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just right builds a little bit more
around the loop each time. Noise
with a phase that isn’t just right
eventually dies out because it is not
reinforced. As a result, the output
builds up to a sine wave at the
desired frequency.
To keep the oscillator from
building up to an infinite output
voltage (or trying to), the circuit is
usually a little non-linear so that loop
gain stabilizes precisely at one when
the output reaches the desired
voltage.
A Phase-Shift
Oscillator
Gain is easy to obtain over a
wide range of frequencies. What
about phase shift? The required
phase shift of 360° can be distributed
around the circuit. For example, if the
amplifier is an inverting amplifier, it
contributes 180° of phase shift. This
leaves the remaining 180° to be
created in the feedback circuit
and/or the filter.
Figure 2 shows a phase-shift
oscillator. To be sure, there are other
circuits with better performance, but
this one is the closest to the basic
circuit we’ve just discussed.
Let’s start with the feedback and
filter circuit formed by the three pairs
of 10 KΩ resistors and 0.1 µF
capacitors. Each pair forms a low
pass RC (resistor–capacitor) filter that
shifts the phase of the input signal
from 0° to 90° as frequency is
increased. At some frequency, the
phase shift will be 60°.
The frequency at which each RC
section contributes 60° of phase shift
is:
f = (tan 60°) / 2πRC = 1.73 /
6. 28 RC = 0.28 / RC
For our combination of 10 KΩ
and 0.1 µF, that frequency is 275 Hz.
When three identical sections are
cascaded, each contributes its own
60° of phase shift, making up the
remaining 180° to form a 275 Hz
oscillator.
At the frequency for which 60°
of phase shift occurs, the filter also
reduces the amplitude of the input
signal by half. If three sections are
connected back to back, then the
total reduction in signal level is 1/2
x 1/2 x 1/2 = 1/8 = 0.125, which is
our value of β.
To make |Aβ| at least 1, A must
then be at least 8, and that is
controlled by the ratio of Rf to Ri. Rf
is made variable to allow for
adjustment in gain to account for
component variations and other
effects as we shall see.
Building a Phase-Shift
Oscillator
For this circuit, you will need a
power supply that can provide both
positive and negative DC voltages of
6V to 12V. Since current draw is low,
you can use batteries to provide
power. An oscilloscope (stand-alone
or sound-card based) is required to
see the waveforms produced by the
oscillator and to make adjustments.
• Start by building the circuit of
Figure 2. The 10 µF capacitors
filter out noise to prevent
feedback through the op-amp
power supply pins. Set the 1
MΩ potentiometer for the
highest resistance between its
connections. A 10-turn trimpot
will be the easiest to adjust,
but a single-turn panel pot will
work if you use a knob to
make adjustment smoother.
• Connect power; you should
see something that looks like a
square wave at the output of
the op-amp. This shows the op-amp output swinging back and
forth between the power
supply voltages as the circuit’s
gain of 1M/10K = 100 is too
high for the current in Rf to
balance that coming through Ri
from the feedback network. As
a result, the output jumps
between the power supply
voltages.
• Reduce the potentiometer
resistance to obtain an
60 March 2015
FIGURE 2. The phase-shift oscillator
circuit. Each pair of 10 KΩ resistors and
0.1 µF capacitors in the feedback
network adds 60° of phase shift at the
frequency of oscillation.
Two Spurious Emissions
The value of 2798 used in the January 2015 column to compute the “free-space” length of
an antenna in inches was a typo. The correct value is 2952. In addition, the Wireless Institute of
Australia (WIA — www.wia.org.au) is the world’s oldest national amateur radio society,
founded in 1910. It was followed by the Radio Society of Great Britain (RSGB – rsgb.org) in 1913,
and only then by the ARRL in 1914.
