Digital controllers - Intelligent Buildings and Building Automation - page 19

Measurement Band

R = (2-1)

AD /

21

n

−

The precision of the conversion increases and therefore the error band
reduces with more bits used. For example, if a resolution better than 0.1 per
cent is required, a minimum of 10 bits must be used. However, the greater the
number of bits, the more expensive the A/D converter. Selection of the type
of A/D converter therefore depends on the relative importance of precision
and cost for the particular device concerned.

Example

A signal ranging from 0 to 10 V comes from a temperature sensor cor-
responding to the temperature ranging from -20°C to 80°C. What is the
resolution of an 8-bit A/D converter?

Solution

Resolution may be defined as the change in the input signal for the digital
output to change by the least significant bit (the last bit on the right of a
binary number). An 8-bit word can be used to represent in binary the num-
bers from 0 to 255 (2 8 numbers including 0), so the resolution is:

10/(2 8 -1) = 0.0392 V = 39.2 mV

or (80-(-20))/(2 8 -1) = 0.392 K

(Note: the resolution of this A/D, 0.392 K, is too low for many applications,
indicating the 8-bit length is not sufficient for many applications.)

2.4 Output unit
Having sensed the measurements via the sensors and the input section, the
control outstation has to send a signal to control a valve or switch a device.
This can be done simply by sending out a pulse. To move a valve by a certain
amount a number of pulses will need to be sent to move the valve for a certain
time. This is valve movement on an incremental basis. This approach used to
be the most popular method for moving valves in the past.
However, the most common approach to conduct such modulating control
actions, nowadays, is to use an analogue signal. If a valve needs to be moved
to a definite position, a corresponding analogue signal is generated to move
it to the defined position. In this case a digital to analogue (D/A) converter is
required to generate the analogue signal. The resolution of the D/A converter
can be determined by the formula, given in Equation (2-2), similar to that
used for an A/D converter.