The Phase-Shift Oscillator for Tremolo
Tremolo, or slow amplitude modulation, is a simple and popular effect used
to add texture and character to the guitar sound, in the same way that
vibrato (pitch modulation) is used by vocalists, violinists and other
string players to add body to an otherwise unvarying note. Many popular
amps have included this effect, notably the Marshall 18W and Fender
Vibroverb / Vibrochamp etc. models. (Note that despite the misleading
names, these amps employed tremolo and not vibrato, which requires
much greater circuit complexity.) Nearly all use the same basic tremolo
circuit. The effect requires a low frequency oscillator (LFO), which
produces a wave (usually a sine wave) of around 0.5 to 10Hz- the "trem'
signal". This is then mixed with the audio signal in some way, so that
its amplitude (volume) increases and decreases in sympathy with the
trem' signal. The effect usually has controls to vary both the frequency
(speed) and amplitude (depth / intensity) of the tremolo, allowing the
effect to be used quite subtly or very vividly.
It is worth mentioning, that of all the stages in an amplifier the trem'
oscillaor is the most sensitive to valve ageing. If you have a very
weak sounding tremolo it can usually be ammended by plugging in a new
Most oscillators works by means of positive feedback around one or more gain stages. Provided the feedback signal is in phase with the input signal, and the total loop gain is unity or greater, the circuit will oscillate at a constant frequency indefinitely. Note that the trem' signal does not have to be a sine wave; more elaborate circuits allow the user to vary the waveform of the trem' signal. Square and triangular waves give a well defined tremolo, or even a stutter effect. However, a sine wave is easy to create and has a natural sound. For a more elaborate trem' it's probably easier to just add an effects loop to the amp and use an off-board, dedicated trem' unit.
Literally dozens of oscillator circuits
can be found in textbooks, but by far the most popular for guitar is
the "phase-shift oscillator". This comprises a single amplifier stage
(itself providing 180 degrees of phase shift) and a feedback network
of capacitors and resistors (providing a further 180 degrees phase shift,
= 360 degrees total shift). The feedback network usually consists of
three CR filters- C1/R1, C2/R2, C3/R3. Ideally, each filter provides
60 degree of phase shift at one particular frequency, and this is the
frequency at which the circuit will oscillate. A four stage CR network
could also be used, each filter providing 45 degrees of shift.
The total loop gain must be unity or greater, so any loss in the feedback
network must be compensated for by the gain of the amplifier. Without
going into the maths of the network (which would require either some
lengthy equations or vector analysis) it can be shown that the gain
of a three-stage CR network, at a frequency where each filter provides
60 degrees shift, is -0.034. Since 1 / -0.034 = -29, this is the minimum
necessary gain we need from the amplifier to sustain oscillations. (In
a four stage network a gain of only -18.4 would be required.) If the
amplifier has a gain of exactly this value it will produce a near perfect
sine wave. However, the stage would be highly unstable and would quickly
stop working as the valve aged and gain fell, and would require continual
adjustment- especially if we want to vary the frequency. Instead, the
amplifier is set up for a gain level much greater than -29. The drawback
is that the output signal will be somewhat distorted as high harmonics
are introduced. Stray capacitance will eliminate some, but in any case it is of no great concern for something as crude as a trem' oscillator.
Immediately we know we require either a high gain triode,
or a pentode. The ECC81 is a favourite choice for oscillator circuits,
and in most cases can be directly substituted for an ECC83. The following
example uses the more common ECC83, and the HT is 300V. Note that the
HT does not have to be particularly well filtered since we are not amplifying
audio signal currents, and the circuit will even work at supply voltages
as low as 100V.
A fairly large anode resistor is in order, to maximize gain and output
swing, and 100k is typical. For the purest waveform the stage should
be biased for maximum linear swing, although it is not critical. To
keep the output impedance as low as possible, and to maximize gain,
the cathode should be fully decoupled well below the oscillation frequency.
A 100uF to 220uF capacitor will usually suffice (even larger values are
available, but tend to be unreliable as well as unnecessary). With the usual 100k anode resistor
we can make an estimation of gain as:
Av = (mu * Ra) / (Ra + ra)
Av = (100 * 100000) / (100000 + 55000)
This is plenty of gain, although it does not yet take account of the
loading effect of the feedback network or any other external circuit.
Draw load line.
The load line shows a bias of -1.5V would be suitable. The cathode resistor
would therefore be:
1.5 / 0.0011 = 1363 ohms, but this is only an oscillator not an audio stage, so let's go with a nice round 1k.
The load line also indicates that the gain will be 60, close to our earlier calculation,
and that the maximum oscillation amplitude will be just over 200V peak-to-peak.
The input impedance of the feedback network needs to be high to avoid loading the stage too heavily, and ideally is should be at least five times the value of anode resistor. In this case the output impedance will be roughly:
Zout = ra || Ra
= 55000 || 100000
The input impedance of the feedback network is approximately equal to 2 * R1, so 220k would probably be the minimum acceptable value but 1Meg is better still, as it allows small value capacitors to be used, is below the maximum allowable grid-leak value, and results in a negligible input impedance of about 2Meg.
If all three CR stages are identical, the frequency of oscillation is given by:
f = 1 / (15 * R * C)
So, for a frequency of 6Hz we would require a value of:
C = 1 / (15 * R * f)
= 1 / (15 * 1000000 * 6)
So we would use 10nF as the nearest standard, giving about 6.7Hz. C1 must have a high voltage rating.
So far we have a fixed frequency oscillator, producing a reasonable
sine wave at about 6Hz. The beginner may pause to wonder how the oscillator
starts in the first place, since the circuit gets its input signal from
its own output. In fact the oscillations will build up gradually from
zero, due to inherent noise within the circuit when it is actually built.
Note that at such a low frequency and relatively low gain, after switch-on
it will take many seconds for the oscillations to begin.
The frequency / rate control:
To vary the frequency of oscillation it is merely necessary to vary one
or more of the filter components- usually the shunt resistors since
variable capacitors are uncommon. To get even and predictable variation
it would be necessary to vary all three resistors simultaneously by
means of a ganged pot, but thankfully that level of accuracy is not
required for tremolo. Fender tend to vary R1, while most Vox amps make
R2 variable, and there is no reason why R3 couldn't be varied- it makes
little difference, provided the loop gain is high to begin with. The
practical range of frequencies is limited to a ratio of about 1:3 when
using a single pot. The usual approach is to design the oscillator for
a frequency that is midway between the highest and lowest desired frequency,
then add a series limiting resistor to prevent the total shunt resistance
being reduced to zero. Thus the frequency can then be varied both above
and below the initial chosen frequency (increasing resistance causes
decreasing frequency). It will usually be necessary to experiment with
the value of this limiting resistor, in order to get the maximum range
without oscillations actually stopping. The oscillator designs found
in the classic amps use wildly varying component values, and were almost
certainly chosen by experimentation rather than calculation.
Adding a footswitch to allow the user to toggle the tremolo on or off
is quite simple, and the following method has been used in countless
amp designs. To turn the oscillator 'off', the footswitch simply shunts
the feedback signal directly to ground. The switch is connected to the
junction of C2 and C3, and is therefore isolated from the high anode
voltage, and also cannot not interfere with the valve's bias. Because
the cathode is fully decoupled, it is at ground potential as far as AC
is concerned. This means we can connect the lower end of R2 to the cathode
and it will make no difference to the AC operation of the circuit. However,
when the switch is now thrown open the upper end of R2 instantly rises
to the cathode's DC potential (about 1.5V in this case). The sudden voltage-transient shocks
the oscillator into starting instantly. If this were not done, it would
take several seconds for the oscillations to begin after the footswitch
A visual frequency / rate indicator:
There is one useful modification that can be made to this otherwise ancient circuit- LED biasing. By replacing the cathode resistor with an LED we eliminate the need for the large bypass capacitor, and obtain maximum gain and minimum output impedance at all frequencies in one fell swoop. A red LED will be suitable in most cases, providing about 1.6V bias, although other colours can be experimented with of course. Additionally, because the oscillations extend to cut-off, the LED will flash in time with the trem' signal giving a novel and useful visual indication of the frequency, and that the circuit is actually working! The circuit [right] shows this, using an ECC81 this time.