OP297_06 Datasheet, PDF (12/16 Pages) Analog Devices – Dual Low Bias Current Precision Operational Amplifier

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.
V_T1ln_{⎜⎜⎝⎛}
I _IN
I _S1
⎟⎟⎠⎞ ^{+ VT2ln}⎜⎜⎝⎛
I _IN
I_S2
⎟⎟⎠⎞ ^{= VT3ln}⎜⎜⎝⎛
I_O
I_S3
⎟⎟⎠⎞ ^{+ VT 4ln}⎜⎜⎝⎛
I _REF
I_S4
⎟⎟⎠⎞
All the transistors of the MAT04 are precisely matched and at
the same temperature, so the IS and VT terms cancel, where
2 ln IIN = ln IO + ln IREF = ln (IO × IREF)
Exponentiating both sides of the equation leads to
( ) _{IO =}
I _IN ²
I _REF
Op Amp A2 forms a current-to-voltage converter, which gives
VOUT = R2 × IO. Substituting (VIN/R1) for IIN and the above
equation for IO yields
V_OUT
= _{⎜⎜⎝⎛}
R2
I _REF
⎟⎟⎠⎞⎜⎝⎛
V_IN
R1
⎟⎞²
⎠
A similar analysis made for the square root circuit of Figure 36
leads to its transfer function
V_OUT = R2
(V_IN )(I_REF )
R1
C2
100pF
R2
33kΩ
R1
33kΩ
V_IN
2
1
Q1
3
6
7
Q2
5
6_–
1/2 7
I_{O OP297}
5₊
V_OUT
MAT04E
C1
100pF ^V+
2_– ⁸
1/2 1
OP297
3_{+ 4}
8
Q3 ⁹
10
R3
50kΩ
14
I_{REF Q4} ¹³
12
R4
50kΩ
V–
–15V
Figure 35. Squaring Amplifier
R2
33kΩ
C2
100pF
6_–
1/2 7
I_{O 5 OP297}
+
V_OUT
I_REF
R1
33kΩ
V_IN
C1
100pF
V+
2_– 8
1/2 1
OP297
3_{+ 4}
Q1 ¹
3
7
6 _Q2
5
MAT04E
8
Q3 ⁹
10
13
14
Q4
12
R3
50kΩ
R4
50kΩ
V–
–15V
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%.
Rev. F | Page 12 of 16