handbook of modern sensors

186 5 Interface Electronic Circuits
output analog voltage V c , which is an approximation of the input signal. This voltage
is subtracted from the input signal and amplified by the amplifier to the value
V D = (V m − V c )A. (5.36)
The voltage V D is an amplified error between the actual and digitally represented
input signals. For a full-scale input signal, the maximum error (V m − V c ) is equal to
a resolution of an A/D converter; therefore, for an eight-bit conversion V D = 19.6A
mV. The multiplexer connects that voltage to the A/D converter, which converts V D
to a digital value C:
C = V D
R 0
= (V m − V c ) A R 0
. (5.37)
As a result, the microprocessor combines two digital values: M and C, where C
represents the high-resolution bits. If A = 255, then for the 5-V full-scale, LSB ≈
77 µV, which corresponds to a total resolution of 16 bits. In practice, it is hard to
achieve such a high resolution because of the errors originating in the D/A converter,
reference voltage, amplifier’s drift, noise, and so forth. Nevertheless, the method is
quite efficient when a modest resolution of 10 or 12 bits is deemed to be sufficient.
5.5 Direct Digitization and Processing
Most sensors produce low-level signals. To bring these signals to levels compatible
with data processing devices, amplifiers are generally required. Unfortunately, amplifiers
and connecting cables and wires may introduce additional errors, add cost to
the instrument, and increase complexity. Some emerging trends in the sensor-based
systems are causing use of the signal conditioning amplifiers to be reevaluated (at
least for some transducers) [5]. In particular, many industrial sensor-fed systems are
employing digital transmission and processing equipment. These trends point toward
direct digitization of sensor outputs—a difficult task. It is especially true when a
sensor-circuit integration on a single chip is considered.
Classical A/D conversion techniques emphasize high-level input ranges. This
allows the LSB step size to be as large as possible, minimizing offset and noise error.
For this reason, a minimum LSB signal is always selected to be at least 100–200 µV.
Therefore, a direct connection of many sensors (e.g., RTD temperature transducers
or piezoresistive strain gauges) is unrealistic. Such transducers’ full-scale output may
be limited by several millivolts, meaning that a 10-bit A/D converter must have about
1 µV LSB.
Direct digitization of transducers eliminates a dc gain stage and may yield a
better performance without sacrificing accuracy. The main idea behind direct digitization
is to incorporate a sensor into a signal converter, (e.g., an A/D converter or an
impedance-to-frequency converter). All such converters perform a modulation process
and, therefore, are nonlinear devices. Hence, they have some kind of nonlinear
circuit, often a threshold comparator. Shifting the threshold level, for instance, may
modulate the output signal, which is a desirable effect.