December 1958 Popular Electronics
Table
of Contents
Wax nostalgic about and learn from the history of early electronics. See articles
from
Popular Electronics,
published October 1954  April 1985. All copyrights are hereby acknowledged.

There is an old adage
that goes thusly: "If you want to build an oscillator, design an amplifier. If you
want to build an amplifier, design an oscillator." Its basis is the difficulty that
can be experienced in obtaining the right combination of feedback phase and amplitude.
Of course experience, use of simulators, and careful circuit construction minimize
the opportunity for validating that saying. The basic requirement for an oscillator
is feedback from the output to the input that is inphase and great enough in amplitude
to maintain, via the amplifier's gain factor, a constant output level. Tuned LC
(inductorcapacitor) tank circuits are often used as simple frequencydetermining
elements because of their combined resonance characteristics. Phase shift oscillators
are a type of oscillator that can be built without inductors. Instead, they rely
on the phase shift of a series of capacitors and resistors to obtain the 180degree
phase shift needed from output to the input to sustain oscillations. Frequency control
is not typically as stable as with a tank circuit or a crystal, especially as temperatures
change. This type of oscillator definitely feeds the aforementioned adage more so
than those with circuits exhibiting high Q factors. This article from Popular Electronics
covers some of the fundamentals (pun intended).
After Class: Working with PhaseShift Oscillators
By Harvey Pollee
Special Information on Radio, TV, Radar and Nucleonics
Most oscillators that utilize resistancecapacitance tuning generate triangular,
trapezoidal, or square waves. When one thinks of the generation of sine waves, he
usually visualizes an inductancecapacitance tuned type such as the Hartley or Colpitts
circuit. There is a class of RC oscillators, however, that is capable of yielding
excellently formed sine waves and, because of the absence of coils or transformers,
these oscillators are very attractive to the experimenter.
Of the three common circuits in the latter group (the Wien bridge, the bridgedT,
and the phaseshift oscillator), the phaseshift type is the simplest to build,
contains the fewest components, and is very easy to get working.
Fig. 1  Theoretical phaseshift oscillator circuit. See
text. Practical circuits are shown in Figs. 2 and 3.
Basic Oscillator
The fundamental circuit of the phaseshift oscillator is given in Fig. 1.
Like all oscillators, action is initiated by some random fluctuation in the tube
current or voltage, such as is due to thermal or shot effect.
To explain the operation, let us assume that the grid of the triode becomes very
slightly positive for an instant. When this happens, the plate current increases
slightly, causing the voltage drop across plateload R_{L} to increase somewhat
above its standby value. The extent of this increase depends upon the voltage gain
of the tube; the greater the gain, the larger the change in voltage drop across
R_{L}.
A voltage drop of this nature causes the plate voltage of the tube to go down,
thus making the plate negativegoing. Since a positivegoing grid has caused a negativegoing
plate, we can say that the "signal" on the plate is out of phase with the signal
on the grid by 180 degrees.
The plate variation is now fed back to the grid through three RC groups: C1R1,
C2R2, and C3R3. Each group can produce a voltage phase shift of its own. Considering
only the first group (C1R1), the voltage appearing across R1 will lead the signal
voltage pulse from the plate by an amount determined by the ratio of the capacitive
reactance (Xc) of C1 and the resistance (R) of R1. Capacitive reactance depends
on frequency as well as on capacitance, so that there must exist some frequency
for which the phase shift for C1R1 will be exactly 60°.
Now the voltage that appears across R1 is applied across the C2R2 group. Assuming
equal capacitors and resistors throughout the circuit, then the phase shift across
C2R2 will also be 60° for this special frequency, making a total phase shift of
120°.
Finally, a third 60° phase shift across the last group (C3R3) results in an
overall voltage change of 180° from the time the signal leaves the plate to the
time it returns to the grid. Adding the normal triode phase change of 180° described
above to the CR phase shift of 180° gives us a total inversion of 360° between
the initial voltage fluctuation and the amplified pulse that returns to the grid.
This, of course, is exactly what is needed for sustained oscillation  feedback
in phase with initial signal, or positive feedback  so that a sinewave voltage
appears between the plate of the triode and B. This voltage may be taken from the
plate through a capacitor (C4) as the oscillator output.
PhaseShift Frequencies. The frequency of the output voltage is automatically
"selected" by the oscillator circuit to conform with the required 60° phase shifts
just discussed. This means, of course, that control of frequency is obtainable by
varying either the resistances or the capacitances.
In practice, anyone of the resistors may be a potentiometer to provide a relatively
narrow range of control. Frequency variation over a substantially wider range may
be realized by varying all three resistors simultaneously; a threegang potentiometer
is ideal for this purpose.
The versatility of a welldesigned phaseshift oscillator is evident when we
consider that it can be constructed for frequencies as low as one cycle per minute
and as high as 100,000 cycles per second. Phaseshift oscillators can't be beaten
for audio testing, code practice, gain control (as in guitar vibrato amplifiers),
or for any other application requiring a stable, reliable, pure sinusoidal output.
Fig. 2  Pentode phaseshift oscillator. Capacitors labeled
"C" have same value; resistors labeled "R" are equal in resistance. Refer to Fig.
4 for "C" and "R" values for given frequencies.
Fig. 3  Dualtriode phaseshift oscillator. All "C's" are
equal and all "R's" are equal. The nomogram will help you choose values for given
frequencies.
Practical Circuits
It can be shown mathematically that a minimum voltage gain of 29 is necessary
to provide satisfactory performance at a single frequency. To insure strong oscillation
over a range of frequencies, the gain must be somewhat higher than this. Hence,
a practical phaseshift oscillator requires either a highgain pentode or two triodes
in cascade for surefire operation.
An example of a pentode oscillator is shown in Fig. 2, and a dualtriode
type is shown in Fig. 3. In the latter circuit, the feedback voltage for sustaining
oscillation is taken from the cathode of the second triode. Since there is zero
phase shift between the grid input and cathode output voltage of a vacuum tube,
the second triode does not introduce any complications when used this way. Instead,
it provides a lowimpedance source for the feedback voltage and prevents the output
load (headphones, speaker, etc.) from causing oscillator instability due to loading
effects.
The nomogram given in Fig. 4 will provide you with the required R and C
values for any frequency between 5 cps and 100,000 cps. Merely select a value for
C (all three capacitors are equal), then lay a straightedge from this value of
C through the desired frequency. The intersection of the edge with the Raxis on
the nomograph tells you the value of all three phaseshifting resistors. The same
procedure is used for finding f if R and C are known, or finding C if R and f are
known.
Fig. 4  Nomogram for obtaining required component
values.
To determine either "C," "R," or "f" if the other two values are known, lay straightedge
to intersect vertical axis at known figures and read unknown figure from the remaining
axis.
Posted October 22, 2020 (updated from original post on 8/27/2013)
Nomographs / Nomograms Available on RF Cafe:

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Earth
Curvature Nomograph 
Coil Winding Nomogram 
RC TimeConstant Nomogram 
Coil Design
Nomograph 
Voltage, Power, and Decibel Nomograph 
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Resistance and Reactance Nomograph 
Frequency / Reactance Nomograph
"After Class" Topics
