REV. B

–12–

AD2S81A/AD2S82A

During the reset period the input continues to be integrated, the

reset period is constant at 400 ns.

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

scaling factor:

= 7.9 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 O/P 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 current must

be:

(100

× 4096) / (7900) = 51.8 µA

Thus, R6 would be set to: 5/(51.8

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 –1.22 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

57 k

Ω. As

Max Current

=

1.1

× 10

6

7.9

× 10

3

= 139 µA

Min Value R6

=

8

139

= 57 kΩ

VCO OUTPUT

In order to overcome the “freeplay” inherent in a servo system

using digitized position feedback, an analog output voltage is

available representing the resolver shaft position within the least

significant bit of digital angle output.

The converter updates the output if the error is an LSB or

greater and the VCO output gives the positional error smaller

than 1 LSB.

INPUT

ANGLE

0

VCO

OUTPUT

+3V

–3V

+LSB

–LSB

Figure 5.

Figure 5 illustrates how the VCO output compensates for in-

stances where, due to hysteresis, there is no change in the digital

count output for 1 LSB change in input angle. The sum of the

digital count output and VCO output equals the actual input

angle.

Transfer Function

By selecting components using the method outlined in the

Component Selection section, the converter will have a critically

damped time response and maximum phase margin. The

Closed-Loop Transfer Function is given by:

θ

OUT

θ

IN

=

14 (1

+ s

2

π

s

choice of external components).

K

2

sec

−2

The normalized gain and phase diagrams are given in Figures

6 and 7.

12

9

6

3

0

–3

–6

–9

–12

0.02

0.04

0.1

0.2

0.4

0

2

FREQUENCY –

Figure 6. AD2S81A/AD2S82A Gain Plot

180

0

–45

–90

–135

–180

0.02

0.04

0.1

0.2

0.4

0

2

FREQUENCY –

135

90

45

Figure 7. AD2S81A/AD2S82A Phase Plot