AND8054 Datasheet, PDF (6/28 Pages) ON Semiconductor – Designing RC Oscillator Circuits with Low Voltage Operational Amplifiers and Comparators for Precision Sensor Applications

AND8054/D
Ratio State Variable Oscillator
The ratio state variable oscillator [6] is used for dual
capacitive sensors when the oscillation frequency is
proportional to the ratio of sensor capacitances C₃ and C₄ (i.e.
freq. α C₃ / C₄). The block diagram and schematic of the ratio
circuit are shown in Figures 7 and 8. This circuit consists of
two integrators and a differentiator circuit. The integrators
formed by amplifier A₁ and A₂ are identical to the integrators
used in the absolute circuit. Amplifier A₃, resistors R₃, R₄ and
R₅, and the sensor capacitors C₃ and C₄ form the
differentiator stage which provides a 180_ phase shift. The
values of resistors R₃, R₄ and R₅ are selected to set the break
frequencies of the differentiator stage, so that the gain of the
stage is equal to –C₃/C₄. Resistor R₅ provides a DC current
path through capacitor C₃ in order to initiate oscillation at
power–up. Because R₅ is relatively large (MΩ), it can be
replaced with a three resistor “Tee” network in order to use
readily available resistors, as shown in Figure 9.
Limit Circuit
Integrator
V₁
6 θ = 90°
Integrator
V₂
6 θ = 90°
Differentiator
V₃
6 θ = 180°
Figure 7. Ratio Oscillator Block Diagram
Limit Circuit
C1
C2
C3
R1
A1
–
R2
+
V₁
A2
–
R3
R5
+
V₂
C4
R4
– ^A3
+
V₃
The differentiator amplifier is formed by the dual sensor capacitances C3 and C4.
Figure 8. Ratio Oscillator Schematic
C4
C1
R1
A1
–
R2
+
V₁
C2
C3
– ^A2
+
R3
V₂
R5a
R5b
R5c
R4
A3
–
+
V₃
A Tee network provides a method to replace a large resistor (i.e. MΩ) with three small resistors (i.e. kΩ).
R5a
R5b
R5c
R5_equivalent
⇔
R5_equivalent
+
R5a
)
R5b
)
R5aR5b
R5c
Figure 9. Ratio Oscillator Schematic with R5 Tee Network
http://onsemi.com
6