13.1 Capacitive and resistive sensors
Capacitive sensors consist of two
parallel metal plates in which the dielectric between the plates is either air
or some other medium. The capacitance C is given by C = ε0εrA/d,
where ε0 is the absolute permittivity, εr is the relative
permittivity of the dielectric medium between the plates, A is the area of the
plates and d is the distance between them. Capacitive devices are often used as
displacement sensors, in which motion of a moveable capacitive plate relative
to a fixed one changes the capacitance. Often, the measured displacement is
part of instruments measuring pressure, sound or acceleration. Alternatively,
fixed plate capacitors can also be used as sensors, in which the capacitance
value is changed by causing the measured variable to change the dielectric
constant of the material between the plates in some way. This principle is used
in devices to measure moisture content, humidity values and liquid level, as discussed
in later chapters.
Resistive sensors rely on the
variation of the resistance of a material when the measured variable is applied
to it. This principle is most commonly applied in temperature measurement using
resistance thermometers or thermistors, and in displacement measurement using
strain gauges or piezoresistive sensors. In addition, some moisture meters work
on the resistance-variation principle.
13.2 Magnetic sensors
Magnetic sensors utilize the magnetic
phenomena of inductance, reluctance and eddy currents to indicate the value of
the measured quantity, which is usually some form of displacement.
Inductive sensors translate movement
into a change in the mutual inductance between magnetically coupled parts. One
example of this is the inductive displacement transducer shown in Figure 13.1.
In this, the single winding on the central limb of an ‘E’-shaped ferromagnetic
body is excited with an alternating voltage. The displacement to be measured is
applied to a ferromagnetic plate in close proximity to the ‘E’ piece. Movements
of the plate alter the flux paths and hence cause a change in the current
flowing in the winding. By Ohm’s law, the current flowing in the winding is
given by I = V/ωL. For fixed values
of w and V, this equation becomes I = 1/KL, where K is a constant. The
relationship between L and the displacement, d, applied to the plate is a
non-linear one, and hence the output-current/displacement characteristic has to
be calibrated.
The inductance principle is also used
in differential transformers to measure translational and rotational
displacements.
In variable reluctance sensors, a
coil is wound on a permanent magnet rather than on an iron core as in variable
inductance sensors. Such devices are commonly used to measure rotational
velocities. Figure 13.2 shows a typical instrument in which a ferromagnetic
gearwheel is placed next to the sensor. As the tip of each tooth on the
gearwheel moves towards and away from the pick-up unit, the changing magnetic
flux in the pick-up coil causes a voltage to be induced in the coil whose
magnitude is proportional to the rate of change of flux. Thus, the output is a
sequence of positive and negative pulses whose frequency is proportional to the
rotational velocity of the gearwheel.
Eddy current sensors consist of a
probe containing a coil, as shown in Figure 13.3, that is excited at a high
frequency, which is typically 1 MHz. This is used to measure the displacement
of the probe relative to a moving metal target. Because of the high frequency
of excitation, eddy currents are induced only in the surface of the target,
and the current magnitude reduces to
almost zero a short distance inside the target. This allows the sensor to work
with very thin targets, such as the steel diaphragm of a pressure sensor. The
eddy currents alter the inductance of the probe coil, and this change can be
translated into a d.c. voltage output that is proportional to the distance between
the probe and the target. Measurement resolution as high as 0.1 µm can be
achieved. The sensor can also work with a non-conductive target if a piece of
aluminium tape is fastened to it.
13.3 Hall-effect sensors
Basically, a Hall-effect sensor is a
device that is used to measure the magnitude of a magnetic field. It consists
of a conductor carrying a current that is aligned orthogonally with the
magnetic field, as shown in Figure 13.4. This produces a transverse voltage
difference across the device that is directly proportional to the magnetic
field strength. For an excitation current I and magnetic field strength B, the
output voltage is given by V D KIB, where K is known as the Hall constant.
The conductor in Hall-effect sensors
is usually made from a semiconductor material as opposed to a metal, because a
larger voltage output is produced for a magnetic field of a given size. In one
common use of the device as a proximity sensor, the magnetic field is provided
by a permanent magnet that is built into the device. The magnitude of this
field changes when the device becomes close to any ferrous metal object or
boundary. The Hall effect is also commonly used in keyboard pushbuttons, in
which a magnet is attached underneath the button. When the button is depressed,
the magnet moves past a Hall-effect sensor. The induced voltage is then
converted by a trigger circuit into a digital output. Such pushbutton switches
can operate at high frequencies without contact bounce.
13.4 Piezoelectric transducers
Piezoelectric transducers produce an
output voltage when a force is applied to them. They are frequently used as
ultrasonic receivers and also as displacement transducers, particularly as part
of devices measuring acceleration, force and pressure. In ultra[1]sonic receivers,
the sinusoidal amplitude variations in the ultrasound wave received are
translated into sinusoidal changes in the amplitude of the force applied to the
piezoelectric transducer. In a similar way, the translational movement in a
displacement transducer is caused by mechanical means to apply a force to the
piezoelectric transducer. Piezoelectric transducers are made from piezoelectric
materials. These have an asymmetrical lattice of molecules that distorts when a
mechanical force is applied to it. This distortion causes a reorientation of
electric charges within the material, resulting in a relative displacement of
positive and negative charges. The charge displacement induces surface charges
on the material of opposite polarity between the two sides. By implanting
electrodes into the surface of the material, these surface charges can be
measured as an output voltage. For a rectangular block of material, the induced
voltage is given by:
V =
kFd/A (13.1)
where F is the applied force in g, A
is the area of the material in mm, d is the thickness of the material and k is
the piezoelectric constant. The polarity of the induced voltage depends on
whether the material is compressed or stretched.
The input impedance of the instrument
used to measure the induced voltage must be chosen carefully. Connection of the
measuring instrument provides a path for the induced charge to leak away.
Hence, the input impedance of the instrument must be very high, particularly
where static or slowly varying displacements are being measured.
Materials exhibiting piezoelectric
behaviour include natural ones such as quartz, synthetic ones such as lithium
sulphate and ferroelectric ceramics such as barium titanate. The piezoelectric
constant varies widely between different materials. Typical values of k are 2.3
for quartz and 140 for barium titanate. Applying equation (13.1) for a force of
1 g applied to a crystal of area 100 mm2 and thickness 1 mm gives an output of
23 µV for quartz and 1.4 mV for barium titanate.
Certain polymeric films such as
polyvinylidine also exhibit piezoelectric proper[1]ties.
These have a higher voltage output than most crystals and are very useful in many
applications where displacement needs to be translated into a voltage. However,
they have very limited mechanical strength and are unsuitable for applications
where resonance might be generated in the material.
The piezoelectric principle is
invertible, and therefore distortion in a piezoelectric material can be caused
by applying a voltage to it. This is commonly used in ultrasonic transmitters,
where the application of a sinusoidal voltage at a frequency in the ultra[1]sound range
causes a sinusoidal variation in the thickness of the material and results in a
sound wave being emitted at the chosen frequency. This is considered further in
the section below on ultrasonic transducers.
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