Measure Capacitive Sensors With A Sigma-Delta Modulator

Capacitive sensors supply high accuracy at a relatively low cost. But system designers attempting to use them have been forced to first convert the capacitance to a voltage, then convert the voltage into the digital domain using a precision analog-to-digital converter (ADC). The complex circuit design, lengthy prototype evaluation, and demanding system test usually cause the designer to look for a different sensor. They often select one that's more expensive, less accurate, or both.

While many applications use capacitive sensors, multiple options exist when interfacing to them, which leads to problems with the signal-conditioning circuitry. However, a new approach employs an industry-standard sigma-delta modulator, traditionally used in high-resolution ADCs, that's modified to measure capacitance directly. Before anything, though, it's important to understand where capacitive sensors are used.

Capacitive sensors exhibit a change in capacitance in response to a change in physical stimulus. Used in many areas of industry, their range of applications is astounding, going from the very high-performance end-including industrial, medical, and manufacturing equipment-to the low-performance end, such as key-touch applications. Common examples consist of humidity, pressure, and position sensors. On a broader scale, applications include non-touch switch technology, proximity sensing, fingerprinting, liquid-level measurement, materials property, oil quality, and all kinds of motion sensors.

Interfacing Capacitive Sensors

Traditionally, the challenge for system designers attempting to use capacitive sensors has been to implement a high-performance, low-cost, capacitive-input front-end. In general, measurements are executed by applying an excitation source to the capacitor electrodes. The variation in capacitance is then turned into a variation in voltage, current, frequency, or pulse width. There are several typical methods of capacitance measurement:

• A "direct" method charges the capacitor from a defined current source for a known time, then measures the voltage across the capacitor. This method requires a very low current, high-precision current source, and a high-impedance input to measure the voltage.
• A second method uses the capacitor to create an RC oscillator, and then measures the time constant, frequency, or period. This method is simple, but it usually doesn't achieve high accuracy.
• Another method involves measuring the capacitor's ac impedance. A sine-wave source excites the capacitance, and the capacitor's current and voltage are measured. Using a four-wire ratiometric connection to the capacitor, a synchronous demodulator then provides one of the most accurate results available. However, the circuit is very complex and has the highest part count.
• The most common method for interfacing to precision low-capacitance sensors is using a charge amplifier that converts the ratio of the sensor capacitor to a reference capacitor into a voltage (Fig. 1). This circuit can be found integrated into an ASIC in some high-volume applications.

In all of these methods, the capacitance is first converted to a voltage, which is then converted to digital by a precision analog-to-digital converter (ADC). A digital output is used in most applications, but there's an advantage in digitizing the information even if the required sensor output is an analog signal-either a voltage or an industrial-standard 4 to 20 mA. That's because sensor linearization, temperature compensation, and system calibration are much easier to implement in the digital domain than in the analog domain.

A very important aspect in any precision capacitive-sensor application is the way the sensor is connected to the rest of the circuit. Space at the sensor site is often restricted, so the signal-conditioning circuit must be small enough to fit into the very small space. Or, the sensor must be connected to the circuit with a relatively long cable. Parasitics of long connections can be large in comparison to the measured sensor changes, which can be on the order of a picofarad or less. Moreover, as the distance between the sensor and converter lengthens, conversion methods that are sensitive to the connection capacitance or leakage current to ground will make accurate measurements increasingly difficult.

Sigma-Delta ADC A well-proven technology, sigma-delta has been used for years in high-performance (>18 bits) ADCs. Figure 2 shows the simplified architecture of an industry-standard single-chip sigma-delta ADC. The capacitors CIN and CREF are periodically switched to the voltage and reference inputs VIN and VREF, and they pump charge into the integrator CINT. The comparator checks the integrator output and controls the phase of the input switches to close the feedback loop, which balances the charges flowing through the voltage and reference path.

A stream of zeros and ones, which can be seen on the comparator output, varies with the charge needed for the loop balance. The charge is proportional to voltage and capacitance. And because the capacitors have fixed values, the density of zeros and ones represents the ratio between the input voltage (VIN) and the reference voltage (VREF). The digital filter then extracts the information carried by the time-domain pattern of zeros and ones to form the digital result.

This architecture inherently features superior performance for linearity and accuracy, but there's a tradeoff between resolution and speed (output data rate). When more zeros and ones are allowed to be processed in the digital filter, it takes longer to get the result but produces more stable bits on the output. Only system noise limits the converter resolution. And, the output data rate is limited by the maximum clock frequency that can be accommodated by the switches' speed, integrator's bandwidth, and comparator's settling time.

Look into the portfolio of available converters to glimpse typical sigma-delta ADC performance. There are no missing codes at 24 bits (relates to differential nonlinearity); greater than 18-bit resolution (peak-to-peak resolution, i.e., a noise-free, stable digital result); 4-ppm integral nonlinearity; and data rates from 10 Hz to 40 kHz.

Sigma-Delta Capacitance To Digital Converter (CDC) The standard sigma-delta ADC is implemented by switching on-chip fixed capacitors and balancing charge between a variable voltage input and a defined voltage-reference input. Well, if the charge is proportional to voltage and capacitance, why not use a fixed input voltage and vary the input capacitor instead?

The modified sigma-delta circuit is shown in Figure 3. The fixed input voltage can be understood as an excitation voltage. The variable capacitor, which is moved off-chip, can be a capacitive sensor. As a result, the output data will represent the ratio between the sensor capacitance and CREF.

This novel idea permits direct interfacing between the capacitive sensor and the sigma-delta converter, which brings inherent features such as high resolution, accuracy, and linearity. Other features related to this circuit architecture are realized when interfacing capacitive sensors in the real world:

• The interface isn't sensitive to capacitance between the sensor nodes and ground or leakage currents to ground, both up to defined limits based on a practical circuit implementation.
• The complete capacitance-to-digital converter can be realized on one silicon chip, resulting in high integration, easy system implementation, high repeatability, high reliability, and last but not least, significantly lower system cost.

Capacitive Length Sensor Example A capacitive length/position sensor was chosen as an example of a simple and low-cost capacitive sensor. The principle of the sensor is elementary: A strip made from a dielectric with defined permittivity moves between two fixed plates. The capacitance measured between the plates changes with the strip's position (Fig. 4).

The sensor can be designed as a simple sandwich of double-sided pc boards. Two copper strips on the inner sides of the top and the bottom pc boards form the capacitor (Fig. 5a). Two fixed pc-board strips in the middle of the sandwich set the distance between the capacitive plates and create a tunnel for the moving part (Fig. 5b). The outer layers, the unused copper area inside the sandwich, and the through-hole vias are grounded to form a shield, which protects the sensor from interaction with the outside world. The moving dielectric strip is made from the same pc-board material with no copper.

Application And Performance This example's capacitive length sensor has been included on an evaluation board built with a usual 1.5-mm-thick, double-sided pc-board material (Fig. 6). The moving strip is 10 mm wide with an initial 0-mm capacitance of approximately 4.5 pF. The capacitance changes by about 0.126 pF/mm as the strip moves between the plates.

The sensor interfaces directly to an integrated sigma-delta CDC, which reduces the complete analog front end to a single-chip solution (Fig. 7). The converter is located relatively close to the sensor. The complete circuit shares the pc board with one sensor plate. CDC insensitivity to any capacitance to ground makes shielding the sensor and connections very easy. Even the pc-board tracks between the sensor and converter can be surrounded by ground, creating a structure similar to a coaxial cable.

The AD7746 CDC used in this example has a capacitive input with full range of ±4 pF. The range can be shifted (offset) programmably by up to 17 pF. Typical resolution in the ±4-pF range is 18 bits (noise-free). Integral linearity is better than 0.01% and factory-calibrated to a gain error of less than 4 fF.

Comparing the sensor and the converter specifications provides the system's theoretical performance: full range of approximately 65 mm, resolution of 0.25 mm, and integral linearity of ±7 mm. Again, these numbers are only theoretical, and the low-cost sensor used for this example doesn't allow for such a high accuracy. The sensor's mechanical precision and robustness are the major factors affecting system performance. Also, deformation of the electric field at the ends of the sensor may cause nonlinearity.

Another aspect of system performance is drift versus temperature. The permittivity of the moving dielectric varies with temperature, and the dimensions of the sensor change with temperature. The silicon-based CDC features typical gain drift of -25 ppm/°C. However, these system errors can be compensated. If the temperature drift of the sensor is known and the temperature is measured, an algorithm in the host software can compensate the system temperature errors. An alternative method for compensating temperature drift is to measure a second fixed capacitor with the same sandwich structure as the main sensor, and then basing the result on a comparison between the moving and fixed part of the sensor.

The AD7746, with its on-chip temperature sensor and a second capacitive channel, supports both temperature-compensation methods. The part is specified for an operating temperature range of -40°C to +125°C, allowing it close location to the sensor itself. In this situation, the silicon temperature and the sensor temperature can be considered equal in most applications. But the part also has standard differential voltage and reference inputs, enabling an easy interface to an external temperature sensor (e.g., a thermistor or RTD).