John Broskie's Guide to Tube Circuit Analysis & Design

07 June 2015


Autoformers in General
In a recent post, number 321, I mentioned autoformers, which provoked some head scratching by some readers. An autoformer is like a transformer, a truly odd transformer, one with but a single winding that offers at least three taps (or connections or lead-out wires); if it presented only two connections, it would be an inductor (a choke). Adding an additional tap along the length of wire make all the difference in the world.

Like a transformer, an autoformer can decrease or increase AC voltages and AC currents, along with impedances. Like a transformer, an autoformer can never increase power, although like a transformer, alas, it can lose some power, due the wire's resistance and core losses. Like a transformer, an autoformer is usually made from solid-core, enameled copper wire and a laminated steel core. Like a transformer, an autoformer can either hold or not hold an air-gap in the core's structure, so some autoformers can sustain a DC current flow, while other are strictly AC devices. Unlike a transformer, an autoformer provides no isolation; hence, its relative rarity.

The reason we audiophiles should care about the autoformer is that it can easily outperform its more famous brother, the transformer. Autoformers are smaller, lighter and offer wider bandwidth and less phase shift and insertion losses than a comparable transformer.

Making sense of how the autoformer works is not really any harder than making sense of how a transformer works. Let's begin with a super simple autoformer whose center tap is at exactly 50% of the single winding—think of it as a center-tapped choke.

The inductance and DC resistance measured from the ground tap to the center tap equals the inductance and DC resistance measured from the input tap to the center tap. As a result of this 50% division of turns of wire about the core, the output AC voltage measured from the center tap to the ground tap will be 50% of what is presented to the input tap and ground.

In the example above, we see that 16Vac is applied across the entire winding and 8Vac appears from the center tap to the ground tap. Because we can only alter the form energy takes, never destroying it, the current flow available at the center tap will be twice that which is applied across the entire winding. In other words, with the exception of some core and copper losses, which will turn a small portion of the input power into heat, the autoformer is a constant-power device. In this example, 4W goes in at the top and 4W comes out at the center tap.

The impedance ratio is equal to (1/tap-ratio)²; thus, in this example, 1/0.5 equals 2, which squared equals 4, so the impedance ratio is 4:1. In other words, an 8-ohm loudspeaker placed across the center-tap and the ground tap will be reflected as a 32-ohm load to the entire winding. This is a godsend for those running OTL and Circlotron amplifiers, as 8-ohms is a brutally low load impedance for any tube to work directly into. Of course, we do not have to place a tap at 50%, as we can pick any ratio we need. For example, I have been tempted to have the following autoformer custom made for tube-headphone-amplifier use.

As far as the tube-based headphone amplifier is concerned, the load is 1200 ohms, even if the actual headphone impedance is only 16 ohms. Needless to say (so why am I saying it?) 1,200 ohms is a much more gentle load than 16 ohms. As far as the coupling capacitor is concerned, the load is 1,200 ohms, so its value need only be about 10µF, not the 500µF that the 16-ohm headphones would seem to imply.

Do not forget the strict laws of physics: you never get anything for free. In this case, the headphone amplifier must deliver a output voltage swing of 8.66Vpk and 7.2mA peak to get 1Vpk and 62.5mA peak into the 16-ohm headphones. Note how 8.66Vpk against 7.2mA equals 58mW (avg) and 1Vpk against 62.5mA equals the same peak wattage, save for some small rounding errors along the way. No free lunches here, just a better matching of impedances and, thus, a greater realization of power transfer.



Autoformers and Speakers
Now that we have a good understanding of how an autoformer works, let's look at some unusual audio applications. An obvious use for an autoformer is to make better matches between speakers and amplifiers—and not just tube-based amplifiers. For example, a solid-state class-A power amplifier that works flawlessly with an 8-ohm load may misbehave with a 4-ohm load, as the output stage, which was already running hot enough to toast bagels, becomes even hotter with the 4-ohm load, which draws twice the current and twice the power (but sees the same voltage) that the 8-ohm load did. Moreover the class-A amplifier may employ an auto-bias circuit that the 4-ohm load will throw off, as it will provoke current swings outside the amplifier's class-A window of conduction. Even the 16-ohm speaker is a bad match, as only half of the 30W amplifier's power can be delivered into that impedance.

With the above autoformer, the solid-state class-A power amplifier designed to deliver 30W into 8-ohms can now deliver 30W into both 16-ohm and 4-ohm speakers with no problems. A slightly less obvious use for an autoformer is to make an 8-ohm speaker more compatible with an OTL amplifier. Believe me, if all speakers held such an autoformer, 300B OTL power amplifiers would be common.

(Here is a quick quiz: what is the winding ratio needed to make the 8-ohm speaker appear as a 128-ohm load to the OTL?)

Now, fasten your mental seatbelts. Ribbon tweeters can deliver amazing high-frequency response, which is why they often appear in super expensive speaker systems. The big problem for the maker of these tweeters is getting the impedance up to 8 ohms, as very little metal foil is needed in their construction and even the thinnest short strip of metal foil offers little resistance, far less than 8 ohms worth.

Remember from my explanations on the topic of current output amplifiers, the force that compels a speaker's diaphragm's movement is due to flow of current within a magnetic field.

      F = B·l·i

Where B is the magnetic flux density; l the wire length in the magnetic field; and i is the current flow. Notice that Voltage and Resistance do not appear in the formula. The more current flowing, the more movement. Ideally, a speaker would present a DCR and an impedance of only a few milliohms, as resistance only adds heat to the mix. (Now, if there were a thermal speaker, whose movement was the direct result of heat being generated, say some expanding and contracting gases, then resistance would not be a waste, but an essential and productive part of the creation of sound. For normal speakers, heat is just wasted energy.) Thus, the makers of ribbon tweeters are in a bind, as they dare not go much below 4-ohms in impedance and yet they could make a much better tweeter but it might present only 1-ohm (or much lower) of resistance. The solution would be an autoformer, with a tap at 35% of the winding.

In the above illustration, we see a conventional 8-ohm woofer wed to a 1-ohm ribbon tweeter. As far as the amplifier is concerned, the load is 8 ohms. As far as the 5µF capacitor is concerned, the tweeter is an 8-ohm type; but as far as the 0.16mH inductor is concerned, the tweeter presents only 1-ohm of resistance. This saves us money both ways, as a 1-ohm tweeter would require a 40µF capacitor to crossover at the same frequency; and an 8-ohm tweeter would require a 0.8mH inductor. In other words, not only do we get the benefit of a high-current ribbon tweeter, we save on crossover parts.

Note the phase reversal on the tweeter, which is due to the 2nd-order crossover imposing a 90-degree phase shift at the crossover frequency on both the woofer and tweeter, which would otherwise result in the tweeter being out of phase with the woofer, thereby creating a deep null at the crossover frequency.

Okay, after that mental warm-up, let's have a brief cool-down period. The following is a generic speaker, nothing fancy, just a big woofer and small midrange and dome tweeter—a speaker your grandfather would recognize and might have bought or, even, built.

First-order filters are used throughout and the crossover frequencies are at 500Hz and 5kHz. Now what would happen if we stacked four of these speakers, one atop the other? Well, we could end up with a 32-ohm load, if all the speakers were wired up in series; or, a 2-ohm load, if wired in parallel; or an 8-ohm load, if we used the series/parallel configuration.

The impedance remains unaltered, in this series/parallel configuration, but what happens to the efficiency, with four speakers blaring at once? Well each speaker only sees 50% of the voltage the amplifier puts out, so we incur a -6dB loss; but as we have quadrupled the radiating surface, we gain a +12dB boost in SPL, so we end up with net gain of +6dB. For example, four 90dB speakers placed in this series/parallel configuration will effectively present an SPL of 96dB with 1W at one meter. Nice for those with wimpy tube amplifiers.

By the way, do not imagine that this is too silly of an idea. One of the best sounding systems I have ever heard was when four small, high-quality, mini monitors were stacked up four high, with one facing forwards, one facing backwards, and two facing the adjoining wall. Amazing stereo image. That's great, John, but what happens if you have kids or a dog or a spouse that sleepwalks and you don't want your tower of speaker to fall over? I see your point, but a speaker stand could be devised that securely held all four speakers together. The easy solution, however, would be to build a bigger speaker enclosure that could house all 12 drivers.

If nothing else, such a design would save 75% on the crossover parts, as four identical crossovers would not be needed.

Now it is time to return to the topic of autoformers. Given the above speaker, how could we exploit an autoformer? One possibility is the following.

The amplifier attaches to the 8-ohm tap and ground—that is if the amplifier is a conventional solid-state or transformer-coupled tube amplifier, as the load presented to the amplifier is 8 ohms. If an OTL amplifier is used, then we would use the 128-ohm tap and ground tap. That was the simple part. Now the harder part.

Beginning with the woofers, four 8-ohm woofers in parallel will equal a 2-ohm load, a brutally-low load impedance even for solid-state amplifiers. But the amplifier sees an 8-ohm load due to the autoformer. The woofers all see the same voltage, but only one half of what the power amplifier put out, thus we incur a -6dB loss; but we have four times the radiating surface area of one woofer, so we gain +12dB in SPL, thus making a final total of +6dB. Why did we take this giant step sideways? The inductor is lower in value by four over the inductor that worked with an 8-ohm load. Smaller is cheaper and better, as lower inductance means lower DCR; of course, this reduction in DCR is somewhat mitigated by the 2-ohm load impedance.

Moving on to the midranges, we started with 8-ohm drivers and we ended up with an 8-ohm load. so the exact same crossover parts are used. But, due to the series/parallel arrangement, we gain +6dB of SPL per watt. In addition, the four midranges can handle four times the power that a single midrange could.

Ending with the tweeters, we see a 32-ohm load imposed by the four tweeters in series. Since each driver sees one fourth of the signal voltage, we suffer a -12dB loss, but we gain +12dB due to the fourfold increase in emitting surface, so a wash obtains, as -12dB + 12dB equals 0dB. Note, however, that the autoformer delivers twice the signal voltage, so we gain +6dB in SPL, bringing the tweeters inline with woofers and midranges. Most importantly,we got away with a 1µF crossover capacitor, rather than the 4µF capacitor an 8-ohm load demands. Is this a big deal? It can be if you are buying $50 capacitors. I am not sure that a copper-foil 1µF crossover capacitor cost only one fourth as much as 4µF copper-foil capacitor, but I am sure it cost a lot less.

In sum, by using an autoformer we not only made the speaker OTL friendly, we saved some money on the crossover.



Autoformers as MC Step-Up Devices
Returning to the topic of moving-coil pre-preamplifiers, an autoformer could be used as step-up inductive circuit. (Notice how I didn't write "transformer.")

Let's say that we need a step up of 10 (+20dB). The autoformer would need to be tapped at 10%. I would definitely keep whatever shunting capacitance is required on the cartridge's side. What about the load resistor, which might be 100 ohms? I would definitely load the top of the autoformer, rather than across the cartridge. Why? All inductive devices desire low-resistance termination, ideally zero ohms, a dead short; just as all capacitors prefer high-resistance termination, ideally infinity. Well, do we use a 100-ohm resistor? No. Instead, we must work out the impedance ratio of the autoformer. In this example, the impedance ratio is 1:100, as the step ratio was 1:10 and 10² is 100. Thus, the resistor's value must equal 100 against 100, or 10k.


Why Do Autoformers Cost So Much?
If you have priced an audio autoformer, you probably have been shocked by the high prices. Odd, isn't it that once something is intended for home audio, the price goes way up. (A friend once told me that he was buying a bunch of flowers and he was happy with the cost, until he mentioned that the flowers were for his daughter's wedding, whereupon the florist told him that the same flowers must now nearly double in price because they were now wedding flowers, not funeral flowers.) well, here is an interesting and impressive autoformer:

This baby boasts the following features:

• 50 Amp – double phase, 12,000 Watts capacity 
• Fully automatic 10% boost when needed (95v-115v) 
• Park power diagnostic light 
• Boost indicator lights for each line (2) 
• Spike and surge protection 
• U.L. listed Autotransformer 
• Size: 12”H x 8 ½“ W x 5½” D 
• Weight: 35 Lbs. 
• Two-year limited warranty 
• Made in U.S.A.

What would an audiophile expect to pay for 50A and 12,000W delivery and 35lbs? A good guess would be $1,000 per pound. Well, as this autoformer is meant to be used by those who own RVs, as in recreational vehicles, the price is only $548, not $35,000. Remember my faux advertisement for Sonic Gold cables? Some never get my jokes, which prompts me to wonder how many wanted to buy Sonic Gold cables from Artifice Audio, a bargain at only $12,349 for 20-foot lengths.

The high audio prices are due to two factors, rarity and troubling psychological issues. If only a handful of iPad-like tablets were sold each year, then they would cost $10,000 each. There is amazing efficiencies to be gained by mass production. For example, if Honda made millions of large, tall, full-range ribbon speakers, they would cost $1,000 each, not $40,000. Electronic parts that cost over a dollar each had be had for 25 cents, if you buy 1,000 of them. Do not forget that handmade is expensively made. When you seek out hand-wound autoformers, you must expect to pay far more than what a machine-made autoformer would cost—lots more.

While this explains much of the high cost, it cannot explain all of it. For example, audio autoformers made for sound-distribution systems are reasonably priced. If these autoformers were sold to audiophiles, however, they would have to be housed in zebra-wood boxes, wreathed in Teflon, and and soaked in gold, as they would cost ten to twenty times more. The question—Who would pay so much more for a fancy box?—does not need to be answered, as we all know the answer: we would. For almost all audiophiles, the media is the message, the wrapper is the candy bar, the fancy enclosure is the sonics.

In the year before his death, the late Dr. Gizmo (Harvey Rosenberg) and I became friends. Long ago, before I sold PCBs and kits, when my only audio endeavors were writing the Tube CAD Journal and creating tube-related software, he contacted me to tell me that I had won the Triode Guild's "Platinum Brain" award. (I wanted to get a personalized license plate that read: "Pt Brain," but it could not pass the wife acceptance factor.) Here is what I wrote at the time:

Last words: does it strike you as odd that Dr. Gizmo is endorsing a hardcore, almost academic set of tools to better understand and create tube audio gear? It shouldn't. He and I are really the two sides of the same coin. He jokes, shocks, and teases his readers, and their inertia, because he is deadly serious about the ultimate aim of all our efforts: the complete enjoyment of the musical experience. Experiencing all that the music can bestow is his goal and mine as well, but as my task is different—the teaching of tube circuitry—I must present a serious face about what tickles and pleases my soul.

I ended with a quote:

"The style is the man. Rather say the style is the way the man takes himself… If it is with outer seriousness, it must be with inner humor. If it is with outer humor, it must be with inner seriousness."

Robert Frost

I never met Gizmo in person, but we did swap many long phone conversations. He was a triode evangelist, an audio-ecstasy crusader. His sincere desire, hope, and longing was for the joys of tube-based audio to be extend beyond the small clusters of old, well-off men with more money than common sense. His goal was that one should be able to buy a fantastically great-sounding audio system for about $2,000; that was $2,000 for everything, speakers and amplifiers and CD player or turntable, not just one interconnect or power cord.

What he thought the world really needed was new Stereo-70, but with a larger chassis, a chassis far wider and deeper than it need be, an almost silly spaciousness, so it would not only allow modification, but it would positively invite it. As he saw it, American teenagers needed something to hotrod, something to modify that would personify and exemplify the modder's character, temperament, emotions, and personality. And since cars were now too expensive and too complicated and too regulated (is it even legal to create a hotrod today?) for ready modification, something else would have to take their place. As he saw it, tube-based audio gear could fill that void, as it was simple and yet yielded deeply satisfying results. Thus, our long phone calls, while we discussed how a universal Stereo-70 could be designed and built.

During one such call, he told me what I already knew. He had originally manufactured toys and he had decided to create a tube-audio company named "Tube God." His plan was simple: he would hire the best electronic designers and use the best parts to build the best audio equipment, which would then be housed in ugly boxes, as he wanted to sell sonic performance, not jewelry boxes. His effort failed. A few years later, he came out with the same products in fancier boxes and he was successful. Audiophiles will not buy ugly boxes. See at the bottom the excerpt I took from Harvey Rosenberg's little booklet, Tube God, to get a good idea of the battle he was fighting against, amongst other things, the notion that "People listen with their eyes."*

About 25 years ago, a famous audio personality took me aside and told me that he didn't make any money in this business until he discovered the secret to success in audio: at least 50% of the cost of a piece of equipment must go into its cosmetics.

I cannot resist the urge to quote myself. From blog number 278:

If the Honda Accord held to the same pricing model as the $27,000 speakers, its price would probably be just under one million dollars. But then cars are not high-end audio gear, which abide by a different set of rules. For the race in high-end audio isn't so much to higher technological achievement, but to higher cosmetic extravagance. The more lavish the exterior, the higher the price, and, thus, the better the sales. I know that this is true, as I have seen products whose guts remain unchanged, but whose enclosure have grown ever more elaborate and expensive, and whose prices have doubled—and which now flourish due to their enhanced perceived value! How is that possible? Isn't it the sound that matters most? No, not really; no more than a pearl necklace is meant to provide warmth to the wearer. High-end audio has become to men the equivalent of what jewelry is to women: a means of designating and illuminating one's social status and wealth.


A few More MC Pre-Preamp Circuits
The well is no where near dry yet. Like a sea giving up its dead, my computer's hard-drive gives up more and more MC pre-preamplifiers. I quite like the following design, as it is so simple.

Why does the name include the word "Aikido?" This circuit sidesteps power-supply noise, rather than employ brute-force means to quell the noise. At each transistor's collector there is plenty of noise, but as long as the power-supply rails present equal but out-of-phase ripple, the noise nulls at the junction of the two 1µF coupling capacitors. Even a simple, non-regulated, RC-filtered bipolar power supply will work surprisingly well.

Another circuit that I found hiding was the following, a somewhat conventional design—well, conventional at least for me.

The only snazzy portions are the inclusion of the extra PNP transistor at the current mirror at the circuit's top and the addition of the rectifier in between the NPN differential pair. The latter device was added as voltage-offsetting device that would allow the DC feedback loop to force the left differential transistor's collector to +5.46Vdc. (Bypassing the MUR410G with a 1kµF capacitor will lower the distortion a tad.)

By the way, we can forgo the use of the emitter follower, with the addition of a pull-up resistor, but the distortion will rise, albeit in a single-ended fashion, with more 2nd harmonic content.

The constant-current source's idle current was pumped up to 10mA. Why? The naked differential amplifier must now drive the negative-feedback resistors. Let's now move on to more interesting circuits.

The above circuit is a Triadtron variation. The 2N5551 transistor at the cathode resistor acts to prevent any alteration in current flow through the input triode. The only way that a triode can maintain a fixed current flow in the face of a change in grid voltage is for there to be a countering change in either its cathode voltage or plate voltage. Well, since the transistor strives to prevent a change in cathode voltage, the plate voltage must change. By how much? That is easy: by the mu (the amplification factor) of the triode. For example, if a triode sees a 1V increase in grid voltage and its cathode voltage is fixed, then its plate voltage must fall by mu volts to maintain the same current flow. But what if we do not need a gain of 33, which is what the 6DJ8 would deliver? We could use a lower-mu triode, such as the 6H30, 12AU7, or ECC99.



Next Time
More departing from recognized, conventional electronic designs, of course.



*An Excerpt from Harvey Rosenberg's Tube Bible
Harvey Tube God effort printed a small booklet that was a kick to read back in 1982, as it stood in the sharpest contrast to the prevailing high-end-audio glossy ads and brochures. Here he explains why you are an audio cynic:



PROBLEM: High quality tube electronics are ridiculously expensive.

We know that many audiophiles are unhappy and angry. They are unhappy because high quality electronics are expensive, and they are angry because there is a general lack of integrity on the part of manufacturers. These attitudes are totally justifiable because of the following set of circumstances:

There seems to be an unspoken and unwritten set of rules in the audio industry that most companies subscribe to as the formula for success.
Here are the rules:

(1) Always describe your products as the ultimate development, the finest sounding, clearest, most musical, most accurate, and of course made with the finest parts available. This rule is followed by the cheapest and most expensive manufacturers, and because everyone says exactly the same thing about their product, no one is believable. The corollary of this rule is - even though every piece of equipment is a compromise, never admit that you equipment has any compromises, or Rule 1A "WHAT THEY DON'T KNOW WON'T HURT ME."

(2) Design your products so that they can be updated later. A manufacturer can make more money on that "latest" $300 mod than he can on the original sale of the equipment because he gets the whole $300. He does not have to pay a sales commission to his rep or give the "retailer's discount" on this. He gets his money in advance so he doesn't have to borrow money from the bank. A good way to make a profit - except it is at your expense. We want to suggest to you that every audio manufacturer today knows exactly how to design his product right the first time, knows about the latest power supply designs, knows about polypropylene capacitors and the latest network analysis — and doesn't incorporate these features because he wants that extra "Latest Mod" money.

You should be angry about this. The general feeling that audiophiles have that manufacturers are bullshitting them is correct. This doesn't help the audio industry much.

(3) An educated audiophile is a dangerous customer. Audio manufacturers have the attitude that audiophiles want platitudes and not facts. Equipment is sold as if it were magic black boxes that performed miracles rather than simple machines that either amplify voltage or current and do some impedance matching in the process.

We think it is the responsibility of the equipment manufacturer to give detailed facts about the machines they manufacture. While we believe that listening is the ultimate test that every piece of equipment should be judged by, and specifications are meaningless, it is also essential that our customers be better educated about the investments they are making. The general cynicisms on the part of the audio consumer are directly related to the bullshit claims and hocus pocus manufacturers use to describe and sell their equipment.

(4) People listen with their eyes. Every manufacturer must decide how much glitter he must add to his product in order for it to be a sexy sell. These manufacturers believe that you are generally deaf, and if they include enough knobs, LEDs, and pretty face plates you will think they make great equipment.




User Guides for GlassWare Software
Just click on any of the above images to download a PDF of the user guides.

For those of you who still have old computers running Windows XP (32-bit) or any other Windows 32-bit OS, I have setup the download availability of my old old standards: Tube CAD, SE Amp CAD, and Audio Gadgets. The downloads are at the GlassWare-Yahoo store and the price is only $9.95 for each program.

So many have asked that I had to do it.


I do plan on remaking all of these programs into 64-bit versions, but it will be a huge ordeal, as programming requires vast chunks of noise-free time, something very rare with children running about. Ideally, I would love to come out with versions that run on iPads and Android-OS tablets.



Kit User Guide PDFs
Click image to download

BCF User Guide

Download PS-3 User Guide

Janus regulator user guide

E-mail from GlassWare Customers

Hi John,

I received the Aikido PCB today - thank you for the first rate shipping speed.
    Wanted to let you know that this is simply the best PCB I have had in my hands, bar none. The quality is fabulous, and your documentation is superb. I know you do this because you love audio, but I think your price of $39 is a bit of a giveaway! I'm sure you could charge double and still have happy customers.
     Looking forward to building the Aikido, will send some comments when I'm done!
   Thank you, regards

Mr Broskie,

I bought an Aikido stereo linestage kit from you some days ago, and I received it just this Monday. I have a few things to say about it. Firstly, I'm extremely impressed at the quality of what I've been sent. In fact, this is the highest quality kit I've seen anywhere, of anything. I have no idea how you managed to fit all this stuff in under what I paid for it. Second, your shipping was lightning-quick. Just more satisfaction in the bag, there. I wish everyone did business like you.

Sean H.

9-Pin & Octal PCBs

High-quality, double-sided, extra thick, 2-oz traces, plated-through holes, dual sets of resistor pads and pads for two coupling capacitors. Stereo and mono, octal and 9-pin printed circuit boards available.

Designed by John Broskie & Made in USA

Aikido PCBs for as little as $24

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TCJ Push-Pull Calculator has but a single purpose: to evaluate tube-based output stages by simulating eight topologies’ (five OTL and three transformer-coupled) actual performance with a specified tube, power supply and bias voltage, and load impedance. The accuracy of the simulation depends on the accuracy of the tube models used and the tube math model is the same True Curves™ model used in GlassWare's SE Amp CAD and Live Curves programs, which is far more accurate than the usual SPICE tube model.

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