OP497

Rev. E | Page 13 of 16

NONLINEAR CIRCUITS

Due to its low input bias currents, the OP497 is an ideal log

amplifier in nonlinear circuits, such as the squaring amplifier

and square root amplifier circuits shown in Figure 40 and

Figure 41. Using the squaring amplifier circuit in Figure 40

as an example, the analysis begins by writing a voltage loop

equation across Transistors Q1, Q2, Q3, and Q4.

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

+

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

=

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

+

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

S4

REF

T4

S3

O

T3

S2

IN

T2

S1

IN

T1

I

I

In

V

I

I

I

In

V

I

I

In

V

I

I

In

V

All the transistors in the MAT04 are precisely matched and at

giving

Exponentiating both sides of the thick equation lead to

()

REF

IN

O

I

I

I

2

=

Op amp A2 forms a current-to-voltage converter which results

2

⎟

⎠

⎞

⎜

⎝

⎛

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

=

R1

V

I

R2

V

IN

REF

OUT

1

2

3

6

7

5

C1

100pF

V+

2

3

8

1

4

V–

6

5

7

9

8

10

Q1

Q3

Q2

14

12

Q4

13

MAT04

1/4

OP497

1/4

OP497

A2

A1

R1

133k

Ω

–15V

R3

50k

Ω

R4

50k

Ω

C2

100pF

R2

33k

Ω

Figure 40. Squaring Amplifier

A similar analysis made for the square root amplifier circuit in

Figure 41 leads to its transfer function

( )(

)

R1

I

V

R2

V

REF

IN

maintain accuracy, the negative supply should be well regulated.

For applications where very high accuracy is required, a voltage

the squaring circuit is that a sufficiently large input voltage can

force the output beyond the operating range of the output op

be varied to keep the output voltage within the usable range.

1

2

3

6

7

5

V+

2

3

8

1

4

6

5

7

9

8

10

Q1

Q3

Q2

14

12

Q4

13

MAT04

C2

100pF

1/4

OP497

1/4

OP497

R2

33k

Ω

C1

100pF

–15V

V–

R5

2k

Ω

R3

50k

Ω

R4

50k

Ω

R1

33k

Ω

Figure 41. Square Root Amplifier

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%.