In TUT3 The Ultimate Tone vol.3 we introduced the notion of "transconductance multiplication" output stages. Simply put, this is just the use of paralleled output tubes. The sonic difference between what most guitar amp hobbyists and players might refer to as a "50W" output stage and a "100W" output stage are explained using the tube characteristics. Most players encounter this sonic difference in the 50W and 100W models within the same brand, say as Marshall plexi or 800 amps, or as a Fender Pro versus a Twin.
"Transconductance" (gm) is a characteristic relating the input stimulus of an active gain element (BJT, jfet, triode) to the resulting output, where the input and output quantities are different "domains". For example, transconductance for a tube is the relationship between the voltage at the control grid and the current at the cathode (equals plate current). Voltage and current are two different domains. A BJT used in a gain stage often has the opposite condition, of a current at the base and an output voltage at the collector.
With a standard tube output stage, we can view the voltages on a scope or measure them with a meter, but we can see a signal voltage at the grid causing a much larger signal voltage at the plate. This voltage gain is the result of the transconductance of the tube and the resistance or impedance of the load. If we double the transconductance by paralleling similar tubes, the voltage gain doubles. We can add more tubes, and use dissimilar tubes, in which case we add all the individual gm values and multiply by the load to find the new voltage gain.
If we place a feedback resistor from the plate to grid, we lose voltage gain and alter the circuit performance. For one thing, we must usually insert a DC blocking cap in series with the feedback resistor in order to keep the idle condition the same. The direct resistive link would otherwise cause the bias to shift dramatically positive and melt down the tube and OT. In many examples of this circuit form, the feedback resistor is taken to the input side of the grid coupling cap. which is often the plate output of the driver or splitter. In any case, the local feedback around the output tube decreases its output impedance and distortion contribution. The reduced drive impedance into the OT helps improve the OT frequency response and the OT parasitics (leakage inductance, coil capacitances) become less problematic.
The DC blocking cap introduces a problem of its own in that another RC constant is added to the circuit, which potentially decreases stability at low frequencies. The next post will show a very simple SE PA that overcomes the problems and illustrates the basic principles of the "trans-tube" amplifier.
Very interesting. I've been using TUT3 style four output tube but 50W Plexi type power section in amps for a long while now. I personally prefer the bigger sound the four-tube output configuration. I look forward to seeing the next post on this topic.
In the attached PDF are six figures which show a progression from a concept to a working circuit using a single-ended output stage.
Fig-1: VE stage
We see a basic opamp gain stage configured as a "virtual earth" amplifier. IN+ is grounded and IN- receives Ein via Rin. Feedback is applied via Rfb which goes from IN- to the opamp output.
The opamp is ideal and has infinite input resistance at its input pins, so there will be no current in or out of these pins. The opamp has infinite gain, so the feedback loop will be accurate. In this case, Ein is connected to the left-hand end of Rin and the right-hand end of Rin is held at ground potential as the opamp maintains zero voltage difference between its input pins. The current through Rin has nowhere to go except through Rfb. The opamp makes its output be the correct polarity for the current to flow as it should.
Voltage gain is set by the feedback loop, as A = Rfb / Rin
Fig-2: Gm input
Here, we have replaced Rin with a transconductance element that will accept a voltage input and produce a current output. Let's say this ratio is 1mA out for 1V in, which is then a transconductance gm = 1mA/V
Rfb has a value of 220k, so if we apply 1V of input to the gm element, its current can only go through Rfb, which will generate a voltage at the output of the opamp of 1mA x 220k = 220V. This is an impressive opamp!
Fig-3: Basic SE tube stage
A standard single-ended (SE) tube power amp circuit is shown with typical values.
Va = 320V
Vs = 320V via 1k
Vk = 32V via Rk
Vg = 0 (ground via Rg=220k)
Rk = 510R
Ik = 63mA
Pa = 20W
The voltage gain of this circuit is typically 10 or less, and we can use Vk as a guide to the peak Ein required to achieve clipping. In this case, we will say Ein max is 32V.
Fig-4: SE tube stage as VE
Now we have added feedback elements around the SE tube stage.
Note that we are calling the signal at the tube plate driving the output transformer (OT) Eout.
Any tube stage that provides gain is inherently inverting, just as the VE stage inverts the signal. So, adding the Rin and Rfb is pretty straight-forward. With the opamp, the reference pin IN+ is at ground and then IN- is made to be at this same voltage. The tube has asymmetrical input pins, as it were, where the cathode is the reference and is sitting at +32V. Were we to somehow get the control grid g1 to be at the same voltage, the tube would pull uncontrolled current and melt itself down. To keep the universe stable, the g1 must be negative with respect to the cathode for the cathode current to be in a useful range. Ideally we want the same 32V difference between G1 and k as the stock circuit had.
We can add Rin quite easily since the tube grid is effectively at ground potential. Rfb ties to the Rin but we need a capacitor to block the 320V at the plate. This seems reasonable enough.
Now we encounter problems.
The raw gain of the stage is only 10 as we saw above and the feedback loop can only make the closed-loop gain LOWER than the open-loop gain. This tells us right away that where we might have already needed a hefty input signal of 32V peak, with feedback we will need even more. Say we make the gain A = 2. If Rfb is 220k as in Fig-2, then Rin would be 110k. Where the tube grid itself may not draw any current from Rin, the grid-leak Rg=220k definitely will. Rg introduces a serious complication to the circuit: it is absolutely needed to keep the tube biased properly by tying g1 to ground, but it forms a voltage divider with Rin and Rfb.
Because the tube gain is so low, the feedback loop has very little "power" inasmuch as we have hardly any gain to sacrifice to make the loop accurate.
The asymmetry of the input pins of the tube is also an issue. The control grid can be deemed as having infinite impedance, where the cathode has an impedance of the reciprocal of the tube's transconductance. In the case of a 6L6, gm=5 or so, and the reciprocal is then about 200R. It would be ideal if the circuit could be given a lot of extra gain to make the feedback loop behave better.
Fig-5: SE with Gm input
We have added the same magical transconductance element that we used in Fig-2. We have moved the DC blocking cap to be between the virtual-earth node 'X' and the tube grid and its grid-leak resistor.
We will assume the Gm element can handle whatever voltage is at the end of Rfb, which should be 320V. The gm element is a current source that can be varied with a voltage input. Like all current sources, its output impedance is ideally infinite.
There is still the issue of Rg stealing away a bit of the input current and making the circuit inaccurate, but it is much better than for the previous figure.
The DC blocking cap is still within the feedback loop and cause phase issues that lead to instability. Fortunately, the OT is outside this loop and we do not have to contend with its primary and parasitic elements.
Fig-6: Practical but imperfect " Transie"
" Transie" is the name Menno van der Veen applied to the small SE version of the Trans Tube Amp.
In this form, the Gm element is shown as an n-channel jfet. This is done to emphasise the fact that it must be a depletion-mode fet type, but it is more likely to be a mosfet in a real circuit. The LND150 is a candidate here. Menno used a surface-mount type device, which suited his ultimate circuit realisation where an extensive input buffer and bias control circuit are fashioned as a module.
Rfb is directly connected to the tube grid, which looks a bit scary.
Rk has been increased in value so there can be voltage across QJN and R2, its source resistor. ideally, R2 has a voltage across it that is greater than peak Ein so that the QJN current never goes to zero. We see that the operating Vgk is still 32V as the original circuit had.
A safety diode is added so that during start-up the tube grid can never be too positive with respect to the cathode. Fortunately, as soon as Va appears, there will be current through R2, QJN, Rfb and the OT primary and QJN will, for the most part, keep 'X' at a reasonable voltage.
Rg is still shown but is entirely unnecessary. We could leave it in as a 1M or higher, if it placates our mind to do so.
The overall circuit performance is now quite transformed, as is usually the case with hybrid circuits of tubes plus solid-state elements. The output impedance at the tube plate is greatly reduced and the OT is driven very well and its distortions are reduced.The tube's distortion is also reduced and the circuit sensitivity with respect to Ein requirements has gone from tens of volts to ones of volts.
We still have the problem of Rk and Ck. Remember that k is an input terminal for the tube and the gain from k to A is the same as from g1 to A, meaning that the RC constant of Rk + Ck telescopes through the tube. There are a number of ways to reduce or eliminate this effect, each with its pros and cons.
Hifi hobbyists are enamored with using 3-terminal voltage regulators to bias tubes through their cathodes. The regulator is configured as a current source. This has a huge negative impact inasmuch as the regulator's frequency response is superimposed upon the circuit. This is not a good thing. The usual bandaid is to parallel the regulator with a massive-value cap, which is needed even if the regulator is made out of discrete components which is a much better implementation. Either approach requires dealing with potential instability while the tube warms up.
An alternative is to configure a fixed-voltage supply to replace Rk+Ck. Again, there must be a very wide bandwidth control and output impedance for this to be useful, plus it requires another PT or winding on the PT.
A further alternative is to reduce Rk to 10R or less and use a bias control circuit to help control the circuit during turn-on and maintain the operating point during operation. This is how Menno tackled the issues, and his Trans Tube Amplifiers book explores the experiments and the results.
It should be obvious that the trans-tube amp concept has similar requirements to any feedback-controlled circuit. The most important being that the gain element within the feedback loop should have as much gain as possible.
A typical power tube is either a triode, tetrode or pentode. A triode has only one connection option to the load via its plate, so the triode's theoretical maximum voltage gain is its mu. A tetrode can be tied to the load in three ways: strictly via the plate, with the screen tied to a fixed voltage; wired using an ultralinear tap for the screen; or with the screen and plate linked for triode performance. A pentode is wired similarly to the tetrode as its suppressor grid is typically tied to its cathode.
The triode voltage gain is lowest. Its plate impedance is also lowest of the three wiring modes.
Ultralinear allows local feedback over a portion of the transformer primary, which reduces the plate impedance of the tube compared to tetrode/pentode mode but not as low as triode mode. Voltage gain is higher than triode mode.
Tetrode/pentode mode has the highest output impedance and the highest voltage gain.
The open-loop distortion of the three modes are from lowest to highest: triode, UL then tetrode/pentode.
Low-z drive into the OT is preferred whenever possible, which is why hifi tube users prefer triode output stages when minimal use of feedback is desired. The low-z drive helps the OT perform better and not having it within a feedback loop means that it has the least impact on the sound. The lowest impedance drive possible without hybrid circuitry is cathode drive. This connection requires a very high drive voltage to the power tube, which adds zero voltage gain of its own and actually introduces a slight voltage loss, and then the drive stage design becomes crucial to low overall THD.
The trans-tube circuit uses feedback up to the drive point of the OT and can reduce the drive impedance to cathode-drive-like values, which is phenomenal as we still retain the voltage gain of the tube. Is there any advantage to enclosing the OT in an overall feedback loop? There could be, but the stability of both the inner loop (trans stage) and outer loop have to be carefully dealt with. The trans-tube approach allows overall open-loop functionality and stability but at low-THD.
The Gm element adds its own THD to the mix, and this will be relatively benign if the element itself is linear and/or simple. Menno experimented with opamps and found that the harmonic profile of the THD and IM was fatiguing despite there being relatively lower numbers than for the plain tube circuit. Obviously that approach could be greatly improved upon were one motivated to do so. Since the trans-tube amp is a hybrid already, how far you go with that is up to each hobbyist. Menno did retain opamps for the bias servo loop, but went discrete for the Gm element and grid buffer.
Very interesting! Thanks for sharing. Perhaps I'm a bit unenlightened, but I wonder why we'd want to reduce THD in a guitar amp, if that is the application you have in mind. I thought IMD was the nasty stuff and THD was generally desirable in the right proportions. I notice you mentioned that the OT will affect the sound less. Do "Transie"-style circuits give us more power over shaping pleasing THD then, since we have less factors to concern ourselves with?
The Trans-Tube amp approach is primarily aimed at hifi, hence a reference to "hifi hobbyists".
But... there is always a "but"...
Guitar amps were originally hifi applications using hifi circuits, where the guitar amplifier itself was meant to be a local public address system with many older amps having a mix of inputs for guitar, bass, accordion, organ and voice. As the amplifiers became more affordable, dedicated PAs got larger and players began overdriving the amps, the needs of guitar players changed and products for them became more focused.
I always look beyond MI for ideas that can be applied to audio and to MI. It makes sense to me to know what the bigger picture is and to try not to have tunnel vision limiting design choices. That's why we have Power Scaling, Super Scaling, GmX, RmX, better effects loops, better bass amps, better guitar amps, better speaker cabinets, etc.
It is well-known that if an OT is driven by a low-impedance that the OT distortions will be reduced and its parasitic elements will be less problematic. Where we are used to the traditional tube wiring modes to reduce tube distortion and to a small extent some OT distortion, the Tans Tube approach is counterintuitive where we use the tube in its nominally most distortive mode to be able to make the greatest overall distortion reduction. This is not just a reduction of the tube THD itself, but one that results in dramatically lower-THD than an all-tube circuit can achieve. It is the way of hybrids, as mentioned above.
We use tubes in MI because we like their distortion, their nonlinearities, and their near-organic qualities. However, there are good and bad distortions, so it is good to have a tool box filled with tethers and controls we can apply as needed to achieve our desired goals. Besides, we may have aesthetic ideals that we wish to explore, even if that becomes a hurdle in attaining an overall sound.
Not all THD is good. Not all power tube distortion is good. Power tube distortion is not "better" or "worse" than preamp tube distortion - it is just different.
IM (intermodulation distortion) is definitely always bad. It causes ghost notes. It causes nonmusical harmonics. It causes fatigue for the listener. It results in a loss of resolution and smearing of the sound.
TUTs explore all of these issues and the best defense against unwanted distortions, especially IM, is to use Galactic Grounding as TUT3 details. Apart from that, anything that reduces THD also reduces IM, and ultimately in hifi, will reduce every other type of distortion, too.
Ahhh, it seems I read that as "hobbyists" the first time, thanks for clarifying! Of course your other points are great as well, thanks for the additional info.
A warm welcome to tube amp modding fans and those interested in hi-fi audio! Readers of Kevin O'Connor'sThe Ultimate Tone (TUT) book series form a part of our population. Kevin O'Connor is the creator of the popular Power Scaling methodology for amplifiers.
Please remember these three principles: respect, sharing, community.
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