AND8054 Datasheet, PDF (4/28 Pages) ON Semiconductor – Designing RC Oscillator Circuits with Low Voltage Operational Amplifiers and Comparators for Precision Sensor Applications

AND8054/D
Table 1. Summary of Capacitive Sensors
Sensor Configuration
Absolute
ÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁ _{Schematic Representation}
CMEAS
ÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁ _{Sensor Applications}
• Absolute Pressure
• Humidity
ÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁ _Circuit
ÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁ ^{Oscillation Frequency}
Absolute Oscillator
freq. T CMEAS
Dual
CMEAS
CREF
• Acceleration
• Oil Level
• Oil Quality
• Differential Pressure
Ratio Oscillator
freq.
T
CMEAS
CREF
Differential
C1
C2
• Displacement
• Proximity
Typical Circuit – Multivibrator
freq. T C1 * C2
OSCILLATOR THEORY
An oscillator is a positive feedback control system which
does not have an external input signal, but will generate an
output signal if certain conditions are met. In practice, a small
input is applied to the feedback system from factors such as
noise pick–up or power supply transients, and this initiates the
feedback process to produce a sustained oscillation. A block
diagram of an oscillator is shown in Figure 3.
The poles of the denominator of the transfer equation T(s),
or equivalently the zeroes of the characteristic equation,
determine the time domain behavior of the system. If T(s)
has all of its poles located within the left plane, the system
is stable because the corresponding terms are all
+
V_IN
–
A ≡ Amplifier Gain
V_OUT
b ≡ Feedback Factor
exponentially decaying. In contrast, if T(s) has one pole that
lies within the right half plane, the system is unstable
because the corresponding term exponentially increases in
amplitude. An oscillator is on the borderline between a
stable and an unstable system and is formed when a pair of
poles is on the imaginary axis, as shown in Figure 4.
If the magnitude of the loop gain is greater than one and
the phase is zero, the amplitude of oscillation will increase
exponentially until a factor in the system such as the supply
voltage restricts the growth. In contrast, if the magnitude of
the loop gain is less than one, the amplitude of oscillation
will exponentially decrease to zero.
T(s)
+
VOUT
VIN
+
1
A
* Ab
+
1
A
* LG
+
A
Ds
+
A
N(s)
D(s)
where A b + LG 5 loop gain
Ds 5 characteristic equation
If VIN + 0, then T(s) + Rwhen Ds + 0
At the oscillation condition of Ds = 0, referred
to as the Barkhausen stability criterion,
|LG| + 1 (magnitude) and éLG + 0 (phase).
Imaginary (jω)
Figure 3. Block Diagram of an Oscillator
Imaginary (jω)
Real (ω)
Real (ω)
2nd Order Oscillator
3rd Order Oscillator
Figure 4. Pole Locations for a 2nd and 3rd Order Oscillator
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