[time-nuts] uC ADC resolution (was: Poor man's oven)

Bob kb8tq kb8tq at n1k.org
Sat Jun 10 15:50:27 EDT 2017


The next issue is that “noise” has a pretty broad definition in this case. 
If you are looking at set point, it also would include temperature drift and
aging. Neither one seem to show up on the standard MCU ADC data sheets :)
It can even be a bit difficult to find them on some (but certainly not all)  
standalone ADC specs.

Next layer to the onion:

If we want to hold the oven at some temperature +/- 0.1 C, the control loop 
needs to go from full on to full off over that range. For grins, let’s assume
that the output is a 16 bit DAC. You will map (somehow) the full range of the
output into a 0.2 C input range. 

If you have a P only controller, the output will step at the granularity of the 
ADC over the 0.2C range. If you have 4 extra bits, you will get 16 x 2 = 32
output levels. That’s not really making the 16 bit DAC earn it’s living. 

A PI controller can (at least theoretically) fill in all of the states of the 16 bit DAC regardless
of the input granularity. If the P is very small and the I is very large it will 
do this fairly seamlessly. In the example above setting P to  < 1/ 2^11 would 
likely do the trick. This all may (or may not) let you hit the P value (or P to I ratio) 
you desire. 

Why does the output DAC matter? Each time the DAC steps, the current
in the heater changes. That power change times the thermal resistance gives
you a temperature step. It is yet another source of “noise” to the crystal. 
Minimizing thermal noise is one of the many things that gets you better ADEV.


> On Jun 10, 2017, at 3:24 PM, Chris Albertson <albertson.chris at gmail.com> wrote:
> On Sat, Jun 10, 2017 at 11:33 AM, Magnus Danielson <
> magnus at rubidium.dyndns.org> wrote:
>> Hi,
>> I was about to make this very point myself. The resolution of the ADC
>> needs to be higher than the limit you try to achieve. There is several ways
>> to reason about it, but one is that the system is a bit slugish you want to
>> have higher resolution in order to react of changes before they overshot
>> the limits you want to keep. Another benefit is that you get away from the
>> bang-bang behavior you get when having too few bits.
>> For an oven you can however cheat some by not requiring linearity in the
>> "too cold" region of temperature. You do want some linearity as you start
>> to come into the right range in order to slow down the heating in order not
>> to do a big overshot.
>> I have seen a little too much cases where there been too few bits both on
>> ADC and DAC sides. Some of it you can overcome, but it runs into trouble.
>> Get good dynamics, it makes the rest of the design easier.
> OK, following the advice both above and below.  Let's try some real-world
> numbers...
> Lets say my goal is regulation within 0.1C.  After filtering I have 10
> "good" bits in my ADC.  That is 1024 counts.   My set point is S.
> I scale the ADC so that 0 == (S - 0.5) and 1023 == (S + 0.5)    This means
> that each ADC count is 0.001 degree C and within the 0.1C range there are
> 100 ADC counts.
> But what if there are only 8 good bits after filtering   The each count is
> 0.004 degree C and there are 25 counts within the 0.1C range.
> The uP's ADC is nominally 12 bits.   Getting 10 "good" noise free bits
> might be asking to much but 8-bits is pretty reasonable.
>> Cheers,
>> Magnus
>> On 06/07/2017 08:32 PM, Bob kb8tq wrote:
>>> Hi
>>> There is a gotcha with the initial assumption: You want the loop to be
>>> *quiet* at a level well below 0.1C. If it is bouncing around that much,
>>> the second order (rate defendant) tempco of a normal crystal will
>>> become a pretty major issue.
>>> Simple rule of thumb - add at least two bits past whatever the target is.
>>> More or less, if you *are* after 0.1C and that comes out to 6 bits, you
>>> need
>>> eight solid bits to get things to work properly.
> -- 
> Chris Albertson
> Redondo Beach, California
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