Datasheet

AD2S1205
Rev. A | Page 18 of 20
The step response to a 10° input step is shown in Figure 14.
Because the error calculation (see Equation 2) is nonlinear for
large values of θ − ϕ, the response time for such large (90° to
180°) step changes in position typically takes three times as long
as the response to a small (<20°) step change in position. In
response to a step change in velocity, the AD2S1205 exhibits
the same response characteristics as it does for a step change
in position.
06339-012
1
5
0
–40
–35
–30
–25
–20
MAGNITUDE (dB)
–15
–10
–5
–45
10 100 10k1k
FREQUENCY (Hz)
100k
Figure 12. RDC System Magnitude Response
06339-013
1
0
–20
–180
–160
–140
–120
–100
PHASE (Degrees)
–80
–60
–40
–200
10 100 10k1k
FREQUENCY (Hz)
100k
Figure 13. RDC System Phase Response
06339-014
0
20
18
2
4
6
8
10
ANGLE (Degrees)
12
14
16
0
12 43
TIME (ms)
5
Figure 14. RDC Small Step Response
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
=
(25)
Conversely,
a
K
onAcceleratiInput
ErrorTracking =
(26)
Figure 15 shows tracking error vs. acceleration for the AD2S1205.
The units of the numerator and denominator must be consistent.
The maximum acceleration of the AD2S1205 is defined as the
acceleration that creates an output position error of 5° (that is,
when LOT is indicated). The maximum acceleration can be
calculated as
2
2
rps000,103
)/rev(360
5)(sec
≅
°
°×
=
−
a
K
onAcceleratiMaximum (27)
06339-015
0
10
9
1
2
3
4
5
TRACKING ERROR (Degrees)
6
7
8
0
40k 80k 160k120k
ACCELERATION (rps
2
)
200k
Figure 15. Tracking Error vs. Acceleration