Hardware Reference
In-Depth Information
Because of its balanced speed and precision, this method has become one of the most
popular A/D conversion methods. Most microcontrollers use this method to implement the
A/D converter. The HCS12 MCUs also use this technique to implement A/D converters.
An A/D converter needs a
low reference voltage
(
V
RL
) and a
high reference voltage
(
V
RH
) to
perform the conversion. The
V
RL
voltage is often set to ground, whereas the
V
RH
voltage is often
set to
V
DD
. Some microcontrollers simply tie
V
RL
to the ground voltage and leave only the
V
RH
voltage programmable. Most A/D converters are
ratiometric,
for the following reasons:
•
A 0-V (or
V
RL
) analog input is converted to the digital code of
n
0s.
•
A
V
DD
(or
V
RH
) analog input is converted to the digital code of 2
n
2 1.
•
A
k
-V analog input will be converted to the digital code of
k
3 (2
n
2 1) 4
V
DD
.
Here,
n
is the number of bits used to represent the A/D conversion result.
The A/D conversion result would be most accurate if the value of the analog signal covers
the whole voltage range from
V
RL
to
V
RH
. The A/D conversion result
k
corresponds to an analog
voltage
V
k
given by the following equation:
V
k
5
V
RL
1
(range
3
k
)
4
(2
n
2
1)
(12.1)
where range 5
V
RH
2
V
RL
.
Example 12.1
▼
Suppose that there is a 10-bit A/D converter with
V
RL
5 1 V and
V
RH
5 4 V. Find the corre-
sponding voltage values for the A/D conversion results of 25, 80, 240, 500, 720, 800, and 900.
Solution:
Range 5
V
RH
2
V
RL
5 4 V 2 1 V 5 3 V
The voltages corresponding to the A/D conversion results of 25, 80, 240, 500, 720, 800, and
900 are
1V 1 (3 3 25) 4 (2
10
2 1) 5 1.07 V
1V 1 (3 3 80) 4 (2
10
2 1) 5 1.23 V
1V 1 (3 3 240) 4 (2
10
2 1) 5 1.70 V
1V 1 (3 3 500) 4 (2
10
2 1) 5 2.47 V
1V 1 (3 3 720) 4 (2
10
2 1) 5 3.11 V
1V 1 (3 3 800) 4 (2
10
2 1) 5 3.35 V
1V 1 (3 3 900) 4 (2
10
2 1) 5 3.64 V
▲
Some of the transducer output voltages are in the range of 0,
V
Z
, where
V
Z
,
V
DD
. Because
V
Z
sometimes can be much smaller than
V
DD
, the A/D converter cannot take advantage of the available
full dynamic range (0 to 2
n
2 1, where
n
is the number of bits used to represent the conversion result),
and therefore conversion results can be very inaccurate. The voltage scaling (amplifying) circuit can
be used to improve the accuracy because it allows the A/D converter to utilize its full dynamic range.
The diagram of a voltage scaling circuit is shown in Figure 12.6. Because the OP AMP has an infinite
input impedance, the current that flows through the resistor
R
2
will be the same as the current that
flows through
R
1
. In addition, the voltage at the inverting input terminal (same as the voltage drop
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