John Broskie's Guide to Tube Circuit Analysis & Design
10 February 2009

Stimulus: It's Not What It Used To Be
I imagine that somewhere atop a seldom-traveled mountain or deep inside some unruly jungle there people who do not know that the World’s economic fortunes have turned bleak. I envy them. Okay, it is far too easy to be just nagging and cynical; it’s much harder to actually make sober suggestions. Here are my six off-the-top-of-my-head solutions to our current woes:

Eliminate the minimum wage and greatly limit employment discrimination and harassment lawsuits. Stop the eight-hour day limit and allow workers to work four-hour days. Why? As we have regulated our work life today, you must work an forty-hour week to count for retirement or benefits or insurance. Why? Why cannot one parent or an old person or a student work a good four-hour day? Or why cannot a young fellow work an eight and four hour job in one day? If he wants to, why can’t he? One size does not fit all. Besides, having two different four-hour jobs is a much safer bet, in these company-closing times. All of these measures would make more jobs available instantly. What about the poor workers? The poorest workers are those with no jobs.

Greatly reduce the burden of laws and regulations on small businesses. A big company, like Microsoft or GE, actually loves big government and its onerous regulation, as it knows that its smaller competitors cannot employ the same huge army of lawyers that it does. The bigger the company, the bigger the legal weight it should endure. But it is insane to expect a small business to survive under the mountain of legal paper heaped on it daily.

Enact real tort reform. Let anyone who wants to sue do so, but make plaintiffs pay the defense if they lose (a fixed fee, perhaps, or a percentage of the desired setlement). A jury trial and the lottery should not be as similar as they are today. Ultimately, we must also try to reduce the number of lawyers. Imagine instead if out of every ten people one was a brain surgeon. If we had that many brain surgeons, many more heads would be sawed opened than need be, but at least we would only fear being misdiagnosed, not sued off the face of the planet.

Raise the Fed’s interest rate, say to 6%, and promise to support the dollar against any decline by putting in place a de facto gold standard. Let the Fed pick an arbitrary price for gold (and few other rare minerals and commodities in the mix) in US dollars, say $1,000 an ounce, then stick to it. If gold goes up, stop printing money; if gold goes down, start printing. Thus, if I lent you $1,000 and I expected to be paid back in ten years, I would know that my $1,000 would be returned with the same value as when I lent it. This is not true today. Imagine doing electrical engineering with a non-constant volt. Imagine what a nightmare it would be if the same voltage reading didn’t produce the same dissipation over time, as the volt was allowed to deflate or inflate. Yet, most economist subscribe to the theory that a little inflation, say 2% per year, is not only acceptable, it is desirable. This is the same as saying 2% of your money will be burned every year (or two out of every 100 NOS tubes you have in your stash must be stepped on each year.) Madness, sheer madness.

Fix the tax mess.  How? Install a flat tax rate. Better still, eliminate all income and corporate taxes and just add national sales tax. Why? Defining "income" is almost impossible these days. Movies that take in a billion dollars make "no income" on paper. Consumption is not debatable; if you buy a BMW, you bought a BMW. In addition, I like the idea of hit men, prostitutes, drug dealers, and the Mafia paying taxes; now, they don’t. (Twenty years ago, I used to know this fellow whose girlfriend made $140K tax free selling illegal drugs; she owned two houses and fantastic artwork and she collected welfare and food stamps.) But what would those millions who worked for the IRS and accounting firms and tax preparation offices and in the large tax divisions of companies do? They would get jobs that actually increased the country’s wealth, rather than just dragged it down. (Want to give the poor a break? Charge no sales tax on medicine or food sold in stores.) No tax code should take more than a single piece of paper to print it on.

Return sanity to the patent and copyright system. Greatly limit the terms of both, say fourteen years; that's it, then it's gone. Sorry Mickey.

So if I am often right, but too soon, might all of this be too drastic, too much real change for anyone to audaciously hope for? Perhaps. But I do know that it would actually stimulate real economic growth and greatly improve the quality of life in the USA. Instead, however, I expect us to follow the Obama economic plan of being wrong and too late. Recessions can be painful, but they are also often necessary, as nothing else allows business to reboot once it is stuck in an unresponsive program, such as the railway investment dead end in the 19th century or the bubble in the 90s. If we just let the economy reset itself, things would improve in a year or two. Instead, we want the same craziness that led to the current fiasco to continue forever. No nation has ever triumphed by suing itself silly and having most of its people work for the government.


Wait a Minute...
While reading page 834 of the Stimulus Package, there in section Q.2D, sub-section 52, I find this: “In order to further the thermionic arts in America, whose energetic and lively furtherance is an absolute necessity to national recovery, tax-free federal grants, which are not to exceed $12,540,000.00 or fall below $990,840.00 are to be yearly granted to those individuals who have worked diligently to further said arts by educating the public and by having created original thermionic circuitry for at least, but not limited to, nine years.” Wow! In other words, never mind the above rant—it looks like I am getting my share after all. Care for some stimulus rinds? They may not be healthy, but they sure are habit forming. Hell, what's a measly $800,000,000,000 between friends.


Getting Electronic Parts

By the way, if you do not use, you should. This site will search through many more electronic part suppliers than you can remember. For example, I performed a search for 5687s and Octopart revealed that an industrial instrument supply house had 8 NOS RCA 5687s for only $6 each collecting dust for the last 30 years. Think outside the the Mouser/Digi-Key box.


Back to Power Boosters
This will be the last post on the topic of power-booster amplifiers (well, at least for a few months). Let’s pull back a bit and think about power and power amplifiers and loudspeakers. It’s a dang pity that amplifiers hold a power rating, as power is confusing, because it doesn’t linearly correlate well with our perception of acoustic power. For example, a 20W power amplifier does not play nearly twice as loudly as a 10W power amplifier, something closer to 200W would be needed. In addition, power isn’t linearly related to output voltage, as a doubling of the output voltage will quadruple the wattage. The following graph shows the voltage and current relationship to power with sine wave into an 8-ohm load.

into 8-ohm Loads
Peak Power Power Ipeak Vpeak Vrms
0.125 0.0625 0.125 1 0.71
0.5 0.25 0.25 2 1.41
2 1 0.5 4 2.83
8 4 1 8 5.66
32 16 2 16 11.32
128 64 4 32 22.63
512 256 8 64 45.26
2048 1024 16 128 90.52

As we can see from the chart, a 1024W amplifier only puts out 32 times more voltage than a 1W amplifier. Worse still, our ears do not perceive it as being 32 times more powerful. I would still welcome only a voltage or current rating on power amplifiers, as it would help flatten the exponential climb. In other words, no one can hear the difference between a 60W and a 64W amplifier, which a voltage rating of 21.9Vrms and 22.63Vrms, respectively, would better help to reveal.

The next step is to factor a loudspeaker’s SPL into the mix. If you double the output voltage, the SPL gains 6dB. For example, an 88dB efficient loudspeaker will put an SPL of 88dB at one meter with a 2.8Vrms input signal. Doubling the signal voltage to 5.6Vrms increases the SPL to 94dB and the wattage from the power amplifier goes from 1W to 4W. The following graph includes SPL.

into 8-ohm Loads
Peak Power Power Ipeak Vpeak Vrms SPL in dB
0.125 0.0625 0.125 1 0.71 76
0.5 0.25 0.25 2 1.41 82
2 1 0.5 4 2.83 88
8 4 1 8 5.66 94
32 16 2 16 11.32 100
128 64 4 32 22.63 106
512 256 8 64 45.26 112
2048 1024 16 128 90.52 118

Note how much power is required to get to 118dB. Also note how starting with a higher-efficiency loudspeaker, say 100dB, would require only a 64W power amplifier to reach the same 118dB SPL. On the other hand, an 82dB loudspeaker would need a 4096W power amplifier! (By the way, what is the limit to a loudspeaker’s efficiency? If I remember correctly, about 128dB SPL would equal unity power transfer.)

Now the interesting question is what happens if two 88dB loudspeakers were placed in series, effectively presenting a 16-ohm load to the amplifier, what would be the effective efficiency of the pair? If a solid-state or tube OTL power amplifier were used, each driver would see half of the 2.8Vrms signal, so each driver would lose 6dB in SPL, but at the same time we would have doubled the driver surface area, which would give rise to a +6dB boost; thus, we would end up where we started, 88dB for 2.8Vrms.

If both drivers are placed in parallel, each driver will still see the same 2.8Vrms, but the doubled surface area will deliver its +6dB boost, so the SPL will increase to 94dB. We didn’t just get something for nothing, as the current into the loudspeaker pair has doubled (4 ohms versus 8 ohms). Of course, if our amplifier can deliver the doubled current, we will gladly take the increase in SPL. Now what happens if we place four drivers in series/parallel, for a combined impedance of 8 ohms?

Each driver will see half the signal voltage, so each driver’s SPL goes down 6dB, but we increased the surface area by fourfold, so we gain +12dB of SPL, assuming that the drivers are close to each other and the frequencies reproduced are large relative to space between drivers. So, -6dB added to +12dB yields a final SPL increase of +6dB, so our normally 88dB SPL speakers will behave as 94dB cluster. In addition, the power amplifier delivers the same voltage and current into this cluster of drivers that it would into a single driver.

The next 8-ohm combination of drivers is nine 8-ohm drivers, with three rows of parallel atop each other, as 8/3 x 3 = 8.

Each driver will now get its third of the power amplifier output voltage, so each driver will lose 9.5dB of SPL, but with nine times the radiating surface area, we gain +19dB in SPL, so the final SPL for 2.8Vrms will be +97.5dB, with our 88dB drivers.

Okay, this is all interesting, but where are the tube power amplifiers with 2A3s or 300Bs? Where can I buy a “Where’s the tubes?” bumper sticker? We can now return to the idea of using a flea-powered tube amplifier with a big solid-state beast of an amplifier. If you are as old as I am, you will remember the huge fuss the Bose 901 loudspeakers created decades ago. Back then, when you told someone that you were an audiophile, they would more than likely instantly respond with, “Oh, you own Bose 901s!” I was never a fan, but then I was in the minority. Dr. Bose used exploding wires, if I remember correctly, to discern the ratio between direct and indirect sound from a point source, the imagined theoretically perfect loudspeaker polar dispersion pattern. His conclusion was that only 11 percent of the signal reaching our ears was direct, the rest coming from reflections. Thus, he placed one driver facing the listener and eight facing backwards.

Now, imagine a modern day copy of the famous 901, with the same driver placement, but with the front-firing driver getting its signal from our 2.5W flea-powered champ and the remaining eight drivers configured as a 4-ohm cluster, driven by a 100W solid-state brute of an amplifier. In other words, our 2.5W has effectively become a 200W amplifier (4-ohm load for solid-state amplifier double power output). But won’t all that stinky solid-state power just overwhelm the bejeweled glory from the tube amplifier’s output? Perhaps, but I doubt it, as the ear will give the first arriving sounds precedence over the latecomers. This just might work and today’s full-range drivers are vastly superior to those made 30 years ago.

Since we are getting whimsical here, I will mention that I would like to build a line-source dipole loudspeaker that held nine full-range drivers (and one 98dB horn tweeter), which would allow switching between 8 ohms or 72 ohms, with all the drivers in series. Who the heck would want a 72-ohm loudspeaker? I would, as I could then build a simple OTL amplifier that would welcome the high load impedance. And at the flick of a switch, the loudspeaker would return to 8 ohms, for easier selling or to bring over friends house to try with their solid-state monsters. By the way, 88dB would still equal 88dB with the 72-ohm configuration; but with the 8-ohm configuration, +9.5dB boost in SPL would result. On the other hand, our OTL amplifier would certainly swing much more voltage into the 72-ohm load than any solid-state power amplifier, so effectively the tube amplifier play plenty loud.

The Last Idea for Now
I just realized that I have far too much more to cover than I want to, as this blog entry is getting far too long. (Of course, when my stimulus grant comes through...) So, here is the last idea. Many will have seen some variation on the following circuit used to power boost an OpAmp so that it can drive low-impedance headphones.

The two power transistors are turned off at idle, but when the OpAmp’s output voltage signal gets high enough they begin to conduct, greatly increasing the possible power delivery into the low-impedance headphones. At low signal levels, however, the transistors contribute nothing to the output signal. Think of them as turbo chargers. Now imagine a 1-ohm loudspeaker, such as the old Apogees. Such a loudspeaker will kill even the burliest of solid-state power amplifiers. Well, that actually isn’t true. All amplifiers can drive a 1-ohm load—they just cannot drive it very far. For example, if the power amplifier holds a 2A current limit, only 2Vpk will be possible into the 1-ohm speaker, which equals only 2W. But if we put in place some big power transistors, our 2A current swing could equal 25V of peak voltage swing into the 1-ohm load, which would equal 312W of power. Ideally, the transistors should reside in the 1-ohm loudspeaker’s cabinet, but such an arrangement would make hooking up the small power amplifier’s feedback all but impossible. And if the transistors fell outside the feedback loop, the distortion would be high, as the switching transition is a harsh one. Perhaps staggered arrays of MOSFETs would prove more effective at lowering distortion.







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