SENSORS FOR VIBRATION AND SOUND MEASUREMENTS
Strain-Gage Accelerometers
Strain-gage accelerometers contain a small, calibrated mass attached to the free end of a cantilever beam (Also see chapter 7). One strain gage sits on the top of the cantilever beam, and another sits opposite it on the underside. Both strain gages measure the bend of the cantilever, one in compression and the other in tension when the device accelerates in a direction perpendicular to the plane of the gages. First, the product of the mass and acceleration converts to force (F = ma) then force converts to an electrical signal. The gages are calibrated to generate an output signal proportional to the amount of acceleration, typically measured in gravity units or gs. The accelerometers’ natural frequency is usually in the order of several kHz, and in an undamped system, the cantilever-mass combination forms a harmonic resonator with Q near 100,000.

A system with an extremely high Q excited near its resonant frequency produces large oscillations, which can mask the true acceleration signal, produce inaccurate measurements, and damage the sensor. Consequently, oil or a similar material is frequently added to control the damping. Figures 8.01 and 8.02 show the frequency response of harmonic resonators with Q = 1 and 100,000. For Q = 100,000, the accelerometer is accurate within 10% to 1/3 of its resonant frequency. In contrast, for Q = 1, the accelerometer is accurate within 10% to half of its resonant frequency.

Most strain gages in accelerometers are wired in Wheatstone bridge circuits. Signal conditioners for a common strain-gage bridge also apply to this type of transducer since it resembles a strain-gage circuit in a load cell.

Piezoelectric Transducers
Piezoelectric materials also are used in accelerometers and microphones. They generate electrical charges on opposite faces of the crystal under dynamic mechanical forces including compression, tension, and twisting. A variety of transducers, such as microphones use piezoelectric elements to convert sound energy picked up by a diaphragm into electrical signals. Conversely, sonic transducers use piezoelectric elements to convert electrical signals into sound energy. Quartz is one of the most common materials applied in piezoelectric transducers and are readily available. Another common material is a piezoceramic material, composed of lead, zirconate, and titinate (PZT).

From an electrical viewpoint, a piezoelectric device resembles a capacitor containing a time varying charge, Q(t). The charge is proportional to the force on the crystal and is usually measured with either a voltage or charge amplifier.

Voltage Amplifier
In Figure 8.03, the voltage amplifier’s gain is 1. Adding feedback resistors or increasing the number of amplifier stages changes the gain. The amplifier converts the high-impedance voltage input to a low-impedance voltage output. The voltage is Q/C, where Q is the charge in coulombs, and the C is the capacitance in Farads, which includes both the sensor and the lead capacitance. When calibrating a charge amplifier, the cable capacitance is part of the charge equation, so replacing the cable without recalibration can change the instrument’s output accuracy.

Charge Amplifier
The charge amplifier shown in Figure 8.03 is extremely versatile because its output voltage is V = Q/C where Q is the charge, and C is the feedback capacitance. When the operational amplifier has an extremely large open-loop gain, the output voltage is independent of the cable capacitance. This lets the amplifier work well even when it’s located several meters away from the sensor. However, because electrical noise increases in proportion to cable length, noise susceptibility determines the maximum permissible cable length more than does device sensitivity. The charge amplifier doubles as a high-pass filter with lower corner frequency f = 1/(2pRC), but this represents a trade-off between sensitivity and frequency response. Decreasing C increases sensitivity, but it also increases the lower corner frequency.

PZT-type sensors can’t make static measurements because of its leakage resistance and high output impedance, which ranges from 10¹⁰ to 10¹² W. Such leakage resistance combined with a capacitance of several hundred pF, yields a time constant of a few seconds.

Low-Impedance Transducers
Most modern piezoelectric transducers contain integrated signal conditioning amplifiers (See Figure 8.04). Also known as integrated-circuit piezoelectric transducers, these units have a low impedance output and require an external power supply. The manufacturer usually specifies their sensitivity and frequency range. Users need only connect a supply to the power terminals and the output to a voltmeter circuit. The voltage is then scaled to the measured engineering units.

The most common application for piezoelectric-type accelerometers is in measuring a wide range of accelerations and mechanical vibrations. They monitor automobile deceleration (and deploy the air bag at the correct millisecond) in safety systems, lift-off acceleration and motion during space-shuttle missions, and mechanical vibration in numerous machines. Piezoelectric sensors, however, cannot measure constant acceleration as do strain-gage sensors.

Low-impedance piezoelectric transducers also measure pressure or force. The accelerometer circuit requires only two wires to handle both power and signals. Due to the sensor’s low impedance, the system is not sensitive to externally introduced or triboelectric-cable noise or cable length. Piezoelectric sensors have resonant frequencies as high as 120 kHz giving them a usable frequency range of less than 1 Hz to more than 40 kHz.

Figure 8.05 shows a simplified connection scheme between an accelerometer and signal-conditioning card. The voltage developed across R is applied to the gate of the MOSFET, which receives power from a constant-current source of 2 to 4 mA. The MOSFET circuits bias off at approximately 12 V in the quiescent state. When the system is excited, voltage develops across the crystal, which is applied to the gate of the MOSFET. The voltage produces linear variations in the MOSFET’s impedance, which, in turn, produces a proportional change in the bias voltage. This voltage change couples to the input amplifier through capacitor C. The value of R and the internal capacitance of the piezoelectric crystal control the low-frequency corner. Units weighing only a few hundred grams generate high-level outputs to 10 mV/g with response to frequencies from 0.3 Hz to 2 kHz. Smaller units with less sensitivity respond to frequencies from 1 Hz to 35 kHz.

The constant-current source provides a source-to-gate bias for the FET. As the gate current responds to changes in applied pressure on the crystal, the drain-to-source voltage (Vds), and the voltage out of the preamplifier change proportionally. An ac coupling circuit or a high-pass filter is always necessary because of the high dc offset at Vds that develops from the bias current. The cutoff frequency of the high-pass filter depends on the application and the particular accelerometer (See Figure 8.06).

To eliminate the need for an outboard preamplifier, some accelerometers contain the current source and the ac coupling circuitry. This feature also lets accelerometers connect to the data acquisition system through simple BNC connectors. Most accelerometers, however, require an amplifier and filter on the output before the analog to digital conversion stage. Also, the programmable-gain amplifier lets the operator adjust the gain for optimum response.

Along with programmable amplifiers, programmable low-pass filters reject unwanted high-frequency signals. The signals typically come from noise or high-frequency vibrations that do not relate to the application. When developing the front-end circuitry for this type of measurement, noise rejection and bandwidth are primary concerns. As the bandwidth increases, the noise can increase as well. Low-pass filters also should be used in most accelerometer conditioning circuits to reduce noise and aliasing effects. The cutoff frequency of the low-pass filter should be close to the system’s maximum useful operating frequency.

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