AD2S83 datasheet(13/19 Pages) AD

13 / 19 page

AD2S83

–13–

REV. D

During the VCO reset period the input continues to be inte-

grated. The reset period is constant at 40 ns.

The VCO rate is fixed for a given input current by the VCO

scaling factor:

= 8.5 kHz/

µA

The tracking rate in rps per

µA of VCO input current can be

found by dividing the VCO scaling factor by the number of LSB

changes per rev (i.e., 4096 for 12-bit resolution).

The input resistor R6 determines the scaling between the con-

verter velocity signal voltage at the INTEGRATOR OUTPUT

pin and the VCO input current. Thus to achieve a 5 V output at

100 rps (6000 rpm) and 12-bit resolution the VCO input cur-

rent must be:

(100

× 4096)/(8500) = 48.2 µA

Thus, R6 would be set to: 5/(48.2

× 10–6) = 103.7 kΩ

The velocity offset voltage depends on the VCO input resistor,

R6, and the VCO bias current and is given by

Velocity Offset Voltage = R6

× (VCO bias current)

The temperature coefficient of this offset is given by

Velocity Offset Tempco = R6

× (VCO bias current tempco)

where the VCO bias current tempco is typically +0.22 nA/

°C.

The maximum recommended rate for the VCO is 1.1 MHz

which sets the maximum possible tracking rate.

Since the minimum voltage swing available at the integrator

output is

±8 V, this implies that the minimum value for R6 is

62 k

Ω. As

Max Current

1.1

× 10

8.5

× 10

= 129 µA

MinValue R6

129

× 10

–6

= 62 kΩ

Transfer Function

By selecting components using the method outlined in the sec-

tion “Component Selection,” the converter will have a critically

damped time response and maximum phase margin. The

Closed-Loop Transfer Function is given by:

OUT

14 (1

+ s

N )

( s

N + 2.4 ) ( sN

2 + 3.4 s

N + 5.8 )

where, sN, the normalized frequency variable is given by:

N =

f BW

and fBW is the closed-loop 3 dB bandwidth (selected by the

choice of external components).

The acceleration constant KA, is given approximately by

A = 6 × ( f BW )

sec

–2

The normalized gain and phase diagrams are given in Figures 5

and 6.

FREQUENCY – fBW

–12

–3

–6

–9

0.0

0.04

0.1

0.2

0.4

Figure 5. Gain Plot

FREQUENCY – fBW

180

–180

135

–45

–90

–135

0.0

0.04

0.1

0.2

0.4

Figure 6. Phase Plot

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