Datasheet

AD2S1210
Rev. A | Page 33 of 36
Table 29. Loop Transfer Function Parameters vs. Resolution
(f
CLKIN
= 8.192 MHz)
Resolution (Bits) t
1
(ms) t
2
(ms) K
a
(sec
−2
)
10 0.4 42 39.6 × 10
6
12 1 91 6.5 × 10
6
14 2 160 1.6 × 10
6
16 8 728 92.7 × 10
3
Note that the closed-loop response is described as
)(1
)(
)(
sG
sG
sH
+
=
(17)
By converting the calculation to the s-domain, it is possible to
quantify the open-loop dc gain (K
a
). This value is useful to
calculate the acceleration error of the loop (see the Sources of
Error section).
The step response to a 10° input step is shown in Figure 10,
Figure 11, Figure 12, and Figure 13. The step response to a 179°
input step is shown in Figure 14, Figure 15, Figure 16, and
Figure 17. In response to a step change in velocity, the
AD2S1210 exhibits the same response characteristics as it does
for a step change in position.
Figure 18 and Figure 19 in the Typical Performance Characteristics
section show the magnitude and phase responses of the AD2S1210
for each resolution setting.
SOURCES OF ERROR
Acceleration
A tracking converter employing a Type II servo loop does not
have a lag in velocity. There is, however, an error associated
with acceleration. This error can be quantified using the
acceleration constant (K
a
) of the converter.
ErrorTracking
onAcceleratiInput
K
a
=
(18)
Conversely,
a
K
onAcceleratiInput
ErrorTracking =
(19)
The units of the numerator and denominator must be consistent.
The maximum acceleration of the AD2S1210 is defined by the
maximum acceptable tracking error in the users application.
For example, if the maximum acceptable tracking error is 5°,
then the maximum acceleration is defined as the acceleration that
creates an output position error of 5° (that is, when LOT is
indicated).
An example of how to calculate the maximum acceleration in a
12-bit application with a maximum tracking error of 5° is
≅
°
°×
=
−
)/rev(360
5)(sec
2
a
K
onAcceleratiMaximum
90,300 rps
2
(20)
Figure 20 to Figure 23 in the Typical Performance Characteristics
section show the tracking error vs. acceleration response of the
AD2S1210 for each resolution setting.