AND8054/D
Designing RC Oscillator
Circuits with Low Voltage
Operational Amplifiers and
Comparators for Precision
Sensor Applications
Jim Lepkowski
Senior Applications Engineer
Christopher Young
Engineering Intern, Arizona State University
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APPLICATION NOTE
INTRODUCTION
The design of RC operational amplifier oscillators
requires the use of a formal design procedure. In general, the
design equations for these oscillators are not available;
therefore, it is necessary to derive the design equations
symbolically to select the RC components and to determine
the influence of each component on the frequency of
oscillation. A design procedure will be shown for two state
variable oscillator circuits that can be used in precision
capacitive sensor applications. These two oscillators have
an output frequency proportional to the product of two
capacitors (C
1
*C
2
) and the ratio of two capacitors (C
1
/C
2
).
The state variable oscillators have been built using ON
Semiconductor’s new family of sub–1 volt operational
amplifiers and comparators. The MC33501, MC33503, and
NCS2001 operational amplifiers, and the NCS2200
comparator are the industry’s first and only commercially
available analog components that are specified at a voltage
of 0.9 volts. These components can be powered from a single
NiCd, NiMH or alkaline battery cell. The wide operating
temperature range of –40_C to +105_C makes these devices
suitable for a wide range of applications.
ON Semiconductor’s family of low voltage operational
amplifiers and comparators help solve the analog limitations
that have resulted from the industry’s movement to low
power supply voltages. The ON Semiconductor family of
analog components provide a solution for the analog I/O
interface circuits that are required for emerging low voltage
DSP and microcontroller ICs.
There are a number of advantages that result from
lowering the power supply voltage such as lower power
consumption and the reduction of multiple power supplies.
Low voltage analog design also results in new challenges for
the designer and care must be taken to transfer existing
higher voltage circuits to the lower voltage levels. For
example, device parameters such as the bandwidth and slew
rate decrease as the voltage is reduced and are modest in
comparison to traditional devices operating at voltages such
as
±10
V. Also, there is a limited voltage swing range
available at low voltages; however, this problem is
minimized by the rail–to–rail single voltage range of both
the input and output signals of the ON Semiconductor
devices.
The MC33501 and MC33503 are designed with a
BiCMOS process, while the NCS2001 and NCS2200 are
implemented with a full CMOS process. The main attributes
of these devices are their low voltage operation and a full
rail–to–rail input and output range. The rail–to–rail
operation is provided by using a unique input stage that is
formed by a folded cascade N–channel depletion mode
differential amplifier. A simplified schematic of the
MC33501 and MC33503 is shown in Figure 1.
©
Semiconductor Components Industries, LLC, 2002
1
February, 2002 – Rev. 1
Publication Order Number:
AND8054/D
AND8054/D
V
CC
IN–
Offset
Voltage
Trim
IN+
Out
V
CC
V
CC
Output
Voltage
Saturation
Detector
V
CC
Clamp
Body
Bias
Figure 1. Simplified Schematic of the MC33501/MC33503
ON Semiconductor’s Family of Low Voltage Operational Amplifiers and Comparators
Part
Number
MC33501
MC33503
Component
Operational
Amplifier
Process
BiCMOS
Features
Package
TSOP–5
Availability
Available NOW
Production Release 4Q2000
•
•
•
•
•
•
@ Single Supply Operation of 1.0 V
Gain Bandwidth Product = 3 MHz (typ.)
Open Loop Voltage Gain = 90 dB (typ.)
NCS2001
Operational
Amplifier
CMOS
@ Single Supply Operation of 0.9 V
Gain Bandwidth Product = 1.1 MHz (typ.)
Open Loop Voltage Gain = 90 dB (typ.)
TSOP–5
Available NOW
Production Release 1Q2001
NCS2200
Comparator
CMOS
@ Single Supply Operation of 1.0 V
Propagation Delay 1.1
ms
(typ.)
Complementary or Open Drain Output
Configuration
TSOP–5
Product Preview
Production Release 1Q2002
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AND8054/D
TRANSDUCER SYSTEM
A wide variety of different circuits can be used to
accurately measure capacitive sensors. The design choices
include switched capacitor circuits, analog multivibrators,
AC bridges, digital logic ICs and RC operational amplifier
oscillators. The requirements for a precision sensor circuit
include high accuracy, reliable start–up, good long–term
stability, low sensitivity to stray capacitance and a minimal
component count. State variable RC operational amplifier
oscillators meet all of the requirements listed above; thus,
they form the basis for this study.
A block diagram of a capacitive sensor system is shown
in Figure 2. The oscillation frequency is found by counting
the number of clock pulses (i.e. MHz) in a time window that
is formed by the square wave oscillator output (i.e. kHz) of
a comparator circuit. The counter circuit can be
implemented with a digital logic counter circuit or by using
the Time Processing Unit (TPU) channel of a
microprocessor. If necessary, temperature correction can be
accomplished by implementing a curve fitting routine with
data obtained by calibrating the sensor over the operating
range. An analog IC sensor can be used to monitor the sensor
temperature or for very precise applications a second
oscillator could be built with a platinum resistive
temperature device (RTD) sensor.
In addition, it is often important for the sensor system to
compute the ratio of two capacitors. Calculating the ratio of
the capacitors reduces the transducer’s sensitivity to
dielectric errors from factors such as temperature. In other
cases, such as in an air data quartz
DP
pressure sensors, the
desired measurement is equal to the ratio of two
capacitances (C
MEAS
/ C
REF
). Furthermore, dual sensors are
typically designed to double the C
MEAS
in capacitance,
while C
REF
may vary less than one percent. Thus, the
transducer’s accuracy is increased if a circuit such as the
ratio state variable oscillator can directly detect the C
MEAS
to C
REF
ratio.
C
MEAS
C
REF
Clock
RC Op–Amp
Oscillator
Comparator
Counter
Circuit
Temperature
Sensor
Algorithm:
Count the number of clock pulses in a time window set by oscillator pulses.
Clock
Signal
Oscillator
Signal
EEPROM:
Temperature
Compensation
Coefficients
Micro–Processor
Figure 2. Block Diagram of Capacitive Sensor Application
SENSOR APPLICATIONS
RC operational amplifier oscillators can be used to
accurately detect both resistive and capacitive sensors;
however, this paper will only analyze capacitive applications.
The three basic configurations of capacitive sensors and their
attributes are shown in Table 1. The absolute and dual
capacitive sensors will be used with the absolute and ratio
oscillator circuits, respectively. Differential capacitive
sensors typically are not used in precision applications;
therefore, they will not be analyzed in this paper.
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AND8054/D
Table 1. Summary of Capacitive Sensors
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Sensor Configuration
Absolute
Dual
Differential
CMEAS
CREF
Schematic Representation
CMEAS
C1
C2
Sensor Applications
•
•
Absolute Pressure
Humidity
•
•
•
•
Acceleration
Oil Level
Oil Quality
•
•
Displacement
Proximity
Differential Pressure
Circuit
Absolute Oscillator
freq.
T
CMEAS
Ratio Oscillator
Typical Circuit – Multivibrator
freq.
T
C1
*
C2
Oscillation Frequency
C
freq.
T
MEAS
CREF
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
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.
V
A
A
A
T(s)
+
OUT
+
+
+
A
+
N(s)
Ds
VIN
1
*
Ab
1
*
LG
D(s)
where
A
b
+
LG
5
loop gain
Ds
5
characteristic equation
If VIN
+
0, then T(s)
+ Rwhen
Ds
+
0
b
≡
Feedback Factor
At the oscillation condition of
Ds
= 0, referred
to as the Barkhausen stability criterion,
|LG|
+
1 (magnitude) and
éLG +
0 (phase).
Figure 3. Block Diagram of an Oscillator
Imaginary (jω)
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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AND8054/D
CIRCUIT DESCRIPTIONS
Absolute State Variable Oscillator
The absolute state variable oscillator is used when the
measurement is proportional to either one or two capacitors
(i.e. freq.
α
C
1
*C
2
). The block diagram and schematic of the
absolute circuit are shown in Figures 5 and 6. This circuit
consists of two integrators and an inverter circuit. Each
integrator has a phase shift of 90_, while the inverter adds an
additional 180_ phase shift; thus, a total phase shift of 360_
is fed into the input of the first integrator to produce the
oscillation. The first integrator stage consists of amplifier
A
1
, resistor R
1
and sensor capacitance C
1
. The second
integrator consists of amplifier A
2
, resistor R
2
and sensor
capacitance C
2
. Resistor–capacitor combinations R
1
and C
1
,
and R
2
and C
2
, set the gain of each integrator stage, in
addition to setting the oscillation frequency. The inverter
stage consists of amplifier A
3
, resistors R
3
and R
4
and
capacitor C
4
. Capacitor C
4
is not essential for normal
operation; however, it ensures oscillator startup under
extreme ambient temperature conditions.
Limit Circuit
V
1
Integrator
6
q
= 90°
Integrator
V
2
Inverter
6
q
= 90°
V
3
6
q
= 180°
Figure 5. Absolute Oscillator Block Diagram
C4
Limit Circuit
C1
C2
R4
R1
–
+
A1
V
1
R2
–
+
A2
V
2
R3
–
+
A3
V
3
The absolute sensor capacitances C1 and C2 are used by the integration amplifiers.
Figure 6. Absolute Oscillator Schematic
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