AND8054 Datasheet, PDF (25/28 Pages) ON Semiconductor – Designing RC Oscillator Circuits with Low Voltage Operational Amplifiers and Comparators for Precision Sensor Applications

AND8054/D
Ratio Oscillator
R11
R1
V11
C1
A1
R2
V₁
C2
C3
A2
R3
R5
V₂
C4
R4
A3
V₃
Figure 30. Schematic of the Ratio Oscillator with Rll that is Used to Obtain T(s),
using Mason’s Reduction Theorem.
Ratio Circuit
Assume R₁ >> R₁₁ , then R₁ + R₁₁ ` R₁
ǒ Ǔǒ Ǔǒ Ǔ P1 + LG + A1
A2
A3 +
–
1
sR1C1
–
1
sR2C2
–
R4(sR5C3 ) 1)
(sR3R5C3 ) R3 ) R5)(sR4C4
)
1)
P1
+
LG1
+
s4R1R2R3R4R5C1C2C3C4
)
s3^ƪǒR3R5C3
*
)
(sR4R5C3 ) R4)
R3R4C4 ) R4R5C4^ǓR1R2C1C2^ƫ
)
s2^ǒR3
)
R5^ǓǒR1R2C1C2^Ǔ
s4R1R2R3R4R5C1C2C3C4 ) s3^ƪǒR3R5C3 ) R3R4C4 ) R4R5C4^ǓR1R2C1C2^ƫ ) s2^ǒR3 ) R5^ǓǒR1R2C1C2^Ǔ ) sR4R5C3 ) R4
Ds + 1 * LG1 +
s4R1R2R3R4R5C1C2C3C4 ) s3^ƪǒR3R5C3 ) R3R4C4 ) R4R5C4^ǓR1R2C1C2^ƫ ) s2^ǒR3 ) R5^ǓǒR1R2C1C2^Ǔ
ǒ
*(sR4R5C3)R4)
Ǔ
ǒ Ǔ ^T(s)
+
V3
V11
+
P1
Ds
+
s4R1R2R3R4R5C1C2C3C4)s3ƪǒR3R5C3)R3R4C4)R4R5C4ǓR1R2C1C2ƫ)s2^ǒR3)R5^ǓǒR1R2C1C2Ǔ
s4R1R2R3R4R5C1C2C3C4)s3ƪ^ǒR3R5C3)R3R4C4)R4R5C4^ǓR1R2C1C2ƫ)s2^ǒR3)R5^ǓǒR1R2C1C2^Ǔ)sR4R5C3)R4
s4R1R2R3R4R5C1C2C3C4)s3ƪ^ǒR3R5C3)R3R4C4)R4R5C4^ǓR1R2C1C2ƫ)s2^ǒR3)R5^ǓǒR1R2C1C2^Ǔ
+
* (sR4R5C3 ₎ R4)
s4R1R2R3R4R5C1C2C3C4 ) s3^ƪ (R3R5C3 ) R3R4C4 ) R4R5C4) R1R2C1C2^ƫ ) s2^ǒR3 ) R5^ǓǒR1R2C1C2^Ǔ ) sR4R5C3 ) R4
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