AD2S1210CSTZ datasheet(33/36 Pages) AD

33 / 36 page

AD2S1210

Rev. 0 | Page 33 of 36

Table 29. Loop Transfer Function Parameters vs. Resolution

(fCLKIN = 8.192 MHz)

Resolution (Bits)

t1 (ms)

t2 (ms)

Ka (sec−2)

0.4

39.6 × 106

6.5 × 106

160

1.6 × 106

728

92.7 × 103

Note that the closed-loop response is described as

)

(

)

(

)

(

(17)

By converting the calculation to the s-domain, it is possible to

quantify the open-loop dc gain (Ka). 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 (Ka) of the converter.

Error

Tracking

Accelerati

Input

a =

(18)

Conversely,

Accelerati

Input

Error

Tracking

(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

)

(sec

Accelerati

Maximum

90,300 rps2

(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.

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