies to a sinusoidal voltage V.sub.IN by means of lines 12 and 14 and resistors 16 and 18 to an inverting input of a pair of operational amplifiers 20 and 22. Each of the operational amplifiers 20 and 22 includes a feedback circuit indicated at 24 and 26 that includes pick-off capacitors C.sub.P1 and C.sub.P2. Since C.sub.P1 and C.sub.P2 are located in the negative feedback loops of amplifiers 20 and 22, they are effective in combination with the resistors 16 and 18 to control the gain to the output voltages V.sub.1 and V.sub.2 of the operational amplifiers 20 and 22. Due to the fact that the operational amplifiers 20 and 22 in effect utilize the capacitor plates of the pick-off capacitors C.sub.P1 and C.sub.P2 as feedback elements, the amplifier gain will be an inverse function of the capacitance of the pick-off capacitors C.sub.P1 and C.sub.P2 and the outputs V.sub.1 and V.sub.2 of the amplifiers 20 and 22 will be linear functions of the capacitor plate gaps.

In the preferred embodiment of the invention shown in FIG. 1 noninverting inputs of each of the operational amplifiers 20 and 22 are connected to ground by means of resistors 28 and 30. In addition, capacitors 32 and 34 are provided in a feedback relationship between the output terminals and the noninverting terminals of the operational amplifiers 20 and 22. Capacitors 32 and 34 can be used to balance out stray capacitances in the circuit.

A differential amplifier 36 provides a means for combining the outputs of operational amplifiers 20 and 22 to generate a signal representing the difference in capacitance between capacitors C.sub.P1 and C.sub.P2. The output V.sub.1 of amplifier 20 is applied through a resistor 38 to an inverting input of amplifier 36. Similarly, the output V.sub.2 of amplifier 22 is applied through a resistor 40 to a noninverting input of amplifier 36. The noninverting input of amplifier 36 is connected to ground by means of a resistor 42 and a feedback circuit including a resistor or impedance 44 connects the output of amplifier 36 with the inverting input. The output terminal of the capacitive pick-off circuit of FIG. 1 is connected by means of a capacitor 46 to the output of amplifier 36 and produces thereon the output voltage V.sub.O.

Operation of the differential pick-off circuit illustrated in FIG. 1 is described by the following equations where the input voltage V.sub.IN is represented by:

The output voltages V.sub.1 and V.sub.2 of amplifiers 20 and 22 are then represented by: ##EQU1##

Since the output voltage of the differential amplifier 36 is equal to

the substitution of Equations (2) and (3) in Equation (4) results in the following expression for the output voltage V.sub.O : ##EQU2## By including the formula for the capacitance of a parallel plate capacitor ##EQU3## where A is the area of the capacitor plates, D is the gap or distance between the plates and .epsilon..sub.o is the permitivity constant, for the pick-off capacitors C.sub.P1 and C.sub.P2 in Equation (5) the following relationship emerges: ##EQU4## Then if the resistances R.sub.16 and R.sub.18 are equal and if the areas of A.sub.1 and A.sub.2 of the pick-off capacitors are equal as well, the output voltage V.sub.O will be directly related to the distance between the plates as shown below: ##EQU5## Therefore it can be appreciated that the output voltage V.sub.O of the circuit illustrated in FIG. 1 will represent in a linear manner the difference in gaps between the plates of capacitors C.sub.P1 and C.sub.P2.