# AD2S1200: Maximun phase shift that can be tolerated between the reference excitation and the sin/cos signals?

Document created by analog-archivist on Feb 23, 2016
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### Q

We want to have an error due to Phase shift of less then 1 lsb with these
parameters: RotationRate=6000rpm ReferenceFrequency=10Khz. What is the maximun
phase shift that can be tolerated between the reference excitation and the
sin/cos signals.

### A

The Error you are referring to is caused by the rotation of the resolver.
Basically at high rotation rates the resolver starts to act like an electric
motor and produces speed voltages. This are in quadrature to the main signal
and result in an additional error through the RDC.

The formula to calculate this error is on page 17 of the datasheet:
Error = Phase shift x [rotation rate / reference frequency]

The main factor in the formula is the Phase shift, which is the phase shift
between the reference signal and the Sin/Cos inputs. This phase shift is
primarily caused by the resolver itself i.e. resistance of the rotor coil
causes a phase shift from what is applied to the rotor to what is then
generated across the stators.

The AD2S1200 internally generates a synthetic reference to compensate for this
phase shift. It can reduce a phase shift of +/-45 degrees down to 10 degrees.

However for you this is not quite enough as he would then have the following
with the speed and freq conditions he outlined :
Error = 10 degrees x [100rps / 10kHz]
= 0.1 degrees = 6 arc min
One lsb = 5.3 arc min.

The reduce this error still further you need to further reduce the phase shift
between the
reference and the Sin/Cos signals. So after all that explanation the answer to
your
questions is:

Error = Phase shift x [rotation rate / reference frequency]
=> Phase shift = Error x [reference freq / rotation rate]
=  [0.088 degrees] x [10,000/100]
= 8.83 degrees.

i.e. You need to keep the phase shift below 8.8 degrees to be able to keep the
additional error below 1 lsb [5.3 arc min.]