[sdiy] Possibly useful reference data

[Antti Huovilainen]

On Thu, 31 Dec 2009, Magnus Danielson wrote:

> 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)

Not quite. I did have a couple typos in the formulae tho. The correct 
formula for how many time constants it takes for an RC filter to settle 
within 0.5 lsb is

RC_n = -ln(1/2 * 2^-bits) = ln(2 * 2^bits)

and

bits = -log2(exp(-RC_n)*2) = log2(exp(RC_n))-1

For 8 bits, the first formula gives RC_n = 6.238.
exp(-6.238) * 256 = 0.5 lsb

Just to be sure, I double checked the result with spice.

Antti

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