OP297

Rev. F | Page 12 of 16

7

6

5

–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

–

+

1/2

OP297

–

+

1/2

OP297

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.

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

+

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

=

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

+

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

4

4

3

3

2

2

1

1

S

REF

T

S

O

T

S

IN

T

S

IN

T

I

I

ln

V

I

I

ln

V

I

I

ln

V

I

I

ln

V

All the transistors of the MAT04 are precisely matched and at

the same temperature, so the I and V terms cancel, where

S

T

Exponentiating both sides of the equation leads to

()

REF

IN

O

I

I

I

2

=

Figure 36. Square Root Amplifier

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 I

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

equation for

I

.

O

yields

REF

2

1

2

⎟

⎠

⎞

⎜

⎝

⎛

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

=

R

V

I

R

V

IN

REF

OUT

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 I

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

leads to its transfer function

REF

or R1; R2 can be varied to keep the output

voltage within the usable range.

()( )

1

2

R

I

V

R

V

REF

IN

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%.

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

R1

33kΩ

C1

100pF

R3

50kΩ

R4

50kΩ

C2

100pF

R2

33kΩ

Figure 35. Squaring Amplifier