Classic Aikido Topology

Here is how I described the Aikido amplifier topology at its introduction:

"The broad-stroke explanation of the Aikido amplifier was that the circuit eliminated power-supply noise from the output, by injecting the same amount of power-supply noise into the top and bottom of the two-tube cathode follower circuit; that the input stage (the first two triodes in series with each other) defines an AC and DC voltage divider of 50%, so that 50% of the power-supply noise is presented to the top cathode follower’s grid, while two equal-valued resistors in series also define a voltage divider of 50%, which feeds the bottom triode's grid the same 50% of the power supply noise. Since both of these signals are equal in amplitude and phase, they cancel each other out, as each triodes sees an identical increase in plate current, so the output remains steady in spite of the power supply voltage fluctuations."

Then in blog number 13, I introduced an array of "Aikido" circuits that, once again, did not look like Aikido amplifier circuit of blog number 11. Thereafter, blog post after blog post displayed more "Aikido" circuits that didn't look alike. In fact, back in 1999, in the first article in first issue of the old-style webzine Tube CAD Journal, I explained how to design a tube-based "Aikido" cascode stage, although I didn't use the Aikido label. In the April/May 2001 issue, I revealed an amazing hybrid amplifier that used an OpAmp frontend and a single-ended tube output stage, standing the hybrid convention on its head, which also offered autobias. I described it thus: "Therefore, we have by injecting noise into the amplifier lowered the noise at the output: not Zen, but Aikido applied to electronics."

And in the last issue, I described an "Aikido" grounded-grid amplifier. And in my post on the Einstein's tube power amplifier back in 2006, I described my own Aikido-inspired amplifier for Einstein, which held three audio Aikido techniques, including a clever Aikido long-tail phase splitter. Moreover, I have explicated two different Aikido cathode followers. Indeed, the whole of my 2001 article, Totem-Pole Output Stage PSRR Enhancement, deals with Audio Aikido techniques applied to OTL circuits. (Unfortunately, I made use an odd schematic symbol, a square with a capital N inside to denote either a triode, a pentode, a N-channel MOSFET, or a NPN transistor, which few understood that it represented either a triode or a pentode or..., which confused many. We alter convention at our peril.)

Many different circuits, but only one name: Aikido. How is this possible? Surely there can be only one Aikido circuit? No, not at all. Audio Aikido is a family of many electronic techniques that all share the same characteristic: the power-supply noise is used against itself, rather than relying on brute force techniques, such as using huge, massive inductors and Foster-beer-sized capacitors or complex high voltage regulators to purge power-supply noise at its source—or using tons of negative feedback within the amplifier to reduce the power-supply noise after the fact, i.e. once the noise has already leaked into its output. All of which leads us to the question, Why do I use the "Aikido" label and just what is Aikido?

 

Aikido History
Aikido is a relatively new Japanese martial art created back in the 1920s by Morihei Ueshiba (1883 – 1969).

Photo from Wikimedia Commons

Originally, this martial art was named "Aikijutsu," but in 1942 its name was changed to "Aikido." From Wikipedia, we learn that he word "aikido" is formed of three kanji:

• ai – joining, unifying, combining, fit
• ki – spirit, energy, mood, morale
• dō – way, path

Thus "Aikido" translates to something along the lines of the way of joining with the spirit, the energy. As you can guess from its name, Aikido is more than just a martial art, as it is also a religious philosophy, one that compels an ethical treatment of one's attacker; so, unlike many other martial arts, gratuitous maiming and, indeed, killing one's opponent are forbidden, not on legal grounds, but ethical, spiritual ones.

I first encountered Aikido when I was a young teenager. I had found a beautiful Japanese book on Aikido in a used bookstore, which I still own (somewhere in a box in my garage). Its binding was the first thing to catch my eyes, as it was covered in coarsely woven white cloth. I read the book with great interest and with much suspicion, as much of what it said seemed too metaphysical for my tastes. To my surprise, the techniques described in the book actually worked.

One demonstration of the importance of the mental (spiritual) aspect of Aikido was giving by having a subject hold his arm out straight, with complete rigidity, locked tightly against being bent. Then, with not that much effort, I would bend his arm. So much for brute force. Next, he was told to loosely hold his arm out straight and to imagine that his arm was a fire hose and that a furious torrent of water rushed through it; now, his arm could not be bent. Not by me, not by anyone else.

(While I was in college, I made this demonstration before a group of friends, which including a thickly muscled Taekwondo student. He was brute force personified and he wasn't about to let me bend his arm. At time I was bulked up enough (and taller) to make the match fair. He was not short of mental energy, as he quickly summoned an instant anger and a fierce stubbornness to his aid, nonetheless I was still able to, after almost a full minute of strenuous effort, bend his arm back. As my hand pulled away from his skin above his elbow, his blood was revealed; the pressure had been so great that some of his blood had transpired through his skin, leaving my fingerprints in red. I have to admire such stubbornness, so stupendously stupid, so perfectly male.)

The key aspect of the Aikido martial art is that it uses an opponent's force against him. The key aspect of Audio Aikido electronic techniques is that they use the power-supply noise against itself, obtaining a null at the output. Confusion, I hope, diminishes.

 

 

Aikido Single-Ended Output Stage
Now here is another topological technique to add to the family of Audio Aikido. I have long wanted to assemble a single-ended amplifier that held a grounded-grid output stage, wherein the grid was grounded and the cathode received the input signal. Why? If nothing else, no Miller-effect capacitance. Recent correspondence with my good friend Vance Lohoff has revived my interest in the grounded-grid amplifier output stage.

I knew that I had to come up with a way of nulling the power-supply noise from the output stage's output. The key word in the last sentence was "output." Many have terminated a negative feedback loop at the output tube's plate, which indeed will lower the distortion and output impedance, but at the expense of a worse PSRR. Remember, we do not want the loudspeaker to see any of the power-supply noise and that the speaker does not attach to the plate, but the transformer secondary. This means that the output transformer must not see any power-supply-noise induced current variations, which means, in turn, that the output tube's current conduction must remain independent of any perturbations in the power supply's voltage. In other words, at idle, the output stage must draw a steady current, in spite of the noise riding on the B+ voltage. Because of the triode's relatively low plate resistance, how is a constant current draw possible?

If the plate voltage increases, then so too must the triode’s current conduction; if this voltage decreases, then so too will its conduction. In other words, the plate resistance acts like a resistor placed across a varying voltage. Thus, the only way we can assure that a triode’s conduction is immune to power-supply voltage fluctuations is by varying either the grid or the cathode voltage in sync with the power-supply noise. But by how much? By definition, a triode’s amplification factor (mu or µ) is a measure of its grid’s effectiveness over its plate in controlling current flow. Thus, for example, if a triode’s mu equals 10, then a positive 10V increase in plate voltage can be countered by decreasing its grid voltage by -1V, as ΔVp/mu = Δ-Vg for a fixed current. (Do not be frightened by the Δ symbol; it stands for the delta, the change in a variable, in this case, for a change in either plate, grid, or cathode voltage, depending on the variable symbol that follows it.) Or, we could restore the same current draw by meeting the 10V increase in plate voltage by increasing the cathode voltage by 1(mu + 1), or by 0.090909, which equals 10V/11, as ΔVp/(mu + 1) = ΔVk for a fixed current.

Why the different formulas for grid and cathode? The answer is that the cathode is slightly more effective than the grid in controlling plate current; with a high-mu triode, such as the 12AX7, this makes little difference, as 101 versus 100 is not a big difference; but with a low-mu, such as a 6AS7, the difference is huge, as its mu equals a paltry 2 and 2 versus 3 is a large difference. The cathode's effective amplification factor is equal to mu + 1. Thus, the power supply noise must be divided by mu + 1, if applied to the output tube’s cathode, which means that some sort of voltage divider will be needed.

My suggestion is that an identical triode be used as part of the voltage divider, as a triode’s mu is not nearly as constant as many imagine, varying as it does with changes in plate voltage and current. The additional triode will also come in handy by offering a low-output impedance at its cathode for driving the output tube’s cathode. Moreover, the input triode works in anti-current phase to the output tube. As the input triode draws more current, its cathode pulls up in voltage, which effectively makes the output triode's grid more negative relative to the its cathode, decreasing its conduction. And since no triode is perfectly linear, being easier to turn on than to turn off, the two departures from linearity tend to cancel.

The trick to making this magic happen lies in using a constant-current source to load the input triode’s cathode, as the constant-current source will force the input triode do the required voltage division to maintain a fixed idle current for us. A cathode resistor, on the other hand, would not yield the desired 1/(mu + 1) ratio, as it would define a two-resistor voltage divider with the input triode. On the other hand, a cathode resistor could lower the distortion, but at the expense of a worse PSRR.