Let's
imagine that we need to digitize an analog input signal in the range of 0-1V
and that digital samples of the input signals will be represented as 8-bits
values.
- This means that a digital
representation of continues analog signal in the range of 0-1V has to be
represented with only 2^^8 (256) different values. Foe example:
- 0V is represented with a minimum 8
bit value decimal 0 or in binary 8'b0000_0000 and
- 1V is represented with maximum 8'bit
value decimal 255 or in binary 8'b1111_1111
Since we have only 256 possible digital 8-bit values
to represent continues analog signal in the range of 0-1V obviously
we will represent a sub-range of an input voltage with a single 8-bit
value.This subrange/step size of the converter defines the converter's resolution.
e.g.
- 8'b0000_0000 digital value represents 0V analog input and first next digital value is 8'b0000_0001 that will represent 1V/255 = 0.003922 V if we assume precision on 6 decimal places ( meaning 0.003922 V is the resolution of our ADC in this example )
- This means that we have to adopt a criteria
that any input voltage, in the range bigger or equal to 0V and less than 0.003922,
will be digitally coded with a value of 8'b0000_0000.
- Further, any input voltage in the range bigger
or equal of 0.003922 but less than 0.007843( represents result
of 2/255) it will be digitally coded with a value of
8'b0000_0001 etc. etc.
=>
The final table looks like this:
- There will be 256 ( for example 0, 1,
2....253, 254, 255 ), 8-bit digital values representation of
the analog input in the range of 0-1V :
Decimal digital value
|
Binary digital value
|
Input analog voltage [V]
|
Comment
|
||||
0
|
8'b0000_0000
|
0
|
0 /255 = 0 V
|
||||
1
|
8'b0000_0001
|
0.003922
|
1 /255 = 0.003922 V
|
||||
2
|
8'b0000_0010
|
0.007843
|
2 /255 = 0.007843 V
|
||||
3
|
8'b0000_0011
|
0.011765
|
3 /255 = 0.011765 V
|
||||
.....
|
…..
|
…..
|
…..
|
||||
253
|
8'b1111_1101
|
0.988235
|
253 /255 = 0.988235 V
|
||||
254
|
8'b1111_1110
|
0.996078
|
254 /255 = 0.996078 V
|
||||
255
|
8'b1111_1111
|
1
|
255 /255 = 1 V
|
||||
And
finaly Successive Approximation Register ADC algorithm to output for
example a digital value 8'b0000_0001 when input signal is 0.003922 V
looks like this:
1.
if
0.003922 V would be bigger or equal than 0.5 V ( this is maximum analog signal
voltage of 1V divided by 2 ) MSB bit ( or bit 7) of a digitized result
would be 1 ( but that is not the case so result is 0 )
=> so far the digital result is: 8'b0xxx_xxxx
2.
if 0.003922
V would be bigger or equal than 0.25 V ( this is maximum analog signal voltage of
1V divided by 4 ) bit 6 of a digitized result would be 1 ( but that
is not the case so result is 0 )
=> so far the digital result is: 8'b00xx_xxxx
3.
if 0.003922
V would be bigger or equal than 0.125 V ( this is maximum analog signal voltage of
1V divided by 8 ) bit 5 of a digitized result would be 1 ( but that
is not the case so result is 0 )
=> so far the digital result is: 8'b000x_xxxx
4.
if 0.003922
V would be bigger or equal than 0.0625 V ( this is maximum analog
signal voltage of 1V divided by 16 ) bit 4 of a digitized result would be
1 ( but that is not the case so result is 0 )
=> so far the digital result is: 8'b0000_xxxx
5.
if 0.003922
V would be bigger or equal than 0.03125 V ( this is maximum analog signal
voltage of 1V divided by 32 ) bit 3 of a digitized result would be
1 ( but that is not the case so result is 0 )
=> so far the digital result is: 8'b0000_0xxx
6.
if 0.003922
V would be bigger or equal than 0.015625 V ( this is maximum analog signal
voltage of 1V divided by 64 ) bit 2 of a digitized result would be
1 ( but that is not the case so result is 0 )
=> so far the digital result is: 8'b0000_00xx
7.
if 0.003922
V would be bigger or equal than 0.0078125 V ( this is maximum analog signal
voltage of 1V divided by 128 ) bit 1 of a digitized result would be
1 ( but that is not the case so result is 0 )
=> so far the digital result is: 8'b0000_000x
8.
if 0.003922
V would be bigger or equal than 0.00390625 V ( this is maximum analog signal
voltage of 1V divided by 256 ) LSB bit or bit 0 of a digitized result
would be 1, which is the case.
=> and the final result is: 8'b0000_0001
© 2011-2020 ASIC Stoic. All rights reserved
© 2011-2020 ASIC Stoic. All rights reserved
