Dave Wuchinich, Modal Mechanics, Yonkers, NY; Edited by Brad Thompson and Fran Granville -- EDN, 11/23/2006
A typical piezoelectric sensor comprises a disk of PZT-5A ceramic material with metallized electrodes on its
surfaces. Applying electrically conductive epoxy to the electrodes connects external wiring to the sensor. An insulating adhesive attaches the assembly to the structure under test and isolates the sensor from ground-referenced potentials. The disk faces the direction of the expected acceleration. When you mount the piezoelectric disk on a target structure, it serves as a simple force sensor and accelerometer by producing a voltage that's directly proportional to the force acting parallel to the disk's direction of polarization. A piezoelectric disk's capacitive impedance presents a large reactance at low frequencies, making the disk and its wiring susceptible to interference that surrounding electrical equipment and power lines produce. Placing the sensor in a remote location requires shielded interconnecting cable, but even shielding is not entirely effective in removing common-mode signals because noise pickup can still occur at the disk's conductive surfaces.
One method of extracting the sensor's signal employs an instrumentation amplifier, which amplifies only the potential the sensor produces; the amplifier rejects common-mode-coupled noise potential that appears on each of the sensor's terminals.
A typical miniature piezoelectric- disk sensor that's 0.125 in. in diameter and 0.0075 in. thick presents a capacitance of approximately 500 pF. If the measurement application requires a dynamic response to force excitation frequencies of 10 Hz or below, the sensor's output reactance ranges into the tens of megohms. The circuit's pc-board insulating substrate and ambient humidity impose a practical limit of approximately 10 MΩ on the amplifier's input resistance.
You must carefully choose insulation and apply guarding potentials, and you must use an amplifier with picoampere input-bias currents. Otherwise, the sensor's capacitance and the amplifier's input-bias-current resistors impose a phase shift on the signal you apply to the instrumentation amplifier. To eliminate guarding and elaborate insulation requirements, the circuit in Figure 1 uses an instrumentation amplifier with feedback to measure the sensor's short-circuit current and not its open-circuit voltage. VCM, the common-mode voltage between the sensor and the signal ground, results from nearby noise sources resulting from stray capacitive coupling. The following equation relates the sensor's output current, i, and its open-circuit output voltage, ES:
where A represents IC1's voltage gain, and R="R1"=R2 in Figure 1. Resistors R1 and R2 provide feedback and input-bias-current-return paths for IC1, an INA121 instrumentation amplifier, and resistor RG sets the amplifier's gain. The INA121's input-bias-offset current of 0.5 pA produces 5 μV of voltage offset across its 10-MΩ feedback resistors. At an amplifier gain of 500, IC1's output offset amounts to 2.5 mV. Amplifier IC2, a TL081, provides unity-gain signal inversion.
jωCS, then i≈jωCSES, and amplifier IC1's input voltage, VI, vanishes because the amplifier's input terminals act as a virtual short circuit across the sensor. Taking the sum of voltages around the loop comprising the instrumentation and inverting amplifiers' output, the two feedback resistors and the instrumentation amplifier's input terminals, whose potential difference is zero, yields eO="j"ωRCES, where eO represents IC1's output and also the negative value of IC2's output.
An operational-amplifier-based integrator, IC3, delivers the value for ES at IC3's output, E' in the following equation.
For the component values in Figure 1, IC1 provides a gain of 500. Resistors R1 and R2 are equal at 10 MΩ, and the piezoelectric sensor's capacitance measures 500 pF. For the highest frequency of interest, 10 Hz, the quantity 2RωCS=0.6<<2A+1=501 and the sensor's output, ES, appear without phase error as E'. This circuit can measure quasistatic force changes; the circuit's ability to sustain a charge on C1 imposes the ultimate limit on the circuit's frequency response.