AD2S81A/AD2S82A
The small signal step response is shown in Figure 8. The time
from the step to the first peak is t1 and the t2 is the time from
the step until the converter is settled to 1 LSB. The times t1 and
t2 are given approximately by
Input Acceleration[LSB/sec2]
Error in LSBs =
KA[sec–2
]
100[rev/sec2] × 212
2.7×106
=
= 0.15LSBs or 47.5seconds of arc
1
t1 =
f BW
To determine the value of KA based on the passive components
used to define the dynamics of the converter, the following
should be used:
5
R
t2 =
×
f BW 12
4.04 × 1011
2n R6 R4 (C4 + C5)
K A
=
where R = resolution, i.e., 10, 12, 14 or 16.
OUTPUT
POSITION
t2
Where n = resolution of the converter
R4, R6 in ohms
C5, C4 in farads
SOURCES OF ERRORS
Integrator Offset
Additional inaccuracies in the conversion of the resolver signals
will result from an offset at the input to the integrator as it will
be treated as an error signal. This error will typically be 1 arc
minute over the operating temperature range.
TIME
t1
A description of how to adjust from zero offset is given in the
Component Selection section and the circuit required is shown
in Figures 1a and 1b.
Figure 8. AD2S81A/AD2S82A Small Step Response
The large signal step response (for steps greater than 5 degrees)
applies when the error voltage exceeds the linear range of the
converter.
Differential Phase Shift
Phase shift between the sine and cosine signals from the resolver
is known as differential phase shift and can cause static error.
Some differential phase shift will be present on all resolvers as a
result of coupling. A small resolver residual voltage (quadrature
voltage) indicates a small differential phase shift. Additional
phase shift can be introduced if the sine channel wires and the
cosine channel wires are treated differently. For instance, differ-
ent cable lengths or different loads could cause differential
phase shift.
Typically the converter will take three times longer to reach the
first peak for a 179 degrees step.
In response to a velocity step, the velocity output will exhibit
the same time response characteristics as outlined above for the
position output.
ACCELERATION ERROR
A tracking converter employing a type 2 servo loop does not
suffer any velocity lag, however, there is an additional error due
to acceleration. This additional error can be defined using the
acceleration constant KA of the converter.
The additional error caused by differential phase shift on the
input signals approximates to
Error = 0.53 a × b arc minutes
where a = differential phase shift (degrees).
b = signal to reference phase shift (degrees).
Input Acceleration
K A
=
Error in Output Angle
This error can be minimized by choosing a resolver with a small
residual voltage, ensuring that the sine and cosine signals are
handled identically and removing the reference phase shift (see
Connecting the Resolver section). By taking these precautions
the extra error can be made insignificant.
The numerator and denominator must have consistent angular
units. For example, if KA is in sec–2, then the input acceleration
may be specified in degrees/sec2 and the error output in degrees.
Angular measurement may also be specified using radians, min-
utes of arc, LSBs, etc.
Under static operating conditions phase shift between the refer-
ence and the signal lines alone will not theoretically affect the
converter’s static accuracy.
KA does not define maximum input acceleration, only the error due
to it’s acceleration. The maximum acceleration allowable before
the converter loses track is dependent on the angular accuracy
requirements of the system.
However, most resolvers exhibit a phase shift between the signal
and the reference. This phase shift will give rise under dynamic
conditions to an additional error defined by:
Angular Accuracy × KA = degrees/sec2
KA can be used to predict the output position error for a given
input acceleration. For example for an acceleration of 100 revs/
sec2, KA = 2.7 × 106 sec–2 and 12-bit resolution.
Shaft Speed (rps) × Phase Shift (Degrees)
Reference Frequency
REV. B
–13–
ADI [ ADI ]
