[sdiy] Possibly useful reference data

[Veronica Merryfield]

Thanks guys - I found an error that pushed the count up a few, although for my case, it doesn't change the number of clocks I need to allow for the sample period.

I get 
bits  time constants
8      7
10     8
12     10
14     11
16     12


On 2009-12-31, at 5:29 AM, Magnus Danielson wrote:

> Antti Huovilainen wrote:
>> 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.
> 
> No, it was apparent something was wrong...
> 
>> 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
> 
> Is that from a full-scale step (step response) or a full-scale spike (impulse response)? I think you mean the step-response.
> 
>> RC_n = -ln(1/2 * 2^-bits) = ln(2 * 2^bits)
> 
> Thus, RC_n = ln(2)*(bits + 1) = ln(2) + ln(2)*bits which should be a more convenient form for most.
> 
> Infact, assuming full-scale step response I found it more convenient to churn out t/tau = ln(2)*(bits+1) than what you got, but maybe thats me.
> 
>> and
>> bits = -log2(exp(-RC_n)*2) = log2(exp(RC_n))-1
>> For 8 bits, the first formula gives RC_n = 6.238.
> 
> That matches what I get from my derivation yes. It still does not match Veronicas results, which makes me wonder what kind of processing she did.
> 
>> exp(-6.238) * 256 = 0.5 lsb
>> Just to be sure, I double checked the result with spice.
> 
> Again, testing with step-responses.
> 
> Cheers,
> Magnus