20 March 2023                                                              Post Number 578

Artificial Intelligence
In the news these days, we hear a lot about AI (artificial intelligence). For example, we learn that students can use AI engines to write their school papers, which brings plagiarism to a new level, as the newly written paper for the student didn't previously exist, which sidesteps the potential snares imposed by anti-plagiarism software and websites. (I understand that teachers will soon have access to an AI engine that can spot those AI-generated essays.) Well, I read that the generated papers produced were easily B worthy. Thus, I signed up to use the new Micro Soft Bing AI. Here is what I asked it:

First, what is the difference between a single-ended amplifier and a push-pull amplifier? Second, is the circlotron amplifier a single-ended amplifier or a push-pull amplifier?

Hello, this is Bing. I can help you with your questions.

A single-ended amplifier is an amplifier that uses a single device (such as a tube or a transistor) to amplify the entire signal. A push-pull amplifier is an amplifier that uses two devices (such as tubes or transistors) to amplify each half of the signal. The advantages of push-pull amplifiers are lower distortion and higher efficiency than single-ended amplifiers.

A circlotron amplifier is a type of push-pull amplifier that uses a special arrangement of transformers and feedback loops to achieve high performance and low distortion. It is not a single-ended amplifier.

I hope this helps. Do you have any other questions about amplifiers?

Who is John Broskie and what does he have to do with audio amplifiers?

 John Broskie is a tube-audio expert and writer who has contributed to amplifier design by creating new and innovative tube-circuit topologies, such as the Aikido pre-amplifier. He has also published hundreds of articles on his website, TubeCAD Journal, where he discusses various aspects of tube-audio theory and practice. He has also designed and sold PCBs for his circuits.

He is well-known and respected among tube-audio enthusiasts for his knowledge, creativity and pragmatism. He has influenced many amplifier builders who have used his designs or learned from his writings.

What is an Aikido preamplifier?

 The Aikido pre-amplifier is a tube-audio circuit that uses internal symmetry to achieve low distortion, low output impedance, high PSRR (power supply rejection ratio) and feedback-free amplification. It was created by John Broskie and is based on his philosophy of balancing imperfections with imperfections.

The Aikido pre-amplifier can use different types of tubes, such as 6DJ8/6922, 12AU7/12AX7, 6SN7/6SL7 etc.. It can also be combined with other circuits, such as cascode or cathode follower, to create different variations of the Aikido topology.

The Aikido pre-amplifier is popular among tube-audio builders and enthusiasts for its sound quality, flexibility and simplicity.

The end.

Not bad, but not exactly right, as single-ended amplifiers can use many output devices in parallel. As I painstakingly pointed out in my last post, the true defining difference is that of the phasing of the output devices. Single phase means single-ended; two phases, push-pull. If some of the output devices work in anti-current phase to the other output devices, then we get push-pull operation. In addition, Bing assumed that all push-pull output stages were class-B types, ignoring class-A push-pull operation. I should have also asked, is the circlotron ipso facto a class-A amplifier?

As for Bing AI's account of the Aikido preamp and me, not bad at all, and it's probably better than what Stereophile or TAS could produce. (Stereophile has referred to me as an audio historian.)

Once again, thank you Rene.

Hidden Push-Pull Operation
Sometimes push-pull operation is hard to see. For example, the patent (US 10,256,776) granted for a putatively single-ended amplifier, which amazingly enough delivers twice the power than any other single-ended output stage loaded by a constant-current source (CCS). The secret is found in the "steering" of the constant-current source, which of course, means alleged CCS is not a constant-current source, but just another output device that runs in AC current anti-phase to the other output device; in short, push-pull operation. If we cannot make sense of the current phases within the output stage, as some schematic elude easy comprehension, we can still perform a simple test on the putatively single-ended amplifier.

A true single-ended output stage cannot deliver symmetrical output current swings greater than its idle current. It can, sometimes, deliver an asymmetrical peak output current greater than its idle current.

The constant-current source and the inductor set a strict limit to how current can flow through them; in contrast, the output MOSFET can draw more than twice its idle current as long as the power-supply rail voltage allows it. Okay, what if we measure the output from a putatively single-ended power amplifier that is actually a class-A push-pull amplifier, wouldn't we run into the same peak symmetrical current limit? We would, but only if we used the intended load impedance. For example, a 16W class-A amplifier must be able to deliver 2Apk and 16Vpk into an 8-ohm load. Well, if we attach a 2-ohm load instead, we should see the same symmetrical 2A peak current output, which implies a peak voltage swing of 4V. If, on the other hand, we measure 8Vpk and 4Apk, we are most probably testing a push-pull output stage.

With tube-based single-ended output stages, this test is 99% definitive, but not with solid-state-based putatively single-ended output stages. Why the difference? With vacuum tubes delivering so few watts, we up the tube dissipation to the limit, sometimes well beyond the published limit. True, the tubes will not last as long as they would otherwise, but they seldom melt down. In contrast, solid-state output devices can only be operated at their data-sheet dissipation limit if the device is refrigerated enough to bring its external temperature down to room temperature (25C or 77 Fahrenheit). On the other hand, solid-state output devices are sand cheap when compared output tubes.

All of which leads to the obvious solid-state design decision to use big heatsinks and many parallel output devices. In other words, where 16W single-ended solid-state output stage loaded by either a constant-current source or an inductor need only idle at 2A to ensure 16W of output into an 8-ohm load, the amplifier designer might run it at 4A, so that 4-ohm load can be driven to 32W, or he just might choose 3A, as that produces the sweetest highs to his ears. If we know what the idle current is, however, say by measuring the current draw from the wall socket and doing some simple math or by directly measuring the voltage drop across the emitter or source resistors, we can determine just what is the strict single-ended limit to symmetrical output current swings.

Another exception to this rule is the bridge output stage loaded by two constant-current sources. It, too, will exhibit symmetrical output current limits, due to the hard limits imposed by the constant-current sources, but it is nonetheless a push-pull output stage.

You can see why marketing departments like terms such as "class-A" and "single-ended," since making sense of them requires more mental work than most are willing to undertake. Obviously, if you have read this far, you eat this sort of mental challenge for breakfast.

About five years ago, I received a request for potential modifications to the Nelson Pass AMP CAMP Amplifier #1, as he built the amplifier in the hope that he could give his NOS 300B-based single-ended power amplifiers a rest, but the solid-state amplifier fell too short of the single-ended glory to which he had grown accustomed. Here is the schematic he sent me and link to another builder's experience.

Now, here is my redrawing of the schematic, which will help those who are used to my schematic sensibility (accent, manner, style...).

What is going on here is that the bottom MOSFET provides all the signal gain. The input FET is configured as a source follower that drives the IRFP240's staggeringly high input impedance. An inverting negative feedback loop returns the output to the FET, which in turn delivers the negative feedback signal to the bottom MOSFET, resulting in less distortion and a lower output impedance.

The ZTX450 NPN transistor in the middle is there to auto-bias the output stage's idle current. The way it works is that the transistor strives to maintain a fixed voltage differential between its emitter and its base, about 0.6 volts. If it see to great a voltage, its collector voltage drops,which in turn lowers the top MOSFETs current conduction until the emitter-to-base voltage returns to 0.6V. Conversely, if the emitter-to-base voltage is below 0.6V, the collector voltage rises until the Top MOSFET conducts enough current to create the 0.6V voltage drop across the two resistors. Auto-bias is wonderful feature, which is made easy due to the class-A idle current flow.

This 0.6V voltage drop across the 0.575 ohms resistance implies a current flow of about 1.05A, the result of dividing 0.6V by 0.575 ohms. (The 0.47 and 0.68 ohms in series-parallel reduce to 0.575 ohms.) The two unmarked resistors represent the potentiometer.

Here is the mod I came up for him.

My goal was to retain as much of the original amplifier as possible, while giving him more control over the resulting sound by coupling capacitor choice. This explains why 0.1µF coupling capacitors have replaced polarized electrolytic coupling capacitors. If I remember correctly, his entire stereo CAMP amplifier cost about $300, which is less than what many would see as the starting price for a pair of boutique high-end designer coupling capacitors. So did my mod improve the sound? I do not know, for as far as I know, he never implemented it.

Why not?

We would have to ask him, but my guess is that I had insulted him by pointing out that his amplifier was not a single-ended amplifier, but a push-pull one. Blasphemy, I know. If we examine the output stage, we see that is an SRPP design, with the top MOSFET running in AC anti-current phase with the bottom MOSFET. Had it been a single-ended output stage, it would more like this.

The NPN transistor still auto-biases the idle current flow through the MOSFETs, but the top MOSFET only functions as constant-current source. Alternatively, we could make an auto-biased constant-current source based on a P-MOSFET.

No one would confuse this amplifier for a push-pull one, whereas the SRPP version confuses many into believing it's a single-ended affair. Mind you, there's nothing wrong about the SRPP topology; indeed, it must be run in strict class-A, but it is nonetheless a push-pull design, which can symmetrically deliver twice the output current that the equivalent single-ended output stage can at the same idle current and with the same B+ voltage.

The SRPP, however, will not produce the same seductive single-ended cascade of harmonics. If it was that sweet cascade that prompted the purchase of a $5000 300B single-ended amplifier, then the SRPP will not prove an adequate substitute. If, on the other hand, the tonality of PIO coupling capacitors pleased your ears most of all, then my mod might save you $4500.

It's time for me to prevent any misunderstanding here. I am not slamming the Pass CAMP AMP #1 in any way. In fact, I know several who have built one and they love them. It is an amazing bargain in the audiophile world where a set of four tweak replacement feet can cost more than the entire amplifier. In fact, this would make a perfect first electronics project for the novice.

Before leaving the Pass CAMP AMP #1, let's look at a version that uses two OpAmps to both set the idle current and center the output stage.

Click on schematic to see enlargement

The B+ voltage is so low that we should have zero problems running the typical FET-input OpAmp, such as the AD712 dual OpAmp, off it directly. (I understand that the current version of the Pass CAMP AMP comes with a 24Vdc switching power supply, which is still OpAmp-safe.) The OpAmp on the left centers the output stage's DC output voltage to half of the B+ voltage. The OpAmp on the right sets the idle current flow through the MOSFETs by comparing the voltage drop across the two emitter resistors in series to the base-to-emitter voltage of the PNP transistor.

Other Solid-State SRPPs
Making an SRPP out of solid-state output devices, such as bipolar transistors or MOSFETs is easy enough. The first time I showed one that I can remember was in 2004 in post 16.

The design, which I discovered later, dates back to 1964.

In 2005 in post 37, we see an SRPP based on lateral MOSFETs.

The logic is exactly same as it was in the tube and transistor version, namely the current-sense resistor between output devices generates the needed anti-phase signal to drive the top output device.

Post 172 from 2009 show a MOSFET-based SRPP.

By time we get to 2014, we see something far more interesting in post 307, a hybrid SRPP that uses a triode as the input stage. Moreover, the arrangement produces a super-triode effect, as the triode superimposes its transfer curve upon the MOSFETs. Put differently, the triode's own plate resistance becomes the negative feedback loop.

What will follow is a SRPP design similar to the Pass CAMP AMP, which I came up with long ago. My goal was to make use of my Aikido-based headphone amplifier for 300-ohm headphones.

I wanted the unit to double as the driver stage for a small power amplifier robust enough to drive 4-ohm computer loudspeakers to 12W.

Where I write these posts

The critical design stipulation, however, was the tube portion could not be gratuitous. In other words, the solid-state power amplifier needed to be powered by the headphone amplifier's relatively high idle current and low output impedance.

Unlike the CAMP AMP, the bottom MOSFET's gate is directly coupled to the negative feedback loop with no help from a FET source follower. The 2N4403 PNP transistor auto-biased the bottom MOSFET's idle current, not the top MOSFET's. Note the 300-ohm input resistor. This resistor is effectively terminating into ground at the other end, so the headphone amplifier will be driving a 300-ohm load. In other words, the tube-based headphone amplifier is not being used gratuitously. Here is the SPICE-generated Fourier graph.

The THD is below 1% with 4W of output into an 8-ohm load. The push-pull nature of the output stage is revealed for all to see in the transient graph.

Note the anti-phase current conduction between top and bottom output MOSFETs. If this were a single-ended output stage, the top MOSFET's plotline would flat-line, while the bottom plot-line would exhibit twice as big current swings. Speaking of the current, the output MOSFETs idle at 1.3A, which ensures easy class-A amplification into a 4-ohm loudspeaker. Here is the Fourier graph with a 4-ohm load.

There's not much difference, which is a testament to glory of high-current class-A operation. Next, we see the transient graph for a 4-ohm load.

Note than neither MOSFET ever ceases to conduct current. (The balanced could be improved by tweaking the MOSFET's source resistor values, but I restricted myself to commonly available 5% resistor values.) By the way, the adventurous could use a rotary switch and a handful of resistors to create an array of operating modes, from pure single-ended to pure push-pull.

The switch should be the shorting type, and we could add more positions. At the leftmost position, the output stage runs in single-ended fashion, as the top MOSFET behaves like a constant-current source (or gyrator). At the rightmost position, the output stage runs in push-pull.

Okay, what if do not need any signal gain, as our signal source already delivers sufficient gain? What we need is a unity-gain power buffer. Here is one possibility that uses the same output MOSFETs.

The top MOSFET functions as a source follower, while the bottom MOSFET functions as a constant-current source. The NPN transistor works to establish a fixed DC voltage across the 0.43-ohm source resistor. The PNP transistor works as an emitter follower. This unity-gain follower is "bootstrapped" by the 1kµF capacitor, which allows for greater positive output voltage swings from the power buffer. On the other hand, if the signal source, say a buffed tube-based line-stage amplifier, offers a low enough output impedance and can deliver the needed current to charge and discharge the top MOSFET's high input capacitance, then we can go naked, i.e. forgo the input emitter follower stage.

The idle current is set by dividing 0.6V by the source resistor's resistance. In this example, 0.6/0.42 = 1.4A. More than enough to drive an 8-ohm loudspeaker to 4W. To drive a 4-ohm speaker to 4W, we would use a 0.36 to 0.39 ohm resistor.

Okay, lets stray from the obvious into the obscure. The SRCFPP. The SRCFPP was my effort to create the missing brother circuit to the White cathode follower and SRPP. The White cathode follower places the current-sense resistor at the top triode's plate; the SRPP, between the two triodes. Thus, I concluded that the missing circuit would place the current-sense resistor at bottom triode's cathode, thereby completing the Trinity of Lazy push-pull topologies. See post 228 for more details. Here is the tube-based version.

This is a unity-gain buffer that delivers a low output impedance and distortion. Like the White cathode follower and SRPP, it must be run in strict class-A idle current flow; and also like its two brother circuits, it is load dependent. In other words, it must be optimized for one load impedance. (Laziness is seldom free.) It's key feature is that output is floating, i.e. floating, not terminated to ground. Thus, a balanced connector is needed to attach to the low-impedance load, for example, headphones. Note the DC offset present on both outputs, which is not a problem, as no net DC voltage potential exists between the outputs. Here is the MOSFET-based version.

The NPN transistor at the bottom provides the auto-biasing of the MOSFETs; in this example, 1.1A. The PNP transistor once again works as an emitter follower to drive the top MOSFET's high input capacitance. Each MOSFET gets its own 0.24-ohm source resistor, which lowers the MOSFET's effective transconductance to about 2.9A/V. With 8Vpk output-voltage swing (4W) into an 8-ohm load the THD is about 0.1%.

We clearly see the push-pull artifacts, as the 2nd and 4th harmonics are greatly reduced. The Transient graph reveals the anti-phase current conduction.

With a 4-ohm load, the THD worsens slightly to 0.15%.

The distortion could be lowered by raising the idle current. The transient graph show how close the MOSFETs come to shutting off.

They are still well within the class-A window of current conduction; thus, an increase in idle current draw isn't needed to qualify for class-A certification. An increase in idle current, however, will move the MOSFET into range of greater linearity—but at the cost of greater heat dissipation. By the way, increasing the current to improve the sound is a great example of how the Law of Diminishing Returns applies to audio. For example, if we doubled the idle current, the distortion will not halve. In fact, the sonic improvement will prove subtle and most will not hear it. Here is another example: you like your $300 headphones, but desire even better sound. But $600 headphones will not deliver twice as good sound. Perhaps, $3000 headphones still not would deliver twice as good sound. A worthy counter example is found at the bottom of the price range. For example, $6 earbud might sound twice as good as $3 earbuds.

Here a longish quote from a letter I wrote 20 years ago to an editor of an electronics trade magazine, which speaks to the issue of marginal improvements in sound.

Charming as these stories no doubt are, how does this justify $2,000 interconnect cables and magic rocks? First of all, I believe that anyone who sells $2,000 interconnects should not be allowed to die a natural death, failing that, horsewhipped with the cords. But at the same time, I have no quarrel with the audiophile who tells me that those same cables transformed his system or, at the other extreme of expense, that four sheets of toilet paper in between his loudspeaker and their stands made his system sound ten times better.

In fact, I believe he is understating the difference. For the difference between recognizing and not recognizing is infinity. As Vanna White turns just one more letter, which is after all maybe only 2% of the available letters, the contestant recognizes the quote: “These are the times that try men’s souls...” Prior to turning that letter, there was no recognition; afterwards, total recognition. The result was not linearly related to effect. Marginal differences do not necessarily have only marginal results.

In Jude Wanniski’s great book, The Way the World Works, he develops his theory of marginality: marginal differences can, in human affairs, have hugely disproportional effects. The camel's back is fine until the extra piece of straw, which is only a 0.00000001% increase in weight, breaks its back. The fastest runner in the world is famous and receives fat promotional deals; the second fastest runner, the one who is 99.993% as fast, is largely ignored and is offered no Nike endorsement jobs. The model who works for your local department store makes $200 per photo shoot, not the $200,000 that Cindy Crawford makes; yet she is only marginally less attractive than Cindy Crawford. If she were marginally more attractive, she would make $2,000,000 per photo shoot and we would worship her as a freshly born deity.

The whole of high-end audio lives in the realm of marginality: the $30,000 vacuum-tube amplifier's output is only marginally different from the average $200 Chinese receiver's output; as seen on the scope, no difference can be discerned. But, like the extra letter revealed by Vanna, small audible differences can have large effects.

Schiit Gjallarhorn Amplifier
The quote from Paul Klipsch that us tube-loving folk love to repeat is: "What the world needs is a good 5-watt amplifier." Indeed, so true. Since this post has been largely devoted to low-power solid-state amplifiers, it make sense to mention the new $299 10W stereo amplifier from Schiit Audio, the Gjallarhorn. We learn from Wikipedia,

"In Norse mythology, Gjallarhorn (Old Norse: [ˈɡjɑlːɑrˌhorn]; "hollering horn" or "the loud sounding horn") is a horn associated with the god Heimdallr and the wise being Mímir. The sound of Heimdallr's horn will herald the beginning of Ragnarök, the sound of which will be heard in all corners of the world. Gjallarhorn is attested in the Poetic Edda, compiled in the 13th century from earlier traditional material, and the Prose Edda, written in the 13th century by Snorri Sturluson."

We learn from the Schiit website that the Gjallarhorn stereo power amplifier holds:

Exotic, Fully Discrete Topology
Gjallarhorn may be smaller than our other amps, but that doesn't mean it skimps on quality. It features an exotic, fully discrete, current feedback gain stage with our exclusive Continuity S™ output stage, as well as a fully linear power supply—including a toroidal transformer with stacked rails and 30,000uF of filter capacitance. No Class D, no switching supplies, no fans. Pick it up—it’s a heavyweight!

No chip amplifiers, no class-D amplifiers—instead we find discrete parts and current-feedback topology with a constant-gm output stage. If this amplifier were entirely the same but with the exception of being housed in a huge enclosure with massive heatsinks, it could be sold for $2990 easily, and would no doubt create a cult following. Being priced at $299, however, it may fly below the average audiophile's perceptual radar, as many think that $299 is too little to pay for a decent power cord.

Looking side the amplifier's chassis, we see the big power toroid.

If we exclude the power output, the amplifiers are quite impressive:

Power Output:
   Stereo, 8 Ohms: 10W RMS per channel
   Stereo, 4 Ohms: 15W RMS per channel
   Mono, 8 ohms: 30W RMS

Frequency Response:
   20Hz-20Khz, +/-0.01db, 3Hz-500KHz, +/-3dB

THD:
   <0.004%, 20Hz-20KHz, at 1V RMS into 8 ohms

IMD:
   <0.005%, CCIR, at 1V RMS into 8 ohms

SNR:
   >117dB, unweighted, referenced to full output

Damping Factor:
   >100 into 8 ohms, 20-20kHz

Gain:
   10 (20dB)

Input Sensitivity:
   AKA Rated Output (Vrms)/Rated Gain. Or, 9/20. You    do the math.

Input Impedance:
   20k ohms SE, 40k ohms balanced

Crosstalk:
   >80dB, 20-20kHz

Inputs:
   L/R RCA jacks for stereo input, single XLR for mono    input

Topology:
  Continuity S output stage; fully discrete, fully
  complementary current feedback, no capacitors in the
  signal path

Oversight:
   over-current and over-temperature sensors with relay
   shut-down for faults

Power Supply:
   80VA transformer, 30,000uF filter capacitance, plus    boosted, CFP-regulated supply to input, voltage gain    and driver stages

Power Consumption:
   80W maximum

Size:
   9” x 6” x 2.5”

Weight:
   8 lbs

I have yet to hear the amplifier, but I have heard the Aegir and Ragnarok plenty and they impressed me greatly. A mere 10W of output power may not seem like much, but most 300B-based single-ended power amplifier cannot deliver 10W, yet they fill rooms with lovely sound. With high-efficiency loudspeakers, they thunder as well.

Of course, the obvious use for the Gjallarhorn is to power a bedroom system or computer speakers. But what I immediately thought of when I saw the Gjallarhorn was bi-amping. Two 10W amplifiers in a bi-amp setup will sound more like a 40W amplifier. Indeed, if the tweeter amplifier never clips, they might sound like a 100W amplifier. To  understand why this is so, read my article, Active Crossovers and Filters and post 573. Passive crossovers, if truth be told, are a nightmare. Why? Loudspeaker drivers are not purely resistive loads. A nominally 8-ohm speaker might only present 8 ohms of impedance for a few tens of Hertz. The truth of the matter is that speaker driver are complex loads. In contrast, active crossovers do no care what the speaker impedance plot-line looks like.

Imagine one stereo Gjallarhorn amplifier sitting atop a speaker enclosure or right behind it or, possibly, mounted on its back, supplying its power output through wonderfully short speaker cables. (I would solder the cable to the speaker drivers directly, and then send the cable out without using an terminals.)

Music Recommendation: Amazing Piano Music
I tend to burn through female singers and piano music, constantly needing a new happy fix. I found one in Paul Wee, a lawyer and concert-grade pianist, piano playing in his album, Mozart & Beethoven Transcribed. Franz Liszt transcribed Beethoven's 3rd symphony for piano long ago. You might think that is impossible, but it is and it sounds amazing. Alkan made a transcription of Mozart's piano concerto N0. 20, which also works. The second I saw that the recording label was BIS, I knew the sound would prove excellent. It did. Great music, great performance.

Coming from the Jazz world, the famous jazz pianist Brad Mehldau has released a fine live album, Your Mother Should Know Brad Mehldau Plays The Beatles. Jazz music thrives on good melodies, which the beatles managed to deliver over and over again. Thus, we have seen many jazz covers of famous Beatles songs, but this album stands out, as he plays with such understanding and grace that nothing sounds forced or derivative. Each track is small jewel. If you were expecting his famous 20-minute tracks you will only be slightly disappointed by the relative brevity. I hope he comes out with a second (and third) Beatle album.

If you want to hear something a bit more retro and sonically outlandish, be sure to give Ramsey Lewis's 1968 album, Mother Nature’s Son, a listen. If nothing else the stereo effects are intriguing.

//JRB

4,600 Words

13 New Schematics

8 Graphs

Days spent in its creation

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