AD538

–10–

REV. C

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 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).

ARC-TANGENT APPROXIMATION

The circuit of Figure 17 is typical of those AD538 applications

In an approximate arc-tangent function, the AD538 will accu-

rately compute the angle that is defined by X and Y displace-

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:

VV

V

V

V

REF

Z

X

θθ

θ

=−

() ()

()

















121

.

where:

θ= Tan−1

Z

X









capacitor connected around the AD547’s 100 k

Ω feedback

resistor frequency compensates the loop (formed by the ampli-

25k

25k

LOG

RATIO

100

25k

25k

ANTILOG

LOG

OUTPUT

100

AD538

INTERNAL

VOLTAGE

REFERENCE

( )

( )

Z

X

1.21

1

2

3

4

5

6

7

8

9

18

17

16

15

14

13

12

11

10

I

B

+10V

+2V

A

D

C

PWR

GND

SIGNAL

GND

IN4148

RATIO MATCH 1% METAL

FILM RESISTORS FOR BEST

ACCURACY

*

1 F

1 F

+15V

–15V

V

AD547JH

R2

*

100k

+15V

–15V

0.1 F

100k

1 F

118k

R1

*

100k

10k

FULL-SCALE

ADJUST

931 , 1%

Figure 17. The Arc-Tangent Function

one-quadrant divider circuit, except that the resulting quotient

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.