Electronics Guide

Wheatstone Bridge Fundamentals

A Wheatstone bridge consists of four resistive elements arranged in a diamond pattern with excitation voltage applied across one diagonal and the output signal measured across the other. When all four resistors are equal, the bridge is balanced and produces zero output voltage. Changing one or more resistor values unbalances the bridge, producing an output voltage proportional to the resistance change.

The basic bridge output equation is:

Vout = Vex [(R1/(R1+R2)) - (R3/(R3+R4))]

For small resistance changes in a single active element, this simplifies to approximately:

Vout = Vex (deltaR/4R)

This output is inherently ratiometric: if the excitation voltage changes, both the bridge output and the reference used for measurement change proportionally, canceling the effect of excitation variations.

Bridge Configurations

Bridges can employ one, two, or four active sensing elements, each configuration offering different sensitivity and compensation characteristics:

• Quarter bridge: One active element, three fixed resistors. Provides the simplest implementation but offers no inherent temperature compensation and half the sensitivity of a half bridge.
• Half bridge: Two active elements in adjacent or opposite arms. Adjacent-arm configuration doubles sensitivity; opposite-arm configuration provides temperature compensation when sensors experience the same temperature but opposite strain.
• Full bridge: Four active elements, all sensing. Provides maximum sensitivity (four times quarter bridge) and excellent temperature compensation when properly configured. Common in load cells and pressure sensors.

Excitation Methods

Bridge excitation can use voltage or current sources, each with distinct characteristics:

Voltage excitation is simpler to implement and provides constant output sensitivity regardless of total bridge resistance. However, resistance changes in the cable connecting the bridge to the excitation source introduce errors by dropping voltage before it reaches the bridge.

Current excitation eliminates lead resistance errors because the excitation current flows equally through all resistive paths. The output sensitivity depends on the absolute resistance values, making it more susceptible to sensor-to-sensor variations but less susceptible to cable effects.

Remote sensing techniques can compensate for lead resistance in voltage-excited bridges by using additional wires to measure the actual voltage at the bridge rather than at the excitation source.

Bridge Linearization

The basic bridge equation contains an inherent nonlinearity: output voltage is not strictly proportional to resistance change, particularly for large changes. For a quarter bridge with one active element:

Vout/Vex = (deltaR/R) / (4 + 2(deltaR/R))

Several techniques address this nonlinearity:

• Keep changes small: For deltaR/R less than 1%, nonlinearity remains below 0.5%, acceptable for many applications.
• Constant current excitation: Using current rather than voltage excitation provides inherent linearization for single-element changes.
• Feedback linearization: Placing the bridge in an op-amp feedback loop with current-source drive achieves excellent linearity.
• Digital correction: Characterizing the nonlinearity and applying polynomial correction in firmware can achieve arbitrary accuracy.

Bridge Amplifier Design

Instrumentation amplifiers are the standard interface for bridge outputs, offering high input impedance, excellent common-mode rejection, and precise differential gain. Key design considerations include:

• Common-mode voltage: The bridge output rides on a common-mode voltage of approximately half the excitation voltage. The amplifier must handle this common-mode level while accurately amplifying the small differential signal.
• Gain selection: Choose gain to utilize the full input range of the following ADC while maintaining adequate noise margin.
• Offset adjustment: Bridge imbalance produces offset voltage that may require nulling before or after amplification.
• Filtering: Low-pass filtering after amplification rejects high-frequency noise while preserving measurement bandwidth.

Thermocouple Principles

When two dissimilar metals join at a point, the junction generates a voltage that depends on temperature and the metal types. This Seebeck voltage typically ranges from microvolts to tens of millivolts over the sensor's operating range, requiring high-gain, low-noise amplification.

Different thermocouple types offer various temperature ranges and sensitivities:

• Type K (Chromel-Alumel): Most common general-purpose type, -200 to +1260 degrees Celsius, approximately 41 microvolts per degree Celsius
• Type J (Iron-Constantan): Popular for moderate temperatures, -40 to +750 degrees Celsius, approximately 52 microvolts per degree Celsius
• Type T (Copper-Constantan): Excellent for cryogenic to moderate temperatures, -200 to +350 degrees Celsius, approximately 43 microvolts per degree Celsius
• Type E (Chromel-Constantan): Highest sensitivity, -40 to +900 degrees Celsius, approximately 68 microvolts per degree Celsius
• Types R, S, B (Platinum-based): High-temperature applications up to 1800 degrees Celsius, lower sensitivity

The Cold Junction Problem

The measured thermocouple voltage depends on both the sensing junction temperature and the cold junction temperature. If the cold junction is at 0 degrees Celsius (the traditional ice-bath reference), standard thermocouple tables directly convert voltage to temperature. In practical circuits, the cold junction is at ambient temperature, which varies.

The solution requires measuring the cold junction temperature with a separate sensor and either adding a compensating voltage or correcting the measurement in software:

Tsensing = f(Vmeasured + Vcompensation)

where Vcompensation is the voltage the thermocouple would produce if the cold junction were at its actual temperature and the sensing junction were at 0 degrees Celsius.

Hardware Compensation Techniques

Hardware cold junction compensation adds a temperature-dependent voltage to the thermocouple signal before amplification:

• Thermistor-based compensation: A thermistor in a bridge or voltage divider network generates a voltage that varies with cold junction temperature. Component values are chosen to match the thermocouple's Seebeck coefficient over the expected ambient temperature range.
• Semiconductor temperature sensor: Linear temperature sensors like the LM35 or AD590 provide voltages or currents proportional to temperature that can be scaled and added to the thermocouple signal.
• Integrated compensation ICs: Specialized chips combine temperature sensing with precision voltage generation, optimized for specific thermocouple types. Examples include the AD594/AD595 series for types J and K.

Software Compensation

Digital cold junction compensation measures both the thermocouple voltage and the cold junction temperature independently, then combines them mathematically:

1. Measure cold junction temperature with a precision sensor (RTD, thermistor, or IC sensor)
2. Convert cold junction temperature to equivalent thermocouple voltage using polynomial or lookup table
3. Add this voltage to the measured thermocouple voltage
4. Convert the total voltage to sensing junction temperature

Software compensation offers flexibility (any thermocouple type with appropriate tables), accuracy (can use high-order polynomials for linearization), and the ability to handle nonstandard reference temperatures.

Thermocouple Amplifier Design

Thermocouple amplifiers face demanding requirements:

• Low offset voltage: With signals as low as tens of microvolts, input offset voltage directly affects accuracy. Chopper-stabilized or auto-zero amplifiers achieve sub-microvolt offsets.
• Low drift: Offset voltage drift with temperature must be small compared to the thermocouple sensitivity, typically below 1 microvolt per degree Celsius.
• High common-mode rejection: Ground loops and electromagnetic interference can create large common-mode voltages that must not appear as signal errors.
• Input protection: Thermocouples may connect to grounded objects at different potentials, requiring protection against large common-mode voltages.
• Open thermocouple detection: When a thermocouple fails open, the amplifier input floats, potentially giving false readings. A small bias current or detection circuit should identify this condition.

RTD Characteristics

RTDs use the predictable resistance-temperature relationship of pure metals, most commonly platinum. The platinum RTD (often called a PRT or Pt100/Pt1000) serves as the industrial standard for precision temperature measurement:

• Pt100: 100 ohms at 0 degrees Celsius, sensitivity approximately 0.385 ohms per degree Celsius
• Pt1000: 1000 ohms at 0 degrees Celsius, ten times higher signal levels reduce lead resistance effects
• Temperature range: -200 to +850 degrees Celsius for industrial grades
• Accuracy classes: Class A (plus or minus 0.15 degrees Celsius at 0 degrees Celsius) to Class C (plus or minus 0.6 degrees Celsius)

The Callendar-Van Dusen equation describes RTD resistance versus temperature:

R(T) = R0[1 + AT + BT^2 + C(T-100)T^3]

where coefficients A, B, and C are standardized for platinum RTDs, and the cubic term applies only below 0 degrees Celsius.

RTD Excitation and Self-Heating

RTD interfaces must measure resistance without causing significant self-heating. Power dissipation in the sensing element raises its temperature above ambient, introducing measurement error. The self-heating coefficient, typically 0.1 to 1 degree Celsius per milliwatt depending on sensor construction and thermal environment, determines acceptable excitation levels.

For a Pt100 at 1 mA excitation current, power dissipation is approximately 0.1 mW, causing negligible self-heating in most applications. Higher currents improve signal-to-noise ratio but increase self-heating; the optimal balance depends on the specific sensor and required accuracy.

Lead Resistance Compensation

The relatively low resistance and sensitivity of RTDs makes lead resistance significant. Various wiring configurations address this:

• 2-wire connection: Simplest but includes lead resistance in measurement. Acceptable only for short leads or when lead resistance is known and stable.
• 3-wire connection: Adds a third wire to measure and compensate for lead resistance, assuming both leads have equal resistance. Most common industrial configuration.
• 4-wire (Kelvin) connection: Separate pairs for current excitation and voltage sensing completely eliminate lead resistance effects. Required for highest accuracy.

Thermistor Characteristics

Thermistors are ceramic semiconductor devices exhibiting large resistance changes with temperature. NTC (negative temperature coefficient) types decrease resistance with increasing temperature and are most common for measurement applications:

• High sensitivity: Typically 3-5% resistance change per degree Celsius, ten times higher than RTDs
• Nonlinear response: Resistance varies exponentially with temperature, requiring linearization
• Fast response: Small thermal mass enables rapid temperature tracking
• Limited range: Most accurate over a 50-100 degree span within their operating limits
• Interchangeability challenges: Resistance tolerance and beta variation require individual calibration for precision work

Thermistor Linearization

The highly nonlinear thermistor response requires linearization for practical use. Several techniques apply:

• Parallel resistance: Adding a fixed resistor in parallel with the thermistor straightens the response curve over a limited range. The optimal parallel resistance equals the thermistor resistance at the center of the desired range.
• Voltage divider optimization: Choosing the series resistor in a voltage divider to equal the thermistor resistance at mid-range provides approximately linear voltage output over that range.
• Steinhart-Hart equation: The polynomial relationship 1/T = A + B(lnR) + C(lnR)^3 accurately models thermistor behavior over wide ranges, enabling software linearization.
• Lookup tables: For digital systems, storing measured resistance-temperature pairs and interpolating provides arbitrary accuracy without complex calculations.

RTD and Thermistor Interface Circuits

Common interface approaches include:

• Bridge circuits: Place the sensor in a Wheatstone bridge for differential output and reduced sensitivity to excitation variations. Works well with 4-wire RTD connection using remote sensing.
• Current source excitation: Drive the sensor with a precision current source and measure the resulting voltage. Simplifies 4-wire RTD measurement and provides consistent sensitivity across the temperature range.
• Ratiometric measurement: Use the same reference for both sensor excitation and ADC reference, canceling effects of reference drift.
• Sigma-delta ADCs: Modern sigma-delta converters with integrated current sources and multiplexed inputs provide complete RTD interface solutions with minimal external components.

Strain Gauge Fundamentals

A strain gauge consists of a resistive element (typically metal foil or semiconductor) that changes resistance when mechanically stretched or compressed. The gauge factor relates resistance change to applied strain:

GF = (deltaR/R) / epsilon

where epsilon is the mechanical strain (change in length divided by original length). Metal foil gauges typically have gauge factors of 2-4, while semiconductor gauges can achieve factors of 50-200 but with poorer temperature stability.

For a gauge factor of 2 and typical measurable strains of 1000 microstrain (0.1%), the resistance change is only 0.2%, producing millivolt-level signals from a bridge with typical excitation voltages.

Bridge Configuration for Strain Measurement

Strain gauges almost universally operate in bridge configurations to maximize sensitivity and provide temperature compensation:

• Quarter bridge: Single active gauge with three completion resistors. Requires external temperature compensation and offers lowest sensitivity.
• Half bridge (bending): Two gauges on opposite surfaces of a beam in adjacent arms. Provides temperature compensation and doubles sensitivity for bending strain while rejecting axial strain.
• Half bridge (axial): Two gauges in opposite arms, one axial and one transverse (Poisson gauge). Temperature compensated with sensitivity between quarter and full bridge.
• Full bridge: Four active gauges in a complete bridge. Maximum sensitivity, excellent temperature compensation, and ability to reject unwanted strain components. Standard configuration for load cells and force transducers.

Excitation Considerations

Strain gauge excitation involves trade-offs between signal level, self-heating, and stability:

• Voltage versus current excitation: Voltage excitation is simpler but sensitivity decreases as gauge resistance increases with temperature. Current excitation maintains constant sensitivity but requires more complex circuits.
• AC versus DC excitation: DC excitation is standard for most applications. AC excitation at carrier frequencies (1-10 kHz) offers improved noise rejection and enables the use of transformer coupling for isolation, but adds circuit complexity.
• Excitation level: Higher excitation improves signal-to-noise ratio but increases self-heating. Typical excitation voltages range from 1 to 10 volts, with power dissipation limited to perhaps 50 mW per gauge.

Amplifier Requirements

Strain gauge amplifiers must meet demanding specifications:

• High gain: Full-scale bridge outputs typically range from 2 to 20 mV, requiring gains of 100-1000 to produce full-scale voltage for an ADC.
• Low noise: Noise referred to the input should be small compared to the resolution required. For 16-bit measurement of a 10 mV signal, input-referred noise must be below about 150 nV RMS.
• Excellent CMRR: The bridge output rides on a common-mode voltage of half the excitation. With 5 V excitation and 10 mV differential output, achieving 0.01% accuracy requires CMRR exceeding 100 dB.
• Low drift: Offset and gain drift with temperature should not exceed the desired measurement stability.
• Wide bandwidth: Static strain measurements require only DC response, but dynamic strain measurement may need bandwidths from Hz to kHz depending on the application.

Practical Amplifier Topologies

Several amplifier configurations suit strain gauge applications:

• Discrete instrumentation amplifier: Three op-amps in the classic in-amp topology provide flexibility in gain selection and the ability to optimize each stage independently.
• Integrated instrumentation amplifier: Devices like the INA114, AD620, or AD8421 offer excellent performance with minimal external components. Internal laser-trimmed resistors ensure high CMRR.
• Programmable gain amplifiers: PGAs with multiple gain settings enable auto-ranging to maximize resolution across varying signal levels.
• Integrated signal conditioners: Complete strain gauge conditioner ICs include excitation, amplification, filtering, and sometimes digitization in a single device.

Noise Reduction Techniques

Achieving the signal-to-noise ratios required for precision strain measurement requires attention to multiple noise sources:

• Shielding: Shielded cables and shielded bridge enclosures reduce electromagnetic interference pickup.
• Twisted pairs: Twisting the excitation and signal wires minimizes magnetically-induced noise.
• Filtering: Low-pass filters at the amplifier input and output reject high-frequency noise. The bandwidth should match the signal requirements.
• Synchronous detection: With AC excitation, synchronous demodulation rejects noise at frequencies other than the carrier.
• Averaging: Digital oversampling and averaging improve effective resolution beyond the ADC's native capability.

Capacitive Sensing Principles

Capacitance depends on geometry and material properties:

C = epsilon * A / d

where epsilon is the permittivity, A is the plate area, and d is the separation. Capacitive sensors exploit changes in any of these parameters:

• Variable gap: Position and pressure sensors vary the plate separation, changing capacitance inversely with distance.
• Variable area: Linear and rotary position sensors vary the overlapping plate area, producing linear capacitance change with position.
• Variable dielectric: Level sensors, humidity sensors, and material analyzers detect changes in the dielectric material between plates.

Excitation Methods

Capacitive sensors require AC excitation, typically at frequencies from 1 kHz to 1 MHz:

• Sine wave excitation: Provides clean, well-defined excitation but requires linear amplifiers and precision rectification for demodulation.
• Square wave excitation: Easier to generate and enables simple switching circuits for charge-based measurement.
• Pulse excitation: Charging a capacitor through a known resistance and measuring charge time provides a simple frequency or time-domain output.

Higher excitation frequencies improve signal levels (capacitive reactance decreases with frequency) and reduce noise susceptibility, but increase power consumption and may cause electromagnetic compatibility issues.

Impedance Measurement Approaches

Several circuit topologies measure capacitance or capacitance changes:

• AC bridge: Similar to resistive bridges but using capacitors as bridge elements. The output voltage varies with capacitance imbalance and excitation frequency. Requires phase-sensitive detection to separate reactive and resistive components.
• Charge amplifier: Measures the charge transferred to a capacitor when switched between voltage levels. Output voltage is proportional to the ratio of sensor and feedback capacitance.
• Oscillator frequency: Using the sensor capacitance as part of an LC or RC oscillator produces frequency output proportional to capacitance. Simple and noise-resistant but requires frequency measurement.
• Sigma-delta modulator: The capacitor-switching action in sigma-delta converters naturally measures capacitance ratio, making them well-suited for capacitive sensor interfaces.

Synchronous Demodulation

Synchronous (or phase-sensitive) demodulation extracts the capacitance-related signal while rejecting noise at other frequencies:

1. The sensor is excited with a sinusoidal or square wave at a known frequency
2. The resulting signal is amplified to useful levels
3. A synchronous demodulator multiplies the signal by a reference at the excitation frequency
4. Low-pass filtering extracts the DC component, which is proportional to capacitance

This technique provides excellent noise rejection because only signals at exactly the excitation frequency and in phase with it produce DC output. Noise at other frequencies averages to zero.

Parasitic Capacitance Handling

Capacitive sensors typically produce very small signals (femtofarads to picofarads of change), making them susceptible to parasitic capacitance from cables, PCB traces, and sensor construction. Several techniques minimize these effects:

• Driven shields: Surrounding the sensitive node with a conductor driven to the same potential eliminates the capacitance between them. The shield "follows" the sensor signal, preventing current flow.
• Differential measurement: Using two sensors in a differential configuration cancels common-mode parasitic effects.
• Ratiometric techniques: Measuring the ratio of two capacitances rather than absolute values cancels many error sources.
• Short connections: Mounting the interface electronics close to the sensor minimizes cable capacitance.

Integrated Capacitive Interface ICs

Several integrated circuits provide complete capacitive sensor interfaces:

• Capacitance-to-digital converters: Devices like the AD7745/AD7746 and FDC1004 directly convert capacitance to digital values with resolution approaching 4 aF (attofarads).
• Capacitive touch controllers: Specialized ICs for proximity sensing and touch interfaces handle multiple channels with automatic calibration.
• Programmable analog front-ends: General-purpose analog front-ends can be configured for capacitive measurement with appropriate firmware.

LVDT Operating Principles

An LVDT consists of a primary winding and two secondary windings wound on a hollow cylindrical form. A ferromagnetic core slides within the bore, coupling the primary to the secondaries. The position of the core determines the differential voltage between the two secondaries:

• At center position, equal coupling to both secondaries produces zero differential output
• Moving the core toward one secondary increases its coupling while decreasing the other's
• The magnitude of the differential output indicates displacement from center
• The phase of the output (0 or 180 degrees relative to excitation) indicates direction

LVDT Excitation

LVDTs require sinusoidal excitation, typically at frequencies from 50 Hz to 20 kHz, with 1-10 kHz being most common:

• Frequency selection: Higher frequencies provide faster response but increase core losses. The frequency should be at least 10 times higher than the maximum rate of position change.
• Voltage level: Typical excitation is 1-10 V RMS. Higher voltage increases output signal level but also increases power dissipation.
• Stability requirements: Because LVDT sensitivity depends on excitation voltage, ratiometric measurement (comparing output to excitation) provides best accuracy.

LVDT Signal Processing

Processing the LVDT output involves several stages:

1. Differential amplification: Amplify the difference between the two secondary outputs, rejecting common-mode noise.
2. Synchronous demodulation: Multiply by the excitation signal to extract magnitude and sign. This converts the AC signal to DC proportional to position.
3. Low-pass filtering: Remove the residual carrier frequency and its harmonics, leaving only the position-dependent DC component.
4. Ratiometric processing: Dividing by the excitation amplitude or summed secondary outputs improves accuracy when excitation varies.

Resolver Principles

A resolver is a rotary transformer that provides absolute angular position measurement. It contains one rotor winding (excited with AC) and two stator windings oriented 90 degrees apart:

• The rotor winding couples to both stator windings, with coupling depending on rotor angle
• One stator output varies as sin(theta) times the excitation amplitude
• The other stator output varies as cos(theta) times the excitation amplitude
• Together, sine and cosine signals provide unambiguous angle measurement over a full rotation

Resolver-to-Digital Conversion

Converting resolver outputs to digital angle requires extracting the angle from sine and cosine signals:

• Tracking converter: A feedback system adjusts a digital angle estimate until a resolver pattern generator produces signals matching the actual resolver outputs. Provides continuous tracking with update rates in the tens of kHz and resolutions to 16 bits or higher.
• Direct conversion: Sample both sine and cosine channels and compute arctangent digitally. Modern converters can achieve 14-16 bit resolution with update rates exceeding 100 kHz.
• Integrated RDCs: Resolver-to-digital converter ICs like the AD2S1210 combine excitation generation, analog signal processing, and digital conversion in a single device.

Synchro and LVDT Signal Conditioning ICs

Specialized ICs simplify LVDT and resolver interfaces:

• AD598: Complete LVDT signal conditioner with on-chip oscillator, synchronous demodulator, and ratiometric output.
• AD698: Similar to AD598 with improved specifications and differential output capability.
• AD2S1210: Resolver-to-digital converter with programmable resolution from 10 to 16 bits and tracking rate to 3125 revolutions per second.

Photodiode Operating Modes

Photodiodes can operate in two distinct modes:

• Photovoltaic (zero-bias) mode: No external bias, the photodiode generates its own voltage. Offers lowest noise but highest junction capacitance and slowest response. Best for precision low-speed measurements.
• Photoconductive (reverse-bias) mode: External reverse bias reduces junction capacitance and improves speed, but increases dark current (leakage current) and associated noise. Preferred for high-speed applications.

Transimpedance Amplifier Design

The basic transimpedance amplifier connects the photodiode to the op-amp's inverting input, with a feedback resistor setting the gain (transimpedance):

Vout = -Iphoto x Rf

The op-amp maintains the inverting input at virtual ground, so the photodiode operates at essentially zero bias (or constant bias if a reference voltage is applied to the non-inverting input).

Key design parameters include:

• Feedback resistance: Determines sensitivity (volts per amp). Higher Rf increases gain but also increases noise and reduces bandwidth.
• Feedback capacitance: Required for stability when photodiode capacitance is significant. Must be carefully chosen to balance stability against bandwidth reduction.
• Op-amp selection: Low input bias current prevents offset errors; low noise minimizes equivalent input current noise; adequate gain-bandwidth product ensures stability and desired signal bandwidth.

Stability Considerations

The photodiode's junction capacitance in parallel with the op-amp's input capacitance creates a pole in the feedback network that can cause instability. Without compensation, the transimpedance amplifier may oscillate or show excessive peaking in its frequency response.

Compensation approaches include:

• Feedback capacitor: Adding Cf in parallel with Rf creates a zero that compensates for the input capacitance pole. The optimum value depends on Rf, total input capacitance, and op-amp gain-bandwidth product.
• Optimal Cf calculation: For a critically damped response, Cf approximately equals the square root of (Cin / (2 x pi x Rf x GBW)), where Cin is total input capacitance and GBW is the op-amp's gain-bandwidth product.
• Integrated transimpedance amplifiers: Some op-amps are specifically designed and internally compensated for transimpedance applications.

Noise Analysis

Three primary noise sources affect photodiode amplifier performance:

• Johnson noise from Rf: The feedback resistor contributes thermal noise with RMS current in = sqrt(4kT*BW/Rf). This noise decreases with increasing Rf, favoring higher feedback resistance for low-noise design.
• Op-amp current noise: Input current noise appears directly at the output multiplied by Rf. Select op-amps with low current noise for high-gain applications.
• Op-amp voltage noise: Input voltage noise is amplified by the noise gain, which increases with frequency due to input capacitance. This makes voltage noise the dominant source at high frequencies with large input capacitance.

Total noise optimization requires balancing these sources against bandwidth and stability requirements.

Wide Dynamic Range Considerations

Light intensity can vary over many orders of magnitude, requiring special techniques for wide dynamic range:

• Switchable gain: Multiple feedback resistors with analog switches enable gain ranging. Care is needed to minimize switch leakage and on-resistance effects.
• Logarithmic amplifiers: Replace the feedback resistor with a diode or transistor junction to produce output proportional to the logarithm of photocurrent, compressing dynamic range.
• Integration mode: Integrate photocurrent on a capacitor for a fixed time, then measure the accumulated voltage. Dynamic range is limited by capacitor size and ADC resolution but can be extended by varying integration time.

Application-Specific Considerations

Different applications emphasize different performance aspects:

• Optical communications: Highest bandwidth (GHz range) with moderate noise performance. Uses reverse-biased PIN or avalanche photodiodes with specialized wideband amplifiers.
• Spectroscopy: Low noise and excellent linearity over wide dynamic range. Often uses zero-bias operation and lock-in detection with chopped light sources.
• Position sensing: Multiple photodiodes in arrays or quadrant configurations. Matching and ratiometric measurement minimize errors from intensity variations.
• Power measurement: Precision current measurement with calibrated responsivity. Often includes temperature compensation for the photodiode's temperature-dependent sensitivity.

Piezoelectric Sensor Characteristics

Piezoelectric sensors behave electrically as a charge source in parallel with a capacitance (the sensor's own dielectric):

• Charge sensitivity: Expressed in picocoulombs per unit input (pC/g for accelerometers, pC/N for force sensors). Typical values range from 1 to 100 pC per unit.
• Sensor capacitance: Typically 100 to 2000 pF, affecting cable and amplifier design.
• Frequency response: Extends from very low frequencies (limited by amplifier time constant) to the sensor's resonance frequency, which can exceed 100 kHz.
• Temperature effects: Sensitivity and capacitance vary with temperature, requiring compensation for precise measurements.

Charge Amplifier Operating Principle

A charge amplifier places a capacitor in the feedback path of an inverting op-amp configuration. The op-amp maintains virtual ground at its inverting input, forcing all sensor charge to transfer to the feedback capacitor:

Vout = -Q / Cf

where Q is the charge from the sensor and Cf is the feedback capacitance. The output voltage is independent of sensor capacitance and cable capacitance, providing consistent sensitivity regardless of cable length.

Low-Frequency Response and Bias

Without a DC path, the charge amplifier output would drift to the supply rails as input bias current accumulates on the feedback capacitor. A high-value resistor in parallel with Cf provides the necessary bias path:

This resistor creates a high-pass filter with cutoff frequency:

fc = 1 / (2 x pi x Rf x Cf)

For measuring low-frequency vibrations, large Rf and Cf values are needed. A 1 Hz cutoff with 100 pF feedback capacitance requires 1.6 gigohms of feedback resistance, necessitating special high-value resistors or active bias techniques.

Practical Charge Amplifier Design

Key design considerations include:

• Input protection: Large transients can generate damaging charge levels. Input clamping diodes or resistors limit voltage excursions.
• Cable considerations: Special low-noise cables minimize triboelectric noise (charge generated by cable flexing). Keep cable runs short when possible.
• Shielding: High-impedance charge inputs are susceptible to electromagnetic interference. Use shielded cables with the shield connected to signal ground.
• Feedback capacitor selection: Use low-leakage capacitors (polystyrene, polypropylene, or C0G ceramic) to minimize drift and maintain low-frequency response.
• Op-amp selection: Choose op-amps with low input bias current (FET input or electrometer types), low noise, and adequate bandwidth for the application.

IEPE (ICP) Sensors

Integrated Electronics Piezoelectric (IEPE), also known as ICP (Integrated Circuit Piezoelectric, a PCB Piezotronics trademark), sensors incorporate a charge amplifier within the sensor housing, providing a voltage output that is easier to interface:

• Constant current excitation: IEPE sensors require constant current bias (typically 2-20 mA) through the signal cable. The internal amplifier modulates this current to superimpose the signal on the bias voltage.
• AC coupling: The output includes a DC bias (typically 8-12 V) that must be removed with AC coupling to reveal the signal.
• Simplified interface: Standard coaxial cable can be used over long distances without the noise sensitivity of charge-mode operation.
• Limited temperature range: The internal electronics limit operating temperature compared to charge-mode sensors.

Applications

Piezoelectric sensors and charge amplifiers find use in:

• Vibration measurement: Accelerometers for machinery monitoring, modal analysis, and seismic sensing
• Dynamic force measurement: Force sensors for impact testing, cutting force measurement, and ballistic studies
• Dynamic pressure: High-frequency pressure transducers for combustion analysis and acoustic measurements
• Acoustic emission: Ultrasonic sensors for non-destructive testing and condition monitoring
• Ultrasonic applications: Transducers for medical imaging, NDT, and sonar systems

System-Level Considerations

Successful sensor interface design requires attention to the complete signal path:

• Grounding: Establish a clear grounding strategy early in design. Separate analog and digital grounds, connect at a single point, and use ground planes to minimize impedance.
• Shielding: Shield sensitive signals from interference sources. Connect shields at one end only (usually the amplifier end) to prevent ground loop currents.
• Power supply considerations: Provide clean, stable power to analog circuits. Use separate regulators for analog and digital sections and include adequate decoupling.
• Temperature management: Consider heat sources in the system and their effect on precision components. Thermal gradients across matched components degrade matching.

Component Selection

Component quality significantly affects interface performance:

• Resistors: Use metal film or thin film for low noise and tight tolerance. Consider temperature coefficient for precision applications.
• Capacitors: Film capacitors (polypropylene, polystyrene) for precision timing and filtering. Avoid general-purpose ceramic types in signal paths.
• Connectors: Choose connectors rated for low-level signals. Gold plating minimizes contact resistance and oxidation.
• PCB material: FR-4 suffices for most applications, but high-frequency or very low leakage designs may require specialized materials.

Calibration and Testing

Proper calibration ensures accuracy:

• End-to-end calibration: Calibrate the complete system including sensor, wiring, and electronics rather than individual components.
• Known reference inputs: Use traceable standards appropriate for the measurement type (calibrated weights, temperature baths, precision resistors).
• Multi-point calibration: Characterize nonlinearity with measurements at multiple points across the operating range.
• Temperature characterization: Measure performance across the expected operating temperature range to enable compensation.