FIGURE 6.35 A practical charge amplifier. The effective feedback resistance is a function of other resistances. It is possible to reduce the output drift substantially by selecting the resistors suitably. The accuracy of this circuit can be improved further by cascading two or more amplifiers, thereby substantially improving the signal-to-noise ratio.

Pulse Width Modulation

As in the case of some capacitive vibrational displacement sensors, the output of the sensor may be an amplitude-modulated wave as shown in Figure 6.36. When rectified, the average value of this wave gives the mean separation of the plates. The vibration amplitude around this mean position may be extracted by a demodulator and a low-pass filter circuit. The output of the low-pass filter is a direct indication of vibrations, and the waveform can be viewed on an oscilloscope.

Square Wave Linearization

Another linearization technique applied in capacitive pressure transducers and accelerometers is pulse width modulation. The transducer consists of two differential capacitors as shown in Figure 6.37. The voltages of these capacitors, e1 and e2, switch back and forth with a high excitation frequency (e.g., 400 kHz) between excitation voltage and ground. The system is arranged in such a way that the output voltage is the average voltage difference between e1 and e2. At null position, e1 = e2, the output is a symmetrical square wave with zero average value. As the relative positions of the plates change, due to vibration, the average value of the output voltage shifts from the zero average value and becomes positive or negative depending on the direction of the displacement. Hence, the output voltage can be expressed by:

© 1999 by CRC Press LLC

FIGURE 6.36 A amplitude modulated signal. It is possible to configure some sensors to give a amplitude-modulated signals, as in the case of capacitive vibrational displacement sensors. When rectified, the average value of this wave gives the mean separation of the plates. The vibration amplitude around this mean position can be extracted by a demodulator and low-pass filter circuit. The output of the low-pass filter is a direct indication of vibrations.

FIGURE 6.37 Block diagram of a square-wave linearization circuit. This is particularly useful for differential capacitance type sensors. The voltages of these two capacitors are made to switch back and forth with a high excitation frequency between excitation voltage and ground. As the relative positions of the plates change due to vibration, the average value of the output voltage becomes positive or negative, depending on the direction of the displacement.

yields

Thus, the output is directly proportional to the variable xi.

Feedback Linearization

Linearization of a capacitance transducer can also be obtained using a feedback system that adjusts capacitor current amplitude so that it stays constant at a reference value for all displacements. This is accomplished by obtaining a dc signal proportional to capacitor current from a demodulator, comparing this current with the reference current, and adjusting the voltage amplitude of the system excitation oscillator until the two currents agree. If the capacitor current is kept constant irrespective of capacitor motion, then the voltage amplitude is linearly related to x as:

© 1999 by CRC Press LLC