6.2 Analogue meters
Analogue meters are relatively simple
and inexpensive and are often used instead of digital instruments, especially
when cost is of particular concern. Whilst digital instruments have the
advantage of greater accuracy and much higher input impedance, analogue
instruments suffer less from noise and isolation problems. In addition, because
analogue instruments are usually passive instruments that do not need a power
supply, this is often very useful in measurement applications where a suitable
mains power supply is not readily available. Many examples of analogue meter
also remain in use for historical reasons.
Analogue meters are electromechanical
devices that drive a pointer against a scale. They are prone to measurement
errors from a number of sources that include inaccurate scale marking during
manufacture, bearing friction, bent pointers and ambient tempera[1]ture variations.
Further human errors are introduced through parallax error (not reading the
scale from directly above) and mistakes in interpolating between scale
markings. Quoted inaccuracy figures are between ±0.1% and ±3%. Various types of
analogue meter are used as discussed below.
6.2.1 Moving-coil meters
A moving-coil meter is a very
commonly used form of analogue voltmeter because of its sensitivity, accuracy
and linear scale, although it only responds to d.c. signals. As shown
schematically in Figure 6.2, it consists of a rectangular coil wound round a
soft iron core that is suspended in the field of a permanent magnet. The signal
being measured is applied to the coil and this produces a radial magnetic
field. Interaction between this induced field and the field produced by the
permanent magnet causes a torque, which results in rotation of the coil. The
amount of rotation of the coil is measured by attaching a pointer to it that
moves past a graduated scale. The theoretical torque produced is given by:
T = BIhwN (6.2)
where B is the flux density of the
radial field, I is the current flowing in the coil, h is the height of the
coil, w is the width of the coil and N is the number of turns in the coil. If
the iron core is cylindrical and the air gap between the coil and pole faces of
the permanent magnet is uniform, then the flux density B is constant, and
equation (6.2) can be rewritten as:
T = KI (6.3)
i.e. the torque is proportional to
the coil current and the instrument scale is linear.
As the basic instrument operates at
low current levels of one milliamp or so, it is only suitable for measuring
voltages up to around 2 volts. If there is a requirement to measure higher
voltages, the measuring range of the instrument can be increased by placing a
resistance in series with the coil, such that only a known proportion of the
applied voltage is measured by the meter. In this situation the added
resistance is known as a shunting resistor.
Whilst Figure 6.2 shows the traditional moving-coil instrument with a long U-shaped permanent magnet, many newer instruments employ much shorter magnets made from recently developed magnetic materials such as Alnico and Alcomax. These materials produce a substantially greater flux density, which, besides allowing the magnet to be smaller, has additional advantages in allowing reductions to be made in the size of the coil and in increasing the usable range of deflection of the coil to about 120°. Some versions of the instrument also have either a specially shaped core or specially shaped magnet pole faces to cater for special situations where a non-linear scale such as a logarithmic one is required.
6.2.2 Moving-iron meter
As well as measuring d.c. signals,
the moving-iron meter can also measure a.c. signals at frequencies up to 125
Hz. It is the cheapest form of meter available and, conse[1]quently, this
type of meter is also commonly used for measuring voltage signals. The signal
to be measured is applied to a stationary coil, and the associated field
produced is often amplified by the presence of an iron structure associated
with the fixed coil. The moving element in the instrument consists of an iron
vane that is suspended within the field of the fixed coil. When the fixed coil
is excited, the iron vane turns in a direction that increases the flux through
it.
The majority of moving-iron instruments are
either of the attraction type or of the repulsion type. A few instruments
belong to a third combination type. The attraction type, where the iron vane is
drawn into the field of the coil as the current is increased, is shown
schematically in Figure 6.3(a). The alternative repulsion type is sketched in
Figure 6.3(b). For an excitation current I, the torque produced that causes the
vane to
turn is given by:
T = I2 dM/2 d0
where M is the mutual inductance and 0 is the angular deflection. Rotation
is opposed by a spring that produces a backwards torque given by:
Ts = K0
At equilibrium, T = Ts,
and 0 is therefore given by:
0 = I2 dM/2K d0 (6.4)
The instrument thus has a square-law
response where the deflection is proportional to the square of the signal being
measured, i.e. the output reading is a root-mean-squared (r.m.s.) quantity.
The instrument can typically measure
voltages in the range of 0 to 30 volts. However, it can be modified to measure
higher voltages by placing a resistance in series with it, as in the case of
moving coil meters. A series resistance is particularly beneficial in a.c.
signal measurements because it compensates for the effect of coil inductance by
reducing the total resistance/inductance ratio, and hence measurement accuracy
is improved. A switchable series resistance is often provided within the casing
of the instrument to facilitate range extension. However, when the voltage measured
exceeds about 300 volts, it becomes impractical to use a series resistance
within the case of the instrument because of heat-dissipation problems, and an
external resistance is used instead.
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