AND8054 Datasheet, PDF (12/28 Pages) ON Semiconductor – Designing RC Oscillator Circuits with Low Voltage Operational Amplifiers and Comparators for Precision Sensor Applications

AND8054/D
RATIO OSCILLATOR DESIGN EQUATIONS
C4
C1
R1
– ^A1
R2
+
V₁
C2
C3
– ^A2
R3
R5
+
V₂
R4
– ^A3
+
V₃
A2
+
–
1
sR2C2
A3
+
–
R4(sR5C3 ) 1)
(sR3R5C3 ) R3 ) R5)(sR4C4
)
1)
V₁
V₂
V₃
A1
+
–
1
sR1C1
Figure 11. Ratio Oscillator Signal Flow Diagrams
Ratio Oscillator
Step 1: Find LG and Ds
The loop gain is found by breaking the loop and inserting a “test’’ voltage into the input.
V_TEST
A1
+
–
1
sR1C1
A2
+
–
1
sR2C2
V₁
A3
+
–
R4(sR5C3 ) 1)
(sR3R5C3 ) R3 ) R5)(sR4C4
)
1)
V₂
LG
+
VOUT
VTEST
+
A1
A2
A3
A3
+
–Z4
Z3
+
R3
R4 ø C4
) (C3 ø R5)
V_OUT
V₃
ǒ Ǔǒ Ǔǒ Ǔ LG +
–
1
sR1C1
–
1
sR2C2
–
R4(sR5C3 ) 1)
(sR3R5C3 ) R3 ) R5)(sR4C4
)
1)
LG
+
*
s4R1R2R3R4R5C1C2C3C4
)
s3[(R3R5C3
)
sR4R5C3 ) R4
R3R4C4 ) R4R5C4)R1R2C1C2]
)
s2(R3
)
R5)(R1R2C1C2)
s4R1R2R3R4R5C1C2C3C4 ) s3[(R3R5C3 ) R3R4C4 ) R4R5C4)R1R2C1C2]
Ds
+
N(s)
D(s)
+
1
*
LG
+
) s2(R3 )
s4R1R2R3R4R5C1C2C3C4
R5)(R1R2C1C2) ) sR4R5C3 ) R4
) s3[(R3R5C3 ) R3R4C4 ) R4R5C4)R1R2C1C2]
) s2(R3 ) R5)(R1R2C1C2)
N(s) + s4R1R2R3R4R5C1C2C3C4 ) s3[(R3R5C3 ) R3R4C4 ) R4R5C4)R1R2C1C2]
) s2(R3 ) R5)(R1R2C1C2) ) sR4R5C3 ) R4
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