AD2S81A/AD2S82A
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.
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
Transfer Function
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).
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:
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 × 10-–6) = 96 kΩ
θOUT
θIN
14(1+ sN )
(sN + 2.4)(sN + 3.4 sN + 5.8)
=
2
where SN, the normalized frequency variable, is:
2
π
s
SN =
f BW
The velocity offset voltage depends on the VCO input resistor,
R6, and the VCO bias current and is given by
and fBW is the closed loop 3 dB bandwidth (selected by the
choice of external components).
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 acceleration constant, KA, is given approximately by
K A = 6 × ( f BW )2 sec−2
The normalized gain and phase diagrams are given in Figures
6 and 7.
The maximum recommended rate for the VCO is 1.1 MHz
which sets the maximum possible tracking rate.
12
9
Since the minimum voltage swing available at the integrator
output is ±8 V, this implies that the minimum value for R6 is
57 kΩ. As
6
1. 1 × 106
7. 9 × 103
3
Max Current =
MinValue R6 =
= 139 µA
= 57kΩ
0
–3
–6
–9
–12
8
139 ×10−6
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.
0.02
0.04
0.1
0.2
0.4
0
2
FREQUENCY – fBW
Figure 6. AD2S81A/AD2S82A Gain Plot
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.
180
135
90
45
0
INPUT
ANGLE
+LSB
–45
–90
0
–LSB
–135
+3V
–180
VCO
0.02
0.04
0.1
0.2
0.4
0
2
OUTPUT
FREQUENCY – fBW
–3V
Figure 7. AD2S81A/AD2S82A Phase Plot
Figure 5.
–12–
REV. B
ADI [ ADI ]
