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 (R1) and add to the in phase output (R2). 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.
What does this calculator do?
The long-tailed-pair phase inverter with negative feedback was used by Leo Fender in the 5F6-A Bassman and subsequently became an overwhelming favorite for classic large amp designs, Marshalls in particular. The basic long-tailed-pair without negative feedback is shown below.
As the input signal voltage increases, the plate current through the left tube increases, causing the inverted output voltage to decrease because of the increased voltage drop across the plate resistor RL1. It also causes the current through the cathode resistor RKand the tail resistor RT to increase, which increases the voltage between the cathodes and ground, thereby making the grid-to-cathode voltage of the right triode more negative, causing its plate current to decrease. This raises the in-phase output voltage. Thus an increase in the phase inverter's input voltage lowers the inverted output voltage and raises the non-inverted output voltage.
Negative feedback from the output transformer secondary can be introduced by splitting the tail resistor into two resistors and driving their connection by a signal taken from the output transformer. This is particular modification is widely used in classic amps.
The calculator takes into account the output load of the power amp's grid resistors RGpa. (These are not the phase inverter grid resistors RG shown in the drawing above.)
To get exactly the same gain in each phase (one positive and the other negative) with identical plate resistors, the tail resistance needs to be infinitely large. (This can be demonstrated, for example, by making the plate resistors equal and setting RT to an unrealistically high value like 1M.) Having a large tail resistance limits the maximum output voltage swing, which is of particular concern for high-power amps. For this reason a smaller tail is often required, which causes the inverted phase to have substantially more amplification than the non-inverted phase. The usual correction is to reduce the size of the inverting plate resistor RL1.
Reference
Table of Contents
Chapter 1. Introducton
Chapter 2. Pentodes and Beam Power Tubes
Pentodes 5 Beam Power Tetrodes 7 Plate Characteristic Curves 8 Power Tubes versus Voltage Amplification Tubes 11 Low Plate Voltage Effects 12 Performance Differences Between Pentodes and Beam Power Tetrodes 13 Plotting Curves for a Specific Screen Voltage 16 Variability of Tube Characteristics 18
Chapter 3. Plate and Screen Circuit Design
The Basic Steps of Power Amp Design 19 The Common-Cathode Amplifier 19 The DC Operating Point 20 Using Triode-Connected Curves 21 Vacuum Tube Response to AC signals 23 Cutoff and Saturation 23 Setting the DC Operating Point 25 The AC Load Line 26 Optimum Load Line for Pentodes 30 Screen Dissipation 33 Maximum Power and Headroom 35 DC Grid Bias Voltage 37 Fixed Bias 37 Cathode Bias 38 Practical Aspects of Using Cathode Bias 39 Cathode Degeneration 40 Selecting the Bypass Capacitor Value 42 The Output Transformer 42 The Screen Grid-Stopper Resistor 44 Plate Circuit Design Procedure for Single-Ended Amplifiers 45
Chapter 4. Grid Circuit Design
A Basic Grid Circuit 47 Preamp Output Impedance 48 Equivalent Grid Circuit for Audio Frequencies 49 Middle-Range Frequency Response 51 Low-Frequency Response 51High-Frequency Response 53 Measuring Parasitic Capacitance 54
Chapter 5. Parallel Tubes and Parasitic Oscillation
Parallel Tubes for More Power 57 Parasitic Oscillation 58 The Effect of RF Suppression on Audio-Frequency Distortion 59
Chapter 6. Push-Pull Power Amps
How a Push-Pull Amplifier Works 61 Class A Push-Pull Operation 63 Class B Push-Pull Operation 65 Class AB Push-Pull Operation 66 Guitar Amplifiers - In a Class All Their Own 67 Power Supply Voltage Excursion 68 Estimating Power Supply Voltage Sag Based on Current Load 68 Design Strategies for Dealing with Class AB Power Supply Sag 73 Drawing Composite Characteristic Curves 75 The Load Line 78 Class AB Power Output 79 Plotting the Effective Load Line for One Tube 80 Computing the Current Load and Plate Dissipation 81 Cathode Bias for Push-Pull Power Amps 83 The Screen Grid-Stopper Resistor 84 The Effects of Mismatched Components 84
Chapter 7. Distortion Characteristics at Full Power
Harmonic Distortion 87 Calculating Percent Harmonic Distortion 90 Intermodulation Distortion 95 Controlling Harmonic Content 95 Rectification Effects 98 Single-Ended versus Push-Pull Distortion 99 Class AB Distortion: Fixed Bias versus Cathode Bias 99
Chapter 8. Distortion in an Overdriven Power Amp
An Overview 102 Headroom 103 The Cushioning Effect 104 Bottoming 105 Positive Grid Voltage Effects 105 Driving a Power Tube Grid Positive with a High-Impedance Source 109 Clipping and Clamping 112 A Different Perspective: How the Circuit Responds over Time 114 Bias Excursion and Recovery 118 The Recovery Phase 120 Bias Recovery Time versus Bass Response 121 An Example of Grid Bias Excursion 124 The Grid Bias Excursion Ratio 127 Bias Excursion Time 130 A Summary of Bias Excursion Formulas 131 Grid Bias Supply Considerations 132 Grid Bias Supply Voltage Excursion and Recovery 133 Bias Excursion for Cathode-Bias versus Fixed-Bias Designs 135 Controlling the Dynamics of Bias Excursion 138 Bias Excursion and Recovery for Some Vintage Amplifiers 138 The Tonal Effects of Overdriving a Power Amp 139
Chapter 9. Crossover Distortion, Blocking, and Blackout
Crossover Distortion 143 Blocking Distortion 143 Minimizing the Likelihood of Blocking Distortion 146 Class AB: Fixed Bias versus Cathode Bias 146 Blackout 147
Chapter 10. The Marshall Model 1967 Head
Pentode-Operated Pentodes 149 Triode-Operated Pentodes 150 Ultra-Linear Power Amplifiers 153
Chapter 11. Real-World Output Transformers
Ideal Single-Ended Transformers 155 Ideal Push-Pull Transformers 156 DC Magnetization Current 157 Hysteresis Losses 158 Middle-Range Transformer Losses 160Low-Frequency Transformer Response 163 High-Frequency Transformer Response 164 Total Response 164 Transformer Power Rating and DC Current Effects 166 Output Transformer Distortion 166 How Real-World Characteristics Affect Power Amp Design 167
Chapter 12. Real-World Loudspeaker Impedance
Nominal Impedance 169 Resonant Frequency and Beyond 170 An Example - The Jensen C12R-8 172 Estimating the Nominal Impedance of a Loudspeaker 172 How Loudspeaker Impedance Affects Power Amp Design 173
Chapter 13. Paraphase Inverters
The Common-Cathode Triode Amplifier 177 Computing the Resistor Values 179 Frequency Response 180 The Gibson GA-20T Inverter 180 Overdriving and Distortion 181
Chapter 14: The Concertina Phase Splitter
The Concertina Phase Splitter, an Overview 183 The DC Circuit 184 Maximum Output Voltage Swing 187 The AC Circuit 189 Phase Splitter Output Impedance for Arbitrary Loads 192 Overdriving and Distortion 197 Nonlinear Distortion Effects 199 Summary of Important Concertina Features 200
Chapter 15: The Long-Tailed-Pair Phase Inverter
The DC Circuit 201 The AC Circuit 204 The Common-Grid Circuit 208 The Common-Cathode Circuit 209 Voltage Gain Imbalance 211 Output Impedance 212Overdriving and Distortion 212 Maximum Output Voltage Swing 213 Adding a Second Signal Input 214 Adding Negative Feedback and a Presence Control 214 Voltage Gain and Input Impedance for Negative Feedback 218 Comparing the Concertina to the Long-Tailed Pair 219
Chapter 16: Negative Feedback
A Generalized Negative Feedback System 221 Loop Gain 222 A Second Look at Cathode Degeneration 223 Negative Feedback from the Output Transformer Secondary 224 Frequency Response with Negative Feedback 226 Other Feedback Effects 228 A Handy Formula for the Long-Tailed-Pair Phase Inverter 229 Stability 230Motorboating 234 An Example of Negative Feedback Design 237
Chapter 17: A Step-by-Step Single-Ended Design Example
The Basic Steps of Single-Ended Design 243 Selecting the Tube and the Screen Voltage 244 Selecting the Idle Plate Voltage 244 Estimating the Cutoff Grid Voltage and Plate Current 245 Setting the DC Operating Point 246 Designing the Cathode Bias Circuit 246 Selecting the Output Transformer Primary Impedance 248 Determining the Plate Circuit Operating Conditions 250 Computing the Harmonic Distortion at Full Power 252 Designing the Grid Circuit 254 The Final Power Amp Design 254
Chapter 18: A Step-by-Step Class AB Parallel Push-Pull Design Example
Accounting for Power Supply Voltage Sag 257 Selecting the Output Transformer Impedance 259 Determining Output Power and Voltage Gain 261 Selecting a Screen Resistor 262 Plotting the Composite Characteristic Curves 262 Plotting the Effective Load Line for One Tube 262 Computing the Average Plate and Screen Current at Full Power 264Computing the Plate and Screen Dissipation 268 Computing the Power Supply Voltage Sag at Full Power 268 Determining the Zero-Signal Characteristics 270 Calculating Third Harmonic Distortion at Full Power 272 Selecting the Grid Resistor Value 273 Applying Preamp Constraints 273 A Paraphase Design 274 Selecting the DC Operating Point 276 Computing the Resistor Values 278 A Concertina Design 279 Selecting the DC Operating Point 280 Examining the Concertina's Nonlinearity 280 Determining the Other Resistor Values 283 A Long-Tailed-Pair Design 283 Tail Resistance and the DC Load Line 284 Selecting the DC Operating Point 285 Examining the Long-Tailed-Pair's Nonlinearity 287 Balancing the Voltage Gains 287 The Final Phase Inverter Design 288 Computing the Coupling Capacitor Value 289 Selecting the Grid-Stopper Resistor Value 289 Computing Bias Excursion and Recovery 291 The Final Power Amp Design 291 Some Last Words About Class AB Design 293
Chapter 19: Epi-Log
Appendices A-G: Vintage Power Amps Listed by Tube Type and Operating Class. Tube Data Sheets
EL84/6BQ5 Power Amps 297 GE 6BQ5 Data Sheet 298 6V6/6AQ5 Power Amps 305 GE 6V6GT Data Sheet 307 7027 Power Amps 313 RCA 7027 Data Sheet 3147591 Power Amps 323 Sylvania 7591A Data Sheet 324 EL34/6CA7/KT77 Power Amps 329 Philips EL34 Data Sheet 331 6L6/5881/KT66 Power Amps 339 Marconi KT66 Data Sheet 342 6550/KT88 Power Amps 353 GE 6550A Data Sheet 354
Appendix H: Derivation of Additional Formulas for the Long-Tailed Pair
Voltage Gains 363 Output Impedance 365
