Created February 4, 2014
Updated February 17, 2014
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Buffers are supposed to be simple and easy aren't they? How hard can it be to simply output the input? Unfortunately, good buffers are as hard to design as good amplifiers, and audio designers are keenly aware of this. In an ideal world, the best buffer is no buffer, but all too often we need them still. Fortunately for us, the low output and power levels of an audio signal buffer make it an ideal application for error correction techniques, since the transistors conform very highly to intrinsic laws at these operating points.
The Kuartlotron is my implementation of a kind of error correction signal buffer. After I had the idea, I discovered Malcolm Hawksford had used an almost identical circuit in his DAC I/V converter. My buffer is like the Tringlotron and many other log-antilog error-correction buffers, but with all of the advantages and few of the shortcomings. It can operate at DC or AC coupled, unlike the Tringlotron, and requires no special biasing, although I have added a biasing arrangement to improve thermal matching.
The top two transistors are a current mirror that feeds the output current into the input transistor. The response of the input transistor to this causes the cancellation of the distortion of the output transistor. For a more in-depth explanation, examine the theory section.
- Total Harmonic Distortion:
Usually .001% or less at audio, measured as low as .00025%
- Linear bandwidth:
THD doubles first at 55KHz and then doubles every octave.
- Distortion under load:
THD doubles first under 1Kohm load and then doubles each time that is halved.
Theoretically 138db at 1KHz
In theory, over 50MHz, if well-constructed and using fast transistors.
- Max output current:
Positive output current has no definite maximum.
- Input impedance:
- Output impedance:
<52R at the output. No more than 5 ohms at the emitter of Q4.
- Output offset:
Advantages of the Kuartlotron
The Kuartlotron is unique in that it doesn't use feedback. It doesn't need feedback, because it cleans up after itself - it subtracts its own distortion. Yet it isn't reliant on its own error correction mechanism either - at frequencies faster than the error correction, it simply operates as a passive buffer. The high degree of efficiency and redundancy in the signal path lends the Kuartlotron virtual immunity to RF interference and an enormous signal bandwidth. Without feedback, it is unfazed by interference because there is little need to load down the internals at high frequencies to prevent oscillation.
What's unusual for this type of circuit however is that it doesn't suffer from the usual complaints about non-global feedback circuits - distortion is vanishingly low and there is no danger of thermal runaway or bias drift. It is fully temperature-compensated and the bias is set by the 1k resistor. Noise is relatively insignificant.
- While the OnSemi BC5xx/BC3x7 transistors come very well-matched out of the box, the same might not be true of other transistors. Since all transistors conform to a logarithmic I/V curve very well at these operating points, any non-conformance causes distortion. Luckily, the nature of this circuit is that even the non-intrinsic qualities of the same-name transistors cancel. For this to work best, you should choose transistors that come well-matched from the factory - manually matching transistors from an unreliable factory could just give you pairs that seem matched but aren't really.
- Thermal Management
- It is theoretically possible that temperature differences between transistors could result in distortion from mismatch. But I have not seen this in practice. The nature of the logarithmic I/V curve means that Vbe mismatches won't actually affect this circuit much, except to cause slight DC offset and different operating points.
- IF you can detect distortion, then it's possible you can trim it down using the trimming scheme in the schematic. The main cause of mismatch seems to be the difference in Vce of Q2 and Q4, causing a mismatch due to Early effect and self-heating differences. In practice I have not found there to be much to gain from trimming, as long as the operating points are right, when using the BC5xx/BC3x7 transistors.
- How do I know when it is working
- The offset voltage should be within 5mV with input shorted, and under 12mV with an input coupling capacitor.
- It does not start properly
- I have not had problems with this after my final build. However it is possible that Q2 may never turn on due to there being insufficient leakage from Q1 and Q3 to turn it on.
- Fit a 1N4148 across the B-E junction of Q1, pointing towards the emitter. If this does not work, then there is a fault elsewhere in the circuit
- Getting help with troubleshooting
If you want to change
something, beware that it may change troubleshooting procedures and
design considerations. That said, if you are confident you do not need
guidance for your application, here are some ideas and helpful
- Increase linear bandwidth
- You can increase the linear bandwidth by increasing the bias through Q1 and Q3. This may be helpful if you use transistors with lower Ft such as the BC3x7. Decrease the R1 and R2. You will need to increase R5 to maintain the Vce balance between Q2 and Q4.
- Use BC337-40 and BC327-40
- The BC3x7 series of transistor are very low noise and have very low internal resistance, so their intrinsic region of operation is much larger. I also know from my Kmultiplier experiments that their Vce/Vbe coefficient is the lowest I have measured. Not only that, but their large die size gives them high thermal inertia, so they will be more immune to dynamic self-heating effects. Theoretically, this makes them the ideal transistor for a log-antilog error correction circuit like the Kuartlotron. They should result in lower output impedance.
In practice I have found that they are slower, so linear bandwidth is halved - to compensate you will want to increase the current of Q1/Q3 to 2mA. The input snubber also needs to be made larger to maintain stability. Lower RC resistance and increase RC corner frequency. In practice, this might achieve lower distortion, but those who have built it so far have preferred to use the BC5xx instead for better sound.
- Increase input impedance
- The input impedance can be increased by making R8 100k. However this will make the DC offset more sensitive to power input drift, at about 20mV/V of power supply error, so a regulated supply would be ideal.
- Reduce output impedance
- Output resistance at the emitter of Q4 may be negative or positive, and it's important to keep it from going negative or else you risk oscillation. For this reason I would recommend at least a 4.7R output resistor. The 47R output resistor was chosen for best compatibility with signal cables. Transmission lines are reactive by nature and without the right termination impedance, become a cascade of series and parallel resonators. Without termination, the cables become antennas for RFI. 22R-47R is a good range for damping cable resonances. Without termination, any buffer will resonate with the cable's series resonance mode; the 47R resistor was chosen to prevent this.
Other adaptions of the Kuartlotron
To be written...
Theory of Operation
After spending most of my hobby work trying to improve feedback circuits I came to realize that circuits which are linear by nature make everything easier. The output distortion of a feedback circuit is the internal distortion divided by the amount of feedback. This means that there are two ways to reduce output distortion: increasing feedback, and increasing internal linearity. The former can usually be done easily, without much effort. However, feedback has a very limited bandwidth, and because of this, most often you increase feedback at the expense of RFI immunity and frequency-dependent distortion. On the other hand, if you increase the internal linearity of the circuit, you sidestep the slowness of a global feedback loop.
But increasing linearity requires use of an entirely different knowledge base than feedback does. With feedback being by far the dominant philosophy for modern designs, it can seem like it's the only option. However super-linear stage design is not an obsolete concept; it has only been largely forgotten.
Before the digital revolution, analog calculator design was a known art. The electronic devices of the time were known to conform to certain mathematical laws and this could be exploited to design analog multipliers, dividers, adders, subtractors, and combinations to calculate any number of things. They usually weren't very accurate, but it's possible.
Even more suitable devices are available today, especially considering how reliable modern fabrication processes have become. I realized, if you can put transistors together to get a reasonably accurate multiplier, why couldn't you put them together somehow to create a buffer just as accurate, without needing feedback? Why use feedback if you can simply take advantage of the transistor's intrinsic nature to do essentially the same thing?
I managed to find a few examples of such a thing. One such example is the Tringlotron.
After several months with these thoughts rolling around in my head, I suddenly came up with the basic circuit:
In a way, this circuit behaves like an ideal transistor. If you see the input as the base, the output as the emitter, and the power input as the collector, it is like a BJT with zero output impedance, very high gain and almost no distortion. The mechanism that causes this result is surprisingly simple - Since Ic(Q2) = Ic(Q4), Vbe(Q2) = Vbe(Q4). Similarly, Ic(Q1) = Ic(Q2), so Vbe(Q1) = Vbe(Q3). Since Vbe(Q3) = Vbe(Q4), this means Vbe(Q1) = Vbe(Q2), which is to say, the Vbe of Q1 is directly cancelled by the correction signal across Vbe(Q1).
This design relies on the matching between the same-name parts - but unexpectedly, not very much. Because of the logarithmic Vbe curve of BJTs, even small Vbe differences will not ruin the matching as long as the transistors are operating within their most intrinsic region - intrinsic meaning, conforming the most to their natural logarithmic transfer curve.
A recent Kuartlotron prototype from my bench:
Joachim Gerhard's Kuartlotron:
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