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We have tried to get position from chip. It gives us quite strange output.
While position sensor is static some bits of output toggles on/off quite
randomly.Output is like 0x4040-> 0x8080 -> 0xC040 etc.
Reference freq is 400 hz, sampling rate 100ms. Mode is 16-bit. sensor rotates
in actual application quite slow.

Do you have 'pseudo' code how to program parallel interface? Just to verife
operation. Now we pull inhibit 500 uS low before pulling enable low and reading
bits out.
Complement & dataload is not used, should ?


Improved, layout, grounding, shielding and or filtering of the Resolver outputs
may eliminate the problems.
Do note that if you do use a filter on the resolver sine / cosine outputs, the
filter should be well matched with corner frequency 2 or 3 decades higher than
the excitation frequency. Otherwise the filter will introduce static errors.
The AD2S83 uses synchronous demodulation and a tracking converter to null an
error signal and produce the digital output. The part is ratiometric with the
excitation (reference) signal in that the absolute amplitude of the excitation
signal has little or no effect on accuracy. However, disturbances on the Sin
and Cosine inputs will affect the demodulator and produce erroneous results.

On the AD2S83 several 'Logic' inputs are referenced to the +Vs(+12V)supply.
These are DATALOAD, SC1 and SC2.
You need to tie DATALOAD and SC2 to +12V instead of +5V to achieve a logic HI.
(These inputs have internal pull-up resistors, and could also be left floating.)

We do not have any code.
There is some background on using the AD2S83 in the applications note  at :

Note that the AD2S83 is an older (mature) IC.
For new designs we are recommending the AD2S1200 which includes the oscillator
circuitry on the chip.