undistorted sine wave that
peaks a volt or so below the
power supply voltages as seen
in Figure 3. (This may be a
touchy adjustment with a
single-turn pot.) If you have a
dual-channel oscilloscope,
observe the input and output
voltages of each RC section,
and verify that each
contributes approximately 60°.
• Measure the period, T, of the
output waveform (one
complete cycle) and calculate
the frequency of the oscillator
(f = 1/ T). Measure the
resistance of the potentiometer
(Rf) after removing it from the
circuit. Compute the
magnitude of the amplifier’s
gain (|A| = resistance / 10
KΩ).
You probably observed that the
frequency was a lot different than the
initial calculation of 275 Hz — my
oscillator’s frequency was 476 Hz.
The voltage drop across each RC
filter section was probably greater
than half. My sections reduced the
output to about 0.27 of the input.
The gain of the amplifier will also be
found to be greater than eight to
compensate for that extra reduction.
My potentiometer’s resistance was
603 kΩ, for a gain of 60. 3 —
approximately equal to 1 / (0.27 x
0.27 x 0.27).
These discrepancies result
primarily from things we overlooked
in the design process. Each RC
section does not contribute exactly
60° of phase shift because it is
loaded by the next section in the
network. That causes
an extra voltage drop
and phase shift. The
op-amp also
contributes its own
small amount of phase
shift, meaning that the
total phase shift
needed from the
feedback circuit will
not be exactly 180° at
the frequency of
oscillation. These two
effects result in a
higher frequency for
the actual circuit at
which |Aβ| = 1.
To see the effects
of op-amp gain
limitations at higher
frequencies, change
the feedback capacitors from 0.1 µF
to 0.001 µF, increasing the 60° phase-shift frequency for each RC section
to about 27. 5 kHz. At this frequency,
a 741 op-amp can’t cause its output
to change rapidly enough to create a
sine wave. (The maximum rate at
which the op-amp can change its
output voltage is called the slew rate,
which is measured in V/µsec.) As a
result, the output waveform will
change to something that looks more
like a triangle wave — no matter how
you adjust the amplifier gain.
The phase-shift and voltage drop
errors caused by the loading effects
of each RC section can be eliminated
by adding a buffer amplifier between
each section. Replace the single op-amp with a quad op-amp such as the
LM324. One op-amp section will
replace the existing LM741. Add a
voltage follower between each RC
Instruments applications
note, Design of op-amp
sine wave oscillators. 3)
Because the voltage follower
presents its very high input
impedance to the preceding circuit,
each RC section can act more like
the ideal filter we envisioned during
the design process.
The resulting frequency of
oscillation and the gain required to
achieve oscillation should change to
be within 20% of the originally
calculated values. (The tolerance of
most 0.1 µF and 0.001 µF capacitors
is typically 10% to 20%, allowing a
lot of variation as well.)
RF Oscillators
The circuits used in RF oscillators
are different than those used for
lower frequencies. RC phase-shift
circuits aren’t generally used above a
few MHz. The values of R or C
become impracticably small, which
leaves the oscillator susceptible to
stray resistances and capacitances
that compromise stability and
consistency. In the MHz range, it’s
much easier to use inductors and
capacitors to form the phase-shifting
circuits which are referred to as
resonators.
Most RF oscillators use discrete
devices such as a bipolar transistor or
FET since most integrated op-amps
March 2015 61
FIGURE 3. The oscilloscope traces show the output
signal from the op-amp and the smaller phase-shifted
signal at the output of the first RC filter section.
Circuit Construction Tutorials
Learning how to build and test circuits at RF is a useful
skill but it does take a little practice. Chuck Adams K7QO
wrote an excellent and detailed tutorial, Manhattan Building
Techniques, that can be downloaded from the QRP ME
website, whose products are popular with low power ham
operators ( www.qrpme.com/docs/K7QO%20Manhattan.pdf).
In addition, you can find all sorts of building tips and
instructions by clicking the Radio Technology Topics link at
arrl.org/tech-portal and in my own Circuitbuilding for
Dummies Do-It-Yourself.
