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.

1

5

0

–40

–35

–30

–25

–20

–15

–10

–5

–45

10

100

10k

1k

FREQUENCY (Hz)

100k

Figure 12. RDC System Magnitude Response

1

0

–20

–180

–160

–140

–120

–100

–80

–60

–40

–200

10

100

10k

1k

FREQUENCY (Hz)

100k

Figure 13. RDC System Phase Response

0

20

18

2

4

6

8

10

12

14

16

0

12

4

3

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

Error

Tracking

on

Accelerati

Input

K

(25)

Conversely,

a

K

on

Accelerati

Input

Error

Tracking

=

(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

rps

000

,

103

)

/rev

(

360

5

)

(sec

≅

°

°

×

=

−

a

K

on

Accelerati

Maximum

(27)

0

10

9

1

2

3

4

5

6

7

8

0

40k

80k

160k

120k

200k

Figure 15. Tracking Error vs. Acceleration