71128 Datasheet, PDF (3/7 Pages) Vishay Siliconix – Simple Solution for Dynamically Programming the Output Voltage of DC-DC Converters

AN731
Vishay Siliconix
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
w
Vxm(Vo2–Vr–aVc2) ) aVc2Vr
Vo2 ) a(Vr–Vxm)–Vr
+
(12)
1(3.4–1.3–1.2 2.7) ) 1.2 2.7
3.4 ) 1.2(1.3–1)–1.3
1.3 _{+ 1.249}
2. To keep V_X equal or less than a maximum value, V_Xm =
3 V:
Vr2
w
VxM(Vo2–Vr–aVc2) ) aVc1Vr
Vo2 ) a(Vr–VxM–Vc2 ) Vc1)–Vr
+
(13)
2(3.4–1.3–1.2 2.7) ) 1.2 0.2
3.4 ) 1.2(1.3–2–2.7 ) 0.2)–1.3
1.3 _{+ 1.13}
V
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
+
Vo2
)
Vr–Vr2
a(Vr2–Vc2)–Vr
+
3.4
)
1.3–1.25
1.2(1.25–2.7)–1.3
+
0.139
m1
+
R2
R1
Ã¥
R2
+
m1R1
+
0.139
(14)
22.1 k + 3.07 kW
Choose R2 = 3.01 kW as a practical value
Calculate R3 and R4:
a
+
m2
m1
+
R3
m1R4
Ã¥
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
+
1.223
ǒ Ǔ ǒ Ǔ b +
1
m1
)
1
Vr–
1
m1
)
a
Vr2 +
ǒ Ǔ ǒ Ǔ R1
R2
)
1
Vr–
R1
R2
)
a
Vr2
(16)
ǒ Ǔ ǒ Ǔ b +
22.1k
3.01k
)
1
1.3–
22.1k
3.01k
)
1.223
1.25 + 0.1389
Document Number: 71128
28-Jan-00
The final result: V_O = aV_C + b = 1.223 x V_C + 0.1389
EXPERIMENTAL RESULTS
A circuit was built and tested (see Figure 5). The result is
tabulated in Table 1 and plotted in Figure 4:
TABLE 1
V_X
V_O
V_C 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
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0
0
V_O
V_X Measured
0.5
1.0
1.5
2.0
2.5
3.0
Control Voltage—V_C (v)
FIGURE 4.
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.
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