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.

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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