[sdiy] Possibly useful reference data

Magnus Danielson magnus at rubidium.dyndns.org
Thu Dec 31 12:38:41 CET 2009


Antti Huovilainen wrote:
> On Thu, 31 Dec 2009, Veronica Merryfield wrote:
> 
>> I recently had to take account of input RC settling time of an ADC and 
>> calculated the number of time constants to wait to allow the RC to 
>> settle to half an LSB. I did this for a couple of bit widths whilst I 
>> had the spreadsheet up.
> 
> The equation to calculate those is RC_n = ln(2^-bits)
> vice versa, bits = log2(exp(-RC_n))

Very strange values appears using those formulas:

bits RC_n
8    -5.545177444
9    -6.238324625
10   -6.931471806
11   -7.624618986
12   -8.317766167

I think the negation should not be there and there should be a multiply 
with 2 for even approaching Veronicas numbers:

RC_n = 2*ln(2^bits)

Using fairly standard reduction a much simpler form turns out:

RC_n = 2*ln(2)*bits
ln(2) is a table item but 2*ln(2) is about 1.386294361

Using this I get:

bits RC_n
8    11.090354889
9    12.47664925
10   13.862943611
12   16.635532333
14   19.408121056
16   22.180709778

I still haven't made any propper analysis thought. What is the assumed 
analysis case?

Cheers,
Magnus


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