AD538
Rev. E | Page 15 of 16
APPLICATIONS INFORMATION
TRANSDUCER LINEARIZATION
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.
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
between the transducer preamplifier output and the next stage
of monitoring or transmitting circuitry. The recommended
procedure 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).
ARC-TANGENT APPROXIMATION
The circuit of Figure 18 is typical of those AD538 applications
where the quantity V
Z
/V
X
is raised to powers greater than one.
In an approximate arc-tangent function, the AD538 will accurately
compute the angle that is defined by X and Y displacements
represented by input voltages V
X
and V
Z
. With accuracy to
within one degree (for input voltages between 100 μV and
10 V), the AD538 arc-tangent circuit is more precise than
conventional analog circuits and is faster than most digital
techniques. The circuit shown is set up for the transfer
function:
( )
( )
( )
21.1
−=
X
Z
REF
V
V
VVV
θθθ
where:
=
−
X
Z
Tan
1
θ
The (V
θREF
− V
θ
) function is implemented in this circuit by
adding together the output, V
θ
, and an externally applied
reference voltage, V
θREF
, via an external AD547 op amp. The
1 μF capacitor connected around the AD547’s 100 k Ω feedback
resistor frequency compensates the loop (formed by the amplifier
between V
θ
and V
Y
).
25kΩ
25kΩ
100Ω
25kΩ
25kΩ
ANTILOG
IN4148
LOG
OUTPUT
100Ω
AD538
I
Y
A
D
I
X
V
X
V
Z
1µF
1µF
V
X
C
V
Y
811
17
16
15
14
13
12
11
10
2
3
4
5
6
7
8
9
LOG
RATIO
INTERNAL
VOLTAGE
REFERENCE
SIGNAL
GND
PWR
GND
I
Z
V
Z
V
O
I
+V
S
–V
S
B
+10V
+2V
00959-019
V
θ
= [V
θREF
–V
θ
] ×
V
Z
V
X
1.21
θ = TAN
–1
Z
X
R
A
931Ω, 1%
V
θ
–15V
+15V
R1*
100kΩ
R2*
100kΩ
118kΩ
1µF
0.1µF
100kΩ
10kΩ
FULL-SCALE
ADJUST
+15V
–15V
7
4
3
6
2
AD547JH
RATIO MATCH 1% METAL
FILM RESISTORS FOR BEST
ACCURACY
*
Figure 18. The Arc-Tangent Function
The V
B
/V
A
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 R
A
(nominally 931 Ω) sets
the power or m factor.
For the highest arc-tangent accuracy the R1 and R2 external
resistors 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 instability
will occur as the output approaches 90° because, by definition,
the arc-tangent function is infinite and therefore, the gain of the
AD538 will be extremely high.
