AND8054 Datasheet, PDF (9/28 Pages) ON Semiconductor – Designing RC Oscillator Circuits with Low Voltage Operational Amplifiers and Comparators for Precision Sensor Applications

AND8054/D
Absolute Oscillator (with C₄)
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
V₂
ƪǒ Ǔǒ Ǔƫ A3 + –
R4
R3
1
sR4C4 ) 1
LG
+
VOUT
VTEST
+
A1
A2
A3
A3
+
* Z4
Z3
+
R4 || C4
R3
V_OUT
V₃
ǒ Ǔǒ Ǔƪǒ Ǔǒ Ǔƫ LG +
–
1
sR1C1
–
1
sR2C2
–
R4
R3
1
sR4C4 ) 1
+
–
R4
s3R1R2R3R4C1C2C4
)
s2R1R2R3C1C2
Ds
+
N(s)
D(s)
+
1
*
LG
+
1
)
R4
s3R1R2R3R4C1C2C4
)
s2R1R2R3C1C2
+
s3R1R2R3R4C1C2C4 )
s3R1R2R3R4C1C2C4
s2R1R2R3C1C2 )
) s2R1R2R3C1C2
R4
N(s) + s3R1R2R3R4C1C2C4 ) s2R1R2R3C1C2 ) R4
Absolute Oscillator (without C₄)
Step 2: Solve N(s) using Method I
Solve Method I: Solve the remainder of: ^N(s)
s² ) w^2o
N(s) + s2R1R2R3C1C2 ) R4
Ǹ ^{s2 ) w2o}
R1R2R3C1C2
R1R2R3C1C2s2 ) R4
* R1R2R3C1C2s2 ) w^2oR1R2R3C1C2
R4 * w^2oR1R2R3C1C2
Set the remainder to equal zero and solve for w_o: R4 * w^2oR1R2R3C1C2 + 0
Ǹ w_o +
R4
R1R2R3C1C2
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