Capacitive Transducers

Capacitive displacement transducers use the electrical quantity of capacitance to convert mechanical movements into a corresponding electrical signal. They are particularly accurate and sensitive transducers and widely used for measuring position, length, or angles. They can also be used in contacting and noncontacting modes. In the former case the movement displacement to be measured is directly connected to one movable element of the capacitor. In the noncontacting mode the object under study is itself made one plate of the capacitor.

ill. 5-1. Basic construction of a capacitor.

A capacitor consists of two plates or electrode areas of conductive material separated by a dielectric filling the gap between them ( ill. 5-1). The capacitance of such a device is the ratio of the current to the potential difference between them and can be calculated from the formula

capacitance = 0.22 - A_k/d

where A is the area of each plate in square inches

d is the gap in inches

k is the dielectric constant of the gap substance

capacitance is given in picofarads (pF).

It follows that the capacitance may be varied by change of area (A) or gap (d). Variation of capacitance with area follows a linear law, but variation with gap follows a reciprocal law (see ill. 5-2).

ill. 5-2. Capacitance is a function of place surface area (A) and also of the gap between the plates (B).

Both forms of working are used in capacitance transducers. Basic configurations for variable area are shown in ill. 5-3 and make use of plain electrodes, cylindrical electrodes, or a moving screen interposed between two plane electrodes. Variable-area transducers are used for both linear and angular measurements, their most useful size being for measuring movements from about 3/16 in. (5 mm) upwards.

ill. 5-3. Three methods of varying the value of a capacitor. At A, one plate is moved; at B, a concentric pair of cylinders, one of which is moved; at C, a movable plate between two fixed plates.

Basic configurations for variable-gap transducers are shown in ill. 5-4. These are normally used for measuring small movements, 3/16 in. (5 mm) or less. They can be extremely accurate for measuring very small movements down to 0.001 micron (1 micron is 0.001 mm).

ill. 5-4. The gap spacing may vary because of movement of a whole plate (A) or because of distortion in the shape of one of the plates (B).

Noncontacting capacitive transducers may work in either mode. With a variable-area type, introducing a screening body between two fixed electrodes (constant gap) varies the capacitance. The actual body introduced may be a conductor or a nonconductor. Also, it does not necessarily have to enter the fixed gap. Introducing it adjacent to one of the fixed electrodes will also vary the capacitance. With a variable-gap proximity transducer the body itself becomes one electrode (or carries the second electrode). These can work with much larger variable gaps than contacting type variable- gap transducers.

A basic configuration for a noncontacting proximity transducer is shown in ill. 5-5.

ill. 5-5. A noncontacting proximity transducer.

LINEARITY

The linearity and repeatability of a capacitance transducer depend on the quality of machining and alignment of electrodes (they are independent of material or magnetic effects). To achieve an accuracy of 0.01 percent means that the gap in electrodes must be accurate to this degree. e.g., with a 0.06 in. gap, the accuracy needs to be 6 micro-inches. Misalignments in the electrodes cause some nonlinearity.

Production transducers of this type are currently made with peak errors less than 0.01 percent for short ranges (up to 5 mm) and 0.005-0.0025 percent for longer ranges (10-100 mm).

Although the noncontacting variable-gap transducers don’t have the linearity of the variable-gap type, they have other advantages that are worth exploiting in terms of stability, sensitivity, and convenience. Certain types of displacement transducers, e.g., have been designed for use at high temperatures (up to 6000 C.). Another advantage of capacitance measurements—namely, that the dielectric does not vary and the transducers can be made mechanically stable over this temperature range—means that very stable measurements of static or slowly changing strain or displacement can be made at high temperatures.

ACCURACY

Accuracy is defined as the maximum error in indicated change of position from zero when compared with a reference standard such as slip gauges. The errors include all sources, such as nonlinearity, slope, resolution, drift, and zero shift.

A wide range of accuracies is possible, depending on the needs and economics of the application. Typical accuracies are

0.1 percent e.g., ± .001” per inch low cost applications

0.01 percent e.g., ± 0.0001” per inch in 1-in, range general measurement or ± 0.001 mm per mm in 10-mm range

.001 percent e.g., ± 0.001 mm per mm in 100-mm range high-accuracy systems

These accuracies are for the transducer. The associated instrumentation may be better or worse, depending on the cost. A typical transducer indicator for 0.001 percent accuracy and six digit readout may be $3000; for .01 percent the price may be below $700; for 0.1 percent, below $150.

SENSITIVITY

Sensitivity can be defined as the smallest change in setting of the transducer that can be read. The overall sensitivity depends on the sensitivities of the transducer itself and the following measuring instrument. The transducer is normally inherently stable, so the onus on achieving high sensitivity lies in the design and construction of a very stable measuring system.

With variable-area transducers a sensitivity of 1 in 10^6 or 10^7 of the transducer range is possible. With variable-gap systems, a sensitivity of 10 times greater, or even more, is possible, because the gaps can be made very small, and the standing capacity higher; thus, the change that must be observed is small. Hence, the sensitivity in absolute terms is very high, although the range of movement is small. e.g., a pair of capacitor plates 2 in. in area with a gap of 0.01 in. has a capacity of 44 pF. A change in the gap of 10^-10 which is 10 ^-12 in., can be observed. At such extremes of sensitivity the stability of construction is critical.

MEASURING INSTRUMENTS

Instrumentation is necessary to convert the setting of the transducer into a readable form. Typically, an ac signal is used to drive the transducer when the amplitude of this signal after passing through the transducer is a measure of the transducer setting. This is in analog form; a digital readout needs analog-to-digital con version.

The most accurate form of transducer-to-digital converter is the self-balancing bridge ( ill. 5-6). This may be accurate to a few parts in a million and give a six or seven figure readout. An alter native is the open-loop transducer-to-dc converter ( ill. 5-7). An ac generator drives the transducer. The output is rectified and filtered and is available as a dc signal that is proportional to the transducer setting. This dc may be digitized to give a five- figure readout. Either the bridge or dc converters may be used to pro vide dc control signals.

ill. 5-7. An open-loop converter for use with a capacitive transducer.

ill. 5-6. A self-balancing bridge circuit for use with a capacitive transducer.

Other forms of measuring instruments are shown in ill. 5-8. At A is an oscillator where the variation in capacitance causes a variation in resonant frequency. This suffers from the problems of stability of frequency, and therefore displacement readout, due to changes in the shunt capacity of the capacitor leads (lead length variations) and drifts in the tuned circuitry.

Shunt capacity is the term given to the capacity between core and screen of the coaxial wires used to drive the transducers.

ill. 5-8. A capacitive transducer, connected in the resonant circuit of an oscillator (A) and in the feedback loop of an amplifier (B). Advantages and disadvantages of both methods are discussed in the text.

Figure 5-8B is a useful circuit, whereby a linear output can be obtained from a variable-gap transducer using it in the feedback loop of an amplifier. Here we have the impedance of the capacitor

Z2 proportional to 1/C2

C proportional to 1/d. Ca 1 Therefore, Z2 proportional to d, where d is the change in displacement between the plates. The closed-loop gain of the amplifier is Z2/Z1

The output voltage of the amplifier is

V=A x Vin = Z2/Z1 x Vin

Therefore

Vout α dVin/Z1 = Kd (where K is a constant)

This means that the output voltage is directly proportional to d. A more stable circuit is shown in ill. 5-9. This is a Blumleine bridge, which uses in its construction inductive voltage dividers as two of the ratio arms. Inductive voltage dividers are a very accurate (1 in 10^6) means of subdividing ac and exhibit very good long-term stability (1 in 10^8). They are therefore ideal components in this in stance for the bridge arms. With this bridge the shunt capacities from the cables don’t affect the accuracy of the measurement because they never appear in parallel with the measuring capacitances. Both the generator and detector can be made with low impedances so that the sensitivity of the instrument is not changed by large changes in shunt capacity (cable length). Another advantage of the bridge circuit is that if the bridge is self-balancing, many sources of drift, such as changes of amplifier gains and carrier level (which would cause a change in the voltage output, and thus apparent displacement, of an off-balance system), are nullified. The balance point of the bridge is independent of the carrier level or amplifier gains. A large dynamic range is also possible with resolution of six decades (1 in 10^6 or 1 m in 10-mm range). Typical full- scale capacitance is around 0.5^-1 pF. Typical cable capacity would be around 200-300 pF for 3 meters (m) of cable. With the correct circuit design a change of 10-6 pF can be measured in 1 pF, shunted by 300 pF with an accuracy (in the case cited) of around 4 x 10^-6 pF.

ill. 5-9. A Blumleine bridge for use with capacitive transducers.

RESOLUTION

Resolution is the least change that can be displayed by a measuring instrument. A transducer system may be capable of sensitivity of one part in 10^6 of the range. If a four decade indicator is used to digitize the transducer, then the system resolution is one part in 10g. A seven decade instrument with a .01-percent transducer accuracy would still have useful resolution in the last three decades for small changes.

STABILITY and DRIFT

Accuracy of measurement also depends on freedom from long- or short-term drifts, that is, the stability of the system. There are numerous potential sources of drift, such as electrical changes, temperature and other environmental changes, and mechanical changes. All these have to be considered in a measuring system requiring high accuracy. With suitable designs it’s possible to achieve accuracy, stability, and resolution of the order of one part per million, but the resulting cost of equipment can be high.

ASSOCIATED CIRCUITS

Associated electronic circuits for capacitive displacement transducers can be relatively simple, due to the high output impedance of the transducer. Figure 5-10A shows a circuit for a differential capacitor with an inductive divider connected to form bridge circuit.

ill. 5-10. Another form of bridge circuit for use with a differential capacitive transducer (A); the equivalent circuit (B).

The transducer draws very little current. Therefore, the impedances of the leads are not significant. Strong capacitance can be minimized by screening, as indicated. It’s not necessary to screen the lead from amplifier to inductive divider because the latter has a low output impedance and is not affected by strong capacitance.

The equivalent circuit is shown in ill. 5-10B. Typical values would be 1 pF on the transducer capacitance and 100 pF strong capacitance in shunt. This would be equivalent to a signal loss of 100 (hence the need for the amplifier).

Carrier phase and amplitude are detected by a phase-sensitive circuit, so that both the sense and amplitude of the displacement can be indicated. This readout may have either the inductive divider calibrated in terms of displacement or a zero-center meter displaying the out-of-balance signal between the two halves of the inductive bridge.

LINEAR DISPLACEMENT CAPACITIVE TRANSDUCER

A linear displacement transducer having variable capacitance is highly linear, stable, and compact. Its performance is generally superior to other comparable length-measuring systems in the range 0 to 250 mm.

ill. 5-11. A capacitive displacement transducer.

It’s possible to measure to accuracies of ± 0.001 percent of full scale— e.g., 1 m in 100 mm. Not only is the transducer linear and stable, but it can also be calibrated in absolute metric or inch units; therefore, all transducers are interchangeable with out adjustment.

ill. 5-12. A circuit for converting the capacitance of a transducer into a variable dc signal.

Resolution is also high. Changes in setting of less than one part per million can be reliably measured (0.01 um in 10 mm). This is possible because of the very stable construction and the drift-free ac ratio measuring system.

An example of a capacitive type displacement transducer is shown in ill. 5-11. It consists of one fixed capacitor and one variable capacitor. The ratio between fixed and variable capacities is measured to give the displacement in electrical form. Because both capacitors are in the same environment and close together, ambient changes such as temperature affect both in the same manner. Hence, the stability and freedom from drift are very good indeed.

The simple and robust structure of the capacitive transducer allows very high accuracy and small size. Typically, a 5-mm-range transducer accurate to 0.5 tm and repeatable to 0.05 m can be less than 10 mm in diameter and 50 mm long. A 100-mm range repeats to 0.2 m and is 33 mm in diameter by 300 mm long.

INSTRUMENTATION

Figure 5-12 shows a dc-dc signal conditioner that converts the variable setting of the transducer into a variable dc signal. Dc power is supplied to the unit. A square-wave generator drives the transducer, and the transducer setting controls the signal amplification. The output of the amplifier is rectified, filtered, and provides a dc signal proportional to the transducer setting. This is an “open loop” method; it’s linear and can be stable to better than 0.02 per cent with a dynamic range of 10,000 at a bandwidth of 250 Hz.

An even more accurate and stable device is the “closed-loop” ac bridge system ( ill. 5-13), where an inductive divider, which is accurate and stable to better than one part per million, is compared with the ratio of the capacitive transducer.

ill. 5-13. Another circuit for obtaining dc from a capacitive transducer.

Any difference or out-of-balance between divider and transducer setting is amplified, synchronously rectified, and available as a direction-sensitive dc output. The instrument is used either with null balance (that is, a position is set on the dials and the transducer moved to balance) or with open loop, in which the dc output is displayed to show the difference between the position called for and the actual position. The great advantage of this is the very high stability and accuracy of the digital setting of the dividers. The transducer setting can be read in digital form to six figures. This system is excellent for closed-loop servo systems.

PREV: Strain Gauges
NEXT: Properties of Piezoelectric Materials

Fundamentals of Transducers (all articles)