Created February 4, 2014
Updated Oct 23, 2017
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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.
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
- 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
- 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
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.
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
- Thermal Management
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
- 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
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 information.
- 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
Theory of Operation
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:
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(Q3), so Vbe(Q1) = Vbe(Q3). Since
Vbe(Q3) = Vbe(Q4), this means Vbe(Q1) = Vbe(Q2), which is to say,
the Vbe error voltage of Q2 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.
recent Kuartlotron prototype from my bench:
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