![](http://datasheet.mmic.net.cn/270000/71128_datasheet_16004890/71128_3.png)
AN731
Vishay Siliconix
Document Number: 71128
28-Jan-00
www.vishay.com FaxBack 408-970-5600
3
To limit the common mode range of V
X
, the following equations
can be used:
1. To keep V
X
equal or greater than a minimum value, V
Xm
=
1 V:
Vr2
Vxm(Vo2–Vr–aVc2)
Vo2
aVc2Vr
a(Vr–Vxm)–Vr
1(3.4–1.3–1.2
2.7)
1.2(1.3–1)–1.3
1.2
2.7
1.3
3.4
1.249
(12)
2. To keep V
X
equal or less than a maximum value, V
Xm
=
3 V:
Vr2
VxM(Vo2–Vr–aVc2)
Vo2
a(Vr–VxM–Vc2
aVc1Vr
Vc1)–Vr
2(3.4–1.3–1.2
3.4
2.7)
1.2
0.2
1.3
1.2(1.3–2–2.7
0.2)–1.3
1.13 V
(13)
So, V
r2
can be any value between 1.249 V and 1.3 V. Choose
V
r2
= 1.25 V.
Calculate m1 and then R2:
m1
Vr–Vr2
a(Vr2–Vc2)–Vr
1.3–1.25
1.2(1.25–2.7)–1.3
Vo2
3.4
0.139
m1
R2
R1
R2
m1R1
0.139
22.1 k
3.07 k
(14)
Choose R2 = 3.01 k as a practical value
Calculate R3 and R4:
a
m2
m1
R3
m1R4
R3
am1R4
(15)
Choose R4, then calculate R3. The value of R4 should be large
enough such that the current going through it will not be so
large as to cause excessive power dissipation under extreme
conditions. On the other hand, R4 should be small enough that
its current will not be overly sensitive to noise and op-amp bias
current.
If R4 is set at 22.1k, then R3 = 3.68 k, and we can choose R3
= 3.60 k as a practical value.
Express V
O
as a function of V
C
, using practical values of R’s:
a
m2
m1
R1R3
R2R4
22.1kx3.68k
3.01kx22.1k
1
m1
1.223
b
1
m1
1 Vr–
a Vr2
R1
R2
1 Vr–R2
a Vr2
b
22.1k
3.01k
1 1.3–3.01k
1.223 1.25
0.1389
(16)
The final result: V
O
= aV
C
+ b = 1.223 x V
C
+ 0.1389
A circuit was built and tested (see Figure 5). The result is
tabulated in Table 1 and plotted in Figure 4:
V
C
V
X
V
O
Measured
Calculated
Measured
Required
0.1
1.43
0.26
0.32
0.2
1.42
0.38
0.42
0.40
0.4
1.38
0.63
0.68
0.64
0.8
1.32
1.12
1.16
1.12
1.2
1.25
1.61
1.66
1.60
1.6
1.19
2.10
2.12
2.08
2.0
1.11
2.58
2.68
2.56
2.4
1.05
3.07
3.11
3.04
2.6
1.02
3.32
3.33
3.28
2.7
1.00
3.44
3.46
3.40
2.8
0.99
3.56
3.58
3.0
0.96
3.81
3.78
0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
0
0.5
1.0
1.5
2.0
2.5
3.0
Control Voltage—V
C
(v)
O
O
(
FIGURE 4.
V
X
Measured
V
O
The measured values are very much in agreement with the
calculated and required values. A negligible error results from
the difference between an ideal op-amp and the actual circuit
with its finite offset voltage and bias current.