AD538
TRANSDUCER LINEARIZATION
1.21
V
X
Z
Z
–1
V
= [V
= TAN (X )
REF
Many electronic transducers used in scientific, commercial or
industrial equipment monitor the physical properties of a device
and/or its environment. Sensing (and perhaps compensating for)
changes in pressure, temperature, moisture or other physical
phenomenon can be an expensive undertaking, particularly
where high accuracy and very low nonlinearity are important. In
conventional analog systems accuracy may be easily increased
by offset and scale factor trims, however, nonlinearity is usually
the absolute limitation of the sensing device.
A
D
I
1
2
3
4
5
6
7
8
18
Z
R
A
LOG
V
Z
25k⍀
931⍀, 1%
V
RATIO
17
Z
B
I
X
16
15
14
13
12
V
X
+10V
V
X
25k⍀
SIGNAL
GND
100⍀
100⍀
+2V
PWR
GND
INTERNAL
+V
S
VOLTAGE
AD538
+15V
–15V
With the ability to easily program a complex analog function,
the AD538 can effectively compensate for the nonlinearities of
an inexpensive transducer. The AD538 can be connected be-
tween the transducer preamplifier output and the next stage of
monitoring or transmitting circuitry. The recommended proce-
dure for linearizing a particular transducer is first to find the
closest function which best approximates the nonlinearity of the
device and then, to select the appropriate exponent resistor
value(s).
1F
1F
REFERENCE
–V
S
C
OUTPUT
IN4148
25k⍀
V
O
I
Y
11
10
V
ANTILOG
LOG
V
Y
I
9
25k⍀
0.1F
+15V
AD547JH
–15V
R2*
100k⍀
R1*
100k⍀
ARC-TANGENT APPROXIMATION
10k⍀
The circuit of Figure 17 is typical of those AD538 applications
where the quantity VZ /VX is raised to powers greater than one.
In an approximate arc-tangent function, the AD538 will accu-
rately compute the angle that is defined by X and Y displace-
ments represented by input voltages VX and VZ. With accuracy
to within one degree (for input voltages between 100 μV and
10 volts), the AD538 arc-tangent circuit is more precise than
conventional analog circuits and is faster than most digital tech-
niques. For a direct arc-tangent computation that requires fewer
external components, refer to the AD639 data sheet. The circuit
shown is set up for the transfer function:
FULL-SCALE
ADJUST
118k⍀
1F
*RATIO MATCH 1% METAL
FILM RESISTORS FOR BEST
ACCURACY
100k⍀
Figure 17. The Arc-Tangent Function
The VB/VA quantity is calculated in the same manner as in the
one-quadrant divider circuit, except that the resulting quotient
is raised to the 1.21 power. Resistor RA (nominally 931 Ω) sets
the power or m factor.
For the highest arc-tangent accuracy the external resistors R1
and R2 should be ratio matched; however, the offset trim
scheme shown in other circuits is not required since nonlinearity
effects are the predominant source of error. Also note that insta-
bility will occur as the output approaches 90° because, by defini-
tion, the arc-tangent function is infinite and therefore, the AD538’s
gain will be extremely high.
1.21
⎡
⎢
⎢
⎤
VZ
(
)
)
⎥
V = V
− V
θ
θ
(
θREF
)
V
⎥
⎦
(
X
⎣
where:
⎛
⎞
Z
−1
θ = Tan
⎜
⎟
⎝
⎠
X
The (VθREF – Vθ) function is implemented in this circuit by
adding together the output, Vθ, and an externally applied refer-
ence voltage, VθREF, via an external AD547 op amp. The 1 μF
capacitor connected around the AD547’s 100 kΩ feedback
resistor frequency compensates the loop (formed by the ampli-
fier between Vθ and VY).
REV. D
REV. C
–10–
ROCHESTER [ Rochester Electronics ]
