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
InV
I
I
IInV
I
I
InV
I
I
InV
All the transistors in the MAT04 are precisely matched and at
the same temperature; therefore, the I
S
and V
T
terms cancel,
giving
2InI
IN
= InI
O
+ InI
REF
= In (I
O
× I
REF
)
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
in V
OUT
= R2 × I
O
. Substituting (V
IN
/R1) for I
IN
and the previous
equation for I
O
yields
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
I
O
9
8
10
Q1
Q3
Q2
14
12
Q4
13
I
REF
MAT04
1/4
OP497
1/4
OP497
A2
A1
I
IN
IN
R1
133kΩ
–15V
R3
50kΩ
R4
50kΩ
C2
100pF
R2
33kΩ
V
OUT
00309-041
Figure 40. Squaring Amplifier
A similar analysis made for the square root amplifier circuit in
Figure 41 leads to its transfer function
)
)
R1
IV
R2V
REFIN
OUT
=
In these circuits, I
REF
is a function of the negative power supply. To
maintain accuracy, the negative supply should be well regulated.
For applications where very high accuracy is required, a voltage
reference can be used to set I
REF
. 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
REF
, or R1 and R2 can
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
I
O
9
8
10
Q1
Q3Q2
14
12
Q4
13
MAT04
C2
100pF
1/4
OP497
1/4
OP497
V
OUT
R2
33kΩ
I
REF
I
IN
C1
100pF
–15V
V–
R5
2kΩ
R3
50kΩ
R4
50kΩ
IN
R1
33kΩ
0309-042
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%.
