Many of SAR ADC’s are
implemented using a switched capacitor array architecture and for an ADC
like that one, here is an equivalent circuit:
Let’s approximate a driving
of this type of SAR ADC input done with an equivalent circuit like
this one:
Here is an example, step by step calculation of maximum value
of the external driving source resistance ( RS ) to achieve a desired accuracy
of our SAR ADC.
·
First
here are some basic characteristics of the SAR ADC used in this calculation/example:
·
Our SAR ADC has 8 bits
output result
·
Our SAR ADC operates on
2 MHz clock frequency
·
Our SAR ADC needs 4
clock cycles to sample a single data
·
Our SAR ADC should have
accuracy of 1/16 LSB
·
Our SAR ADC equivalent
circuit has Ri = 1KΩ, Ci=100pF
1.
Step 1 ( calculation of
the sample time: Ts )
- Ts = 4 *1/2Mhz = 2μs
- 4 represents number of clock cycles that our ADC SAR
uses to sample a data
- 2MHz represents our ADC SAR operation clock frequency
2. Step 2 ( finding a conversion time of our ADC
with the accuracy desired)
·
It
can be proven that our ADC conversion time with the accuracy desired is
calculated using a following formula:
where:
o
Rt =
Rs + RI
o
8
represents how many output bits has our ADC SAR
o
4 is
derived from a desired accuracy. The desired
accuracy is 1/16 and 16 = 2^^4
3.
Step 3, our ADC’s sample time should be always bigger
or equal to our ADC’s conversion time with the accuracy desired :
·
After solving
this last equation per Rs, the conclusion is:
·
The analog source resistance can be no larger than 1.40 kΩ for
1/16 LSB accuracy for the SAR ADC in our example.
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