OP297

Rev. G | Page 12 of 16

NONLINEAR CIRCUITS

Due to its low input bias currents, the OP297 is an ideal log

amplifier in nonlinear circuits such as the square and square

root circuits shown in Figure 35 and Figure 36. Using the

squaring circuit of Figure 35 as an example, the analysis begins

by writing a voltage loop equation across Transistor Q1,

Transistor Q2, Transistor Q3, and Transistor Q4.

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

+

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

=

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

+

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

S4

REF

T4

S3

OUT

T3

S

IN

T2

S1

IN

T1

I

I

V

I

I

V

I

I

V

I

I

V

ln

ln

ln

ln

2

All the transistors of the MAT04 are precisely matched and at

the same temperature, so the IS and VT terms cancel, where

2lnIIN = lnIOUT + lnIREF = ln(IOUT × IREF)

Exponentiating both sides of the equation leads to

()

REF

IN

OUT

I

I

I

2

=

Op Amp A2 forms a current-to-voltage converter, which gives

VOUT = R2 × IOUT. Substituting (VIN/R1) for IIN and the previous

equation for IOUT yields

2

⎟

⎠

⎞

⎜

⎝

⎛

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

=

R1

V

I

R2

V

IN

REF

OUT

A similar analysis made for the square root circuit of Figure 36

leads to its transfer function

()(

)

R1

I

V

R2

V

REF

IN

OUT =

7

6

5

–15V

1

2

3

V+

V–

Q3

Q1

Q2

Q4

13

14

12

8

9

10

4

8

6

5

7

2

3

1

MAT04E

–

+

1/2

OP297

–

+

1/2

OP297

VIN

R1

33kΩ

C1

100pF

R3

50kΩ

R4

50kΩ

IREF

C2

100pF

R2

33kΩ

VOUT

IOUT

Figure 35. Squaring Amplifier

7

6

5

IOUT

–15V

1

2

3

V+

V–

Q1

7

9

10

4

8

3

1

MAT04E

8

Q3

5

6

Q4

13

12

14

Q2

R2

33kΩ

C2

100pF

C1

100pF

R1

33kΩ

R3

50kΩ

R4

50kΩ

VOUT

IREF

–

+

1/2

OP297

–

+

1/2

OP297

VIN

Figure 36. Square Root Amplifier

In these circuits, IREF is a function of the negative power supply.

To maintain accuracy, the negative supply should be well regu-

lated. For applications where very high accuracy is required, a

voltage reference can be used to set IREF.

An important consideration for the squaring circuit is that a

sufficiently large input voltage can force the output beyond the

operating range of the output op amp. Resistor R4 can be

changed to scale IREF or R1; R2 can be varied to keep the output

voltage within the usable range.

Unadjusted accuracy of the square root circuit is better than

0.1% over an input voltage range of 100 mV to 10 V. For a

similar input voltage range, the accuracy of the squaring circuit

is better than 0.5%.