|John Broskie's Guide to Tube Circuit Analysis & Design|
20 April 2013
The the Musical Fidelity 550K is certainly a step in the right direction, albeit a very small step, for the 550K power-booster is only a very powerful voltage amplifier with a 50-ohm input impedance, not a device lets the existing flea-power amplifier's output current flow into the loudspeaker, with an augmentation of current flow and voltage potential from the power booster.
Cascading a small amplifier into a large amplifier is not the same as a small amplifier working side by side with a big amplifier. Thus, what I am describing here is something altogether different. The last posts that I have made on this topic
were all concerned with the idea of the small power amplifier not functioning gratuitously, making sure that it actually did some real work. In other words, at the time all I could imagine was a big booster amplifier that required some real input power to be driven to full output, much as current-feedback amplifiers require serious current flow into their inverting input. But what I am going to cover this time is radically different in that the small power amplifier will actually drive the loudspeaker, notwithstanding that it will do so only partially, as the booster circuit helps it out by augmenting its feeble output, but does not replace it altogether. My last few posts on electronic supercharging were closer to this goal, as the power transistors and MOSFETs help the tube drive the load, but do not do all the work themselves.
Imagine a black box that holds two sets of binding posts. Imagine this black box placed in between your existing power amplifier and your speakers. Now imagine that what your speakers would sound like if they were attached to your amplifier, but which was now much more powerful.
In searching for a good analogy for what I have in mind, cosmetic surgery and enhancements come to mind, but my four or five female readers reading over my shoulder are never forgotten, so a better analogy might be the power steering in your car.
While the car's engine runs, the power steering augments and enhances your own ability to turn the steering wheel. If the engine stops running, you can still steer your car; it won't be easy, particularly if you are old and frail, but it is nonetheless possible. This is possible because power steering does not sever the connection between the steering wheel and the car's tires; instead, it only strengthens your motions—never disuniting your efforts from the task—working only to make it easier for you to turn the wheel. Well, this is what a power booster should do as well, increasing the power delivered to the speaker, but never cutting the flow of current from the small power amplifier to the loudspeaker.
A quick summery: there are four ways to implement a power booster.
All four approaches are valid and have their uses. I like the first approach when the big amplifier is a stripped-down version without an input stage (or even driver stage), what I refer to as a naked amplifier; in fact, a naked push-pull amplifier can even be built that would require a high-gain balanced line-stage amplifier. The second approach also appeals to me, as it could result in fewer stages in the amplification chain. The third approach, version 3a, is complicated, as placing a bigger in parallel with a small amplifier problematic because it requires that both amplifier share an identical amount of voltage gain and that some resistance must be added to the output of both amplifiers, so one amplifier doesn't fight the other. The bigger problem with this approach is that it doesn't yield any more power delivered into the speaker, although it will unload the existing small amplifier. Approach 3b, however, makes sense when the speaker presents an unusually low impedance; it also offers the advantage of unloading the small power amplifier, as the impedance multiplier would make an 8-ohm load appear twice or thrice as large as it really is to the small amplifier. But it is the fourth approach that I am jazzed about right now and is the topic of this post.
The key concept is that the power booster augments—but does not replace—the small amplifier.
An Interesting Design Problem, No?
Thus, approaches one and two could never achieve the goals. My first thought was that an impedance-multiplier circuit (IMC) could be used in either approaches three or four.
Indeed, an IMC, which makes the load impedance appear larger to the amplifier, could increase the power delivered to a low-impedance load, such as 1-ohm ribbon speaker, which the original small power amplifier was never meant to drive. Say that a small tube power amplifier that used a single 300B output tube and put out 4W and which expected to see an 8-ohm load were hooked up directly to the 1-ohm loudspeaker; not much sound would result; and the little sound produced would be woefully distorted. But if an IMC were placed in series with the flea-power amplifier, the small amplifier would still contribute its wee amount of output current and the IMC would deliver the extra needed current to make the 1-ohm load appear as an 8-ohm load to the flea-power amplifier. In this example, the flea-power amplifier would still put out a peak of 8V (at the speaker) and peak current flow of 8V/8-ohms, which equals 1A. The IMC would also put out 8Vpk as well and deliver the missing 7A of current, so the 1-ohm loudspeaker would see a peak current flow of 8A and 32W of power.
On the other hand, if the loudspeaker is an 8-ohm type to begin with, the IMC would do nothing to increase the power delivered, but it would make the 8-ohm speaker appear as a 16-ohm load to the small power amplifier. So the IMC idea was a dead-end? No, not at all, it was just not enough to realize approach four. If the flea-power amplifier is limited to a peak output voltage of 8V, then 8Vpk is the limit that could be delivered to the speaker, so the IMC would bestow no increase in power.
In contrast, imagine that an IMC were used with an inverting power amplifier with a gain of -1. In other words, if the inverting power amplifier were presented with an input signal of +8V, it would develop -80V at its output. Thus, if the loudspeaker were placed in between an IMC and an inverting power amplifier, the loudspeaker would see twice the voltage signal that the small power amplifier puts out.
For example, if the 8Vpk from a flea-power amplifier entered the above circuit, the loudspeaker would see 16Vpk across its inputs, which would imply twice the current flow than the 4W amplifier could deliver, 2A not 1A. So where does the extra 1A of current come from? The IMC would make up the difference on the positive terminal of the speaker and the inverting power amplifier would produce the full 2A of current on the speaker's negative terminal.
Note how the small power amplifier's 4W of output power becomes 16W at the loudspeaker's terminals. Why wasn't the power delivered only doubled? If the current is doubled, the power is quadrupled, as current² against resistance equals wattage. Another way of looking at is that if the current is doubled, so must be the voltage; thus, with twice the voltage and twice the current, the power must go up fourfold, as voltage against current equals power. Think of it this way: I • V = W, so 2I • 2V = 4(I • V) = 4W.
Okay, but could such an amplifier-power booster be built? Nothing exotic is required, just two power amplifiers and some resistors.
That's it. The only out of the ordinary thing is that the IMC uses a unity-gain stable power amplifier (and even this requirement can be bypassed). The two 0.2-ohm resistors set the IMC's impedance ratio to 2, so a 4-ohm loudspeaker will appear as an 8-ohm loudspeaker to the small power amplifier. Wait a minute, the loudspeaker in the schematic is 8 ohms not 4 ohms. True enough, and if the loudspeaker were terminated at the other end to ground, not the inverting amplifier's output, the 8-ohm loudspeaker would appear as a 16-ohm load to the small power amplifier. But since the inverting power amplifier's is the inversion of the small power amplifier's output, the effective ground is located in the middle of the loudspeaker's voice-coil, so effectively the 8-ohm loudspeaker is a 4-ohm speaker as far as the small power amplifier and IMC are concerned. In other words, as far as the IMC can tell, the load it sees is 4-ohms in impedance, so it doubles the 4 ohms to 8 ohms for the small power amplifier.
Actually, the impedance that the small power amplifier sees is a tad bit more than 8 ohms, as the 0.2-ohm series resistor must be included in the calculations. The schematic shows the voltage relationships within the amplifier-power booster.
You can see the small voltage drop of 0.2V across the 0.2 resistors, which implies a load of 8.1 ohms for the small power amplifier to drive. Of course, we could just round the voltage and current values, which I will do in the following schematic that shows the current relationships within the circuit.
Before moving on to more circuits, let's pause to reflect on the possibilities. One idea that immediately comes to mind, well at least my mind, is the power booster could be housed in a loudspeaker enclosure, much in the same way that many subwoofers hold their own internal power amplifiers. Let's start with a high-efficiency, two-way loudspeaker.
Both speaker drivers offer an efficiency of 94dB per watt. Without actually seeing the loudspeaker, we can make some very solid guesses. For example, the enclosure must be huge, if the speaker goes down low in bass frequencies. Or put differently, if the speaker enclosure is small, the speaker cannot go low. Why not? Physics. You can have high-efficiency and low-end extension and big box; or you can have high- efficiency and no bass and a small box; or you can have low-efficiency and low-end extension and small box; but you cannot have high-efficiency and low-end extension and small box.
An analogy might be found with bullets; you cannot have a subsonic bullet that is small and packs a huge punch; but you can have supersonic bullet that is small and packs a huge punch. If you must have a subsonic bullet (no supersonic-to-subsonic tumbling and quieter) that packs a huge punch, then it must be massive. Remember KE = 1/2MV².
The big problem with a big loudspeaker is that is big, which means that it is heavy, expensive, and not spouse friendly. Well, what if we used the high-efficiency tweeter, which can be very small and then used a small box with a low-efficiency woofer that went down deep and then used a power booster to bring the woofer up to the tweeter output?
If the power booster doubles the incoming voltage, then the loudspeaker will see four times more power and produce +6dB more SPL. Thus, the nominally 88dB efficient woofer will put the same 94dB that the tweeter puts out with 2.828 RMS volts (4Vpk) of output from the small power amplifier.
Note how the IMC gets the same inductor that a non-powered woofer would get. The power booster will still present the same 8-ohm load to the inductor that the naked woofer would. It might be possible to impose a low-pass filter on the woofer solely through the inverting amplifier. For example, if the inverting amplifier didn't invert a band of frequencies but passed them along in phase, the woofer would not see a large differential voltage, indeed no differential voltage, so it wouldn't respond to those frequencies. Next time I have a cup coffee, I will think about this more deeply, as there are frequency-selective phase flipper circuits that could be used, such as the following.
In other words, a low-pass or high-pass filter might be made without using a traditional filter. The following just might work, with the phase-shifting circuit bringing the high frequencies in phase the small power amplifier's output, so the woofer sees the same voltage on both of its plus and minus terminals, which means no current flow, which in turn means no sound at those frequencies.
As far as the small power amplifier is concerned, it sees a fairly constant 8-ohm impedance from 20Hz to 20kHz, as the woofer is engaged at low frequencies and the tweeter at high frequencies. As the frequencies go high, the woofer's impedance effectively goes high, much as if a large inductor were in series with it. As I said, I must drink a bit more coffee before I can commit myself to this idea actually working; but it does look promising.
16X Power Boosters Now that we know how to double the small amplifier's output current into the loudspeaker and, thereby, increasing the power delivered into the loudspeaker by fourfold, we will look into how to design a more aggressive power booster that would increase the power deliver by sixteen-fold! Remember I² in the power formula; well, tripling the current will increase the power by nine-fold; and quadrupling the current will yield 16 times more power. The topology doesn't change, but the current and voltage ratios do. In other words, we will have to break the symmetry between the IMC and the inverting power amplifier below it, as the inverting power amplifier will have to swing three times the output signal that the IMC and the small power amplifier will have to swing.
The puny 4W power amplifier still puts out its 1A of peak current flow and 8V of peak voltage. The inverting power amplifier at the bottom applies its gain of three to develop -24Vpk at its output, so the loudspeaker sees a total of 32Vpk across its terminals, which implies a peak current flow of 4A and peak power of 128W or, in average watts that many refer to as RMS watts, 64W. In other words, the flea-power amplifier's 4W have been transformed into 64W. So, all we have to do is alter the inverting amplifier's gain? No, there's more to it than just that.
The IMC no longer just matches the flea-power amplifier's current flow; it must provide three times more current. Thus, the IMC gets a 0.1-ohm series resistor, while the external small power amplifier sees a 0.3-ohm series resistor. The IMC's formula for impedance multiplication is (R1 + R2)/R1, so the IMC make the loudspeaker appear for times bigger in impedance than it actually is.
Wait a minute; I thought the whole point of the power booster was that the small external power amplifier would still be working into the loudspeaker's impedance. It does. This will be a bit confusing at first. Because the loudspeaker sees the differential signal, rather than being terminated into ground at one end, where the effective ground falls is somewhere within the loudspeaker's impedance. In other words, somewhere along the speaker's impedance there is a null point that sees a constant 0V. Examine the following schematic and note how the two load resistors combine to 8 ohms and how each sees the same current flow, but different voltage swings.
This is the load the IMC thinks it is attached to, if you will forgive my personifying an insentient electronic circuit. Indeed, this two-load-resistor version would function identically to the single-loudspeaker version, in terms of voltage and current swings. Here is the same circuit with a negative input voltage swing. Note how the OV connection between load resistors remains at 0V and that no current flows from this point into or out of the ground.
Actually Building a Power Booster
The next easiest approach would be to use power IC amplifiers (GainClone amplifiers), such as the LM4780, which is a stereo 60W power amplifier.
Why not the more famous LM3886? The LM4780 doesn't seem to offer any more phase margin than the LM3886; indeed, their open-loop gain/phase graphs look identical. But the LM4780 data-sheet shows it being run with a gain of only 10 (+20dB), whereas all the other design examples that I have seen for the LM3886 always show a gain of over 20. It is quite possible, however, that an LM4780 consists of two LM3886 amplifiers in one package.
By inspecting the above LM4780 graph, it looks like a gain of only 10 will be safe, which would allow us to build the following circuit.
The LM4780 is not unity-gain stable, so we must let it amplify by at least tenfold. But the IMC circuit requires a unity-gain power amplifier (buffer), so how is that going to work out? The workaround is to let the LM4780 develop a gain of 11 and then reduce the input signal it sees to one 11th. Note the two-resistor voltage divider at the top amplifier's positive input. It is made up of 1k and 10k resistors, so its voltage division equals 1k/(1k + 10k). The top amplifier's feedback resistors pair consists of also 1k and 10k resistors, so the gain it realizes is equal to (1k + 10k)/1k. What the amplifier's gain giveth, the voltage divider taketh away. In other words, unity-gain.
The bottom amplifier is configured as an inverting amplifier and it exhibits two gain settings: for input signals from the external small power amplifier, the gain is -1 (or inverted unity-gain); for the 1k resistor's connection to ground, 10. What we are doing is throwing away potential negative feedback, so that we can trick the amplifier working like an inverted unity-gain amplifier.
How much power could this power booster put out? It depends on several factors, such as the loudspeaker impedance and the external small power amplifier's power output. Let's assume that the external small power amplifier put out a healthy 36W into 8-ohm loads, which implies a peak output of 24V and 3A. The power booster would double both the peak voltage and current, resulting in 144W into an 8-ohm load. That is a lot of power. Indeed, I worry about the LM4780 being over stressed, as the bottom inverting power amplifier effectively sees a 4-ohm load, not an 8-ohm load. The following variation both unloads the LM4780s and gives us more potential power; note the +/-40V power-supply rails.
Note how the IMC portion of the circuit uses 0.2-ohm series resistors, while the small power amplifier gets a 0.1-ohm resistor. The two 0.2 resistors are effectively in parallel, so they present 0.1 ohms of resistance, so the IMC's impedance ratio remains at 2:1.
Of course, even more amplifiers could be placed in parallel. In fact, several high-end solid-state power amplifiers consist of many LM3886 amplifiers in parallel. Remember, about half of the cost of a high-end-audio product goes into cosmetics, and then there is the cost of those glossy ads, which doesn't leave a lot of money to buy expensive parts. So, it isn't surprising that a $7,000 high-end amplifier should hold twelve $3 chip amplifiers. I once met an audiophile who was appalled to learn that the DAC in his very, very expensive CD player cost less than $5 (in 1000 quantities); he wouldn't buy resistors that cost only $5 each, so shouldn't the DAC, the most important part in the CD player, cost at least as much as his favorite coupling capacitors, say $150? He would be even happier if the exact same DAC cost $500, for as all audiophiles know, the more it costs the better it sounds—besides it keeps the audio riffraff from spoiling your picnic. What's the point of having exalted audio tastes, if DACs cost less than $5?
This raises an interesting question: Shouldn't a power booster be used only to boost the power output of small amplifiers, not fairly beefy ones? My leaning is that a power booster should be optimized to work solely with flea-power amplifiers. Why? If you already own a big power amplifier, power booster wouldn't make as much sense as just buying a bigger amplifier. If, on the other hand, you own a 4W, 300B-based, single-ended wonder that sound so sweet that you need to wear bib as you listen to catch all the tears streaming from your eyes, then the power booster makes a lot more sense. (If you haven't heard a good flea-power amplifier, you should, as they can be breathtaking.)
The following schematic shows a power booster that boosts ninefold and that would work with up to 16W external power amplifiers.
First of all, note that the IMC portion gets lower power-supply-rail voltages, +/-20Vdc. Why? Since this power booster is meant to work with a small external power amplifier, larger power-supply-rail voltages will only create extra heat, as the IMC will never swing more than 16Vpk. Indeed, paradoxically enough, if both the IMC and inverting amplifiers used the same +/-40Vdc rail voltages, the bottom inverting amplifiers would run cooler than the IMC amplifiers. Second, note that the IMC's impedance ratio equals 3:1. Third, note that the bottom inverting amplifiers run with a gain of -2, not -1, which results in the speaker seeing three times more voltage and current, which explains the ninefold increase in power.
Other Power Booster Amplifiers
A truly unique chip amplifier, the TDA7293 has the ability to disconnect its input and driver stage, so its output stage can be driven in a slave-like fashion by a master TDA7293.
(Note how the bottom TDA7293's pin 11 attaches to the top TDA7293's pin 11. What would happen if we used only the bottom half of this schematics and drove the slave TDA7293's pin 11 with an Aikido gain stage? We just might get a fine Moskido hybrid power amplifier on the cheap.)
Another interesting chip amplifier is the OPA541 from Burr-Brown. It is not as famous as the LM3886 and it costs about twice as much, but it offers several key advantages.
The OPA541 uses a FET input stage and it is unity-gain stable. Hallelujah! This means that we will not need the extra resistors now do we need to throw away negative feedback. (Once again, we just might be able to build a Transkido hybrid power amplifier on the cheap.) In addition, the OPA541 can be wired up in a master-slave configuration, so greater current delivery is possible and less heat from each OPA541.
Ever since I saw this configuration in a Burr-Brown data-sheet, over 10 years ago, I have been mightily impressed with the results from this topology. It doesn't just double the potential output current; it reduces the distortion by about 20dB, which is always welcome. I have built headphone amplifier based on this configuration and the sound is vastly better than just two OpAmps in parallel (each getting its own 10-ohm series resistor at its output).
The above circuit doubles the potential current swings and must ever so slightly reduce the OpAmp noise, but it doesn't work nearly as well as the following circuit.
This is not a universal solution, as only unity-gain OpAmps can be used; in other words, DO NOT USE THE OPA637. Stop and think about how the number slave OpAmps is not limited to one; we could use one master OpAmp and eight slaves.
Okay, back to power boosters proper. Of course, we could just build discrete solid-state power-amplifier modules. Indeed, we could build hybrid power amplifier modules for the IMC and inverting power amplifier application. Now, the only limits are our wallet and imagination. With +/-100Vdc power-supply-rail voltages, truly frightening and forbidding amounts of power could be delivered—if your wall socket can deliver the current without blowing a fuse.
The following tables list the voltage, current, wattage, and gain relationships in a power booster based on the rail voltages it uses.
Note how the potential output wattage varies depending on the small power amplifier's output. If we didn't expect to work directly into the speaker, we could simply go the Musical Fidelity 550K power-booster route and let the big differential power amplifier do all the work of driving the speaker, which means that the bottom row of each of the above tables would be the power output. But...it wouldn't be the same would it?
I have to stop now, as the sky darkens and my dog needs emptying.
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The Tube CAD Journal's first companion program, TCJ Filter Design lets you design a filter or crossover (passive, OpAmp or tube) without having to check out thick textbooks from the library and without having to breakout the scientific calculator. This program's goal is to provide a quick and easy display not only of the frequency response, but also of the resistor and capacitor values for a passive and active filters and crossovers.
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