The Long-Tail Pair from aikenamps.com

The Long-Tail Pair

General

The Marshall/Fender phase inverter is commonly known as a
“long-tail
pair”, or “Schmitt” type phase inverter, or phase splitter (actually,
the
original Schmitt inverter was a differential pair with a large “tail”
resistor;
the “standard” guitar amplifier phase inverter is a self-biased version
of this circuit that works better with positive-only power supplies and
ground-referenced inputs). 

Following is a schematic diagram of a typical phase inverter found
in
some guitar amplifiers:

The basic circuit is commonly known as a “differential amplifier”,
which
means that it amplifies the voltage difference between the two grid
inputs.  Technically, it is a differential in, differential out
amplifier, because it has differential inputs on the two grids as well
as differential outputs on the two plates (the two plate signals
produce the same voltage signal, but one is inverted, or 180 degrees
out of phase, with  respect to the other).

It should be noted that there are actually three inputs used in
this type of phase splitter. The first input is the obvious one, the
left side of C1. The second
input (the lower end of C2) is useful as a feedback input,  a
reverb
or effects return input, or as a second channel input.  In the
circuit
shown above, the second input  is used as a feedback return input,
taking the signal off the junction of the feedback divider.

The third input is not so obvious; it is the lower end of
R6.
If a signal is input at this point, the phase splitter will produce an
output signal on each output that is in phase with the other,
rather
than 180 degrees out of phase, and also in phase with the signal input
at the lower end of R6.  This means that if a signal of equal
phase
is applied to the first input (C1) and the third input (R6), it will
subtract
from the out of phase output (R2) and add to the in phase output
(R1).
Likewise, if an equal phase signal is applied to the second input (C2),
and the third input (R6), it will subtract from the in phase output and
add to the out of phase output (this is because the out of phase output
is actually in phase for the signal applied to the second input, C2,
and
the in phase output is out of phase).  This third input is useful
for balancing the feedback signal by subtracting from the in phase
output
and adding to the out of phase output in order to compensate the
unequal
gains to each output from the feedback input.  The gain is much
less
than the gain into the first and second inputs.

The two outputs provide (nearly) identical signals, except for a
180
degree phase difference between them.  This is exactly the type of
signal needed to drive a push-pull amplifier, so this circuit is
commonly
seen in higher-power guitar amplifiers.

The plate resistors

The output voltage is developed across the plate resistors
(R1 and R2), and is proportional to the current changes from the tubes
in response to the input signals.  The value of these resistors is
set using “standard” techniques, such as using the load line to
determine
the desired amplification and output range.  A good value to start
with is usually around twice the internal plate resistance of the
triode.
These resistors have a major effect on gain and output impedance of the
phase splitter.  The actual output impedance is equal to the plate
resistor value in parallel with the impedance seen looking into the
plate
of the tube.  Since there is local feedback in this stage, this is
larger than the standard preamp stage output. These resistors also have
an effect on frequency response.  Higher values will result in
less
high frequency response.  When only one signal input is used
(ignoring
feedback inputs) R1 is usually made 10% – 20% lower than R2 to
compensate
the unbalanced gains of the two tube sections and make the two output
amplitudes
equal.

The grid resistors

These resistors (R3 and R4) provide the grid bias reference
voltage.  They are the equivalent of the normal “grid-to-ground”
resistors
in a standard preamp stage, except that they don’t go to ground,
instead,
they go to a different “reference” point, the junction of R5 and R6.

The value of these resistors is not critical, but they should be a
moderately
large value, somewhere around 100K – 1Meg.  Contrary to popular
belief,
in this type of phase inverter, the input impedance is not equal to the
value of this resistor, rather it is around two to five times higher,
depending
upon the amount of negative feedback from the “tail resistor”  and
the amount of  global negative feedback (around two times higher
for
the circuit shown above, with no global negative feedback).  This
is why it is not a good idea to use too large a value of coupling
capacitors
going into the phase inverter input.

This increase in effective input impedance is known as
“bootstrapping”.
It is similar to the effect you get when you have a self-biased cathode
follower. There is an AC signal present at the junction of the grid
resistor
(R3) and the “tail” resistor (R6), since there is current feedback due
to the unbypassed tail resistance. Since this signal is in phase with
the
input signal, the effective current through the grid resistor is
lowered.
The signal at the top and the bottom of the grid resistor is
subtracted,
and that voltage divided by the grid resistance gives the input current
drawn by the stage. If you divide the input voltage by the input
current,
you get the effective input impedance.  For example, if you apply
a 1V AC signal and the signal at the tail node is 0.5V and in phase,
the
input impedance is 2 Megohms, not 1 Megohm, because there is 0.5V
across
the 1Meg grid resistor instead of 1V, which results in a current of
0.5uA
for a 1V input, and Rin = 1V/0.5uA = 2 Megohms.   If the tail
resistor is large enough to be considered a constant current source,
and
there is no global negative feedback, the input impedance will be twice
the value of the grid resistor.

If there is global negative feedback, the signal applied to the
second
input will be in phase with the signal applied to the first input (this
results in a reduction in the output voltage, which means the feedback
is negative).   This signal will add to the cathode voltage
because
it is in phase.  The impedance seen “looking into” the cathode on
each side is (Ra + Rl)/(mu+1). Assuming matched tubes with equal mu’s,
this means the source and load impedances are equal at the cathode, so
the voltage is divided exactly in half.   This means that the
input impedance is dependent upon the amount of negative feedback
applied,
and can get very large for large amounts of negative feedback. For
example,
if 1V is applied to the first input, and 0.5V of feedback is applied to
the second input, the cathode voltage would be V=1/2 + 0.5/2 = 0.75V.
The
resulting input impedance would be 1 Meg/(1-.75) = 4 Meg.

These grid resistors have little or no effect on gain, for normal
values.
If they are too low in value, they will attenuate the input
signal.
They do have an effect on the frequency response.  Higher values
will
result in greater low frequency response for a given input coupling
capacitor,
but this effect is diminished somewhat due to the local negative
feedback.

The input coupling capacitors

These capacitors (C1 and C2) are used to block DC levels
from
previous stages, in order to keep from upsetting the DC bias voltage on
the grids of the phase inverter tubes.

These capacitors also determine the lower -3dB point of the
frequency
response of the phase inverter. If the input impedance is two times the
grid resistor value, for instance, or 2Meg, and a -3dB point of 53Hz is
desired, a capacitor of C = 1/(2*pi*53Hz*2Meg) = 1500pF, or .0015uF,
would
be required.  Too large a coupling capacitor will increase the
tendency
for the phase inverter input to generate “blocking” distortion.
If
C1 is made small (less than .01uF or so, with 1Meg grid resistors), it
will improve the low frequency response balance between the two output
phases if the second coupling cap, C2, is made at least ten times
larger
than the first cap, C1.

An interesting thing can happen, though, when the phase inverter
hits
clipping.  This very high input impedance suddenly drops, and can
severely clip the input waveform (by “clamping” the top to the cathode
voltage level) and raise the lower -3dB point.  For this reason,
when
tapping off the phase inverter input to go to another tube, say, for
instance,
an effects loop or reverb amplifier, a large value (100k or so) series
resistor should be included in front of the grid of the PI, and the
signal
should be tapped off before this resistor to preserve the original
signal.
This resistor can also help smooth out the tone of the PI when it clips.

The bias resistor

The bias resistor (R5) is connected to the two cathodes,
which
are tied together, and sets the bias current for the two tubes.
Since
it has the cathode current for both tubes flowing through it, the value
must be half of what it would normally be for one tube in a “standard”
preamp configuration.  This value is selected by plotting the load
line for the tube in question, and determining the required negative
grid
bias voltage to give the desired operating point and plate
current.
The value is then halved, since both tubes will be drawing current
through
the same bias resistor.

For example, a “normal” 12AX7 preamp stage might have a bias
resistor
of 820 ohms to 1.5K.  If the same bias point is desired for the
phase
inverter, a value from 410 to 750 ohms would be used (using standard 5%
values, pick a resistor from 390 to 820 ohms).  The values might
be
different for a 12AT7, depending upon the desired plate current and
bias
point.

This resistor will determine both the quiescent DC plate voltage
(a
smaller resistor equals more current, which results in a lower
quiescent
DC plate voltage), which determines the symmetry of the clipping, and
the
“headroom” of the PI.  It also determines the headroom of the grid
input, which also determines the point at which the PI clips, relative
to the input grid voltage.  Subjectively, higher currents are
usually
attributed a “warmer” tone.  Too much current results in too much
non-linearity, and adds unwanted harmonic distortion even to clean
sounds.
This resistor is best set to give a fairly decent clip characteristic
for
the PI, or best linearity, or tone.  (Be sure to disconnect any
global
negative feedback before testing this, as the feedback will tend to
correct
distortions present in the phase inverter).  Since this resistor
is
the main controller of the current flow, it will drastically affect the
quiescent DC levels at the plate, the grids and the cathode.  This
resistor has a large effect on gain.

The “tail” resistor

The next resistor is the “tail” resistor (R6).  It is
used as a “pseudo constant current source”, providing local negative
feedback
to the PI.  This resistor is necessary because, without it, the
differential
amplifier would have very unbalanced outputs (the output signal on one
plate having a larger peak-to-peak amplitude than the output signal on
the other plate), because of the low relative gain of the tubes
comprising
the differential cathode-coupled amplifier.  The larger this
resistor
is, the better the balance of the PI outputs.  There is an upper
limit,
however, where the tail resistor drops too much voltage and there is no
headroom left (or perhaps it should be called “footroom”, since it
raises
the DC level of the cathodes of the tubes).  This resistor is best
adjusted by careful attention to PI balance and headroom, settling on a
good compromise between them.

Making the first tube’s plate resistor (R1) 10-20% smaller than
the
second tube’s plate resistor (R2) will compensate the gain difference
between
the two amplifier sections, and should be done before manipulating the
tail resistor.  Note that this should done only if one input is
used
as a signal input, and the second used for a feedback input.  If
both
inputs are used as signal inputs, for channel 1 and channel 2, for
instance,
the plate resistors should be identical, because compensating the
balance
of one channel will make the balance of the second channel even worse.

The tail resistor also “bootstraps” the stage, resulting in a
higher
input impedance, due to the local feedback action, as described in the
grid resistor section above.   Note that the bias resistor,
R5,
sets the current through this tail resistor.  The amount of
current
set by the bias resistor, along with the value of the tail resistor,
determines
the DC voltage dropped across this resistor, which, in turn, partly
determines
the headroom of the circuit.  If no global negative feedback is
used,
the tail resistor should be made as large as practical, with respect to
the amount of current being drawn, and the desired headroom of the
amplifier.
This will give the best balance to the PI outputs.  This resistor
has little effect on gain, but a major effect on balance and headroom.

The feedback resistors

Since this type of phase inverter has two main signal
inputs
(ignoring the third in phase input for a minute), the second one makes
a good spot to introduce global negative feedback from the output
transformer
secondary, to reduce distortion, improve linearity, and lower the
effective
output impedance of the amplifier (increase damping, for “tighter”
bass).
The last resistor is usually a small value, such as 5K (Marshall) or
100
ohms (Fender), and is the shunt element of the feedback voltage divider
for the global negative feedback loop (pot VR1 in the above
schematic).
The feedback voltage applied to the phase inverter is the resultant
divided-down
version of the output voltage.  This resistor directly affects the
amount of negative feedback, and thus, the overall gain of the output
section,
as well as the linearity, input range, and distortion.  The
feedback
divider ratio is the ratio between the series feedback resistor (R7)
and
the shunt feedback resistor (VR1).  The amount of feedback also
controls
the effective bootstrapped input impedance.

The presence control

Potentiometer VR1, in addition to providing the 5K
resistance
to ground for the feedback attenuation network, is also used as the
presence
control.  Capacitor C3 is used to shunt a portion of the feedback
signal high frequencies to ground.  By reducing the amount of high
frequencies being fed back, there is more gain at these
frequencies.
This results in a boost of the upper frequencies, adding “presence” to
the signal.  This is a bit different than just a simple
equalization
boost, because, in addition to boosting the high frequencies, there is
less negative feedback at these frequencies, which means the output
stage
has less damping, and the effective output impedance is raised, which
increases
the interaction between the speakers and the amplifier at these
frequencies.
Increasing the value of the capacitor will lower the corner frequency
of
the boost.

Conclusions

The long-tail pair phase inverter is generally the best
choice
for a push-pull guitar amplifier.  It provides the very good gain
and balance, as well as extra inputs for feedback summing. The best way
to get a feel for this circuit is to replace the bias, plate and tail
resistors
with trimpots, and adjust them interactively while watching both
outputs
on a dual-channel scope.  Alternately, a lot can be learned by
simulating
the phase inverter with different values in PSpice, or another
simulation
program.


Copyright ©
1999,2000,2001,2002,2003,2004  Randall
Aiken.  May not be reproduced in any form without written approval
from Aiken Amplification.

Revised 10/03/04

Read More