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Compared with competing optical, inductive, and piezoresistive transducers, capacitive sensors have many advantages, among them low cost and power usage, and good stability, resolution, and speed. They also have a near-zero temperature coefficient, can be optically transparent, and are easy to integrate into ICs or onto printed-circuit boards (pc boards). Capacitive sensors can detect motion, acceleration, flow, and many other variables, and are used in a wide range of applications.

But many engineers still distrust the technology. Some believe that capacitive sensors are affected by temperature and humidity, sensitivity to noise, difficulties in designing, instability, and nonlinearity. Capacitive sensors do need some specialized design know-how to avoid those hazards. Some sample designs and applications should help dispel this distrust.

Capacitive sensors come in one of three types. Fixed-plate versions maintain the relative position of the two plates, while the capacitive coupling changes as a result of different materials placed near the plates. A grounded conductive material will reduce coupling capacitance, and a high-dielectric material will raise it. These sensors are used for sensing wall studs or determining the composition of materials. An array of multiple fixed plates can form an x-y touch sensor to measure finger or stylus position in two dimensions or even to image fingerprints.

Another technique involves changing the spacing between the capacitor's parallel plates. This geometry's ability to accurately measure small motions down to 10^-14 m makes it useful in electret microphones, tiltmeters, seismometers, and micrometers. Adding a third plate to sandwich the moving plate between two fixed plates, and driving the fixed plates while sensing the moving plate, increases the signal and provides shielding. This arrangement does not handle large motions well since capacitance drops to a difficult-to-measure value with large plate spacing.

The third type, which involves moving the parallel plates so their overlap area changes, can measure greater linear motions. Adding a second fixed plate above the moving plate again improves performance, as first-order spacing dependence is nulled out. To improve accuracy, multiple plate patterns are used, with a demodulator counting plates for a coarse position determination and interpolating between plates for a fine measurement, similar to optical encoders.

Ratiometric position sensing is better still. In this technique, the moving plate, C, is on one side of two fixed plates, A and B. The device measures the ratio of the capacitances C_CA and C_CB. This device is not sensitive to spacing. Adding two more fixed plates A' and B' on the other side of the moving plate, and then connecting A' to A and B' to B, makes the unit self-shielding and first-order insensitive to tilt.

Demodulation Methods

Several techniques are available to convert the capacitance or capacitance ratio to a voltage output. In the direct method, the plates are charged with a dc voltage and feed a very-high-impedance amplifier. This scheme is inexpensive and has good high-frequency response. But it doesn't work at dc unless the amplifier's impedance is infinite, and it is noisy because semiconductors are noisy at low frequencies.

Another method uses the sense plates to create the C in an RC oscillator, and then measures the oscillator's output frequency or period. The result is a simple, low-noise demodulator that rejects low-frequency noise. But if stray capacitance is not nulled, it may swamp the sensor's capacitance, causing a low-amplitude and unstable output.

In a synchronous demodulator, the sensor plates are driven by a square- or sine-wave signal at, for example, 5 V and 100 kHz, rather than a dc signal. Some systems use two square waves at 0°and 180° phases, and a phase-sensitive demodulator. In these systems, the sensor is usually configured for ratiometric measurements for improved stability and precision. The ratiometric synchronous demodulator is the most accurate circuit, but it has the highest part count.

Practical Circuits

In a practical system, the capacitance to be sensed usually ranges from 0.01 pF for ICs to 2-3 pF for a pc board of a square centimeter. Impedance ranges from 1.59 M? at 100 kHz with a 1-pF sensor to 1590 M? at 10 kHz with a 0.01-pF sensor. The amplifier's input impedance should be much larger than the sensor's to avoid shunting the signal, and since typical operational amplifiers have input capacitances of a few picofarads, special low-capacitance amplifiers are needed. These amplifiers can be used with any of the three types of demodulators.

At these extremely high impedances, system noise is usually dominated by amplifier current noise rather than voltage noise. Amplifier voltage noise is generally restricted to a relatively narrow range, between 3 nV/?*Hz and 60 nV/?*Hz. But current noise is much more variable, with extremes of 0.2 fA/?*Hz to 50 pA/?*Hz

The capacitive pickup amplifier will probably need a FET input stage, either a JFET or MOSFET, to get acceptably low current noise. MOSFET current noise is in the range of 0.2 fA-1 fA/?*Hz and will not contribute to output noise with reasonably high sensor plate capacitances (0.5 pF) and excitation frequencies (100 kHz). JFETs are almost as good, 2 to 40 fA/?*Hz, and usually have lower voltage noise and are less sensitive to electrostatic discharge. Bipolar transistor current noise can be over 50 pA/?*Hz. With a sensor impedance of 100 M? and a bandwidth of 10 kHz, this level of current noise will produce over 100 mV rms of input-referred noise.

Designers have three circuit choices for the input amplifier: follower amplifier, virtual-ground amplifier, and all-over feedback amplifier. Their noise performance is similar, but each circuit offers different options for shielding and handling stray capacitance, and each has different amplifier common-mode requirements.

The typical unity-gain follower amplifier uses the ratiometric sensor configuration, with C₁ and C₂ representing C_CA and C_CB (Fig. 1). The circuit has an in-band ratiometric response of:

and it will produce a linear output with area-variation motion.

The response is independent of stray capacitances C_A, the amplifier's internal input capacitance, and C_G, the stray capacitance to ground. The former is bootstrapped out because the negative input follows the positive input exactly, and the latter is nulled by using a driven guard shield. The shield follows the input signal exactly so if the shield completely surrounds the input node no current can flow from the input through stray capacitance to ground.

Handling Stray Capacitance

Stray on-chip capacitance from the positive amplifier input to the substrate often can be handled by bootstrapping the negative power supply through C_V, but not all amplifier types are stable with this connection. Bootstrapping the positive power supply input doesn't work for most IC op amps, but positive supply bootstrap can be used for properly designed discrete amplifiers.

To set the amplifier's bias point, the designer can use an input resistor to ground. It must be large enough for reasonable low-frequency response and to minimize its noise contribution, and small enough so that the amplifier's input bias current doesn't cause an unacceptable dc voltage at the input. It's size should also allow the highpass filter formed by the resistor and the sensor capacitance to reject low-frequency noise such as 60 Hz. The resistor may be 100 M? or higher. This large resistance can be generated with a smaller value for R_L, say 10 M?, by bootstrapping it to the amplifier output with C_Z to increase its apparent ac value. A small resistor may be needed in series with C_Z for low-frequency stability.

Internal Capacitance Reduced

These circuit tricks decrease an IC amplifier's internal capacitance from several picofarads to 0.1 pF or less and provide an ac input resistance in the gigaohm range.

The virtual-ground amplifier keeps the signal at virtual ground, so shields can be at ground potential (Fig. 2). Also, amplifier common-mode input range is not a problem, and power supplies do not need bootstrapping.

But the output voltage is now:

where C₂ is now a fixed capacitor. C_A and C_G do not affect the output, except to produce lower loop gain at high frequencies.

This circuit also can be used ratiometrically, but the problem (with any sensor plate configuration) is that with C₂ a fixed capacitor the output depends on the absolute value of the sensor. In a motion-measurement application, this will cause an unwanted response to spacing change in an area-variation sensor. The locations of the sensor plates and the fixed capacitor can be interchanged to linearize the two types of motion sensors. With spacing-variation sensor plates, the sensor plates should be in location C₂ and C₁ should be a fixed capacitor. The output voltage will then be linear with motion. With area-variation sensor plates, the sensors should be in C₁'s position with C₂ fixed for a linear output.

An all-over feedback amplifier combines the advantages of the follower and virtual-ground amplifiers (Fig. 3). Its shield is at ground; its output is ratiometric instead of absolute, and amplifier common-mode range isn't a problem. In addition, this circuit does a better job of compensating for stray capacitance (C_S1-C_S4, C_A, C_G). This circuit also needs a large input resistor (100 M?) to set the input dc voltage, but it is placed in parallel with C_S4. An analog switch can be used for this purpose.

The moving capacitive plates are often coupled to the amplifier through another air-spaced capacitor (represented in the circuit by C₃) to avoid a moving wire connection. Unlike some circuits, the all-over feedback amplifier's output equation is not affected by this small capacitance. In fact, the output equation (Equation 1) is the same as that for the follower amplifier.

The only important stray capacitance is C_S4, the amplifier's input-to-output capacitance. It may be less than 0.1 pF for IC amplifiers if the input and output pins are on opposite sides of the package, and it can be further reduced to an insignificant value by adding a discrete FET at the amplifier input.

Snares, Hazards, And Pitfalls

Unwanted tilt and spacing sensitivity is a key design issue for area-variation motion sensors. Different sensor-plate geometries exhibit varying sensitivities.

A rectangular plate pattern forms a simple motion detector with low spacing sensitivity if it is used with a follower or all-over feedback amplifier with correct shielding or guarding (Fig. 4a). However, the configuration is sensitive to tilting around the y axis. A triangle pattern transduces motion linearly and resists y- and z-axis tilt (Fig. 4b). Performance improves if dimension A is small. However, x-axis tilt is a problem. The preferred arrangement is a chevron pattern, which also compensates for first-order x-axis tilt (Fig. 4c). If the pickup can be surrounded by driver plates, all tilt and spacing dependencies are reduced, shielding is improved, and the signal is larger.

Another problem is triboelectric charge. This electrostatic charge caused by friction can confuse capacitive sensors in two ways. First, the amplifier's very high input impedance means that even a tiny spark discharge can create a transient output that can be misinterpreted as a sudden large-amplitude input excursion.

In addition, if a sensor plate picks up an electrostatic charge, any mechanical spacing change due to vibration will be converted to an output voltage according to V=Q/C, where Q is the total electrostatic charge on the plates (unchanged by vibration) and C is the sensor capacitance, which changes inversely with spacing. This vibration-induced voltage can be very large, saturating the amplifier. Or if the vibration's frequency spectrum is close to the carrier frequency, the vibration will add to the output signal. The solution to this vibration sensitivity is to eliminate insulators from the region of the sensor plate gap, increase mechanical rigidity, and increase the carrier frequency.

Nanoampere leakage currents also cause problems. They degrade capacitive sensors by adding noise or by upsetting amplifier bias. The worst offender, surface pc-board conduction paths, can be handled effectively by adding ground (or driven-shield) etch paths around the amplifier input. For instance, the input node of the virtual-ground amplifier can be surrounded by a ground implemented as a printed circuit board trace surrounding the sensitive components and connected to ground. Solder mask should be relieved on top of this trace.

Discrete components also can produce leakage currents. Surface-mount MOSFETs all have an integral protection diode that degrades performance by adding current noise, so either diode-less through-hole MOSFETs (protected by a removable wire ring) or JFETs (no diode needed) are preferred. Electrolytic and high-value ceramic capacitors also are noisy and leaky; film or mica types should be used.

Sensor Applications

A good example of a capacitive-sensor application is a very simple finger-touch keyswitch with a low component count (Fig. 5). A microcomputer generates a short positive pulse at plate A and a short negative pulse at plate B. With no finger present, the positive pulse couples through floating plate C to plate D, producing a positive transient at C, which is read by the computer. If a finger touches C, the positive signal path is interrupted, and enough of the negative pulse couples to D to produce a negative output.

The plates can be built on the product's pc board. If the microcomputer has a comparator or analog-to-digital converter (ADC) input, the circuit requires only one discrete component.

Capacitive sensors also can increase device integration. For instance, Analog Devices' ADXL50 is a surface-micromachined accelerometer with integrated signal processing, built on a 9 mm² chip. It measures acceleration in a bandwidth from dc to 1 kHz with 0.2% linearity, and it outputs a scaled dc voltage. The accelerometer is a force-balance device, using electrostatic force to null the acceleration force on the "proof" mass, with advantages in bandwidth, self test, and linearity.

Early accelerometers measured the displacement of a spring-suspended mass. Problems with this approach included the presence of a resonant peak, difficulty in achieving good dynamic range, and the need to carefully calibrate the force-vs.-displacement relationship.

Microscopic Movement

The proof mass in a force-balance device deflects only microscopically. The device detects and amplifies this displacement, then feeds back a force to restore the rest position. With a high-gain amplifier, the mass is nearly stationary and the linearity is determined by the linearity and precision of the voltage-to-force transducer rather than the suspension characteristics. Early versions used piezoresistive sensing of the displacement, but problems with temperature coefficient, dc response, and shock-induced zero shift caused a switch to capacitive sensing in most new accelerometers.

The ADXL50 uses a very small (1 mm²) capacitive sensor element. To increase signal strength, the silicon micromachined electrode design uses 42 moving plates, each 2-µm wide, projecting from a center bar. On either side of each moving plate are fixed plates driven by a 0° and a 180° square wave. The gaps between the fixed and moving plates are 2 µm. The total electrode length is 10 mm, and the mass of the moving plate is 0.1 µg.

The total sensor electrode capacitance, neglecting fringe fields, is about 0.1 pF. This small value would require an extremely low amplifier input capacitance for accurate open-loop sensing, but with closed-loop operation the error contribution due to variations in gain is negligible if the demodulator gain is high (Fig. 6). The open-loop change in capacitance with a 50-g acceleration is 0.01 pF, and the system can resolve a change of 20 aF (20 * 10^-18 F), corresponding to a beam displacement of 20 * 10^-6 µm.

The amplifier is conventional, and the demodulator is a standard synchronous demodulator implemented in bipolar technology.

With a moving-plate dc bias level of 1.8 V, midway between the two fixed-plate dc levels, the electrostatic force on this plate is balanced. As the plate's mass is deflected by acceleration, E_O provides a restoring voltage. The electrostatic restoring force is developed by changing the dc level on the moving plate through the 3-M? load resistor.

An older application of capacitive sensing is a computer graphic input tablet manufactured by Shintron Co., Concord, Mass. The tablet was developed in 1967, but the principles of its operation are still used today. It measured the x, y, and z movements of a small, capacitively coupled pickup stylus relative to a square-wave-driven resistive sheet that generated an electrostatic field over the 11-in. square tablet. Two different methods of producing the orthogonal field lines were investigated, and a phase-locked-loop demodulator was used with ratiometric response. Performance was good at large stylus-to-tablet separations.

The tablet had a 1024-by-1024 resolution, 1% accuracy, and a sample rate of 100 x-y samples/s. The output format was 10-bit parallel digital, and maximum paper thickness was 0.5 in.

Driving a resistive sheet to measure a single axis is simple. If metallic electrodes A and B are placed along opposite sides of the sheet and fed with a 5-V square wave, the sheet will generate a linear ac voltage field just over its surface. A stylus using a small electrode will pick up a signal proportional to the y displacement when moved near the surface of the sheet. A circuit that measures signal amplitude can also measure the z position.

Two-Dimensional Complications

A two-dimensional system is more complicated. If metallic electrodes C and D are added to the remaining two sides, electrodes A and B will be shorted at the corners, or at minimum a very nonlinear field will be produced. One alternative is to drive the corners instead of the sheet's edges, and to use a medium-resistivity material on on the edges and a high-resistivity material for the sheet to produce an orthogonal, linear field.

To measure position in the y axis on this resistive tablet, electrodes A and B are connected together and driven with 100-kHz, 0º signal and electrodes C and D are connected together and driven with 100-kHz, 90º signal. As the stylus is moved in the y axis, the electrical angle will change from 0º to 90º, but displacement in x will not affect the signal. The x-axis position is determined by driving electrodes A and D together and B and C together. Changes in z will change amplitude, but not phase.

Excluding small fringe effects, the field produced by this tablet will be linear and orthogonal if the ratio of the resistives is large. In practice, a large resistivity ratio may be difficult to obtain and a geometric compensation, a slight pincushion shape, will be needed to correct the nonlinearity caused by a low ratio. A linearity correction table can handle a large nonlinearity. The low-resistance strips can be dispensed with, for example, and the resulting over-50% nonlinearity measured and stored.

The stylus pickup used a guarded, coaxial construction with a 2-mm point exposed for writing and sensing (Fig. 7a). It performed well up to 10 cm stylus-to-tablet spacing, at which distance its capacitance to the resistive sheet was less than 0.05 pF, and the signal amplitude was reduced to 10% of the amplitude at the surface due to fringe effects and unguarded stray capacitance. To achieve this performance, the amplifier's input capacitance had to be less than 0.1 pF, a level that attenuated the signal by 3X. The use of ratiometric position detection made this unimportant.

The pickup circuitry used discrete transistors and both guarding and neutralization techniques to minimize input capacitance (Fig. 7b). The guard in the follower circuit did most of the input-capacitance cancellation. A small amount remained due to the finite amplifier gain and the FET's gate-to-drain capacitance. The adjustable neutralizing capacitor, with a value of 0 to 0.1 pF, nulled this residue. Parasitic capacitance is reasonably repetitive and stable, so the neutralizing adjustment is not sensitive to environmental factors once adjusted.

Larry Baxter is a consulting engineer at PictureTel Inc., Andover, Mass. He specializes in the design of electromechanical and electro-optic, analog, and video circuits. He received his BSEE degree from Rensselaer Polytechnic Institute, Troy, N.Y. He has been a founding partner at several companies, including ECHOlab Inc., Kronos Inc., and Everygame Inc.  

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