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

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

compute the angle that is defined by X and Y displacements

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

V

V

V

θ

θ

θ

where:













=

−

X

Z

Tan

1

θ

1 μF capacitor connected around the AD547’s 100 kΩ feedback

resistor frequency compensates the loop (formed by the amplifier

25k

Ω

25k

Ω

100

Ω

25k

Ω

25k

Ω

ANTILOG

IN4148

LOG

OUTPUT

100

Ω

AD538

A

D

1µF

1µF

C

8

1

1

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

B

+10V

+2V

1.21

Z

X

931

Ω, 1%

–15V

+15V

R1*

100k

Ω

R2*

100k

Ω

118k

Ω

1µF

0.1µF

100k

Ω

10k

Ω

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

one-quadrant divider circuit, except that the resulting quotient

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.