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 lnlnlnln
2
All the transistors of the MAT04 are precisely matched and at
the same temperature, so the I
S
and V
T
terms cancel, where
2ln
I
IN
= lnI
OUT
+ lnI
REF
= ln(I
OUT
× I
REF
)
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
V
OUT
= R2 × I
OUT
. Substituting (V
IN
/R1) for I
IN
and the previous
equation for I
OUT
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
IV
R2V
REFIN
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
V
IN
R1
33kΩ
C1
100pF
R3
50kΩ
R4
50kΩ
I
REF
C2
100pF
R2
33kΩ
V
OUT
I
OUT
00300-035
Figure 35. Squaring Amplifier
7
6
5
I
OUT
–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
V
OUT
I
REF
–
+
1/2
OP297
–
+
1/2
OP297
V
IN
00300-036
Figure 36. Square Root Amplifier
In these circuits, I
REF
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 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; 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%.
