Here's the latest on my temperature loop problem, where I have been
advised to use a lookup table rather than an equation to determine what
my latest sampled value is.

   Our crystal experts want an oven where you can set the temperature to
within a few tenths of a degree.  Also, it is desirable to limit the
thermal noise on the crystal to +/- 100 microkelvin.  This is to keep
the response of the crystal to temperature steps below a certain level
and to not contribute to the random-walk-of-frequency characteristics
of the oscillator that we make from the crystal.

   So now we have a target - 100 microkelvin.  Our thermistor bridge and
crystal are at 80 degrees-C and the thermistor value is about 7787 ohms
at this temp.  The resistors in the other three branches of the bridge
must also be at ~7787 ohms so that the bridge puts out zero volts (that
is, it's balanced) when the temperature is at the set-point.

   We need to know how much differential bridge voltage is output to the
A/D converter when the temperature moves by 100 microkelvin.  The
resolution of the A/D converter must be fine enough to resolve that
amount of voltage.  We seek dV/dT which can be expressed as:

    dV   dV   dR
    -- = -- X --   where V is the bridge differential output voltage,
    dT   dR   dT   R is the thermistor resistance, and T is the temperature.


   dV/dR = Vr/4R   where Vr is the bridge reference voltage (2.5V in our
                   case), R = 7787 ohms.

   dV/dR = 80.3E-6 volts/ohm.


   dR/dT = 3.9%/degree (manufacturer's spec) and 3.9% of 7787 ohms is
                       304 ohms.

   dR/dT = 304 ohms/degree


   So dV/dT = 80.3E-6 volts  X  304 ohms  =  24.4 millivolts/Kelvin
                      -----         ----
                       ohm          Kelvin

   For a change in bridge temp of 100E-6 Kelvin,

          dV = 24.4E-3 volts  X  1E-4 Kelvin  =  2.44 microvolts
                       -----
                       Kelvin

   So the bridge voltage changes 2.44E-6 volts for 100E-6 kelvin delta-T.

   We must resolve 2.44E-6 volts with our A/D converter and we have a
   full range voltage swing of 2.5 volts (+/- 1.25 from balance), so we
   need   2.5/2.44E-6 steps or 1.026E6 steps.

   The converter must then have "n" bits where 2^n = 1.026E6 or

   n = log (1.026E6) =  ~20 bits.  The Analog Devices AD7714 offers
          2

   either 16 or 24-bit modes, so the choice is clear (24).


   Now things get a little fuzzy for me.  Can I do some register arithmetic
   in order come up with a "number" which represents how far my latest data
   sample is from the desired set point?  It seems like it should be able
   to be done without a huge equation or a lookup table either.  My desired
   set point is zero volts on the bridge which is 7FFFFF or 800000 (half
   way between 000000h and FFFFFFh, so I need a way to tell my algorithm
   that I am either fairly close to these numbers or still way off.  In
   either case, I believe I can use a simple linear fit to a slope at this
   point with very little loss in accuracy.  If I have several linear slopes
   to deal with depending upon how far I am from the desired point, then
   I can work my way in to the set point a little at a time.

   Well, it's Friday afternoon on St. Patrick's day ... and I'm running out
   of energy (and getting very thirsty!).  I'll chew on this over the
   weekend and see if everything gets clear to me by Monday morning!  At
   this point, any recommendations will be accepted with open arms.

   Thank you folks, see you next week.

   Jim Johnson
   jjohnson@hpl.hp.com