handbook of modern sensors

190 5 Interface Electronic Circuits
5.6 Ratiometric Circuits
A powerful method for improving the accuracy of a sensor is a ratiometric technique,
which is one of the most popular methods of signal conditioning. It should be emphasized,
however, that the method is useful only if a source of error has a multiplicative
nature but not additive; that is, the technique would be useless for reducing, for instance,
thermal noise. On the other hand, it is quite potent for solving such problems
as the dependence of a sensor’s sensitivity to such factors as power-supply instability,
ambient temperature, humidity, pressure, effects of aging, and so forth. The technique
essentially requires the use of two sensors, of which one is the acting sensor, which
responds to an external stimulus, and the other is a compensating sensor, which is
either shielded from that stimulus or is insensitive to it. Both sensors must be exposed
to all other external effects which may multiplicatively change their performance.
The second sensor, which is often called reference, must be subjected to a reference
stimulus, which is ultimately stable during the lifetime of the product. In many practical
systems, the reference sensor must not necessarily be exactly similar to the acting
sensor; however, its physical properties, which are subject to instabilities, should be
the same. For example, Fig. 5.34A shows a simple temperature detector, where the
acting sensor is a negative temperature coefficient (NTC) thermistor R T . A stable
reference resistor R 0 has a value equal to the resistance of the thermistor at some
reference temperature, (e.g., at 25 ◦ C). Both are connected via an analog multiplexer
to an amplifier with a feedback resistor R. The output signals produced by the sensor
and the reference resistor respectively are
V N =− ER
R T
, (5.39)
V D =− ER
R 0
.
It is seen that both voltages are functions of a power-supply voltage E and the circuit
gain, which is defined by resistor R. That resistor as well as the power supply may be
the sources of error. If two output voltages are fed into a divider circuit, the resulting
signal may be expressed as V 0 = kV N /V D = kR 0 /R T , where k is the divider’s gain.
The output signal is not subject to either power-supply voltage or the amplifier gain.
It depends only on the sensor and its reference resistor. This is true only if spurious
variables (like the power supply or amplifier’s gain) do not change rapidly; that is,
they must not change appreciably within the multiplexing period. This requirement
determines the rate of multiplexing.
A ratiometric technique essentially requires the use of a division. It can be performed
by two standard methods: digital and analog. In a digital form, output signals
from both the acting and the reference sensors are multiplexed and converted into
binary codes in an A/D converter. Subsequently, a computer or a microprocessor
performs the operation of a division. In an analog form, a divider may be a part of a
signal conditioner or the interface circuit.A“divider” (Fig. 5.35A) produces an output